THE SEMICONDUCTING PROPERTIES OF SOME BINARY AND TERNARY COMPOUNDS by Ping-Wang Chiang:.. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1965 Doctoral Committee: Professor Donald R. Mason, Chairman Associate Professor Howard Diamond Professor Ernst Katz Associate Professor Robert H. Kadlec Professor Lawrence H. VanVlack

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ACKNOWLEDGMENTS The author would like to express his sincere appreciation to Professor Donald R. Mason for his guidance and assistance during the course of this research. Acknowledgment is also due to Texas Instruments, Inc. and the National Science Foundation for the financial assistance, and the Department of Chemical and Metallurgical Engineering for partial support for this work. The author would like to thank Dr. Do F. O'Kane and the following students, Messrs. R. I. Bassett, C. Herbert Rice, S. J. Lewis, L. K. Murray, and G. A. Schmitt who assisted with various phases of the research. Mrs. M. L. Gersh deserves the credit for typing this manuscript. Finally, the author is indebted to his wife, Theresa, for her encouragement and her patience in his long working hours. ii

THE SEMICONDUCTING PROPERTIES OF SOME BINARY AND TERNARY COMPOUNDS Ping-Wang Chiang ABSTRACT Some of the semiconducting properties, including electrical conductivity, Hall coefficient, and Seebeck coefficient were determined for nine compounds, In Te5, In2Te3, InTe from the In-Te system, InzSe3, InSe from the In-Se system, AgIn Te14 from the Ag Te-InZSe3 system, Cu In9Te17 from the Cu2Te-InTe3 system, CdIn Se4 from the CdSe-In Se3 system, and Ag In8Se 3 from the Ag Se-In Se3 system. The compounds In3Tes, AgIn9Te14, In Se, and InSe have high resistivity at room temperature while InTe, Cu In Te17 and CdIn Se4 are highly conductive. Ag2In8Sel3 has two forms. Form I, the high conductivity material which crystallizes in the chalcopyrite structure, and Form II, the high resistivity material which has a monoclinic structure. A third form may exist for this compound. The observed energy gaps were 1. 09 eV and 0. 75 eV for high and low temperature forms of In3Te respectively, 1.14 eV and 1.65 eV for a and P forms of In Te respectively, 1,51 eVforAgIn Te14s 3. 6 eVfor form of In2Se3, and 1.09 eV for InSe. Impurity activation energies observed were 0.088 eVfor InTe, 0.24 eV for Cu In Te17, and 0.014 eV for CdIn Se. >97 9 1 2 4e The energy gap of Ag2In8Se13 is 1.52 eV. With a cocoon technique developed in this work, it is possible to suppress decomposition of the sample during the measurements as shown in the properties of In3Te5. The cocoon arrangement also make it possible to partially control the atmosphere of measurement. With extra Se sealed in the cocoon, it was possible to restore the original high resistivity of Ag In Sel3 after it had exhibited a high electrical 2 o 13 4 iii

conductivity as a result of heat treatment caused by the measuring cycle. X-ray analyses and density measurements were made on five compounds, In2Te, InTe, In Se3, InSe and AgIn Sel and the lattice 2 3' 2 3 8% 0 1 3 constants are reported. Some of the relations between the crystalline structure and the semiconducting properties are discussed. Differential thermal analysis measurements have been made for the compositions within the In-Se binary system, the Cu Te-In2Te3, and the Ag2Te-In2Te pseudo-binary systems. Phase diagrams, either whole or partial have been constructed, based on the DTA results. iv

TABLE OF CONTENTS Page ACKNOWLEDGMENT...................... ii ABSTRACT o............. e o o o............. o iii LIST OF TABLES. o..................... ix LIST OF FIGURES....O.... *.......O.. x LIST OF APPENDICES..................... xv INTRODUCTION.............. *...... o 1 I. THEORY................ o o o o o o o o............ o 4 A. Equations for Carrier Concentration in a Semiconductor.. 4 B, The Fermi Level Change................. 8 1o Extrinsic Semiconductors,...............* 8 a. Case I, N = 4N............. 9 d c b. Case II, Nd<< N............. 0. 9 d c c. Case II, Nd >> N........ o..... 10 d c 2. Intrinsic Semiconductors.............. 11 3. Summary................ 11 C. Electrical Conductivity and Hall Effect........ o 12 1. General Formulae for Electrical Conductivity and Hall Effect...................... 12 2. Formulae for Intrinsic Semiconductors........ 13 3. Formulae for Extrinsic Semiconductors,....... 17 4. Mobility Ratio from Electrical Conductivity and the Hall Coefficient....... o...... o..... 18 D. Seebeck Coefficient.................. 19 1. General Formulae for the Seebeck Coefficient.... 20 2. Seebeck Coefficient for the Extrinsic Region..... 21 3. Seebeck Coefficient for the Intrinsic Region..... 21 v

Page II. EXPERIMENTAL PROCEDURE................... 23 A. Sample Preparation..................... 23 B. Differential Thermal Analysis............. 24 C. Chemical Analysis.................... 24 D. X-Ray Analysis..................... 25 E. Density Measurement..................... 25 F. Microscopic Analysis................... 25 G. Electrical Measurements............... 26 1. Electrical Specimens.................. 26 2. Description of Equipment.............. 27 a. Modifications of the Equipment........... 27 b. Cocoon Arrangement............... 30 c. Result of the Modification..........30 III. SEMICONDUCTING PROPERTIES OF In3Te......... 31 A. Literature Review................ 31 B. Experimental Results................... 31 C. Interpretation and Discussion of the Results....... 36 IV. SEMICONDUCTING PROPERTIES OF In2Te3......... 38 A. Literature Review................... 38 B. Experimental Results................... 38 C. Discussion..................... 43 D. Summary......................... 45 V. PHASE DIAGRAM OF THE PSEUDO-BINARY SYSTEM OF Ag2Te-In Te3 AND SEMICONDUCTING PROPERTIES OF AgIn Te 14.......................... 47 A. Literature Review.................... 47 B. Experimental Results.................... 47 1. Phase Diagram Study................ 47 2. Electrical Properties............ 51 vi

Page V. (Cont.) C. Discussion n.......... * * 0 0 0 o 55 VI. SEMICONDUCTING PROPERTIES OF In2Se........ 56 Ao Literature Review............ *... o D 56 B. Experimental Results............ 57 C, Discussion............. 0 0 0 0 0 0 0.... 63 VII. SEMICONDUCTING PROPERTIES OF InSe....... 0 65 A, Introduction......... o o 0 0 0 65 Bo Literature Review............. * 65 C, Experimental Results.................... 65 D. Interpretation of the Results........... o 75 Eo Summary. *....................... 81 VIII. ELECTRICAL PROPERTIES OF InTe.............* 84 A. Literature Review................. 0 84 B. Experimental Results............... 0 84 C. Discussion of the Results........... 89 D. Summary.................. 94 IXo PHASE DIAGRAM OF Cu2Te-In Te3 PSEUDO-BINARY SYSTEM AND THE ELECTRICAL PROPERTIES OF Cu7In9Te 17. 0.... 96 A. Introduction..... 0.....0 0 0 0 0 0 0 0 0 96 B. Experimental Results,............... 97 1. Mechanical Properties........... 0 97 2. Chemical Analysis................ 97 3. Differential Thermal Analysis and Phase Diagram.. 100 4. Electrical Properties of Cu7In Te17........ 103 C. Discussion and Interpretation of the Results...... 108 D. Summary. O O O 0 0 0 0 0. 0.......... 0.a 118 vii

Page X. ELECTRICAL PROPERTIES OF CdInzSe4............. 120 2 4 A. Literature Review..................... 120 B. Experimental Results.................... 120 C. Discussion of the Results............. 126 XI. SEMICONDUCTING PROPERTIES OF Ag2In8Se. e....... 130 ^ o130 A. Introduction....................... 130 B. Literature Review..................... 130 C. Experimental Results................... 131 D. Discussion........................ 147 APPENDICES............................ 155 BIBLIOGRAPHY............................ 208 viii

LIST OF TABLES Table Page 1.1 Scattering Exponents and the Seebeck Factors...... 16 5. 1 Summary of the Differential Thermal Analysis Measurements for the Pseudo-Binary Phase Diagram of Ag2Te-In2Te3 System................ 48 6. 1 Summary of DTA Measurements for the In-Se System... 59 9.1 Composition of Zone Refined Samples of Cu7In Te17 Determined by Chemical Analyses............ 98 9.2 Summary of DTA Measurements for the Cu Te-In Te3 Pseudo-Binary System.................. 101 9.3 Summary of the Data on Cu7In8Te 7 Compounds..... 104 11.1 Summary of Calculations on Structure of Ag2In8Se13... 152 11. 2 Bonding Radii and Bonding Lengths in Ag, In, Se Structures......................... 153 F. 1 Line Intensity and Sin a Values of X-ray Results..... 169 Io 1 Hall Coefficient..................... 186 I. 2 Seebeck Coefficient.................... 194 I. 3 Electrical Conductivity of AgIn8Se3........... 201 2 8 13" ix

LIST OF FIGURES Figure Page 1. The Locations of the Compounds Investigated...... 2 2.1 Schematic Diagram of the Measuring Jig and Cocoon Arrangement....................... 29 3.1 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for In3Te5, Showing the Stabilization Effect of The Cocoon Arrangement............ 32 3/2 3.2 Logarithm of IRHT 3/ versus Reciprocal Absolute Temperature for In3Te5, Showing the Stabilization Effect of the Cocoon Arrangement............... 33 3.3 Logarithm of |RH a1 versus Logarithm of Absolute Temperature for In Te................ 35 4.1 Logarithm of Electrical Conductivity and Logarithm of 3/2 RH T 3/ versus Reciprocal Absolute Temperature for In2Te3, Ingot No. 1224, Showing the Properties of InZTe3 with Excess Te in the Compound,............ 40 4.2 Logarithm of Electrical Conductivity and Logarithm of 3/2 RH T / versus Reciprocal Absolute Temperature for In2Te3, Ingot No. 1212, Showing Characteristics of the Congruent Compound................ 41 4. 3 Logarithm of IRH cI versus Logarithm of Absolute Temperature for In Te.................. 42 2 3.42 4.4 Seebeck Coefficient versus Reciprocal Absolute Temperature for In2Te3................. 44 5. 1 Partial Phase Diagram for the Ag2Te-In Te Pseudo Binary System...................... 50 x

Figure Page 5.2 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for AgIn9Te14 Measured Without Cocoon Arrangement.................. 52 3/2 5.3 Logarithm of IRHT | versus Reciprocal Absolute Temperature for AgIn Tel4 Measured Without Cocoon Arrangement...................... 53 5.4 Logarithm of J RH o versus Logarithm of Absolute Temperature for AgIn Te 14 *............. 54 6. 1 Phase Diagram of the In-Se System............ 60 6. 2 Logarithm of Electrical Conductivity versus 1000/T Plot for In2Se3....................... 61 3/2 6.3 Logarithm of RHT versus 1000/T Plot for In Se.... 62 6.4 Logarithm of I RH o Product versus Logarithm of T Plot for In2Se........................ 64 7. 1 Structure of an InSe Major Layer.............. 66 7. 2 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for InSe............... 68 7.3 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for InSe Measured Without Se in the Atmosphere................... 6 69 3/2 7.4 Logarithm of IRHT j/ versus Reciprocal Absolute Temperature for InSe................. 71 3/2 7.5 Logarithm of IRHT 3/ versus Reciprocal Absolute Temperature for Zone Refined InSe Measured Without Se in the Atmosphere.................... 72 xi

Figure Page 7. 6 Logarithm of J RH - I versus Logarithm of Absolute Temperature for In Se.................. 73 7.7 Logarithm of I RH I versus Logarithm of Absolute Temperature for Zone Refined In Se Measured Without Se in the Atmosphere................... 74 7.8 Seebeck Coefficient of InSe............. 76 7.9 Logarithm of | H T | versus Reciprocal Absolute Temperature for InSe, Showing the Activation Energy of Mobility......................... 79 7.10 Energy Diagram of InSe.................. 82 8.1 Structure of InTe..................... 85 8. 2 Logarithm of Electrical Conductivity versus Logarithm of Absolute Temperature for InTe............ 87 8.3 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for InTe............... 88 8.4 Seebeck Coefficient versus Reciprocal Absolute Temperature for InTe.................. 90 8.5 a q T versus Absolute Temperature for InSe, Showing the Change of Fermi Level Along with Temperature.... 92 9.1 Result of Chemical Analysis on Zone Refined CuInTe2, Showing the Composition of Cu7In Te17......... 99 9.2 Phase Diagram of the Cu2Te-In2Te3 Pseudo Binary System.. * *................ 102 9. 3 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Cu7 In9Te17. *' ' ' ' ' ' ' ' ' 103 xii

Figure I 9.4 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Cu7In9Te17..... 9. 5 Logarithm of Electrical Conductivity versus Logarithm of Absolute Temperature for Cu7IngTe 17............ 9. 6 Seebeck Coefficient versus Reciprocal Absolute Temperature for Cu7 In9Te1 7 *....*..... 9. 7 Seebeck Coefficient versus Reciprocal Absolute Temperature for Cu7In9Te17................. 9.8 J a qT versus Absolute Temperature for Cu7In9Te1 7 Showing "A" Type Variation of the Fermi Level.... 9. 9 i a qTJ versus Absolute Temperature for Cu7In Tel7 Showing "A + B" Type Variation of the Fermi Level..... 9. 10 aq - (3k/4) In T versus Reciprocal Absolute Temperature for CuInTe2 and Cu7InTe17................. 10. 1 Phase Diagram of the CdSe-In Se3 Pseudo-Binary System. 10.2 Structure of CdIn Se4................. 10.3 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for CdIn Se4.......... 10.4 Seebeck Coefficient of CdIn2Se4............. 10. 5 -aq - (3k/4) In T versus Reciprocal Absolute Temperature for CdInSe........................ 11.1 Phase Diagram of the Ag2Se-In2Se3 Pseudo-Binary System. 11.2 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se 13............ Page. 106. 107.109.110. 113. 114 116 121. 122 ~ 124. 125 129 132 134 xiii

Figure Page 11.3 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se13 in Low Temperature Region........................... 135 11.4 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se13 (by O'Kane)... 137 11.5 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag In8Se13 (by O'Kane).... 138 3/2 11.6 Logarithm of IRHT / versus Reciprocal Absolute Temperature for Ag2In8Sel3................ 139 3/2 11.7 Logarithm of RHT / versus Reciprocal Absolute Temperature for Ag2In8Se13 (by O'Kane)......... 140 11.8 Logarithm of RH a1 versus Logarithm of Absolute Temperature for Ag In8Se1............... 141 11.9 Seebeck Coefficient of Ag In8Se13............ 143 11.10 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature Measured Under Constant Se Temperature for Ag In8Se 13................ 144 11.11 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature of Se Measured Under Constant Sample Temperature for Ag In8Sel3........... 145 11.12 Logarithm of Electrical Conductivity Character of Zone Refined Ingot for Ag In8Sel 3........... 148 D. 1 Block Diagram Showing Operation of DTA Equipment... 163 G. 1 Electrical Circuit Used for Measuring the Electrical Conductivity, Hall Effect, and Seebeck Coefficient of the Semiconducting Compounds............. 178 xiv

LIST OF APPENDICES Appendix A. Fermi-Dirac Statistics Based on 6F/6e, = 0.... 1 B. The Minimum Value of F(T) = 128 N exp (E - Ed)/kT. c g d C. Preparation of Samples and Zone Refining........ 1. Sample Preparation................. 2. Zone Refining..................... Page 155 i -JO 159 1j c0 iO 160 16.1 D. Differential Thermal Analysi E. Chemical Analysis... 1. Cu-In-Te System.... a. Tellurium Analysis. b. Indium Analysis. c. Copper Analysis. 2. Ag2In8Se13...... F. X-Ray Analysis....... 1. Experimental Method. 2. Experimental Results. 3. Indexing Method... G. Measurements of Hall Effecl and Seebeck Coefficient.. 0 a 0 0 0 0 0 0 9 * * 0 0 1 6 - *..... * S 0......... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 a 0 0 0 0 0 0 0 * 0 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 0* ~ 0 ~ ~~~~ ~ ~~~~~ ~ ~ ~ ~ ~ ~ l'o4 164 1 o4 1 (~166 167 1 68 168 168 17 4 Electrical Conductivity, 0 0 0 0 0 0 0 0 0 0 0 * 0 1. Electrical Circuit................... 2. Sample Holder and Container.............. 3. Measuring Procedure.................. a. Hall Effect................. b. Electrical Conductivity and Seebeck Coefficient. c. Type of Carrier.................. 4. Sample Calculations.................. a. Calculation of the Hall Coefficient........ b. Calculation of the Electrical Conductivity.... 177 177 179 130 180 180 181 181 181 182 XV

Appendix G. 4. (Cont.) Page c. Calculation of the Seebeck Coefficient..... 182 H. The Original Equipment.................. 184 1. Experimental Data,................... 1. Hall Coefficient................. 2. Seebeck Coefficient,................ 3. Electrical Conductivity of Ag2In8Se 13....... 2 o 13' 186 186 194 201 J. Nomenclature....................205 xvi

INTRODUCTION The purpose of this work has been to prepare, measure and interpret the electrical properties of some binary and ternary semiconducting compounds. Initial work was centered on both developing a better experimental technique and a better understanding of the binary compounds which in consequence should lead to a better understanding of the ternary compounds. In order to prepare homogeneous samples, it was necessary to have a knowledge of the phase diagram in which the compounds appear. Knowledge of the structure of the compound provides a basis for understanding of the properties of the material. For the binary compounds, work was centered on the preparation and evaluation of the properties of the compounds in the In-Te and the In-Se systems, In Te5 In2Te3, InTe, InSe, and In2Se3. Four ternary compounds of the I VI-In2VI3 or the CdSe-In Se3 pseudobinary systems were investigated, where I means Group I elements, Ag, Cu, in the present case, and VI is Group VI elements, in the present case Se and Te. Figure 1 gives clearly the location of the compounds investigated. Differential thermal analysis (DTA) was used to determine the solid-liquid transformation of a mixture or a compound as a function of temperature. Since each of the binary constituents is a pure chemical compound, adequate equilibrium relationships can be obtained by investigating only the pseudo-binary plane which joins them in the ternary system. This is not true in general, but appears to be valid in the investigated systems. The phase diagram behavior of a system can be delineated and the conditions necessary for preparation of high purity compounds can be established by DTA measurement in conjunction with chemical analysis, microscopic examination, and x-ray measurement. 1

Se Te CdInZSe 4 Cu7In9Te 7 /Tn aSe3 7 9 17 I \ e InnSe3 2 3 CdSe InTe CdSe n Ag Te or Ag Se or u A AgeIn Se Cu2Te / AgIn9Te An8 e13 Ag or Cu In Ag or Cd In Figure 1. The Locations of the Compounds Investigated.

3 If a congruently melting compound exists in a phase diagram, DTA can provide an estimate of its composition and melting point. Zone refining can be used to produce a high purity compound. Peritectic composition also can be located by DTA measurements. And a zone leveling technique can be used to prepare the samples. Density and x-ray measurements on a single phase material also aid in determining the composition of the material and help in the understanding of the compounds. The sample obtained by zone refining or zone leveling is usually polycrystalline, but of sufficient purity to provide information on the intrinsic electrical properties of the semiconducting compound, Electrical conductivity measurements as a function of temperature indicate the energy gap of the compound as long as certain simplifying assumptions are valid. Hall effect data as a function of temperature also provide an estimate of the energy gap, and it is sometimes possible to determine the majority carrier concentration. Seebeck coefficient in many cases also enable one to estimate the energy gap, the mobility ratio and the carrier concentration. In the course of this work, three kinds of samples, classified according to their electrical properties were investigated: 1) the samples having high resistivity at room temperature which are In3Te., In2Te3, AgIn9Te14, InZSe3, and InSe; 2) samples having low resistivity at room temperature which are InTe, Cu7Inge17, and CdIn Se4; and 3) the compound having both high and low conductivity properties which is Ag2In8Se13. The first kind can be explained in a straightforward manner according to classical semiconductor theory, and therefore are presented first. The second kind is more complicated to explain. The last kind is very complicated, and so is discussed lasto

CHAPTER 1 THEORY In this section, equations relating the electrical conductivity, Hall coefficient, and Seebeck coefficient to the absolute temperature, energy gap, Fermi level, mobilities, carrier concentrations, effective masses, the temperature coefficient of the energy gap variation, donor energy level, and acceptor energy level are developed and summarized. Measurements of the electrical conductivity, Hall coefficient, and Seebeck coefficient as functions of temperature can be used in conjunction with the equations from this section to determine the values of these various properties of semiconducting materials. EQUATIONS FOR CARRIER CONCENTRATION IN A SEMICONDUCTOR Based on the Fermi-Dirac statistics, and on the quasi-free electron model and approximated by the free electron model, it can be (39) shown that the concentration of electrons in the conduction band of a semiconductor is given by * 3/2 / 2 2m (Ei-E /d Ei 1 n = i g__ 12! c 2 I2 l+exp (E -Ef)/kT 2 i i f g where n = concentration of electrons in the conduction band, c electrons / cm m = effective mass of electron, gm n = h/2'T -27 h = Planck's constant, 6. 62 x 10 erg-sec. E = energy gap of the semiconductor, eV g E = Fermi energy level with reference point of zero energy at the top of the valence band, eV 4

5 Ei = ith energy level with the reference zero energy same as Ef = Boltzmann's constant, 1.38 x 10 erg/ K= k 5 8.6 x 10 eV/~K T = absolute temperature, K The Fermi-Dirac statistics used in developing Equation (1) is based on the assumption that, at equilibrium, the entropy of the system has a minimum value. This is good for the adiabatic case. When a constant volume or constant pressure is considered, the Fermi distribution function must be derived on the basis that at equilibrium, the free energy, (Helmholtz free energy for constant volume and Gibb's free (63) energy for constant pressure) has a minimum value. A more detailed discussion is given in Appendix A. Equation (1) can be rearranged to,1 3/2 2 2m kT 1/2 1 n ) x dx n = -(2) C rr2 ' 2 1 + exp [ x+(E-Ef)/kT] f^og where x = (E.-E )/kT i g The integral of Equation (2) has been tabulated by McDougall and (42) (14) Stoner. However when (E -Ef)/kT > - 2, the Ehrenberg approxigf mation, given by 0o Co 1+ exp [x+(E -Ef)/kT] = w//[ l+4exp(E -Ef)/kT] (3) can be used, and Equation (2) becomes n = 8(2ir m kT/h )3 / l+4exp(E -E)/kT] c n g f /[ (E = 8U(m T/m )3/2/[ 1 +4exp (E -E)/kT] = 4N /[ +4exp (E -E)/kT] (4) c g f

6 where U = (2 m k/h)32 = 2.415 x 015 0 N =2U(m /m )3/ T3/2 4.83 x 1015(m T/m 3/2 c n 0 n 0 -28 m = rest mass of electron, 1.9 x 10 gmi 0 In deriving Eq. (4), only the Ehrenberg approximation is involved, and Equation (4) is good for both high and low energy differences between the bottom of the conduction band and the Fermi level. In the valence band, the energy states either must be filled with an electron or else they represent a hole so that the probability of having one or the other is unity, and the concentration of holes in the valence band, analogous to Equation (4), can be shown to be = 4N /[ 1 + 4 exp (Ef-E)/kT] (5) where p = concentration of holes in the valence band, holes/cm v N = 2U(m T/m) v p o m = effective mass of hole n E = energy level of the valence band, is taken as the V reference level = 0 eV For an intrinsic semiconductor, the electrons in the conduction band are excited from the valence band, and the number of the electrons in the conduction band is equal to the number of the holes in the valence band. n = p n, (6) C v 1 where n, = carrier concentration of an intrinsic 1 3 semiconductor, carriers/cm When the semiconductor has a high energy gap so that E >>kT, the exponential factors in the denominators of the right hand side of Equations (4) and (5) are large with respect to the factor of one, and Equations (4) and (5) can be simplified to

7 n = N exp- (E -Ef)/kT c c g f (7) v = N exp- Ef/kT v v f (8) From the viewpoint of kinetic theory, the product of the electron concentration and the hole concentration should be a constant (ni) = (const) = n p (9) i c v i, e. n, = (n )/2 1 c v (10) When Equations (7) and (8) are substituted into Equation (10), the intrinsic carrier concentration is found to be /^T ^T 1/2 n. = (N N )/ 1 c v exp (-E /2kT) g, - 2 3/4 3/2 = 2U (m m / m ) T/ n p o = 4.83x015 (m o/m)/ T3/ 0 0 exp (-E /2kT) g exp (-E /2kT) (g (11) 1/2 where m = mean effective mass = (m m ), gm o n p The concentration of the electrons in the conduction band contributed by the donor, and the concentration of the holes in the valence due to the acceptor are given(55) respectively by due to the acceptor are given respectively by and N = Nd/[ 1 + 2 exp (Ef-Ed)/kTj d d exp(E-Ef)/Td N ~ = N /a 1 + 2 exp (E -Ef)/kTJ a a at 4 - (12) (13) where Nd = ionized donors d = concentration of conduction electrons from donors, electrons/cm3 N = concentration of donors, donors/cm d

8 E = donor energy level, eV d N = ionized acceptors, 8a 3 = concentration of holes due to the acceptors, holes/cm N = concentration of acceptors, acceptors/cm a E = acceptor energy level, eV. a The carrier concentration for an extrinsic semiconductor will be given in Equation (2;;). THE FERMI LEVEL CHANGE The change in Fermi level with temperature will be discussed for both extr:nsic and intrinsic semiconductors. Extrinsic Semiconductors As a basis for discussion, an n-type semiconductor is considered. The same concepts can be extended in a straightforward manner to a p-type situation. Because a semiconductor crystal must be electrically neutral, the tctal elect:ron concentration in the conduction band must be equal to the sum of the activated donoLs and the hole concentration of the valence band. n = p + N ( 4) c v d By substituting Equations (4), (5), and (12) for n, Pv, and Nd Equation (14)) becomes 4N 4N N c, v d 1+4 exp (E -Ef)/kT 1+4 exp (Ef/kT) 1+2 exp (Ef-Ed)/kT Equation (i 5) is rather complex. However it can be simplified according to the situation concerned. In the temperature range where the impurity demoniates, p is + v much smaller: than N and the first term in the right hand side of

9 Equation (15) can be neglected. Therefore Equation (15) can be reduced to 4N N c d (16) 1+4exp (E -Ef)/kT 1+ exp(Ef-Ed)/kT By rearranging Equation (16) as a function of exp - (E -Ef)/kT, and solving for exp - (E -Ef)/kT, and hence (E -E), one obtains g f g ' N N 2 8Nd E -E E -E =- (E-E) kT ln [- 11 -N ) + - N exp g f 9 d 4 4N 4N N kT c c c (17) Case I, N = 4N Noting that (E -Ed) is always positive, and so, exp (E -E )/kT g. g d is always larger than unity, it can be shown that in case N = 4N d c so that (1 - Nd/4Nc) - 0, then Equation (17) can be simplified to d c E -E = (E -E )/2 - (kT/Z) In (Nd/2N) (18) g f gd d c Case II N << N - -d c For a low impurity semiconductor where Nd << N, but when d c the exponent (E -Ed)/kT is so large that g d (8NdlN ) exp (E -E )/kT >> 1 (19) d c g d Equation (17) can also be simplified to Equation (18). However when N << N but the exponent is so small that d c (8Nd/N ) exp (E -Ed)/kT << 1 (20) d c gd By expanding the square root into a series and neglecting the higher order terms of ( 8Nd/N ) exp (E -E )/kT, Equation (17) can be simplified tod c g to E Ef= kT In (Nc/Nd) (z1)

10 and is therefore a linear function of temperature. In the case where N << N but the exponential term under the square root in Equation d c (17) is approximately equal to unity, i.e., (8Nd/N ) exp (E -E )/kT = 1 (22) d c g d By substituting the value of (E -E ) obtained from solving Equation (22) g d into Equation (17), one obtains E - E= (E -Ed) = kT In (5N /4Nd) (23) g f gd c d Case III. N >> N d C ---c An examination for the case Nd >> N shows that Equation (18) d c is valid whenever 128 Nc exp (E -Ed)/kT >> Nd (24) while Equation (21) is valid whenever 128 N exp (E -Ed)/kT << Nd (25) c gd d It is interesting to note that the minimum value of the left hand side of Equations (24) or (25) occurs at T= 2 (E -E )/3k, and has a value m * (E -E) d of 1. 53 x 10 L n g d ] 3/2 The derivation of this result is shown m k in Appendix B, and shows the limits of applicability for using Equations (18) or (21), whenever Nd >> N d c The carrier concentration of an n-type semiconductor in the extrinsic range, where Equation (18) is valid, can be obtained by neglecting p of Equation (14) and substitute Equation (18) into Equation (1 2): n Nd N / /T exp - (E -E )/2kT ~c d c d Vd (UNd)l/ 2 (m /m) 3/4 (T) 4exp -(E -Ed)/2kT d~n 0~ g ~d~ (26) (26)

11 It is easy to understand that changing (E -E ) to Ea N to g d a c N, m to m, and Nd to N on the equations discussed v ' n p d a above will give the equations for p-type semiconductors. Intrinsic Semiconductors To evaluate the position of the Fermi level of an intrinsic semiconductor where impurity conduction is negligible, the second term in the right hand side of Equation (15) can be neglected and Equation (15) can be rearranged and solved to give exp (Ef/kT) = [ -(1-M) + (l-M)+64M exp (E /2kT) ] (27) f8 g where ' N m M - i = -, = effective mass ratio N m c n For semiconductors wherein E > 2kT,the exponential term in the square root is much larger than (1 - M), and Equation (27) can be reduced to Ef = E /2 + (3kT/4) In (m /m ) (28) However, whenever E is not greater than 2kT, then Equation (27) must be used explicitly. Summary The position of the Fermi level thus can be summarized as the following. 1. For an intrinsic semiconductor with E > 2kT gEf = E /2 + (3kT/4) In (m /m ) (28) g p n 2. For an n-type semiconductor a. E -Ef = (Eg-E )/2 - (kT/2) In (Nd/2N) (18) g xL gd d c

12 whenever [ Nd < N and (8N /N ) exp (E -Ed/kT>> 1] d c d c gd or [ N 4N ] d c or [ Nd >> N and 128 N exp (E -Ed)/kT >> Nd] b. E -E = kT In (N /N ) (21) g f c d whenever [ N << N and (8N /N ) exp (E -E )/kT < 1] d c d c g d or [Nd >> N and 128 N exp (E -Ed)/ kT< Nd] d c c g d 3. For a p-type semiconductor, Equations (18) and (21) can be used by replacing (E -E ) with E, N with Nv, m with m, and Nd g d a c v n p d with N a ELECTRICAL CONDUCTIVITY AND HALL EFFECT The electrical conductivity is a measure of the number of current carriers and the ease with which they move in the presence of an electric field. The Hall effect occurs when a magnetic field is applied perpendicular to an electric current, and a potential is induced which is perpendicular to both the magnetic field and the electric current. General Formulae for Electrical Conductivity and Hall Effect The expression for electrical conductivity is given by cr = q n l + q Pv p (29) and for Hall coefficient by 2 2 n (~ /t ) -P (I R c Hnn 1n n nv H,p p1p (30) H q (n L+ Pv 1n where a = electrical conductivity, mho/cm R = Hall coefficient, cm /coulomb H

13 2 = drift mobility of electrons, cm /v-sec. n 2 = drift mobility of holes, cm /v-sec. P 2 = Hall mobility of electrons, cm /v-sec. H, n 2 = Hall mobility of holes, cm /v-sec. H, p -19 q = electron charge, 1.602 x 10 coulombs/electron Equation (30) can be rewritten as 2 2 -cqn vp' RH = -P 03 [c n -v P where P is the ratio of the Hall mobility to drift mobility. This ratio depends on the scattering mechanism and the shape of the energy surfaces in momentum space. For spherical energy surfaces with thermal vibration scattering, p is equal to 3Tr/8. And in the case of impurity scattering, p is equal to 1.93. Formulae for Intrinsic Semiconductors In the intrinsic region, where n = p = ni, Equation (29) can be written as = ni q (pn + p) (32) Substituting Equation (11), which is good for non-degenerate semiconductors, into Equation (32) gives m 3/2 n= q ( + p ) 2U ( ) T3/ exp (-E /2kT) (33) If the mean effective mass m is constant and the electron mobility is popotional to T3/ hich would presume that lattice scattering is the proportional to T (which would presume then Equation (33) is in the fscatteringm of is the predominant mechanism), then Equation (33) is in the form of ~' = (const) exp (-E /2kT) g (34)

14 In general, E is a polynomial function of the absolute temperature. However, if it is assumed that the coefficients of higher than T are very small and can be neglected, E can be written as E = E - T (35) g g,o where E = energy gap at 0 K, eV g, 0 = the temperature dependence of the energy gap, eV/ K and Equation (34) can be written as v = [ (const) exp ( ())] exp (-E /2kT) (36) Equation (36) shows that the slope of log10 c vs i/T plot is equal to -E /4.606 k. g It will be noted that when E < 2kT, Equation (11) is no longer valid. -1.5 In the case where the mobility does not follow T temperature dependency, but follows T - E must be correlated according to g, o d log L C T(-32)] /d(l/T) = - E /4.606k (37) 10 g,o 0 However, when the electrical conductivity changes very rapidly with temperature and y is not very different from 1. 5, then the temperature correction may be neglected. The Hall coefficient of an intrinsic semiconductor can be obtained by substituting ni for n and p in Equation (31). The result gives 2 2 RH = [ 'p ] (38) q ni ([n+|Lp) or R = - t r b- 1 (39) H qn. b+l 1

15 where b = [n /p, the ratio of electron mobility to hole mobility. Combining Equation (11) and Equation (39) gives -3/2 RH g 1 U(mm 32 exp (E /2kT) (40) H q b+1 U(m /2 i. e. 3 2 RHT3 = (const) exp (E /2kT) (40a) H g Analogous to the electrical conductivity equation, it can be seen from Equation (40) that if the mobility ratio and the mean effective mass are constant and if the temperature dependency of energy gap follows Equation (35), then the slope of log10JRHT 3/ vs. 1/T plotwill provide the value of E /4.606k. g,o When the electron mobility is considerably larger than the hole mobility, Equation (32) can be reduced to -. = n, q [ (b >> 1) (41) and Equation (39) to R = - p/q n. (b >> 1) (42) H,i 1 Combination of Equation (41) and Equation (42) gives -RH = 3 n = IHn (b >> 1) (43) Equation (43) gives the relation of Hall mobility to the electrical conductivity and the Hall coefficient for n-type conduction when b >> 1. The analogy will give the similar result for p-type conduction. Whenever b is not very large with respect to unity, then the jRH i ari product gives the value of Pi3 -i LpI which is a measure of the difference between the electron drift mobility and the hole drift mobility. The Hall mobility is usually written as a function of temperature in the form

16 -T - 3 1H 1H,o 300 (44) where pH = Hall mobility H Ho = Hall mobility at 300 K = mobility scattering exponent ~ = mobility scattering exponent The value of y is dependent on the scattering mechanism, and can be (7, 9, 30,31,39, 55, 80) - found elsewhere 30,3139,55,80) and these results are summarized in Table 1- lo TABLE 1L 1 SCATTERING EXPONENT AND SEEBECK FACTOR Scattering Seebeck Scattering Mechanism Exponent (y) Factor (A) Ionized impurity - 3/2-,-1 4.0 Dislocation -1 Ionic lattice kT << h v 2.5 Neuotral impurity Neutral impurity 0 Optical polar 1/2 Ionic lattice kT >> hv 1/2 3.0 Alloy scattering 1/2 Thermal fluctuation y -y + 7/2 Lattice scattering (intra-valley) 3/2 2.0 Lattice scattering (intra + inter-valley) 1. 8^ 2. 5 Constant v vibration 5/2 " 3 1,- 0.5 Electron-hole scattering 5/2 Polar Jo[ exp(E/kT) -1] Hopping electrons J [ exp(-E/kT)] T -7 from the relationship L = oL ( 300)

17 Formulae for Extrinsic Semiconductors For higher impurity semiconductors below moderate temperatures and for low impurity semiconductors at low temperatures, the number of electrons excited from donor levels to the conduction band or excited to acceptor levels from the valence band may far exceed the number of electrons thermally excited from the valence band to the conduction band. If only one type of the carriers dominates the conduction and Equation (26) is valid, the equations of the electrical conductivity and the Hall effect for n-type semiconductors reduce to 1/2 I 3/4 3/4 % = q npB = qji (UNd)l/ (m /m 3/4 T3/4exp-(EE)/2kT q n 11 q Sr (U N)'/Z~ mn /M ] T exp -(E -E )/2kT (45) and R = -/q n Hn c 1/2 * 3/4 -3/4 = -L p/(UN (m /m )3/4] T exp (E -E )/2kT d o g d (46) 3/4 Equation (46) indicates that a log IRHT 3/ vs. 1/T plot gives a slope of (E -E )/4 606 k g d For p-type semiconductors, they become p = q Pv 1 (47) p v p and RH = P/ q P (48) The Icr RH n or Jo- RH, p product gives an equation the same n -n.^ p I p as Equation (43). (68) Smith, in a derivation analogous to that used above for the energy gap, shows that a plot of the natural logarithm of carrier concentration versus reciprocal absolute temperature will have a slope of either AE/2k or AE/k, where AE is the distance between the donor level and the conduction band for n-type, or between the valence band to the acceptor level for p-type semiconductors. Since both donors and acceptors are

18 present, the carrier concentration observed from the Hall effect measurements is the difference between Nd and Na and the energy level d. a observed is that which dominates. When the temperature dependency -3/2 of the mobility is T (lattice scattering), then, aE of the dominating carrier can be estimated from the slope of the plot of logatithm of the electrical conductivity versus reciprocal absolute temperature. Mobility Ratio from the Electrical Conductivities and the Hall Coefficient In a near-intrinsic semiconductor, both holes and electrons contribute to the Hall effect as is shown in Equation (31), And when b is substituted for ~i / p, Equation (31) becomes [n b - ] 13 c v R = - v (49) H q [n b+p ]2 c v Since b is almost always greater than unity, the Hall coefficient for p-type samples must pass through zero before going into the intrinsic range. The temperature at which the Hall coefficient goes through zero is called the Hall inversion temperature. The mobility ratio at the Hall inversion temperature can be estimated in such materials from electrical conductivity and Hall effect measurements made at the Hall inversion temperature and below. Measurement in the temperature region where impurity conduction dominates can yield a value for the acceptor concentration, N, and the Hall mobility, Lp, as a function of temperature. a p Therefore, at the Hall inversion temperature, it is possible to compute the hole component of the electrical conductivity. At this temperature, the total hole concentration p is given by p = n + N (50) v c a And the electrical conductivity at this temperature, (a)R=0 according to Equation (29) is given by

19 ()R0 = qnc + q P p =q nc + q n c + (N ) qip c n c p a p q n (b+ 1) p + o (51) c p p where o- is the portion of conduction contributed by the holes P due to the ionization of the acceptor. However, it follows from Equation (49) at the Hall inversion temperature where R = 0 that n b2 = p (52) c v And, substitution of Equation (52) into Equation (51) gives R =0 b = H (53) RH=0 _ SEEBECK COEFFICIENT The Seebeck coefficient results from the diffusion of electrons and holes inside a material when a thermal gradient is present and the electric current flow is zero. In semiconductors the Seebeck coefficient may be a factor of 100 to 1000 higher than that of metal, such as platinum, which is used in the measuring circuit. This means that it is usually not necessary to distinguish between the absolute Seebeck coefficient and the Seebeck coefficient relative to the metal The Seebeck coefficient, which can vary rapidly with temperature, is a function of Fermi energy level and the scattering mechanism. Since the Fermi energy level is influenced by impurity concentration, mobility, and the effective mass, the Seebeck coefficient is dependent on these factors, and especially on the impurity concentration,

20 General Formulae for the Seebeck Coefficient (39) Mason ) has shown that the complete Seebeck coefficient for a p-type semiconductor can be given by Ak V Ak = P - (54) p q T and for an n-type semiconductor by V -V Ak. g n (55) a -(-A j - -- ) (55) n q T where a = Seebeck coefficient, volt/ K A = Seebeck factor, a constant dependent on scattering exponent, summarized in Table 1. 1 * V = Imref potential for n-type semiconductor, volt. n V = Imerf potential for p-type semiconductor, volt. p V = gap potential for semiconductor, volt, g Since the potential change associated with the change in energy is E = qV (56) Equations (54) and (55) can be rewritten into Ak E* p = ( + _ — ) (57) p q qT Ak E -E a = -(Ak < + g n (58) n q qT (32) Johnson developed an expression for the Seebeck coefficient of semiconductors in terms of the mobility ratio, energy gap, temperature dependence of the energy gap, and the ratio of electron hole effective masses. With assumptions that the classical statistics holds, she gave n p a = - k — ) [ A(n b-p ) - n b n P In (59) q(n b+ p ) c v c N v N c v c v

21 Equations (57) and (58) are more convenient for the discussion of an extrinsic range while Equation (59) is for the intrinsic region. Seebeck Coefficient in the Extrinsic Range When the Imref level is approximated by Fermi level, the Seebeck coefficient of an extrinsic range is obtained by substituting either Equation (18), Equation (21), or Equation (23) into Equation (57), or corresponding equations for p-type into Equation (58). The suitable equation must be chosen according to the condition. More detailed discussion on the change of the Seebeck will be presented in the text of the explanation of the experimental results when it is required. Seebeck Coefficient in the Intrinsic Range For an intrinsic semiconductor, n = c this condition together with the definitions of Equation (44) gives p = n,. Imposing V 1 N and N into c v qk E = _ — (b ( + a q q b+1 { 2kT A(b-l) A(b1) (b+l) 3 4 m In n ] m p (60) If the energy gap is a linear function of temperature as presented in Equation (35), then Equation (60) becomes k ( b-l) a = - ( b+l E m,E g - i- + A + 3(bl) In n 2kT 2k 4(b-l) in, m P (61) Equation (61) shows that the slope, m, and the intercept, c, of the plot of Seebeck coefficient versus the reciprocal absolute temperature are k b-1 I, m = -- ( q b+l 2k k b-1 3 n c = -q (b ) (A- ) In n q b+i 2k 4 m p (62) (63)

22 Using the value of the energy gap obtained from the electrical conductivity or the Hall effect measurements, one can obtain b, the mobility ratio from Equation (62). As the first approximation for the effective mass ratio, the expression b = (m / m ) I (64) p n can be used, which is applicable for semiconductors with spherical energy surfaces in the temperature region where lattice scattering predominates. The value of A can be determined from the temperature dependence of the mobility from RH o plots, and the temperature dependence of the energy gap, (, can be obtained from Equation (63).

CHAPTER 2 EXPERIMENTAL PROCEDURE This section describes the experimental procedures used in obtaining the materials and data. SAMPLE PREPARATION All samples were prepared from the high purity elements, 99. 99+% for Ag and Cd, and 99. 999+% for Te, Se, In, and Cu. The elements used to prepare InSe and In Se3 were moreover, purified by heating in a hydrogen atmosphere. The surfaces of indium, cadmium and copper were etched and dried before used. Stoichiometric quantities of the elements were sealed in a specially cleaned fused silica tube and evacuated to -5 5 x 10 mm Hg or lower before sealing. The sealed elements were fused in a digital temperature programming unit described by Hozak, Cook, and Mason. ( After fusion, each sample for differential thermal analysis (DTA) was ground to a powder and rebottled in a specially cleaned fused silica DTA tube. For each zone refining sample the fused compound was transferred to a zone refiner while it was still hot. Since the tubes containing InSe often cracked during the zone refining, they were sealed in a second fused silica tube which also had been evacuated to 5 x 10 mm Hg or lower, in order to prevent them from being oxidized and spoiled. The zone refiner was operated at a zone travel rate of 3/4 inch per hour with a liquid zone about one inch long. For peritectic compounds, the (9) zone leveling technique described by Cook and Mason was used. The zone travel rate was about 0 3 inch per hour in both directions. A Bridgeman furnace was used to grow a single crystal. A more detailed description of the sample preparation is given in Appendix Co 23

24 DIFFERENTIAL THERMAL ANALYSIS MEASUREME NT The differential thermal analysis measurements were made in a (5) furnace described by Barnes et al. The heating and cooling rates were about 2. 5 C per minute, indium being used as the reference material. The differential temperature between the sample and the reference material was recorded versus the sample temperature on an x-y recorder. The DTA tube was made of 10 mm I. D. fused silica tubing with a concentric 4 mm.lo D. fused silica tube about one inch long in the bottom to accommodate a thermocouple. The more detailed description of DTA is given in Appendix D. The equipment was used to determine the characteristics of the heating and cooling curves for several compositions in the In-Se binary system, the Ag Te-In Te3 pseudo-binary, and CuzTe-In Te pseudo(49) binary system in addition to the information presented by O'Kane and Kulwicki. ( CHEMICAL ANALYSIS A chemically analyzing scheme was designed to analyze for Ag, Cu, In, and Te. Tellurium was reduced and precipitated to elemental form with sulfur dioxide saturated hydrazine solution. Indium and copper were titrated with ethylene-diamine-tetra acetic acid (EDTA) with and without complexing the copper ion by KCN. Silver was titrated by the Volhard Method using KCNS, The detailed procedures are given in Appendix E. The result of the experiment indicated that the tellurium analysis was satisfactory while that of indium, silver, and copper were marginal. The scheme was used to determine the compositions of CuInTe2, In3Tes, and the silver content of Ag2In Se 3.

25 X-RAY ANALYSIS X-ray photographs were taken on powdered samples of InTe, InzTe3, In3Te5, InSe, In Se3, and AgzIn8Se13, using Cu Ka i (K Ka) = 1.54178 A ] or Cu K a radiation with appropriate mean filter (ni for Cu, V for Cr) in a Debye-Sherrer camera of 11.46 cm. diameter. In each case, the sample exposure time was six hours. The x-ray photograph was measured with an accuracy of 0. 01 mm. including the correction for observed sample limes from the standard germanium lines. A more detailed description of the x-ray work is given in Appendix F. DENSITY MEASUREMENT Densities of InTe Te, InTe InSe, In Se3, Ag In8Se13 and Cdln Se4 were measured using a liquid immersion technique with either water or ethanol as the immersion fluid. One InTe density was measured by Beckman air comparison Pycnometer. MICROSCOPIC ANALYSIS The zone refined ingots were polished either on one side or on the bottom first with emery paper and then with Linde polishing powder, type B. The microscopic inspections were performed before and after the surfaces were etched with Dano solution, having the composition 33 ml glacial acetic acid 23 ml concentrated hydrochloric acid 5 ml concentrated sulfuric acid 3 ml concentrated nitric acid 29 ml 15 gm CuC12/100 ml H20 7 ml 33 gm CrO3/100 ml H0 This etching solution was satisfactory for etching compounds CuInTe2, CdIn Se, Ag In Sel, AgIn Te 4, CdIn2Te4, InTe, and In Te3. It was unsatisfactory for etching the compounds InSe, In Se3 and some compositions of the In-Te system. A red strain deposited on the etched surface.

26 Pure nitric acid, sulfuric acid and hydrochloric acid were tried for these compounds. The results were also unsatisfactory, ELECTRICAL MEASUREMENTS Electrical conductivity and Hall effect measurements were carried (38) out by conventional d. c. techniques described by Lindbergo ( The desired current level through the sample was attained by placing external resistors in series with the sample. To eliminate the contact resistance, six separate current and potential leads were applied to the sample for the measurement of the electrical properties. The potential drops across the leads were taken for both the forward and reverse current directions. Hall effect measurements required reversing the directions of both the magnetic field and the electric field, to eliminate the potentials resulting from non-alignment of the Hall probes, the Nernst effect, and the RighiLeduc effect. However, it does not remove the Ettingshausen effect which is generally small in comparison with the Hall voltage. Seebeck voltage and the differential temperature across the specimen were measured to calculate the Seebeck coefficient. Electrical Specimen The electrical specimens were cut from a zone refined ingot or from an ingot grown in a Bridgeman furnace. The dimensions of each specimen were about 0. 7 inch long, 0. 15 inch wide and 0. 1 inch thick. Each specimen was lapped to dimensions with emery paper and polished with Linde B polishing powder, followed by cleaning in an ultrasonic cleaner ("Sonogen" Model AP10, Bronson Ultrasonic Co., Stamford, Conn.). Every specimen was microscopically inspected before the measurement. Six platinum wires (30 or 32 gauge) were fused in the ends and along the sides of the specimen. The two wires fixed in the ends of the specimen served as the path of electric current for the electrical conductivity and Hall effect measurements, and also for reading Seebeck

27 Seebeck voltage. Two wires, each fixed at the center of opposite sides of the specimen served for reading Hall voltage. The remaining two wires, fixed in one side of the specimen, were used to read the potential drop along the specimen to check its homogeniety and compute the resistivityo The dimensions of the polished specimen and the spacing of the platinum wires along the length of the sample were measured with a toolmaker's microscope. More detailed description of the electrical measurements is given in Appendix G. DESCRIPTION OF EQUIPMENT (49) The equipment was originally built by O'Kane. Several parts of the unit have been modified, but the main principle remained the same. The detailed description of O'Kane's equipment is given in Appendix H. Modifications of the Equipment The equipment as originally built by O'Kane had several defects. The sample shield supporting device was made of copper which might cause a contamination of the sample during the measurements at high temperature. The silver wires insulated by ceramic tubing, had to be replaced every two or three measurements. The wire insulation and the connectors were not good enough to permit the measurement of very high resistivity material. Also, it was sensitive to the environmental disturbances. To change the polarity of the magnetic field, the whole permanent magnet had to be rotated 180. The equipment could not be used to measure semiconductors which might decompose at high temperature. The irreversibility of the properties of Ag2In8Se13 reported in O'Kane's thesis is a good example, The following modifications, improving these defects, have been done:

28 1. The shield and the heat reservoirs were machined of molybdenum rod. Fansteel 77 tubing was used for the support. These modifications minimized the possibility of copper contamination in the high temperature measurements. 2. 18-gauge tungsten wires, insulated by fused silica tubing were used as the conducting medium. To prevent the wires from being contaminated or attacked by the vapor of the sample during the measurements, the lower part of the insulation was made of a solid Lavite rod. In this way, the conducting medium could be a permanent one, and the exposing of silver wire to a high temperature was also avoided. Platinum wires were joined to the ends of the tungsten wires to facilitate the connection of the platinum probes of the sample to these conducting media. 3. Highly insulated coaxial wires and coaxial connectors were used in all the external wiring of the equipment. This modification made the equipment capable of measuring very high resistivity material and at the same time, inert of the environmental disturbances. 4. A Varian model 4004 electrical magnet was installed, taking the place of the permanent magnet. Figure 2. 1 shows the construction of the measuring unit after the modification. The Gremar coaxial connectors were mounted on the top of a brass bucket while the multi-lead header assured the system of being air tight. Silica gel was placed in the bucket for keeping the insulator dry. With the "O" ring seal device and a Vycor tube, an inert gas can be introduced into the system for protecting the system from being oxidized. Lavite insulation separated the high temperature portion from the high conduction Fansteel tubing and kept the upper portion cool. The molybdenum heat reservoirs stabilized the sample temperature. By adjusting the power input to the upper and the lower heaters, the temperature and the temperature gradient across the sample could be well controlled.

29 TO VACUUM PUMP OR ARGON TANK LAVITE MOLYBDENUM SHIELD INSULATION VYCOR TUBE AND HEAT RESERVOIR A~ ~~- (\ FAN STEEL 77 TUBING COAXIAL CONNECTOR LOWER HEATER UPPER HEATER COCOON AND SAMPLE TUNGSTEN WIRES O- RING SEAL MULTI-LEAD (INSULATED BY DEVICE HEADER SILICA TUBING) THERMOCOUPLE 's};g DIFFERENTIAL THERMOCOUPLE SAMPLE PLATINUM WIRES FOR HALL EFFECT, PLATINUM WIRES ELECTRICAL CONDUCTIVITY FOR CURRENT Figure 2. 1. Schematic Diagram of the Measuring Jig and Cocoon Arrangement.

30 Cocoon Arrangement A cocoon technique, limiting the free space around the specimen and so suppressing the decomposition of the specimen during the measurements was developed. Figure 2.1 also shows a part of the construction of a cocoon. The specimen, together with a differential thermocouple and a thermocouple (for measuring the sample temperature) was sealed in two halves of a fused silica cyclinder (only one-half is shown in the figure) with Sauereisen cement. After the cement had dried, the cocoon was evacuated and sealed at the tail. The volume of the cocoon was less 3 than two cm. The samples were measured under their own vapor pressure by this technique instead of under vacuum or one atmosphere of an inert gas. By introducing Se or Te into the cocoon, the decomposition of the samples was suppressed in some cases. Result of the Modification The equipment thus modified is now able to detect a voltage drop across the sample at a current of 0. 5. a. Since it is insensitive to the environment disturbances, the galvanometer does not fluctuate during measurement and a precise value can be read from a K-2 potentiometer. The intensity of the magnetic field can be varied up to 8000 gauss and magneto-resistance can be measured if desired, the magnet rotation for changing the polarity of the magnetic field is no longer being necessary. The cocoon technique suppressed the decomposition of some of the samples during the measurement and made the measurements reproducible. This will be demonstrated in discussing the semiconducting properties of In3Te5 Extra Se sealed in the cocoon made the properties of the second heating cycle of InSe different from that of the non-extra Se one. Extra Se in the cocoon also gave a significant difference in the properties of the second heating cycle of AgZIn8Sel3 from the case wherein no extra Se was added.

CHAPTER 3 SEMICONDUCTING PROPERTIES OF In Te -- 3-5 LITERATURE REVIEW A review of the literature on the phase diagram of the In-Te (25) binary system, up to 1956 is given by Hansen, who shows a phase diagram of the In-Te system, including two congruently melting compounds, InTe and In Te, melting at 696 C and 667 C, respectively, and two peritectic compounds, In2Te and In Te5, melting at 460 C and at about 4550C, respectively. Grochowski et al) in clarifying and correcting this phase diagram of the In-Te system, found two new peritectic compounds In3Te4 and In Te, melting at 650 C and 625 C, respectively. Grochowski also claimed that the phase In Te exists at the composition In Te which melts at 462 C peritectically. The melting point of In2Te5 97 2 5 is corrected to be 4670C, the composition of InTe is claimed to be In30Te31, and In2Te is claimed to be In27Te40. Grochowski has measured the electrical conductivity of In3Te5, reporting an abrupt increase of the electrical conductivity at 445 ' 4600 C and an energy gap obtained from the data above 500~C of 0.99 ~- 1.06 eV. His x-ray measurements on the high temperature form shows that In 3Te5 crystallizes in a hexagonal structure with the lattice constants of o o a = 13. 27 A, c = 3.56 A, and c/a = 0. 27. The density of his material was 5o 87 gm/cm. EXPERIMENTAL RESULTS The ingot used in this work was prepared by the zone leveling (9) technique described by Cook and Mason. The microscopic analysis before and after being etched with Dano solution both showed a single phase except at the very ends of the ingot. The electrical conductivity and the Hall coefficient results are shown in Figure 3.1 and Figure 3.2. Specimen No. 207(2A) was 31

32 10 -6 I0 I E 0 So E >-" IO-I - - O 103 0 -J LLJ 10 Figure 3. i64 Figure 3.1. 1-8 I0O 10......r 1 F-'"ctd -E, 'TRS \R I I o-'~ no gTcorrectionf E corrected byReciprocal Absolu 0.37 eV/u 0.43 e5V'rng A e-m0.36 eVn-...._ _ _ _ _ _ _ _ _ ___~~~~~ 10 -1.4 1.8 2.2 2.6 3.0 3.4 3.8 RECIPROCAL ABSOLUTE TEMPERATURE ( IO3/T),(~K)Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for In 3Te 5, Showing the Stabilization Effect of The Cocoon Arrangement.

33 TEMPERATURE, t, (~C) 727 560 441 352 282 227 181 143 III 84 60 39 21 4 -10 I 08 107 ICU cr I n3 Te.. — ____ _ _ _ __a 207 (3) First heating cycle.. = === -- —: — o 207 (2A) First heating cycle I \. ^ ^^^ -- — ^ — o 207(2A) Second heating cycle - ____~____. ___ A 207 ( 3 ) Second heating cycle * o 207 ( 4 ) First heating cycle * i in cocoons ___ I I iuI 105 1.0 1.4 L.8 2.2 2.6 3.0 3.4 RECIPROCAL ABSOLUTE TEMPERATURE, IOO0/T, (~K-) 3.8 Figure 3. 2. 3/2 Logarithm of I RHT | versus Reciprocal Absolute Temperature for In3Te, Showing the Stabilization Effect of the Cocoon Arrangement.

34 measured without the cocoon arrangement under hydrogen atmosphere, After a measurement up to 585 C, the first heating cycle, the specimen was cooled down to room temperature before the second heating cycle was made, to a maximum temperature of 607 C. The specimen has an -4 electrical conductivity of 5 x 10 mho/cm at room temperature and a Hall coefficient of 800 cm /coulomb at 1400C. An abrupt 10-fold increase of the electrical conductivity was observed at 4600 C which agreed with Grochowski's data. It is clearly seen that the properties of the specimen No. 207(2A) in the low temperature range cannot be recovered because of the heat treatment of the first heating cycle. The Hall coefficient at low temperature showed that the specimen was p-type, the Hall inversion temperature occurring at 360 C. The logarithm of the I o- RHI product vs. logarithm of absolute temperature shown in Figure 3.3 indicates that the specimens have a hole mobility of 2 5 20 cm /v-sec. and that at low temperature, the mobility varies as T1. At the transition temperature of about 450 C the mobility decreases abruptly. Specimens No. 207(3) and No. 207(4) were measured with cocoons made of Lavite, sealed with Sauereisen cement, and protected in a hydrogen atmosphere. The electrical properties measured with this cocoon arrangement are reproducible for the second heating cycle of specimen No. 207(3). The rate of the increase of the conductivity with respect to the temperature of these two specimens at the lower temperature range were lower than specimen No. 207(2A). The Hall inversion temperature occurred at 345 C for both specimens. A T * dependency of the Hall mobility was observed for specimen No. 207(3) while T * dependency was observed for specimen No. 207(4) at the lower temperature region. A plot of log RHcr against reciprocal absolute temperature indicates that the mobility may be limited by a Boltzmann activation energy of about 0. 1 eV, but the data scatter too much to establish this conclusion definitely.

35 I 0 LJ U) 0 > C) b a: FI 0 -J -j < I 0 9 8 7 6 5 4 3 2 In3Te5 o 207 (2A) F * 207 (2A) S A 207 (3) F A 207 (3) S o 207 (4) F x in cocoons irst heating cycle iecond heating cycle irst heating cycle f;econd heating cycle irst heatihg cycle * I 100 300 ABSOLUTE TEMPERATURE, T, (OK) Figure 3.3. Logarithm of I RH r versus Logarithm of Absolute Temperature for In3Te 5

36 X-ray analysis made on the low temperature form of In3Te5 indicated that it is not hexagonal as is the high temperature form. Nor it is cubic or tetragonal. The sin a values of In Te of both high and low temperature forms are given in Appendix F. INTERPRETATION AND DISCUSSION OF THE RESULT S 1. In3Te5 specimens measured have the carrier concentrations of about 106 holes/cm at 140 C, calculated according to Equation (48). 2. The T dependency of the Hall mobility of the specimens in the temperature below 500 K indicates that in this temperature range, the ionized impurity scattering dominates the conduction. The mobility of specimen No. 207(4) is rather scattered in the lower temperature region, and the scattering exponent cannot be well obtained. However, -1.5 A-2. 5 is a good estimation. When the logarithm of the Hall mobility vs. 1/T is plotted for specimen No. 207(4), a straight line of negative slope (4) is obtained, indicating that there may be the hopping mechanism with an activation energy of about 0. 10 eV. However the scattering of the data leaves it as a question. 3. The mobility ratio, b = n /Bp, calculated according to Equation (53) gives the values of 3. 9 ^ 10 for all the specimens. Hence the electron mobility may vary from 20 to 80 cm /volt-sec, or from 50 to 200 cm /volt-sec. 4. The abrupt increase of the electrical conductivity at the temperature of 4600 C is associated with the transformation of the crystal structure identified by x-ray analyses which are summarized in Appendix F. 5. The increase of the electrical conductivity and the decrease of the Hall coefficient in the second heating cycle over the first heating cycle for specimen No. 207(2A) which was measured without the cocoon arrangement indicates that the specimen loses an constituent which in turn creates more acceptors by the heat treatment of the first heating cycle, while the reproducibility of the properties for the specimen

37 measured in the cocoon indicates that the cocoon prevents the specimen from decomposing during the measurement. The higher activation energy for electrical conductivity at the low temperature region and the higher Hall inversion temperature of specimen No. 207(2A) over that of specimens No. 207(3) and No. 207(4) arises from the decomposition of the specimen. 1.5 6. Since the specimens showed a T temperature dependence of mobility below 500 K, a T correction of the electrical conductivity must be made for this temperature region in evaluating the acceptor energy level. However, above 500 K the activation energy is much higher and the influence of the pre-exponential factor is less. If this -1.5 mobility has a T temperature dependency (characteristic of lattice scattering) no temperature correction is required. Figure 3. 1 also shows the curves for the corrected electrical conductivity for the specimens which are in arbitrary units. These curves show that there is an acceptor at 0.37 eV. The 0.74 eV appears to be the intrinsic energy gap of the low temperature form of In 3Te5 since it shows up in the temperature region above the Hall inversion temperature. The 1.09 eV probably represents the energy gap of the high Temperature form of In Te5 Flat straight lines appearing between 1000/T of 1.8 '- 2.2 for specimen No. 207(2A), 2.0, 2,.3 for specimen No. 207(2A), and 1.7 ~ 2. 0 for specimen 207(4) show that in this temperature region, the acceptors in each sample were saturated, and the specimens have the constant carrier concentration. The impurity concentrations, N, for the specimens obtained from these a 3 regions are 1.34 x 10 acceptors/cm for specimen 207(2A), 0.9 x 10a acceptors/cm3 for specimen No. 207(3), and 0.7 x 1016 acceptors/cm for specimen No. 207(4),

CHAPTER 4 SEMICONDUCTING PROPERTIES OF In Te 2-3 LITERATURE REVIEW In Te was one of the simplest type of defect structures in which some of the crystallographically equivalent sites are only partially occupied, and has been investigated by many investigators. (22) Hahn and Klinger from x-ray powder photographs and density measurements, found that In2Te3 has a face centered cubic lattice o 3 4 with a lattice parameter a = 6. 158 A, d = 5.75 g/cm and z = -InTe3/ (29) unit cell, Inuzuka and Sugaika later on found that In Te also o 3 exists in 3-modification, with a = 18.40 A, d = 5.78 g/cm and (2) z = 36. 5 In Te3/unit cell. Appel and Lautz measured the electrical conductivity of InZTe3 and showed that there were two activation (26) energies, 1.0 eV and 2.4 eV. Harbecke and Lautz reported E g as a function of temperature from their optical measurements. Gory(18) unova et al reported an energy gap of 1.0 eV from his optical data. (44) Miyasawa and Sugaike on the other hand gave E of 1. 2 eV for g In2Te3 at the room temperature. Sergeeva and his co-workers have (78) investigated the electrical properties, the phase compositions, (77) (52) x-ray analysis, the optical and photo electrical properties, ( (53, 54) and the thermal conductivity of In Te and showed that the a-3 transformation occurs at 500 " 550~C, Their data are in general agreement with the published data although having slightly different numbers. Apparently none of these authors used zone refined ingots for their specimens, EXPERIMENTAL RESULTS The ingots No. 1212 and No. 1224 were prepared by zone refining. Ingot No. 1212 had an original composition of 59. 9% Te, whereas 38

39 ingot No. 1224 had an original composition of 60c 2% Te. Each ingot had 21 zone refining passes and was slowly cooled, Hence ingot No., 1224 should have a higher residual excess tellurium content than ingot No. 1212. The microscopic analysis showed that the ingots were single phase. The density measurements and the x-ray analysis made on specimen No. 1212(1B) gave d = 5.858~.04 gm/cm (crystal segment using water as the immersion medium), and the cubic lattice 0 2 parameter, a = 6, 163 A. The sin a values are listed in Appendix F, The electrical conductivity, Hall effect, and Seebeck coefficient measurements have been made on specimens No. 1212(2) and No, 1224(3) with extra Te in the cocoon and, on specimens No. 1212(3) and No, 1224(2) without Te in the cocoon. Figure 4, 1 shows the 3/2 electrical conductivity and R T /plots for ingot No. 1224 (containing excess Te). Below 420 K, an apparent donor energy level calculated according to Equation (36) and Equation (44) of 0, 96~, 05 eV is observed on the first heating cycle which increases to 1 03 eV on the second heating cycle, For temperatures between 4500K and 600 K, the initial activation energy of 1. 06 eV increases to 1. 1 5~. 04 eV for the second heating cycle. Above 750 K. a very high energy gap of 2 eV or over is observed on the first heating cycle, but it becomes 1. 33~, 03 eV on the second heating cycle, No obvious difference is observed for specimens measured with and without Te in the cocoon., 3/2 The electrical conductivity and R T data for ingot No, 1212 H are shown in Figure 4o 2. Below 450 K, a reproducible donor activation energy of 1 05~, 02 is observed. From 4500K to 7000K. a second activation energy of 1. 1 6~, 08 eV is observed, and these data are also quite reproducible. Above 720 K, a reproducible activation energy of 1, 63~. 03 eV is observed, The first and second cycles are reproducible; with or without tellurium, whereas the third cycle on specimen No, 1212(3) without Te shows an increase in conductivity at low temperature. Figure 4 3 shows the plot of the logarithm of I RH Co of InzTe3 vso the

40 TEMPERATURE, t, ('C) 60 21 -10 i u Iz E bi -i w.I -J 727 441 22 ' I i - I00 _ = o -- 1224(2) First heating cycle =I = _ _._ _ - -* 1224(2) Second heating cycle. 4 __ _. 0- 1224 (3) First heating cycle - o0 1224(3) Second heating cycle 10,- ~,w1.3t7 eVv__ __. | ~~~~1.v i I(~ " '~.... — l.Oe eV —,.,e" %' = 10~- /J=:1.18 /-1.03 eV= \,!.0-4. '7~ 1.04* 1.07, Vi 1.3' e1.|1=^ || | 'o' / 1.36 eV I0'e _ _ _ _ _ _ _ I I__ 10s I I 1.0 1.4 1.8 2.2 2.6 3.0 5.4 RECIPROCAL ABSOLUTE TEMPERATURE, IOOO/T, (~K-') Figure 4. 1. Logarithm of Electrical Conductivity and Logarithm of |RHT3/ versus Reciprocal Absolute Temperature for In Te3, Ingot No. 1224, Showing the Properties of In2Te3 with Excess Te in the Compound.

41 TEMPERATURE, t, (C) 928 181 III 60 797 417 21 -10 100. * I I I I I 10 I0 oz 10 o 0 -j 4 U U bJ W 1d II Ai 5 e\ 5 e\ C~Thl TF F: - i i i f I / 1.14 e a r | | | A4 1212(2) FI|rst heatin cycle 1212 ( 6 eVting oF 1212(3) Flrst heating cycle r 1Ti. v ^ l", e -- -- -- -- - * 4- 1212 (3) Second heoting cycle 1.23I h eV &00 1212(3) First heating cycle * -*- 1212(3) Second heating cycle 1212(3) Third heating-cycle ldo le' le' 10 106 107 loe 10o 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 RECIPROCAL ABSOLUTE TEMPERATURE, 1000/T. (KK') Figure 4. 2. Logarithm of Electrical Conductivity and Logarithm of IRHT3/ Z versus Reciprocal Absolute Temperature for In2Te3, Ingot No. 1212, Showing Characteristics of the Congruent Compound.

42 u i 0n 4.o N E Il 0 - - _I., m J 1000 TEMPERATURE, T (~K) Figure 4. 3. Logarithm of IRH I versus Logarithm of Absolute Temperature for In2Te3

43 logarithm of the absolute temperature. A change in the slope of all the curves is observed at about 600 0K Above this temperature, the -15 -2.5 mobility of In Te has a T to T 5 temperature dependency -1 while below this temperature, it is T. Furthermore, the mobility decreases at low temperature for all specimens on the second (and third) heating cycle, the decrease being more pronounced in ingot No. 1224 (with excess Te). The Seebeck coefficient also shows n-type characteristics. It increases (decreases in the magnitude) as the temperature increases except in the temperature between 550 K to 700 K as shown in Figure 4. 4, where Seebeck coefficients are plotted as a function of reciprocal absolute temperature. At 150 C, the Seebeck coefficients of the specimens are about -1.0 mV/ K, while at 590 C, they are about -0.3 mV/ K. The slopes of the Seebeck curves give activation energies which are in general conformity with those obtained from the electrical conductivity and Hall coefficient data. DISCUSSION 0 1. With the cubic lattice parameter of a = 6. 163 A for In Te3, 3 23 the theoretical density of In Te is 5.78 g/cm, assuming that one 2 35 unit cell contains 4/3 formulae of In Te3. The pycnometric density of 3 In2Te3, 5.858 g/cm indicates that the specimen has interstitial atoms in the structure. Since In Te3 has cation vacancy in the structure, it is possible that the interstitial atom is In. If this is the case, the composition of In Te3 calculated from the x-ray and density data is In 067Te3 or In40 Te59. This result shows a higher medium 2.067 3 40.8 by, 2 concentration than that obtained from chemical analysis by Grochowski (12) et al. 2. At 720~ to 750 K, the rate of increase of the electrical conductivity decreases markedly, then increases much more rapidly than originally. This is associated with the phase transformation from

44 0 -100 -200 y: 0. -300 -. -400 z w ^ -500 Z LUJ o -600 UL w -700 0 0 Y -800 0 -900 m -900 LJU L ~IJnr -- j ^^ =.5o — _ m = 0.65 volt... i - A. - I& - I - AV -........ &7 I I I \ I I /, m = 0.50 volt-= I I I L N x 1 A 1212 (2) A 1212(2) o 1212 (3) * 1212 (3) e 1212 (3) o 1224(2) * 1224(2) o 1224(2) * 1224(2) I I In2 Te3 First heating cycle Second heating cycle - First heating cycle Second heating cycle - Third heating cycle First heating cycle Second heating cycle First heating cycle Second heating cycle -I vvv -1100 - 1200nn I L I I 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 RECIPROCAL ABSOLUTE TEMPERATURE, IOOO/T, (~K-') Figure 4. 4. Seebeck Coefficient versus Reciprocal Absolute Temperature for In2Te3. f 3.

45 a-modification to P-modification. The energy gap of 1.65 eV in ingot No. 1212 apparently is the intrinsic property of 3-modification whereas 1.14 eV is the intrinsic energy gap of the a-modification. The activation energy of 1.35 eV observed from the second heating cycles of specimens No. 1224(2) and No. 1224(2) in the electrical conductivity data and, from the Hall coefficient data, may represent the energy of transformation of a- to 3-modification. The a, P transformation also shows up in the Seebeck coefficient and the mobility data but at lower temperature. 3. The mobility ratio calculated according to Equation (62) is 15.3 for the first heating cycle of specimen No. 1212(3) between 5200 to 620 K, 38 for the second heating cycle of specimen No. 1224(3) between 650 to 800 K, and 15 for the second heating cycle of specimen No. 1224(2) above 6500K. -1.5 -2. 5 4. The T to T temperature dependence of mobility shows that the scattering is predominantely by lattice phonons. 5. Using the observed lattice parameter, a = 6. 163 and the o accepted value of the Te covalent radius, 1.32 A, the In in the structure containing In vacancies has an effective radius of only o o 1.35 A, which is 6-1/ 2% less than its accepted value of 1.44 A. which it exhibits in stoichiometric compounds (as InSb, InAs, etc.). Hence it is concluded that this effective lower value of In must be used for structure calculations when In exists in defect structures containing In vacancies. SUMMARY The x-ray analyses and the density measurements made on a zone refined In2Te3 specimen indicated that In2Te crystallizes in o 3 cubic habit with the parameter a = 6 163 A, that density of In2Te3 is 5.858 g/cm, and that the composition of the material is In0 Teo The electrical conductivty Hall coefficient, and Seebec a coefficien 2 The electrical conductivity, Hall coefficient, and Seebeck coefficient

46 data all indicate that In2Te3 has a crystalline transformation in 720~K to 7900K which agrees with Sergeeva's (53 54 77 78) data. The energy gap estimated from the electrical conductivity and the Hall effect are 1. 14 eV for a-modification and 1, 65 eV for I3-modification. The mobility ratio estimated from the slope of Seebeck coefficient against 1/T are 15~' 40 for In2Te3. The properties and their stabilities on repeated temperature cycling are sensitive to the crystal composition, being more stable as the composition of the congruent melting point is approached. An excess of Te contributes to this variation and instability. Samples with a Te deficiency were not examined.

CHAPTER 5 PHASE DIAGRAM BEHAVIOR OF THE PSEUDO-BINARY SYSTEM OF Ag2Te-In2Te3 AND SEMICONDUCTING PROPERTIES OF AgIn9Tel LITERATURE REVIEW (23) Hahn et al have made x-ray analyses at six compositions within the Ag2Te-InTe3 pseudo-binary system, and reported that all the materials crystallized in chalcopyrite structures. Austin et al( (79) and Zhuze et al made studies on the optical and electrical properties for AgInTe2 and reported that the energy gap is 0. 9 eV for the (49) compound. O'Kane made eight DTA measurements for the compositions within the Ag2Te-In2Te3 pseudo-binary system and proposed a partial phase diagram for the system. O'Kane also investigated the electrical properties of AgIn3Te5. No work has been done on the compound AgIn Te 14' EXPERIMENTAL RESULTS DTA measurements have been made on twelve samples within the Ag2Te-In Te3 pseudo-binary system in addition to the eight (49) compositions made by O'Kane, and a more completed partial phase diagram of the system is composed. The study of the phase diagram indicates that AgIn9Te14 exists as a peritectic compound. Electrical conductivity and Hall effect measurements have been made on the single phase portion of a zone refined ingot of this material. Phase Diagram Study DTA measurements have been made on 2. 5, 5, 8, 10 (2 samples), 12. 5, 20, 35, 45, and 90 mole %o Ag2Te and the zone refined 10 and 30 mole % Ag2Te specimens. The results are summarized in Table 5.1. The 2. 5 mole /o Ag2Te sample showed the transition at 676 C on both heating and cooling and the 685 C transition on heating. 47

48 TABLE 5. 1 SUMMARY OF DIFFERENTIAL THERMAL ANALYSIS MEASUREMENTS FOR THE Ag TenTe PSEUDO-BINARY SYSTEM 2 2 3 CD s:5 (D C) f0 CD Sample Co mpo sit ion Mole Mole Sample Annealing Number Conditions Differential Thermal Analysis Results Heating Cooling Liquidus Transition Liquidus % Ag2Te 0 2. 5 5 8 10 12.5 17 % In2Te3 100 97. 5 95 92 90 87. 5 83 TempC C 147 1322 1606 1607 1608 186 343 1609 672 20 80 1321 25 75 735 30 70 181 35 65 742 40 60 630 45 55 748 50 50 732 60 40 631 80 20 647 90 10 744 None None None None None Zone Refined None None 5 days at 595~C None None Zone Refined None None None 4 days at 480~C None None None 669 676 699 695 696 695 695 699 Temp, 0~ 458 674 694 695 690 I Temp. C 667 676 685 697 697 690 695 699 697 699 700 699 699 692 688 684 664 6 654 770 957 698 698 698 695 690 688 684 676 657 763 957 679, 419, 694 (692) 681 668, 631, 600 (661), 644, (603) (661), 647, 602 640, 535, 517 618, 516 478 135 Transition Temp. 49 431 674 686 687 685 - 49 388 - 49 (693) - 637, 602 647 645 42, 525, 516 620, 516 480 49 49 49 49 100 0 135 25

49 The 5 mole %o Ag2Te sample started and completed liquefaction at 674~C and 699 C respectively on the heating cycles. In the cooling cycle, it began solidifying at 697 C but the large heat effect was not observed until 6850C. The solidification was completed at 674 C. The 8 mole % Ag Te completed the liquefaction at 695 C on the heating cycle. On the cooling cycle, it began and completed the solidification at 697 C and 686 C respectively. Sample No. 1608, 10 mole % Ag2Te liquefiedat 696~C on the heating cycle. But started and completed solidification at 697 C and 687 C respectively in the cooling cycle. Sample No. 343 had the same character as sample No. 1608. The 12. 5 mole % Ag Te sample liquefied from 695 to 699~C in the heating cycle and solidified at 699 C in the cooling cycle. The 20 mole % AgzTe sample showed transitions at 679 C and 694 C and melted at 698 C on the heating cycle. It solidified at 699 C on the cooling cycle, The 30 mole % Ag2Te sample melted at 698~C and solidified at 699 C on the heating and cooling cycles respectively. The 35 mole % Ag2Te sample started and completed liquefaction at 681 and 695 C respectively on the heating cycle and solidified at 699 C on the cooling cycle. The 45 mole /o Ag2Te sample had the transition temperature at 600, 630, and 680 C in both heating and cooling cycles. The liquidus temperature of this sample was 6880C. The 90 mole %o Ag2Te sample had a transition at 480~C and its liquidus temperature was 766 ~ 4 C. Based on these DTA measurements and O'Kane's data, a partial phase diagram as shown in Figure 5.1 is constructed. At low Ag2Te region, In Te3 with Ag2Te in solid solution melts peritectically at 674 C. Two more peritectic compounds exist at 75 mole % Ag2Te melting at 6860C, and at 10 mole % Ag2Te melting at 694~C. The

50 1000 PHASE DIAGRAM OF Ag2Te - In2Te3 BINARY SYSTEM A Transition during heating cycle 0 Transition during cooling cycle 750 cr I — w < 700 LJ aw LF 650 550 500 450 70 6( D 50 40 30 20 10 0 MOLE % OF Ag2Te In2Te3 AggTe Figure 5. 1. Partial Phase Diagram for the Ag2Te-In2Te3 Pseudo Binary System.

51 congruent compound at 25 mole % AgzTe melting at 699 ~ 1 C, has a very wide solubility. By considering 40, 45, 50, and 60 mole %o Ag Te samples together, it appears that in addition to a peritectic compound with decomposition temperature of about 670 C at 50 mole % Ag Te, there may exist two more peritectic compounds, one at about 55 mole % Ag2Te with decomposition temperature at 638 C, and the other at about 60 mole % Ag Te with decomposition temperature at 535 C. The phase diagram of the high Ag2Te region can not be precisely determined at the present time with the DTA data available. Electrical Properties The electrical conductivity and Hall coefficient measurements have been made, without a cocoon arrangement, on specimen No. 186(2), a single phase polycrustalline portion of an ingot with the composition (Ag 2Te)(In2Te3)9, having had ten zone refining passes. Figure 5.2 shows a plot of logarithm of the electrical conductivity versus the reciprocal absolute temperature, and Figure 5. 3 shows a plot of logarithm of R T versus the reciprocal absolute temperature for AgIn9Te14. The material was n-type. At the room temperature, the material has a electrical conductivity of 2. 5 x 10 mho/cm, and it increases as the temperature increases. The intrinsic energy gap of AgIn9Te14 estimated from the slopes of the figures are 1. 50 eV from the electrical conductivity data and 1. 51 eV from the Hall coefficient data. A donor energy level 0. 95 eV below the bottom of the conduction band is observed in the lower temperature range. When log |RH or is plotted against log T as shown in Figure 5. 4, a slope of - 1.0 is obtained for the temperature above 600 K, indicating the lattice scattering domination. The Hall mobility of Agn9 Te14 is 40 cm /volt-sec at 600 K.

52 TEMPERATURE, t, (C) 181 143 727 560 444 352 282 227 III 84 60 39 21 4 I - ' 162 u 0 0 E -I b I lo -i 0.s, ==_ E EE a: A-A a r- -6 A -I3 a 2.t 2a -- o 186 (2) First heating cycle * 186 (2) Second heoting cycle — *~ I I I I I I I I I I ''1 l l l l l l l l l l l %... ~D L t ee e^ ^r a, I LU I.Z 1.6 1L 2.U 2.C.4 2.6 L U. 3OU RECIPROCAL ABSOLUTE TEMPERATURE. I000/T, rK').4 3.6 Figure 5. 2. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for AgInTe14 Measured Without Cocoon Arrangement.

53 TEMPERATURE, t, (~C) I 352 282 227 727 560 181 143 - 109 I s 108 11OIN I107 106' Ag IneTel4 * 186 (2) Second heating cycle Eg,= /.5/ et 1.0 1.2 1.4 1.6 1.8 2.0 RECIPROCAL ABSOLUTE TEMPERATURE, 103/T, 2.2 (OK I) 2.4 Figure 5. 3. 3/2 Logarithm of |RHT | versus Reciprocal Absolute Temperature for AgIn9Te 14 Measured Without Cocoon Arrangement.

54 (n (0) E b7 Ag In9Tel4 70 * 186(2) Second heating cycle 60 50 -J~1 ~~~T 40 30 3 0 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 500 600 (Log) ABSOLUTE 700 TEMPERATURE, (OK) 800 Figure 5. 4. Logarithm of RH a- versus Logarithm of Absolute Temperature for AgIn9Te 14

55 DISCUSSION No x-ray, density, or Seebeck measurements were made on this compound. Hahn( reported lattice parameters at 9% and 20% Ag Te as a = 6. 19 kX, c = 12.38 kX, c/a = 2. 0. These values undoubtedly are characteristic of AgIn9Te 14 The decrease in conductivity and the temperature at which the activation energy changes from 0. 95 to 1. 50 eV on the second heating cycle indicates that donors were lost on the first heating cycle, probably associated with the loss of the most volatile component, Te. The 1.50 eV energy gap of this material is greater than that of 1.1 ~ 0. 1 for AgIn3Te5 reported by O'Kane and that of 1.20 ~.05 observed in Chapter 4 for In2Te3.

CHAPTER 6 SEMICONDUCTING PROPERTIES OF InSe3 LITERATURE REVIEW (72, In Se was first obtained by Thiel and Koelsch, and Klemm and Vogel3 confirmed its existence. But Hahn and Klinger(2) were (z0) the first to study the structure of In Se3. Later on, Hahn suggested 2 3' that In2Se3 might have two structure modifications, and gave the lattice 0o parameters of the high temperature form (hexagonal), a = 3. 99, c = 19. 00 A. (21) Hahn and Frank showed that the high temperature form, a soft, thin, graphite-like crystal with hexagonal symmetry, could be obtained by rapid cooling of the material kept for a long time at 800 C, while the low temperature form, a hard and brittle material, was obtained after the material has been kept at 600 C for a long time. Hahn and Frank also suggested existence of a third modification of In2Se. Sugaike also made an x-ray study on the low temperature form of In Se 3 Miyazawa and (45) Sugaike in investigating the structure, electrical conductivity, Hall effect, Seebeck coefficient and thermal expansion of In Se3, established that a phase transformation of In2Se3 (ac-d) takes place at 197 C, and reported that the graphitic modification of InZSe which is stable at the room temperature but not at high temperature has hexagonal lattice 0 (73) parameters of a = 4.01, c = 19.20 A. Yoshioka confirmed the existence of the phase transformation at 197C from his specific heat (47) data. Newman ) demonstrated the existence of yet another phase above 600-700 C. Semiletov 6) from his electron diffraction works, claimed that the hexagonal a-modification, the low temperature form, has lattice o o parameters a = 16. 00 A, c = 19. 24 A, while for the P-modification, o o a = 7. 11 A and c = 19.3 A. Semiletov also claimed the existence of y and 6 modifications cubic and monoclinic, respectively. Andrievskii also made an electron diffraction study of In2Se3. 23j 56

57 (35) Kulwicki had constructed a phase diagram for the In-Se system, claiming two congruently melting compounds, InSe and In Se3, melting at 614 C and 885 C respectively and two peritectic compounds, InSe46 and In Se5 melting at 553 C and 660 C respectively. These data do not agree with the data of the diagram constructed by Slavnova and his co-workers(64 65) who claimed the existence of the compound In2Se which Kulwicki found to be In54Se46. The melting points of InSe and In2Se3 claimed by the latter are different from that of Kulwicki, being 660 C for InSe and 900 C for InZSe3. Slavnova and the co-workers have (65, 66) also investigated polymorphism and the structure of In Se3, and claimed the phase transformations of In Se a-3 at 195 C, - at 650~C and y~.-6 at 750~C. Kulwicki also reported the latent heat of fusion of In Se to be 14. 0 ~ 1. 9 kcal/gm mol, Brice et al made the optical and electrical measurements on polycrystalline In Se and reported that optical energy gap is 1. 2 eV for (56) the low temperature phase. Radautsan also made the electrical conductivity and Hall coefficient measurements on In Se3 Miyazawa, Brice, and Radautsan all found a sudden jump of the electrical properties of In Se at about 200 C and the phase transformation of In2Se at 197 C from the 23 a to the p modification is thus well established. EXPERIMENTAL RESULTS The x-ray analysis made on the powder pattern of specimen No. 1221(3), the zone refined In2Se3 indicated that In2Se3 crystallizes O O in a hexagonal structure with the lattice parameters a = 7.04 A, c = 19.00 A with c/a = 2. 703. The x-ray data are given in Appendix F. This result does not agree with any of the published data although it indicated that the material might be P-modification. The theoretical density based on 3 the x-ray analysis is 5. 705 g/cm, assuming that one unit cell contains six formulae of In2Se3. The pycnometric density of the same material (using HO0 as the immersion fluid) was found to be 5. 567 g/cm, indicat

58 ing that the material has a non-stoichiometric vacancy. The DTA results indicated that In2Se3 is deficient in Se, and by assuming that the vacancy occurs in Se sites and is responsible for the decreased density, the composition of the material is calculated to be In 41 Se58 8' Several DTA measurements have been made on the compositions within the In-Se system in addition to Kulwicki's data and are summarized in Table 6. 1. A phase diagram, slightly modifying that constructed by Kulwicki is given in Figure 6.1. However, DTA at 59% Se clearly shows the In Se3 to have a composition between 59% and 60% Se. The logarithm of the electrical conductivity vs. 1000/T plot for InzSe3, obtained from the polycrystalline specimen No. 1215(4) measured without any extra Se in the cocoon is shown in Figure 6. 2. The specimen had a crack part way across the center of the sample and the magnitudes of the reported measurements may not be correct. However, when the data are plotted in this form, the slope of the curve is not affected, and the energy gap obtained from the slope should be valid. The a-p phase transformation showed up as an abrupt change in slope from about 0. 15 eV/2k to a slope of about 0. 8 eV/2k which increases gradually to a slope of about 4 eV/2k on the first heating cycle. On the second heating cycle, an abrupt change in the electrical conductivity occurred at about 330 C, having a slope of 2. 6 eV/2k below and above the transition. The non-reproducibility of the transition temperature is not surprising because the x-ray analysis showed that the starting material was the P-modification. Another electrical conductivity change was observed at about 430 C on both heating cycles which does not correlate with any transition in the DTA study. Hence it is presumed that it represents the onset of intrinsic conductivity, and an energy gap of 3. 6 eV is observed for the P-In Se3. 3/22 3 Figure 6. 3 shows the logarithm of R HT vs. 1000/T plot for In2Se3 for the second heating cycle. The material is n-type and it is presumed that the a-Pt transformation is responsible for the discontinuity of the Hall coefficient at about 3300 C. The energy gap evaluated from

59 TABLE 6. 1 SUMMARY OF THE DTA MEASUREMENT FOR THE In-Se SYSTEM Maximum Heating Sample Fusion. Transition Number Temperature Temperature (o C) (~C) Compo sition (At. % Se) 0 10 20 30 40 45 50 50 54 56 58.59 60 60 493 494 495 496 844 497 1200 509 510 846 1303 676* 1215 950 950 950 950 950 950 zone refined 1000 950 1000 159, 521 157, 519 157, 520 1 60,520,553 521, 552 613 605, 614 662 659 (195), 661 660 205, 745, 886 197, 638, 741 Liquidus Temperature ( C) 157 521 518 520 (560) 598 613 614 686 765 850 875 885 888 Cooling Transition Temperature (~C) 158 158 160 158, 553 supercooled 598, 611 606 601 (594) (595) 614 885 727 CD CD CD 35 35 35 35 35 35 3.5 3 5 zo 950 ne refined 35 61 62 64 66 68 70 75 80 85 90 1504 294 533 275 1305 499 1308 500 1309 501 210,218,740 884 1000 203, 220,640,744 865 1000 (221), 744 830 975 205, 221, (645), 744, (740)795 742 771 900 220, 741, (759) 759 - 220,740,750 (860?) 625 210, 221, (650), 744, 759 759 - 220,655,738,750 755? 625 221,744 822 745,730 744, 721 742, 722 744, (725) 748 745 745 742, 733 744 35 35 100 6, All samples were water quenched. 8;C Heat treated 5 days at 595~C. 217

60 P —2.4 atm 900 800 700 crnnI 70/ 760~ \ / 6 I 0 / \ w 5 0:cr /:D^~ 1, 5200~ _ - 500 -- I 400 -i 3001 200!1580 0 0.2 0.4 0.6 0.8 1.0 In ATOM FRACTION SELENIUM Se Figure 6. 1. Phase Diagram of the In-Se System.

61,i 3.6 V.. -2 lI0 A, 2,/3.6 eV 10-3 — 4 eV - U 1072 1631 15 Firs h E E -- 10 o 10 __. ____83 1 R 1L TMEAU.4 3 eV8 10.4.8.2,.6.0.4 3.8.10 o 1215(4) First heating cycle * 1215 (4) Second heating cycle 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 RECIPROCAL ABSOLUTE TEMPERATURE, IOO/T (K-') Figure 6. 2. Logarithm of Electrical Conductivity versus 1000/T Plot for In2Se3. 2* 3

62 TEMPERATURE, t, (~C) 181 III,1727 10 -- 441 282 60 21 -10 10'~ 109 I — 10: ' I 11 IIn2 Se3 ~ ~I ~~ ~ 0 *1215 (4) Second heating cycle & l l l.......1 i 106 1.0 1.4 1.8 RECIPROCAL 2.2 2.6 3.0 3.4 ABSOLUTE TEMPERATURE,'~~T, (~KI') 3.8 Figure 6. 3. 3/2 Logarithm of R T versus 1000/T Plot for In Se H 2 3*

63 this plot according to Equation (40) is 3.3 eV for the P-In2Se3. Figure 6. 4 shows the logarithm of I RHC I vs. logarithm of absolute temperature plot for the second heating cycle on the InZSe3 specimen. The a-p phase transformation causes a sudden increase of the Hall mobility. Above 600 K, a T-1 6temperature dependence of mobility is observed, indicating that lattice scattering may be the dominating mechanism. DISCUSSION The Se vacancies apparently behave as donors in the P-In Se3, since the conductivity is increased on the second heating cycle and no excess Se was in the measuring environment to suppress the loss of Se on the second measuring cycle. The increase in apparent low temperature donor activation energy from 0. 15 eV to 0. 4 eV also supports this conclusion. This model is consistent with that obtained on other compounds in this work. The energy gaps of 3. 3 eV and 3. 6 eV observed in this work are considerably higher than those reported by any other workers, possibly because they have never worked with zone refined material. For future work, a stabilization of P-modification and suppression of donor levels may give a satisfactory high energy gap material.

64 0 a, E u b cr I0 -J -J I 100 200 300 400 500 600 7008009001000 ABSOLUTE TEMPERATURE, T, (OK) Figure 6. 4. Logarithm of J RH - Product versus Logarithm of T Plot for In2Se3.

CHAPTER 7 SEMICONDUCTING PROPERTIES OF InSe INTRODUCTION A review will be given on the structure and the published data on the electrical and optical properties of InSe. The electrical conductivity, Hall effect, Seebeck coefficient, density, and x-ray lattice parameter measurements were made on the zone refined InSe ingots, and the crystal grown in a Bridgeman furnace. The results are discussed. LITERATURE REVIEW InSe crystallizes in a layered hexagonal lattice. Each major layer is built up of four hexagonal sublayers with stacking arrangement -abba-, where "a" represents Se layers and "b" represents In layers. ( (60) Semiletov reported that the lattice constants of InSe are a = 4. 04 kX and c = 16. 90 kX, and that the bonding distances are 3. 15 kX for In-In, 2. 50 kX for In-Se, and 4.16 kX for Se-Se between one major layer to the adjacent major layer. Figure 7. 1 shows the structure of one major layer of InSe in a unit cell. The electrical and optical properties of InSe have been measured (11) by several investigators; Damon obtained an energy gap of 0. 96 eV from his electrical conductivity data measured on a p-type material, and reported a mobility of 5 cm /volt-sec. Mori, (46) from Hall coefficient data, concluded that his n-type material had an energy gap of 1.6 eV and that there was a donor level at 0. 95 eV below the bottom of the conduction (15) (8) band. Fielding and Brice measured the optical properties of InSe and reported respectively that the energy gap was 1. 8 eV and 1. 05 eV. EXPERIMENTAL RESULTS The electrical conductivity, Hall coefficient and Seebeck 65

66 3.46A / 0.92A 8.35 -- 0 3.15A 0 `A 0 -, /0.92A _ 4.03A @ In Qse I \ I \ I \ Figure 7. 1. Structure of an InSe Major Layer.

67 coefficient were measured on polycrystalline specimens from ingots No. 1200, No. 1208, and No. 1201. Ingot No. 1200 was zone refined for eight passes and ingot No. 1208 had 18 passes. Ingot No. 1201 was crystallized in a Bridgeman furnace from a zone refined ingot having 16 passes. Figure 7. 2 shows the temperature dependence of the electrical conductivity of specimens No. 1200(3), No. 1201(a), and No. 1201(b). Sample No. 1200(3) was measured with extra Se in the cocoon. Between 110~ to 160 K (-163~C to 113 C), the electrical conductivity observed in the first heating cycle was substantially constant (not shown in the figure). Then it increased according to d In ar/d(l/T) = 0. 12 eV/2k to 200~K followed by 0.38 eV/2k up to 300 K. Between 3300 to 410~K, the d In ao/d(l/T) gave a value of 0. 18 eV. In the temperature higher than 6700K, an energy gap of 1.09 eV was obtained from the slope of the In - vs. 1/T plot. A lower conductivity in the low temperature range was observed on the second heating cycle as the result of heat treatment during the first heating cycle, while the conductivity above 410 C was reproducible for the first and the second heating cycle. The slope of the log a- vs. 1/T plot in this higher temperature range gave again an energy gap of the intrinsic range of this material of 1.09 eV. Samples No. 1201(a) and No. 1201(b) were measured without extra Se in the cocoon. The conductivities of these specimens decreased on the second heating cycle not only in the low temperature range but also in the high temperature range. The energy gap calculated from log a- vs. 1/T plot varied from cycle to cycle and from specimen to specimen, as shown in Figure 7. 2. The temperature dependence of electrical conductivity for several zone refined InSe specimens which were measured without any extra Se in the cocoons are shown in Fig. 7. 3. The electrical conductivities in the low temperature range increased on the heat treatment for all samples. The electrical conductivities in the higher temperature range were again reproducible and the intrinsic energy gap calculated from the slopes of

,o727 560 441 352 282 227 181 143 III 84 60 39 21 -I -25 -56 -73 -88 -101 -112 -122.k InSe- o 1200(3) First heating cycle~ 1200(3) First cooling cycle *1200(3) Second heating cycle A1201 (a) First heating cycle A 1201 (a) Second heating cycle o 1201 (b) First heating cycle * 1201 (b) Second heating cycle Ii I 1I_ __ _ -, = /09eV_ E o 0 r E tb I0 z 0 0 -J ir 10-, -62 1.49e \''/. 9e V — x IT.- ~ 52 e,,X-In,.,., - \-'~ /'^/. - - - --—./- -— V..... 54r -- g^-:\ ^ ^ -/5g- = --- = --- == = _ -- — ~- -- - - ~49 e -— ^~= ^^. ^^-.o e - ~- -- = = --- --- - === == ^= ^^^ ^^ -~-== = — 00 \ 1d3 * 0./2eV* /I i. — ti -_ _ -- -— _ - _ _ 4 I From log T3/4 VS /T I I 1.0 1.4 18 2.2 2.6 3.0 3.4 3.8 4.2 4.6 5.0 RECIPROCAL TEMPERATURE, I000/T (~K)-l 5.4 5.8 6.2 66 Figure 7. 2. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for InSe. 1200(3): Zone refined specimen measured with Se in the atmosphere. 1201 (a) and (b): Crystal growing in a Bridgeman furnace measured without Se in the atmosphere.

TEMPERATURE, t, (~C) 352 282 227 181 143 III 84 727 561 441 in 60 39 21 -10 -56 -73 -88 -101 -112 *From log 0T 0/s VS. I/T — ~ I - I / —9 o 1 = 0.5s eYV. =,= H o I I Z~~~~~~. JS "!-5 I ZZI ZZI ZIZIZI IZ InSe A 1200(2B) First heating cycle ~ 1200(28)Second heating cycle A 1200 (2B)Third heating cycle o 1200(4A) First heating cycle * 1200(4A) Second heating cycle * 1200(4A) Third heating cycle b 1200(4A) Fourth heating cycle * 1200(4A) Fifth heating cycle o 1208 (3) First heating cycle * 1208(3) Second heating cycle 2 0 I 2 Ib D 0 z 0.J 4 LJ _1 0.45 eV ^A> 1 L ^ -2 10,0./2 el ____ _ _ _ _ _.^ ^ -^^ _ ~ ~ ~~'< _ ___ _ ___ ~ __ _ ^^^ —^^^^^^^^~ OD (,D -4 1 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2 4.6 5.0 5.4 RECIPROCAL ABSOLUTE TEMPERATURE, IOOO/T, (K'l) 5.8 62 66 Figure 7. 3. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for InSe Measured Without Se in the Atmosphere.

70 the log c vs. 1/T plots were again 1.09 ~ 0. 03 eV. A d In -/d(l/T) = 0. 12 eV/2k was observed in the temperature between 180 K to 250 K for the first heating cycle of specimen No, 1200(4A). After the fourth heating cycle, specimen No. 1200(4A) was repolished before the fifth heating cycle was measured. The Hall coefficients indicated that all the specimens were n-type. Figure 7.4 shows the curves of loglRHT 3/2vs. 1/T plots for the same specimens shown in Figure 7. 2. The Hall coefficient of specimen No. 1200(3) in the low temperature region increased after it had been heated in a Se atmosphere, while in the high temperature region, it was reproducible. The intrinsic energy gap calculated from the slope of this plot was 1. 09 eV which was consistent with the electrical conductivity data. The Hall coefficients of specimens No. 1201(a) and No. 1201(b) also increased by heat treatment of the first heating cycle, but in both low and high temperature ranges and the energy gaps did not correlate with those obtained from the electrical conductivity data. Figure 7. 5 shows the same kind of plots for the InSe specimens of Figure 7.3. The Hall coefficient decreased in the low temperature region after these specimens had been heated without a Se atmosphere. Again, they were reproducible in the higher temperature region and gave the values of energy gaps of 1.09 ~ 0.03 eV. Figure 7.6 is a plot of log jRH or vs. log T for the specimens plotted in Figures 7.2 and 7.4. For specimen No. 1200(3), there was no change of the IRH -i product in the second heating cycle from that of the first cycle. In the high temperature region, the temperature -5/2 dependence of IRH I was approximately T. The I|RH I product of specimens No. 1201 (a) and No. 1201(b) increased on the second heating cycle for temperatures below 700 K, showing a T dependence on temperature until the mobility reached a level between 150 and 200 cm /volt-sec. The mobility then remained essentially constant and finally decreased as a function of T3/5. Figure 7.7 shows the RH finally decreased as a function of T. Figure 7. 7 shows the IR-H c |

71 TEMPERATURE (~C) 727 560 441 352 282 227 181 143. -10 111 84 60 39 21 10' 109 10!. I ' InSe o 1200(3) First heating cycle 1200(3) First cooling cycle ~ 1200(3) Second heating cycle A 1201 (a) First heating cycle A 1201 (a) Second heating cycle O 1201 (b) First heating cycle ~ 1201 (b) Second heating cycle cY Irr 107 ~T.-5r lj= I.$3/ e I1.$31 eV02e yEgQ = 1.09 eV If~ 105.0 1.4 1.8 2.2 2.6 3.0 3.4 RECIPROCAL ABSOLUTE TEMPERATURE, 103/T (~K) 3.8 Figure 7.4. 3/2 Logarithm of IRHT 1 versus Reciprocal Absolute Temperature for InSe. 1200(3): Zone refined specimen measured with Se in the atmosphere. 1201(a) and (b): Crystal growing in a Bridgeman furnace measured without Se in the atmosphere.

72 TEMPERATURE, t, (OC) 727 561 441 352 101'O I I cu 1o) InSe A 1200(2B) First heating cycle 79 deV A 1200(2B) Second heating cycle A 1200(28) Third heating cycle o 1200(4A) First heating cycle * 1200(4A) Second heating cycle _ 1200(4A) Third heating cyole 6 1200(4A) Fourth heating cycle __ — 1200(4A) Fifth heating cycle o 1208(3) First heating cycle * 1208(3) Second heating cycle 1.8 2.2 2.6 30 3.4 ABSOLUTE TEMPERATURE, IOOO/T, (~K') 1.4 RECIPROCAL Figure 7. 5. Logarithm of | RHT | versus Reciprocal Absolute Temperature for Zone Refined InSe Measured Without Se in the Atmosphere.

73 400 350, 300 V) 0 250 0 b oh I - 200 0 2 I < 150 100 Figure 7. 6. 450 500 550 600 TEMPERATURE,~K Logarithm' of |RH o I versus Logarithm of Absolute Temperature for InSe. 1200(3): Zone refined specimen measured with Se in the atmosphere. 1201(a) and (b): Crystal growing in a Bridgeman furnace measured without Se in the atmosphere.

74 500 400 300 - InSe A 1200(2B)First heating cycle A 1200(2B) Second heating cycle A 1200(2B) Third heating cycle o 1200(4A) First heating cycle * 1200(4A) Second heating cycle * 1200(4A) Third heating cycle 6 1200(4A) Fourth heating cycle v-1200(4A)Fifth heating cycle o 1208(3) First heating cycle * 1208(3) Second heating cycle 0 - LI (/ 0 C> (O, o >I-J I 200 - 100 80 70 60 50 40 30 100 200 00 TEMPERATURE (oK) Figure 7.7. Logarithm of I RH I versus Logarithm of Absolute Temperature for InSe Measured Without Se in the Atmosphere. Zone Refined

75 dependence on temperature for the specimens shown in the Figures 7. 3 and 7. 5. In the low temperature region, for sample No. 1200(4A), 5 IRH 1 Idepends on temperature by approximately T for the first heating 6. 8 cycle and T for the fifth heating cycle. In the high temperature region, it is almost T -. In the initial measurement, a T phenomenon is observed in the intermediate temperature range which disappears on subsequent measurements after heat treating. Sample No. 1200(2B) on the third measurement shows a T temperature dependency, followed -1/2 -2 by a T/ region and then a T region. Earlier measurements showed a T region between the T and T regions which disappeared on heat treating. Sample No. 1208(3) shows only the T and T variations. Figure 7. 8 shows the Seebeck coefficients of InSe. The data are rather scattered although they all show an n-type coefficient. The density measured by the water immersion method was 5. 4319 gm/cm. The x-ray measurements by the powder pattern method indicated that InSe crystallized in a hexagonal structure with the lattice constants o o of a = 4. 03 A and c = 25. 04 A. The c value does not agree with that of (60) Semiletov. The x-ray data are included in Appendix F, INTERPRETATION OF THE RESULTS 1. Judging by the bonding distances between atoms in the InSe crystal, the In-Se bond is covalent since the distance 2, 50 kX is near o (60) to the sum of the radii of Iniv, 1. 35 A, as deduced from the In Te3 structure, (rather than the value of 1. 44 obtained from the InSb or InAs o structures) and SeTV, 1. 14 A. The Se-Se bonding is Van der Waals rather than covalent since the radius for covalent Se is 1. 14 A, whereas 0 (51) it is 2. 0 A for a Van der Waals' bond. The In-In bonding distance is too great to be explained on the basis of a simple covalent bond 0 (69) (In = 1. 44 A ), but using a correlation given by Suchet, the increased bond length can be explained if resonance is present and the radius increases to 1. A he n-pair ing in this structure the radius increases to 1. 57 A o The In-pair occurring in this structure

76 InSe A 1200(2B) First heating cycle A 1200(2B) Second heating cycle A 1200(2B) Third heating cycle o 1200(3) First heating cycle o 1200(3) First cooling cycle * 1200 (3) Second heating cycle o 1200(4A) First heating cycle * 1200(4A) Second heating cycle a 1200(4A) Third heating cycle 6 1200(4A) Fourth heating cycle - 1200 (4A) Fifth heating cycle O 1208 (3) First heating cycle * 1208 (3) Second heating cycle 0 -0 o "L. E IIL w 0 LLi LmJ 0 0 LJ oo -0.1 -0.2 -0.3 -04 500 600 TEMPERATURE, t, (~C) Figure 7. 8. Seebeck Coefficient of InSe. 1200(3): measured with Se in the atmosphere. Others: measured without Se in the atmosphere.

77 +4 then gives an effective molecule of the form In2, and InSe has a typical semiconductor bonding structure. (35) 2. From Kulwicki's DTA data, the congruently melting compound apparently is deficient in Se. The composition of the material based on the density measurements and the x-ray analysis data is In43Se42 i.e. for every 43 Se sites, there is one Se vacancy. If this number represents the equilibrium condition, then the activation energy of a vacancy at the melting point of InSe is AE = -kT In (1/42) = ( 8. 6 x 105)( 887)(ln 42) = 0.286 eV The compound may be considered as [ In2Se ] 42[ In?2 E ], the indium coupled with the Se vacancy possibly being a donor. 3. The lattice constant c = 16. 90 kX given by Semiletov(60) indicates that the unit cell is composed of two major layers of the structure shown in Figure 7. 1 stacked in sequence -ABAB-. Our o experimental data with c = 25. 04 A shows that a unit cell is composed of three major layers stacked in sequence -ABCABC- and does not agree with Semiletov. We do not consider this to be a serious discrepancy. 4. The RH j product, which is directly proportional to Hall mobility, of specimen No. 1200(3) which was measured with extra Se in the cocoon did not change by the heat treatment of the first heating cycle. The decrease of the conductivity of this specimen on the second heating cycle in the low temperature region resulted from a decrease of the carrier concentration of the material which correlates with the increase of Hall coefficient observed on the second heating cycle. On the other hand, the Hall coefficient of the zone refined specimens measured without a Se atmosphere decreased and the electrical conductivity increased indicating that the carrier concentration increased, It seems that InSe decomposes by a heating treatment without a Se atmosphere and the equilibrium depends on the Se-vapor pressure in the gas phase.

78 5. The increase of the Hall coefficient of the specimens No. 1201(a) and No. 1201(b) on the second heating cycle indicates that the carrier concentration of the material made by the Bridgeman technique decreases by the heat treatment of the first cycle. The increase of the mobility of these specimens suggests that materials are becoming more ordered. The decrease of the conductivity of these specimens is thus explained. 6. The temperature dependence of RH o I product of InSe in low temperature regions of virtually all specimens was approximately by T, which agreed well with Mori's data who reported T. This phenomenon cannot be explained by simple scattering theory. However when log IRH r T3/ 2 is plotted against 1/T as shown in Figure 7. 9, the straight lines with negative slope as indicated in the figure are obtained. This -3/2 indicates that the mobility follows a relationship B = JL T exp(-E/kT). In the energy diagram, this represents that the bottom of the conduction band is not smooth but contains ripples which may vary from 0. 10 to 0. 3 eV. The electrons then require an activation above the conduction band ripples, after which they appear to follow a normal lattice scattering relationship. The electrical conductivity of an n-type extrinsic semiconductor of this type is then expressed by 3/2 -3/4 =o- q p0 U Nd (m /Im )3/ T3 / exp -(2E+E -E )/2kT d n o gd 3/4 and the slope of log o T against 1/T will give the value of -(2E+E -E )/ g d 4.606 k. 7. The IR cr products of all specimens in the higher temperature 1. -2.5 region show a T,, T temperature dependence. This may indicate that the scattering is dominated by lattice scattering or hole-electron scattering. (6) The T dependence of mobility of specimen No. 1200(4A) observed in the first heating cycle disappears in the third heating cycle. This indicates that the neutral impurity scattering is eliminated by the heat treatment during the measurement. The ionic scattering mechanism

79 7 10 lb: m InSe o 1200(3) First heating cycle o 1200(4A)First heating cycle 4 1200(4A)Fifth heating cycle A 1201 (a) First heating cycle A 1201 (a) Second heating cycle * 1201 (b) First heating cycle.27eV \.22eV 28i~ ~ ~ ~ ~ ~ ~ ~ /. 06 I0 2 3 ABSOLUTE TEMPERATURE, IOOO/T, 4 ( K) RECI PROCAL Figure 7. 9. 3/2 Logarithm of I1j TT 1 versus Reciprocal Absolute Temperature for InSe, Showing the Activation Energy of Mobility.

80 may take the place of the neutral impurity one, 8. According to Equation (46), the plot of loglRHT /Ivs. 1/T in the extrinsic region for n-type semiconductors will give a straight line with a slope of (E -E )/2k. When this is made for all specimens, g d an impnurty energy level at 0 49~0. 04 eV below the bottom of the conduction band was observed for InSe in the temperature between 400 to 550 K. This value agrees with the values obtained from the slopes of -3/4 log r T vs. 1/T plots, 0O48 ~ 0.05 eV. 3/4 9. The value (E -E ) obtained from the slope of log RHT3/ vs. g d H 1/T plot for specimen No. 1200(4A) in the temperature between 294 K to 370 K is 0.18 eV, while 2k times the slope of log c- T/4 vs. 1/T plot for the same specimen in the same temperature region is 0. 58 eV. The mobility activation energy, one-half of the difference of these two values is then 0. 2 eV. This value satisfactorily agrees with the mobility activation energy obtained from Figure 7. 9. 10. In the temperature range below 250 K, a value of 0o 12 eV is obtained from the log C- vs. 1/T plot for specimen No. 1200(4A). The same phenomenon was observed in the temperature between 150 K and 190 K for specimen No. 1200(3). The constant electrical conductivity of specimen No. 1200(3) below 150 K may indicate that an unobserved donor exists. 1. Satisfactory correlations could not be made on the Seebeck data, since the data were too scattered. However, a pattern was observed. In the temperature below about 400 K, the magnitude of the Seebeck coefficient increases. Then it becomes constant followed by a rapid decrease in the magnitudes. The change of the magnitude may depend on the scattering mechanism of the electrons although no explicit relationship is deduced. The polycrystalline nature of the specimens also may contribute built-in potentials, because of the anisotropic nature of the crystal structure, which could change erraticly with temperature as a result of recrystallization.

81 12. The scatter of the Seebeck data may also arise from a changing donor concentration, if donors are formed by a Boltzmann activation mechanism. In this case, the deep donor activation of 0.48 eV noted above would become a 0. 24 eV Boltzmann activation energy, which is the same order of magnitude as that computed for the formation of Se vacancies above. SUMMARY The electrical conductivity, Hall effect, and Seebeck coefficient measurements were made, with and without extra Se in the cocoon, on zone refined InSe ingots and one InSe crystal grown in a Bridgeman furnace. When there is no Se in the measuring atmosphere, InSe may decompose and increase the donor concentration by the heat treatment during measurements. However, when extra Se is sealed in the cocoon, the decomposition of InSe appears to be suppressed. The energy band diagram of InSe as a function of temperature deduced from the electrical conductivity and the Hall coefficient data is shown in Figure 7. 10. Four temperature regions were observed. In the temperature range below room temperature, a donor energy level of 0. 12 eV below the bottom of the conduction band was observed. Then the bottom of the conduction band appears to become rippled which is associated with the activation of a donor G0 18 eV below the bottom of the ripples in the conduction band and refuses a mobility activation energy of 0. 1 to 0. 3 eV. The third region shows a donor level of 0.48 eV below the conduction band is activated. Whether the bottom of the conduction band is rippled or not in this temperature range is not certain. At temperatures higher than 700 K, the InSe appears to go into the intrinsic region, and the energy gap observed is 1.09 eV. Both Hall and Seebeck coefficients show that InSe specimens are n-type. However the Seebeck coefficient data were rather scattered, and attempts to correlate it on the basis of a simple model were only marginally successful.

82 E-jo,_, '0 i 2e.v 02eV U V10. 18eV 0.48 eV E TEMPERATURE --- Figure 7. 10. Energy Diagram of InSe.

83 The structure study based on x-ray and density measurements indicated that the InSe specimens are deficient in Se. Hence the In coupled with a Se-vacancy appears to be a donor. Judging by the bonding distances between atoms in InSe, it is concluded that the In-Se bond is covalent, the In-In bond is a resonating covalent bond, and the Se-Se bonds between major layers is a van der Waals' bond.

CHAPTER 8 ELECTRICAL PROPERTIES OF InTe LITERATURE REVIEW InTe is a III-VI compound and has been of possible interest for a thermoelectric material as well as for a superconducting material in a high pressure crystal modification ( 1316 5758) Grochow(19) ski et al in clarifying and correcting the phase diagram of the In-Te system, confirmed its congruent melting point of 696~C, (2) and determined that its composition was 50. 8% Te (In3Te3) at its melting (59) point. Schubert et al deduced that InTe has a tetragonal structure as is shown in Figure 8. 1 with lattice constants of a = 8. 42 kX, c = 7. 12 kX. Two different views of the crystal are shown in Figure 8.1. (17) 0 0 (15) Gerasimov gave a =8.44 A, c = 7.17 A, c/a= 0.85. Fielding et al have measured the electrical properties of this material, and reported that at room temperature, the electrical resistivity and the -.3 3 Hall coefficient of InTe are 14 x 10 ohm' cm and 0. 15 cm /coulomb respectively. However, no temperature dependence of the properties have been given. EXPERIMENTAL RESULTS (19) Grochowski determined the composition of the InTe zone refined ingot to be In30Te 31 Ingot No. 248 was prepared by zone refining In30Te31 ten passes, while ingot No. 738 was prepared by zone refining In50Te50 8 passes. Both ingots were shiny and brittle as they were prepared. Microscopic analyses performed on both ingots before and after etching with Dano solution (see Procedure Chapter) indicated that the ingots were single phase. The density measured for ingot No. 248 by liquid immersion technique, using ethanol, was 6.23 gm/c. c., while the air buoyancy method, applying Beckman Air Comparison Pycnometer gave a value of 6. 27 gm/c. c. The results of 84

85 c o- a (A) mInm1 OTe InI (a) Projection on the basal plane. a 7- i- 7 ___ ______ ___ ___i~ c 0A_ _ _ _ -: I — Z~fl7_Z (B) 4 F o I 9) A5 sac icr I - H- -7C ---;FL ^lti nIn OTe InI (b) Three-dimensional projection. Figure 8.1. Structure of InTe.

86 x-ray measurements on specimen No. 248(5) gave the lattice o o constants a = 8 44 A, c = 7. 13 A which do not agree with either Gerasimov or Schubert's data. The x-ray data are given in Appendix F. The Lane x-ray back-reflection method was applied to three spots of the electrical specimen No. 248(2) to determine that it was a single crystal. The flat cleaned side faces were [ 110] faces and the electrical properties were measured in the [ 111] direction. Specimen Noo 248(3) was prepared from the same ingot in the same condition, and is expected to have the same faces and direction. No x-ray work was done for the specimens from ingot No. 738, However from the similarity in visual appearance and cleavage planes, it is assumed that the measurements were made on single crystals. The temperature dependency of the electrical conductivity of InTe is shown in Figure 8.2 plotted as log or versus log T and in Figure 8.3 as log cr versus 10 /T. All specimens were measured under a hydrogen atmosphere, except No, 738(6) which was measured in an evacuated "cocoon" Each specimen, except specimen No. 248(3), was measured twice (two heating cycles) to see if the heat treatment of the first heating cycle changed the properties of the specimen. The conductivity of specimens No. 738(5) and No, 738(6) were about 200 mho/cm at room temperature, which decreased as the temperature increased to 40 mho/cm at 900 0K No significant change occurred during the heating treatment of the first heating cycle of these specimens, Specimen No, 738(6) showed a T ~ temperature dependency of conductivity above 500 K while specimen Noo 738(5) showed T~75 below 450 K, and T- 0 in the region between 650'-800 K. The electrical conductivity of specimens No, 248(2) and No. 248(3) differed from that of specimens prepared from ingot Noo 738 in several aspects: the electrical conductivity of specimens No, 248(2) and No. 248(3) was substantially constant for a wide temperature range; the magnitude was smaller than that of specimens No. 738(5) and No.

87 E o 0 -.C E b >o:3 0 U I-J _1 LL 300 400 500 600 7 ABSOLUTE TEMPERATURE, T,(~K) Figure 8. 2. Logarithm of Electrical Conductivity versus Logarithm of Absolute Temperature for InTe.

88 TEMPERATURE, t,( C) 727 441 282 181 IIl 62 21 0 0 b I0 0 z 0 () -j 0 I-~J w 10( — 0 InTe A 248 (3) First heating cycle o 248 (2) First heating cycle * 248 (2) Second heating cycle o 738(5A) First heating cycle * 738 (5A) Second heating cycle a 738 (6) First heating cycle * 738(6) Second heating cycle _ _ _ __. I._ I, I I( 1.0 1.4 RECIPROCAL 1.8 2.2 2.6 3.0 3.4 ABSOLUTE TEMPERATURE, IOO/T, ( ~K)' 3.8 Figure 8. 3. Logarithm of Electical Conductivity versus Reciprocal Absolute Temperature for InTe.

89 738(6) at room temperature, being 50 mho/cm for No. 248(2) and 100 mho/cm for specimen No. 248(3); and a change in electrical conductivity occurred as a result of the heat treatment of the first heating cycle. Figure 8.4 shows the Seebeck coefficient of InTe versus 10 /T. Although all specimens showed n-type Seebeck coefficients, there were significant Seebeck differences between the specimens cut from ingot No. 738 and that from ingot No. 248. The magnitude of Seebeck coefficient of specimens No. 738(5) and No. 738(6) increased from 0.100 mV/~K at room temperature to 0. 250 mV/~K at 600 ~C. For specimen No. 248(2), it increased from 0.100 mV/ K at room temperature to about 0.140 mV/0K at about 2500C followed by a decrease to 0. 04 mV/~K at 600 C. Between 1000/T limits of 2.0 to 1.4, the Seebeck coefficient versus 1000/T plot of specimen No. 248(2) for the first heating cycle gave a straight line at the slope of 0. 044 volt. On the second heating cycle, a region with slope equal to 0.1 volts was observed. DISCUSSION OF THE RESULTS 1. Calculation of bonding distances, angles, and positions in the crystal indicates that In atoms exist in two different positions. Half of the In atoms are each bonded to 4 Te atoms with bond distances of 2. 67 A, two 960 bonding angles and four 116. 5 angles, as shown in Figure 8.1. This corresponds approximately to the normal covalent bond angle of 109. 5, and the sp bond length of 2. 67 A of In -Te o VI 0 (In =1.35A, Te =1.32A). The other half of the In atoms are each surrounded by eight Te 0 o atoms with bond distances of 3.48 A and bond angles of 65.4 for Te atoms on the same plant and 71. 6 and 810 for Te atoms on different planes, as shown in Figure 8.1. This suggests that these atoms are +1 2 0 + 0 monoionic since the In Te bond length is 3.53 A (In = 1.32 A, -2 0 + Te = 2.21 A). However, these In atoms are under pressure from o the lattice because of the shorter actual bond length (3.47 A ) and

90 TEMPERATURE, t, (~C) 727 560 441 352 282 227 181 143 III 84.02 -.04 -.06 ^ -.08 ' 0\\ m 0.044 VOLT E z/ w m=OJIVOLT o -.16 ---- u>_ w -18 -20 -/// - o E / InTe Sw -~2 - 2248 (2) First t v) \ I I /I I *? f/ 1 248 (~2 Se'rnn 1.4 1.8 2.2 2.6 3.0 3.4 RECIPROCAL ABSOLUTE TEMPERATURE, 1000/T, (~K 38 Figure 8. 4. Seebeck Coefficient versus Reciprocal Absolute Temperature for InTe.

91 it is postulated that the In vacancies occur in this In position. Each Te atom then is bonded covalently to two In atoms with bond angle of 83. 6 and ionically to four In atoms with bond angles of 62 and 119. The InTe then can be represented as In+L InTe2]. 2 2. If a mobility of 10. 7 cm /volt-sec, calculated from Fielding's ) data according to Equation (43) is used, then the carrier concentrations of the specimens at room temperature, calculated 19 3 according to Equation (45) are 2.7 x 10 electrons/cm for specimen 19 3 No. 248(2), 6.9 x 10 electrons/cm for specimen No. 248(3), 8.4 x 10 electrons/cm for specimen No. 738(5), and 14.3 x 10 electrons/cm for specimen No. 738(6). These values are at the same order of magnitude of N from room temperature (2. 5 x 10 ) to 700 K 19 c (8. 9x 10). 3. According to Equation (58) A E -E _ ( Ak + g ) (58) n q qT and approximating E by Ef, a plot of I a qT| as a function of temperature will show the variation of the energy difference between the bottom of the conduction band and the Fermi level, E - Ef. Figure 8. 5 is a plot of I an q T versus the absolute temperature. The straight line between the temperature of 500 K to 650 K observed in the first heating cycle of specimen No. 248(2) may indicate that in that temperature region, E -Ef is a constant for this specimen. If this is the case, "A" evaluated from the slope of this line is 0. 525, and the value of E - E obtained from the intercept is 0. 045 eV. It has g f been shown that when N = 4N, (E - Ef) is expressed by Equation (18). d c g f E - E = (E -Ed)/2 - (kT/2) In (Nd/2N ) (18) g f g d d c Equation (18) together with Equation (58) shows that a a vs. 1000/T plot gives a straight line with a slope of (E-E)q when Nd is plot gives a straight line with a slope of (E -Ed)/2q when N is

0 -G) vr (D rj 300 400 500 600 ABSOLUTE TEMPERATURE,T, (~K) Figure 8. 5. aqTj versus Absolute Temperature for InTe, Showing the Change of Fermi Level Along with Temperature.

93 approximately equal to 2N. This is the case for specimen No. 248(2) c in the temperature region of 5000C 0 650 K where the slope in Figure 8. 4 is 0. 044 volt. This value agrees with the value of 0. 045 eV found from Figure 8. 5. The impurity energy level is thus concluded to be 0. 090 ~ 0. 02 eV below the bottom of the conduction band. When this value is substituted into Equation (16), Nd/2N is found to be d c 1. 07 for 500 K and 1. 08 for 650 K which agree with the assumption that Nd/2N 1. By assuming that Nd/2N = 1, then the mobility d c 2 d c must be about 50 cm /volt-sec at 650 K. 4. By evaluating the Seebeck data for No. 248(2) from the second heating cycle in a similar manner, a donor level at 0. 2 eV is observed. This donor level apparently appears as a result of the loss of Te during the first heating cycle, as a slight arrest near the 0.09 eV donor is also noted. 5. The value of A = 0. 525, which is very near to 0. 5 suggests that the conduction is dominated by constant v vibration scattering, and the scattering exponent for mobility will be 2. 5 '^ 3. 0. -2.65 6. The T temperature dependence of conductivity of specimen No. 738(6) suggests that the carrier concentration of this specimen is constant, and that this conductivity variation is attributable to a decrease in mobility since the temperature dependency for the mobility agrees with that deduced from the Seebeck data. 7. The theoretical density of InTe based on the x-ray data should be 6.32 gm/cm. The composition of the sample calculated from the x-ray and density measurements is InTe 0 = In4Te = In30Te30.7 and InTe.039 = In26Te = In30Te31.2 based on that the density is 6.27 and 6.23 gm/cm respectively. 8. As deduced from the phase diagram and the preparational procedures, the samples from ingot No. 248 presumably more nearly represent the congruently melting composition than the samples from ingot No. 738. The latter samples have a lower concentration of In

94 vacancies in the structure. However, since the electrical conductivity of the No. 738 samples is significantly higher than that of the No. 248 samples, the filled vacancies (i. e. the compressed In ions) must act as donors. Presuming that all the In vacancies exist in these sites, there is one such (Schottky) vacancy for every 15. 5 In sites. 9. At the melting point of In Te3 696 C, the activation energy of formation of an In vacancy according to (vacancies) = (occupied sites) exp (- AE/kT) AE = -kT In L (vacancies)/(occupied sites)] -5 =- 8.6 x 10 x 969 In (1/14.5) = 0.223 eV 10. Although the compounds InTe and InSe are chemically similar, their electrical properties are very much different. It has been shown that in InTe, one half of the In atoms are ionically bonded and one half are covalently bonded. The ionically bonded In is univalent and can act as a shallow donor, easily liberating a 5s electron to conduction band to produce the observed high conductivity. On the other hand, all In-Se atoms are covalently bonded and the material has normal semiconducting properties. SUMMARY Electrical conductivity, Seebeck coefficient, lattice constants and density measurements have been made on zone refined InTe single crystals. All specimens were n-type with carrier concentrations of 19 20 3 10 100 electrons/cm o Donor levels at 0.090 ~.02 and 0.2 eV below the bottom of the conduction band were found. A mobility scattering exponent of 2. 5 to 3. 0 is predicted from Seebeck data, which agrees with the conductivity variation observed on the higher conducting specimens of ingot No. 738 containing excess In. The composition of the zone refined compound is found to be In30Te31, based on the chemical

95 analysis and the x-ray and density measurements. A detailed discussion on the structure of InTe shows that InTe can be represented as In [ InTe2 -, and that the donor may be the filled vacancies of In+ sites. The structures of InTe and InSe are compared and the cause of the difference in properties between these two compounds is discussed.

CHAPTER 9 PHASE DIAGRAM OF Cu Te-In Te3 PSEUDO-BINARY SYSTEM AND THE ELECTRICAL PROPERTIES OF Cu In Te 7- r ---9 —1 7 INTRODUCTION The compound CuInTe2 is the only compound reported and measured in the Cu Te-In Te pseudo-binary system. CuInTe2 belongs 2 2Iffi VI (23) to compounds of the type A B C and crystallizes in the chalcopy(3) rite structure. It is similar in structure to the well-known semiconductors with diamond and zinc blende structures. The chalcopyrite lattice of CuInTe2 can be considered as being derived from the II-VI zinc blende type compounds, such as CdTe, by replacing a pair of the Group II atoms, Cd, one with a Group I element (Cu) and another with (79) a Group III element (In). ) Two atoms of copper and two of indium form a tetrahedron with the center atom being tellurium; thus, each atom has four nearest neighbors. All energy levels in the s and p shells are saturated with two electrons of opposite spin that share their (74) position and momentum. The experimentally determined lattice o o (23) parameters for CuInTe2 were reported to be a = 6. 16 A and c = 12. 3 A. The c/a ratio of 2, 00, which is an ideal chalcopyrite structure, indicates that the electro-negativity differences between copper, indium and (76) tellurium atoms just compensate each other. By optical measure(3) ments, Austin found that the energy gap, E, of CuInTe2 was 0.95 eV (75) while Zalar reported E = 1.04 eV from the electrical conductivity 9 (76) measurements. Zalar also measured the Seebeck effect of CuInTe2. (79) 2 Zhuze gave E = 0.95 and hole mobility of 100 cm /v-sec. (41) Mason and O'Kane reported that CuInTe did not melt congruently. This means that the compound melts peritectically or that the congruently melting compound does not exist at the composition of 50% Cu2Te - 50% In Te. The electrical properties reported by (75) Zalar are rather complicated. In order to interpret the electrical 96

97 properties, some knowledge of the pseudo-binary phase diagram of Cu2Te-In2Te3 appears to be desirable. Differential thermal analysis, zone refining, chemical analysis, microscopic analysis, electrical conductivity measurements, and Seebeck effect measurements have been carried out in this work, and the results are presented and discussed. EXPERIMENTAL RESULTS In this section the mechanical properties, chemical analyses, phase diagram study and electrical properties of Cu7In9Te17 are presented. Mechanical Properties The zone refined copper indium telluride was coarse polycrystalline. The grain size varied from 1 mm. x 1 mm. x 1 mm. to 3 mm. x 4 mm. x 30 mm. However, the grain boundaries were irregular in shape, and it was very hard to separate a single crystal for the electrical measurements. The material was rather brittle and sometimes contained crack-lines over parts of the zone refined ingot. The electrical specimen often cracked when a platinum wire was welded to it. In many cases, the specimen cracked during the electrical measurements; this might be due to a high coefficient of thermal expansion for the sample. Microscopic analysis indicated that the material was single phase. Chemical Analysis The chemical analysis procedures described in Appendix E were used to determine the composition of the zone refined ingots used in this study. The results of the chemical analyses are presented in Table 9. 1 and plotted in Figure 9. 1. The tail ends of zone refined ingots, Nos. 854, 1033, and 1207 have a higher copper content which indicates that

TABLE 9.1. COMPOSITION OF THE SAMPLES Sample Numbei 182 232 Starting Composition (Cu2Te)45(In2Te3)55 (Cu2Te) 50 (InTe3)50 No. of Z. R. Passes 10 Section Number 4 7 Location of Results the section No. Cu of Chemicdl Analysis,Ato %) )n Te middle near tail 19.0 17.85 26. 9 27.20 54. 2 54.95 10 276 743 854 (Cu2Te50 (In2Te3)50 (Cu2Te) 50(In2Te3)50 7 11 CuIn8Te 16 10 (C2Te 46.8(In2Te3)53 2 +3 Te 855 Cu5In Te 1 1033 (Cu2Te)50 (In2Te3)50 10 9 2+3 8A 1A 3A 7 8D 1 3+4 6+7 3A 8B 1A 4 7 9 near head near tail head middle near tail tail head middle near tail middle tail head middle middle tail 22. 54 22. 75 21.82 22. 50 22.49 35. 9 20.10 21.22 21.23 22. 66 37.66 24.40 22.05 20.89 33.48 26. 70 25. 75 26. 99 26. 35 26.44 14.6 27.81 27. 21 27.46 25. 88 17.81 27. 60 26. 65 27. 32 25. 98 27.3 50. 77 51.49 51.19 51.15 51.07 49. 5 52. 09 51.57 51.30 (0 00 1207 (Cu Te) 45(InTe3) 55* 27 51.46 44. 54 47. 99 51.30 51.79 40. 54 51 5 1210 Cu5In6Te 1 5 Cu7IngTel 7 23 21.2 Indium and tellurium used in this sample were hydrogen fired. Head means the first frozen end while the tail is the last section to freeze (impure end). + Calculated Ato % of Cu, In, and Te.

m start (Cu In Te) / e55 2 33 C~ stort(Cui:e,55 743 o 2+3 / \ E 8A / a start (Cu In Te2) \ 1033 - x3A ~ 88 (toil) 20C — d ^50 start (Cu2Te)( n2Te3),, / 182 4 / ' 07, \ ~ stort(CuTe)9(ln2Te3),, / \ o120 IA (head) c. 25 \ o 77 9 (tail) sta rt(Cu 51n6T,,) - T V'CuTe 5 \- |n2 Te 855 0 1 3+4 Pseudo- Binary Line OA 6+7 30 40 0start (CuulnTe 40 854 - 0 average.o Tail In ~~~~~~~35/-~ ^ 35 Cu Cu-40 I Cu-40 In 05 In 30 Te 55 / ________ \________ ____\Te20 A 10 15 20 25 B MOLE % In ---- Figure 9.1. Result of Chemical Analysis on Zone Refined CuInTe2, Showing the Composition of Cu7In9Te17.

100 the congruently melting compound has less copper than the starting compositions of these ingots. Smaller composition gradients are expected for the ingots having starting compositions nearer the congruent composition. The analyses on ingot No. 854 showed very small composition gradients which suggests that the initial composition of the zone refined ingot is probably near to the congruent composition. The compositions of the homogeneous sections of five analyzed ingots, which excludes the multiphase tail section, show that the congruent melting point is near 44% Cu2Te- 56% In2Te, indicating that the congruently melting compound is Cu7In9Te17. Ingot No. 182 has a composition far off the pseudo-binary tie line when compared with the composition of the other ingots. This indicates that the chemical analysis for this run may be off. Differential Thermal Analysis and Phase Diagram A differential thermal analysis study of the Cu2Te-In2Te pseudo-binary system has been made. The liquidus, solidus, and solid-solid transformation temperatures are summarized in Table 9. 2, Based on these data, a phase diagram for the pseudo-binary system of Cu2Te-In2Te3 is proposed in Figure 9. 2. From the DTA data at 80% In Te3, it appears that a eutectic occurs very close to In2Te3. The DTA data confirms the zone refining and chemical analysis experiments, indicating the presence of a congruent compound, Cu In Tel7 whose melting point is 783 C, and which may have a solid-solid transformation near 650 C. However, the existence of other transformations in the system near this temperature makes the interpretation of the DTA data difficult. The compound CuInTe 2(51. 5% In Te3 - 48. 5% Cu Te, as determined from Zalar's Seebeck data (76 is peritectic at 780 C, and undergoes a solid-solid transformation at 655 C. Another peritectic compound which decomposes at 740~C may exist in the region of 55% Cu Te - 45% In2Te3. A eutectic occurs near (Cu2Te)g0(In Te 3)0 and 638 C. The numerous solid-solid phase transitions at 320 360 phase transitions at 3200, 360, and 570C occur between Cu Te and P2

TABLE 9. 2. DIFFERENTIAL THERMAL ANALYSIS OF Cu2Te-InZTe3 SYSTEM 2s 23 Sample Composition Mole % Sample iTmi rT r DTA Results Heating DTA Results Cooling Liquidus Transition Liquidus Transition Temperature Temperature Temperature Temperature (U U Q) $-4 0) ly. An n m 1 i v (n rc nriA +i ti-i In2Te3 20 20 1& I& L I &J %,,, LL'L7-LJk.J.i.L %..,IIL JIL 20 40 637 6 days at 590~C 663 7 days at 600~C 1 day at 300~C 639 2 days at 580~C 765 803 739, 654 639, 583 360, 320 734, 650 636, 575 465, 360,320 743,655 641,364 49 742 777 734, 637 607, 558 425, 357, 310 740, 647 612, 558 320 49 49 40 669 6 days at 550~C 803 738, 655, 582, 362 772 737, 643,608, 554, 361 50 731 None 801 780, 670 * 654 783 667,654 49 50 232 Zone Refined 57 1501 60 638 80 632 2 weeks at 604~C 6 days at 590~C 2 days at 580~C 783 (melt congruently) 780 810 772 656 638, 662 782, 429 672 783 783 784 760 o45 652, 571 607 49 660 49 100 147 None 669 667 * Sample not annealed and 667-670 C transition apparently arises from non-homogenized In Te3 impurity.

102 0 7800 bLJ {z: 700- 66 Iz A 665 w A638 0a o - 655 600 0] A t570A 0 500 - a o A 400 360 320 3001- I — - I I I I 0 20 40 60 80 100 Cu2Te MOLE % In2Te3 In2Te 2 3 ~ ~~I2Te3 Figure 9. 2. Phase Diagram of the Cu2Te-In2Te3 Pseudo-Binary System.

103 (Cu2Te) 60 (In2Te3) 40 Electrical Properties of CuIn Te7 The temperature dependencies of the electrical conductivity for several zone refined Cu7In Te17 and one crystal grown in a Bridgeman furnace, above the room temperature are shown in Figures 9. 3 and 9. 4. Figure 9. 5 shows a log o- versus log T plot for the same data. All ingots were slowly cooled to room temperature after zone refining except ingot No. 855 which was quenched in air. Specimen No. 1210(0) was the zone refined material used for growing the Bridgeman sample No. 1210(B). Low temperature measurements on specimens No. 232(2B), No. 854(3B), and 855(2A) indicated that Cu7In Te17 has a substantial constant electrical conductivity below the room temperature and a3000K/r800K = 1.0. Above 700 C, the Pt electrical contacts form a solution with the specimens, and the data in this region were of doubtful value. The specimens can be divided into five groups as shown in Table 9. 3 according to the characteristics of their electrical conductivity. Group I, including the first heating measurements of specimens No. 182(6), No. 854(3B) and No. 1210(B) (Figure 9.3) has the highest electrical conductivity. The electrical conductivity of this group shows a T 11 temperature dependence between 300 K to 450 K with electrical conductivity minima at 430 K and 560 K, and maxima at 470 K and 650 K. The electrical conductivity then decreases from 660~K to 900~K and is followed by a rapid increase, showing an apparent intrinsic energy gap of 1.3 eV. Group II includes the first heating measurements of specimens No. 232(2B), 1033(3) and 1210(0) (Figure 9.4). The electrical conductivity of this group has minimum values at 450 K and maxima at 560~K. Above 800 K, the electrical conductivity of this group rises rapidly,

TABLE 9.3 SUMMARY OF DATA ON Cu 7In Te17 COMPOUNDS Comp. after Zone Refining o Original | 0 E T Pc T Q D>) 300 > a E p max Sample Composition - <0 - + a a 2 o Xp CuTe In3Te Te | ~ | cm r v-se e~- ~~ c? 8 54(3B) 46.8 53.2 +3.1 53.9 3. 80 0.37 1 yes 130 D B.24 650 100 1.6 9. 2 67 907 I 1210(B) 45.6 54.4 0.00 1 yes 160 C+B. 18 600 75 1. 4 12.0 39 995 __ 182(6) 45.0 55.0 0.00158.6 7. 92 4.335 1 yes 85 C+B.15 500 75 1.1 9.2 51 1021 1210(0) 45.6 54.4 0. 00 1 yes 5.2 C+B.24 500 6 1.1 3.4 11 100 II 232(2B) 50.0 50. 0 0.00 1 yes 11 A C 905 1033(3) 3 50.0 50.0 0.00 53. 3 3. 32 1.31 1 y ves 3.1 A C ____ I I __ 852 855(2A) 45.6 54.4 -4.35156.1 6. 01 0.14 * yes 135 D C+B. 16 450 40 0. 9 5. 5 45 833 III 854(3B) 46.8 53.2 +3.1 53.9 22 yes 47 D C+B. 24 560 30 1.2 4. 9 38 887 __ 1033(3) 50.0 50.0 0.00153. 3 3. 32 1.31 2" ves 27 A C __ __ _____ 837 743(5B) 50.0 50. 0 0.00153.0 3.00 1.49 1 yes 76 852 V 743(6) 50.0 50. 0 0.00 53. 0 3.00 1.49 1 no 47 A 852 743(4A) 50.0 50. 0 0.00|53.0 3.00 1.49 1 no 27 726 232 50.0 50.0 0. 00 __ _ _ 1 no 9.6 ___ ___ ___ 1 843 276(2A) 50.0 50.0 0. 00 1 yes 0.1 D B.06 400 0. 1 0.7 13.010.05 806 v -l9 700 1. 0 1.6 15. 0. 840 276(2A) 50. 0 50.0 0.00 2 yes B. 20 7~ 10 6 5 840 ___ __.261 800 0.5 2. 2 16.01 0.2 1 quickly cooled O -p-7

105 TEMPERATURE, t, (~C) 560 441 352 282 227 181 I1 977 727 1000 I 43 III 84 60 39 21 A 11 I 100 0 0 I -1 b 0 CD Z 0 0.J wr I0 10 0.21 eV 18 eV Cu7 In9 TeI7 v 182 (6) First heating cycle O 854 (38) First heating cycle A 1210 (B) First heating cycle * 854 (3B) Second heating cycle 0 855 (2A) First heating cycle * 855 (2A) After first cycle _ 1033 (3) Second heating cycle I t I I -— I I I I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. It i I -I 10 1. o-2L 0.8 1.2 RECIPROCAL 1.6 2.0 2.4 2.8 3.2 3.6 ABSOLUTE TEMPERATURE 1000/T, ( K )'I Figure 9.3. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Cu In9Te 1. Group I: 182(6), 854(3B), 1210(B). Group III: 854(3B), 855(2A), 1033(3).

106 TEMPERATURE, ~C 977727 560 441 352 282 227 181 143 III 84 60 39 21 1000, I- I I i ' ' III i 100 E 0. 10 0 b o: I 01 0 0 >r L> -i LU 0.I Oo1i. - Cu7lngTe17, 743(4A) First heating cycle.0 232(2B) First heating cycle " 743 (5B) First heating cycle -o 1033(3) First heating cycle Fir st heating cycle a 1210(0) First heating cycle a 276(2A) First heating cycle * 232 (? ) First heating cycle a 276 (2A) Second heating cycle I I I I I 0.8 Figure 9. 4. 1.2 1.6 2.0 2.4 2.8 3.2:1 3.6 RECIPROCAL ABSOLUTE TEMPERATURE, 1OO0/T, (~K) Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for CuIn9Te17. Group II: 232(2B), 1033(3), 1210(0). Group IV: 232(?), 743(4A), 743(5B), 743(6), 276(6).

107 200 101 90 80 70 60 50 E 40 U T% 30 0 — -o t-i20 1210 ( r_z _o 0 -. - o 2 F heating I cyl Fiue. Lgrtmo Tria Co 7ctvtyes V 182(6) First heoting cycle. __ 4 232(2B) First heating cycle * 232(?) First heating cycle 5 743(4A) First heating cycle - ___'1_ _ o 743(5B)First heating cycle 4 x 743(6) First heating cycle 0 843(3B) First heating cycle '1-i i * 843(3B)Second heating cycle 0 855(2A)First heating cycle _ 3 0 1033(3) First heating cycle * 1033(3) Second heating cycle 0', 1210(0) First heating cycle A 1210(B) First-heating cycle 2 _I I I ___ 100 200 300 400 500 600 700 800 900 1000 ABSOLUTE TEMPERATURE, T, (~K) Figure 9. 5. Logarithm of Electrical Conductivity versus Logarithm of Absolute Temperature for Cu In Tel7.

108 also showing an intrinsic energy gap near 1 3 eV. The electrical conductivity of Group III, including the first measurements of No. 855(2A), and the second heating measurements of No. 854(3B) and No. 1033(3) (Figure 9.3), decreases as the -1.0 -1.5 o temperature increases according to T ' T up to 800 K. Group IV comprise specimens all of which were obtained by zone refining an initial composition of CuInTe2 (Figure 9. 4). Specimens from ingot No. 743 have a sharp maximum electrical conductivity at 6250K followed by a very rapid decrease of the electrical conductivity. The electrical conductivity of No. 232(?) is constant up to 500 K followed by an increase according to d log cr/d(1/T) = 0.42 eV/2k. Group V has only one example, also obtained by zone refining of CuInTe2 for a limited number of passes and specimen No. 276(2A) (Figure 9. 4) has the lowest electrical conductivity, 0, 1 mho/cm from the room temperature up to 500 K followed by a rapid increase to 1.0 mho/cm at 600 K. Then it decreases and increases again followed by a sharp decrease. Figure 9. 6 shows the Seebeck coefficient measurements for the specimens shown in Figure 9.3 and Figure 9. 7 shows it for the specimens shown in Figure 9. 4. All specimens had a p-type Seebeck coefficient, ranging from 0.1 to 0.2 mV/ K at room temperature, increasing as the temperature increases up to about 500 C. Then it decreases as the temperature increases, indicating an intrinsic characteristic. DISCUSSION AND INTERPRETATION OF THE RESULTS 1. The numerous solid-solid phase transitions in the phase diagram between Cu Te and (Cu Te)60(In2Te3)40 at 570~C, 360~C and 320 C can be accounted for by examining the phase diagram for the Cu-Te system, and assuming that the transitions in the binary system of Cu-Te extend into the ternary field of the Cu-In-Te system.

109 TEMPERATURE, t, (~C) 977727 560 441 352 282 227 181 143 III 84 60 39 21 4 ~0.8 l l lCu7 In9Te17 V 182 (6) First heating cycle 0 854 (3B) First heating cycle * 854 (3B) Second heating cycle 0.7- 0 855 (2A) First heating cycle * 1033 (3) Second heating cycle A1210 (B) First heating cycle 0.6 0 E 0.5 z u 0.4 0 0 LL, LLI 0. LL) W. - AL ^ - ' < --- V) nf~ w I Figure 9. 6. Seebeck Coefficient versus Reciprocal Absolute Temperature for Cu7IngTe17.

110 TEMPERATURE,~C 977 727 560 441 352 282 227 181 143 III 84 60 39 21 a n n i I I --- — I ----- ----- I ---- — I --- — r ---- I ------ I ------ --- I.. I I I Cu7 Ing Tel7 I I I.720.640.560 0 E.480 LLU -.400 Li.. LU LLJ 0 C) o.320 La (n O) _I, I __ o 232 (2B) o 1033 (3) A 1210 (0) o 276 (6) 1 276 (6) First heating cycle First heating cycle First heating cycle First heating cycle Second heating cycle 0I 0 "c 0.240.160.080 0.. ""I',kY- --- ^ ~ - -- I 9- A~........-~ l-^^~~~~\.V N-, "^SL~~~~~~~~~. _ _~~ ~ ~~ I____I___I ___ I ___ I 0.8 1.2 1.6 2.0 2.4 2.8 3.2 RECIPROCAL ABSOLUTE TEMPERATURE, I000/T, (~K)' 3.6 Figure 9.7. Seebeck Coefficient versus Reciprocal Absolute Temperature for Cu7In9Te 17

111 The transition at 425 C-4650C and 20% In Te remains unexplained. 23 The congruently melting compound, melting at 783 C exists at 44 mole % Cu Te - 56 mole % In Te3. The compound CuInTe2 is peritectic, and undergoes a solid-solid transformation at 655 C, as seen both on DTA and electrical measurements. With this knowledge of the phase diagram behavior, Zalar's data75 76) on electrical conductivity and Seebeck effect variations can be understood, since the growth of a Bridgeman crystal from 50% In2Te3 should produce a large variation in composition along the crystal. 2. It has been shown that the specimens can be divided into five groups according to the characteristics of their electrical conductivity. When the sample preparation is reviewed, it is found that the specimens of Group I are prepared by slow cooling of zone refined 44. 1 ~. 9 mole % Cu2Te, that the specimens of Group II are by slow cooling of zone refined 50% mole Cu Te (except No. 1210(0)), and that the specimens of Group III are obtained by quick cooling of the material, assuming specimens No. 854(3B) and No. 1033(3) being quickly cooled after the first heating cycles. The chemical analyses indicate that the specimens of Group I contain about 54 mole %o or more of In Te with excess tellurium, that the specimens of Group II contain about 53. 5 mole % In Te3, that the specimens of Group III are similar 2 3 -to those of Groups I or II except that they are quenched rather than annealed. The specimens of Groups IV and V are all obtained by zone refining of 50% In2Te3 ingots, and possibly the zone refining was not sufficiently efficient to produce samples sufficiently close to the congruent composition to exhibit proproperties characteristic of Group II or Group I. This suggests that at the composition near 53. 5 to 54 mole %o In2Te (3. 5%o vacancies) there is a change in the electrical nature of the interaction of the vacancies with the lattice. Below 3. 5% vacancies, they aid the introduction of acceptors, whereas above 3. 5o they may act to decrease the acceptor concentration. Therefore, it can be concluded

112 that Group I is the low temperature form of Cu7In9Te17 with a vacancy concentration greater than 3. 5%. Group II is the low temperature form of Cu7In Te17 with a vacancy concentration less than 3. 5%, and Group III is the high temperature form of Cu7In Te17. Group IV represents specimens which have even lower vacancy concentrations and are relatively far removed below the 3. 5% vacancy concentration. Group V has (74) properties more nearly like those published for CuInTe2 by Zalar, and we assume that it is not representative of Cu7In9Tel7, but of CuInTe2. 3. Specimens No. 1033(3), No. 743(6) and No. 232(2B) (vacancy-deficient samples) increase electrical conductivity by the heat treatment during measurements, while specimens No. 854(3B) and No. 855(2A) (vacancy-rich samples) decreases. This indicates that the vacancy-deficient Cu7In9Te17 increases the acceptor concentration and vacancy-rich Cu7In Te17 with an initial high acceptor concentration as decreased by the heat treatment. 4. Seebeck coefficient of specimens No. 232(2B) and No. 1033(3), which are near the 3.5% vacancy composition, are higher than those for the other specimens at room temperature. This is correlated with the conductivity and compositions of the specimens. Deviations from the 3. 5%o vacancy composition increase the conductivity and lower the Seebeck coefficient. 5. According to Equation (57) a = Ak/q + E /qT (57) p p and approximating E by Ef, a plot of a qT| as a function of temperature will show the variation of the Fermi level when Ak/q is small with respect to a Figures 9. 8 and 9. 9 show the plots for Cu7In Te17. Three kinds of Fermi level variations are observed. The aqT of type "C" increases as the temperature increases as shown in Figure 9. 8. The aqT of Type "B" is constant as shown for specimen No. 276(2A) and the first heating cycle of specimen No. 854(3B)

Cu7Ing Tel7 o 232 (2B) First heating cycle o 1033 (3) First heating cycle * 1033 ( 3 ) Second heating cycle /D-O 4 0.4 — _ gPI G) cK 0.3 '7 t. 0.- I..= 0 100 200 300 400 500 600 700 800 900 1000 ABSOLUTE TEMPERATURE,T, (~K) Figure 9.8. aqTI versus Absolute Temperature for Cu7In9Tel7, Showing "A" Type Variation of the Fermi Level.

0.5 0.4 0.3 G) 0.2 0.1 Figure 9.9. ABSOLUTE TEMPERATURE,T, (~K) ap q T versus Absolute Temperature for Cu7In9Te17, Showing "A + B" Type Variation of the Fermi Level.

115 in Figure 9, 9. Type "C+B" is the combination of type "C" and type "B" as shown by the other specimens in Figure 9. 9. It is found that all the specimens adding acceptors by heat treatment show type "C" characteristics, and the type "B" or type "C+B" specimens decrease the acceptor concentration by heat treatment. Consequently this can be correlated to the composition of the specimen as discussed in section 4. 6. When Equation (18) for a p-type semiconductor is substituted into Equation (57), an equation for the Seebeck coefficient of p-type extrinsic semiconductor is found to be a= Ak/q+ E /2Tq - (k/2q) In (N /2N ) p a a c oj a q = Ak + E /2T - (k/2) In (Nd/2U) + (3k/4) In (m T/mo) p a d p o (9.1) This equation shows that the slope of a q - (3k/4) In T versus 1/T is P equal to E /2. When this is made for the specimens showing type "B" a or type "C+B", the Seebeck coefficient, E of 0. 19 ~ 0. 26 eV are a found in the temperature region where the a qT values shown in Figure 9. 9 are constant. These values are nearly twice the corresponding values seen on the a qT plots, strongly suggesting that the Fermi level lies medway between the acceptor level and the top of the valence band, and that there is an acceptor level at 0, 2 ~ 0. 04 eV. The values of Ea estimated by E = 2E = Za2 qT in the constant a qT region a a f p p are shown in Table 9 3. 7. A plot of a - 3k/4 In T in the low temperature range for specimen No, 855(2) (Group III) shows an acceptor having an ionization energy of about 0, 007 eV as shown in Figure 9. 10. 8. A similar plot for specimen No. 276(2B) (Group V) shows a shallow acceptor level having no activation energy on the first cycle, but increasing to 0. 04 eV on the second cycle. It is not surprising that this behavior is different from that observed above (Cu7InTe 17), since this material is more representative of the CuInTe2 phase.

116 0 - 0 E-0.35 - 0.8 - 41)~It 1.2 1.6 2.0 2.4 2.8 3.2 RECIPROCAL ABSOLUTE TEMPERATURE, I000/T, (~K-') 3.6 -0.2 -0.2 I I I I I Cu7 InTe17 855 (2A)First heating cycle I_ " I _ I r T I I I \ O~ -0. 3 \ - -Ea=?2m 0.007 eV 5n- __ __ _ 7 __ __ II I — n I O a a 7 Q Q IrN II 10 1 1I v C-l J ai j I I / l 1 ~/ I. RECIPROCAL ABSOLUTE TEMPERATURE, IOO0/T, (~K-I) 1 I 4 Figure 9. 10. aq - (3k/4) In T versus Reciprocal Absolute Temperature for CuInTe2 and Cu7In Te17.

117 9, When E = E /2 is substituted into Equation (16) for a f a p-type semiconductor: 4N N v a v 1 + 4 exp (E /2kT) 1 + 2exp (E /2kT) a a and solved for exp E /2kT, one finds a 4N - N v a exp (E /2kT) = (9 3) a 4(N -ZN) a v Since exp (E /2kT) is always positive, therefore, the condition a 2N < N < 4N (9.4) v a v should be satisfied. Equation (9.4) gives the limitsof N for the a E = E /2 situation. f a When the value of E estimated from the Seebeck data is a substituted into Equation (9. 3) and solved for N, the acceptor a concentration of the specimen can be found. Table 9.3 also lists the value of N estimated in this way. Furthermore, the carrier concena tration, p, can be calculated according to Equation (13), and the values are given in Table 9 3. 10. The hole mobility can now be calculated according to Equation (47), and the values are also listed in Table 9.3. 11. A comparison of the log a versus 10 /T and aqT versus T plots for Groups I and II are significant. Over the temperature range wherein aqT is constant and defines an acceptor energy, E /2, the a electrical conductivity increases with essentially the same activation energy. At temperatures where the aqT curves commence to rise again, the electrical conductivity decreases. This phenomenon can be explained by assuming that the acceptor bands are degenerate and nearly empty, until the Fermi level approaches E /2. Conductivity increases by an increase in both hole concentration in the valence band and electron concentration in the degenerate in the valence band and electron concentration in the degenerate

118 acceptor band, until the acceptor band becomes about one third filled. Above this point, the effective mass of the electrons changes and the mobility changes, as indicated by a curvature of the conductivity curves near their maximum values. When the degenerate acceptor band becomes more than half filled, the effective carrier concentration decreases and the conductivity falls with increasing ionization. 12. In the Group III specimens, the evidence indicates that the deep acceptors observed in Groups I and II are at least partially converted to shallow acceptors. Measurements from 77 K to 300 K on specimens No. 232(2B), No. 854(3B) first cycle, and No. 855(2A) (Figure 9. 5) show essentially a constant conductivity, hence this acceptor ionization energy is very small, equal to 0. 007 eV as deduced from Figure 9. 10 from the Seebeck data. SUMMARY Based on chemical analyses and DTA measurements, a phase diagram for the pseudo-binary system of Cu Te-In Te has been proposed. Zone refining, microscopic examinations, and chemical analyses together with DTA measurements indicate that the congruently melting composition is Cu7In Tel7, 44 mole % Cu Te - 56 mole % In Te3. Two peritectic compounds exist near CuInTe2 and 55 mole % Cu2Te - 45 mole % In2Te3. Electrical conductivity and Seebeck coefficient measurements on the congruent compound Cu7In9Tel7 were performed. All specimens were p-type. The electrical conductivity of Cu7In Te17 below 200 C down to liquid nitrogen temperature is substantially constant, indicating the presence of one acceptor level having an activation energy of 0. 007 eV as determined from the Seebeck data. The electrical properties of the material strongly depend upon the compositions and states of the crystals as shown in Table 9. 3. A second acceptor level at 0. 2 ~ 04 eV above the top of the valence band is also found. These acceptor concentrations are about 1020 acceptor/cm

119 and the hole mobility is estimated to be about 10 to 70 cm /v-sec at 250 0C. One sample believed to be from the CuInTeZ peritectic phase was also measured, and its properties are substantially different from those of Cu In9Te17.

120 CHAPTER 10 ELECTRICAL PROPERTIES OF Cdln Se LITERATURE REVIEW CdIn2Se4 is a peritectic compound in the CdSe-In2Se3 pseudobinary system, melting at 915. (4149) Figure 10.1 shows the CdSe-In Se3 phase diagram as determined by O'Kane. It crystallizes in a tetragonal structure (pseudo-cubic) with the lattice constants 0(24 34) a = c = 5.82 A ' as shown in Figure 110.2. The electrical properties of CdIn2Se4 have been investigated by several investigators. (6,34,49,50,71) 2 4 (34) Kolomiets and Mal'kova obtain an energy gap of 1. 3 eV from the slope of the logarithm of the electrical conductivity versus reciprocal absolute temperature while Suzuki and Mori(71) reported 1. 54 eV from the same kind of plot. Without zone refining, Suzuki and Mori found that the starting composition of CdIn2Se4 1 gave a specimen of the highest resistivity. The Hall mobility calculated from Suzuki's data is about 35 cm /v-sec, while Kolomiets and Mal'kova gave 100 cm /v-sec. O'Kane(9) estimated the mobility to be 78 cm /v-sec at 129 C on a normal zone refined specimen. These values compare with 22 cm /v-sec, given by Beun et al. (6) Nobody ever measured a specimen more than two cycles to see if a change occurred by the heating treatment. The optical energy gap given by Kolomiets and Beun was 1.45 eV and 1. 61 eV respectively. EXPERIMENTAL RESULTS Pycnometric density, measured by liquid immersion method using ethanol was 5. 58 ~ 0.04 gm/c. c. for specimen No. 083(2), 5. 56 ~ 0. 04 gm/c. c. for specimen No. 085(7) and 5. 54 ~ 0.05 gm/c. c. for specimen No. 189(4). The electrical conductivity and the Seebeck coefficient of specimens No. 083(2), (measured by O'Kane) No. 085(7), and No.

121 Cd Se - In2 Se3 A From D TA Heating Curves o From D A Cooling Curves I,; I' 1,( 0 w - I,( DI _ c L I w CdSe MOLE % Cd Se In2 Se3 Figure 10.1. Phase Diagram of the CdSe-InZSe3 Pseudo-Binary System.

122 I -. — _ ___ /- - - 1-.-_ 0 Cd * In Se = c = 850 Kx Figure 10.2. Structure of CdIn2Se4.

123 189(4) are shown in Figures 10.3 and 10.4 respectively. No Hall data were taken as the materials were too highly conductive to be measured in our equipment. Ingots No. 083 and No. 085 were prepared by normal zone refining the composition 50 mole o CdSe and 50 mole % In2Se3, and the polycrystalline specimens - from both ingots- were cut from portions without inclusion of a second phase. Specimens No. 083(2A) and No. 083(2B) were measured by O'Kane without the cocoon arrangement. Specimen No. 085(7) was measured with about 40 mg extra Se in the cocoon. The specimen had substantially constant electrical conductivity, 145 mho/cm for below 225 C down to liquid nitrogen temperature. After it had been heated up to 336 C, the specimen was held at that temperature for five hours before it was cooled down and remeasured. During this five hours, the electrical conductivity decreased from 80 mho/cm to 67 mho/cm. The electrical conductivity obtained in the second heating cycle below 430 C was 80 mho/cm, almost a half the value of the first heating cycle. The specimen gave a n-type Seebeck coefficient. The magnitude of Seebeck coefficient of both the first and the second cycles increased as the temperature increased in the whole temperature range, from 0.013 mV0/K at liquid nitrogen temperature to 0.17 mV/~K at 900~K. The magnitude of Seebeck of this specimen was smaller than that of the other specimens. (8) Ingots No. 185 and No. 189 were prepared by zone leveling 50 mole o CdSe and 50 mole lo In Se3. Ingot No. 185 had 10 zone leveling passes while No. 189 had only seven. The zone leveling technique had enabled us to obtain a single phase CdIn Se4. Both polycrystalline specimens No. 185(7) and No. 189(4) were measured in the evacuated cocoon without extra Se. Below 150 C, they had essentially constant electrical conductivity, 240 mho/cm for specimen No. 189(4) and 25 mho/cm for specimen No. 185(7). A decrease of the

124 TEMPERATURE, t, (~C) -10 1000 100 E 0 rE b 0 z 0 -J I (-l u o -J u LI 10 Cd In2Se4 083 (2A) First heating cycle " 083 (2B) First heating cycle * 085(7) First heating cycle 085(7) Second heating cycle 185 (7) First heating cycle 185 (7) Second heating cycle 189 (4) First heating cycle 189 (4) First cooling cycle * measured by O'Kpne 1.4 1.8 2.2 2.6 3.0 34 RECIPROCAL ABSOLUTE TEMPERATURE, IOOO/T, (OK-') TEMPERATURE, t, (~C ) 'a 727 227 60 -23 -73 -106 -130 -148 -162 -173 -183 -190 -196 -201 )I I I I I ___ I(B)I ___ I ___ ___ I _ I 2 3 4 5 6 7 8 9 10 II 12 RECIPROCAL ABSOLUTE TEMPERATURE, IOO/T, (~K-') Figure 10. 3. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for CdIn Se4. (A) High Temperature Range (B) Low Temperature Range.

0 o -ot -0.1 x r r E W X f X-r LI.IL Cd In2Se4 0 -0.3 o (x 083(28) First heating cycle O | A 085(7) First heating cycle\ [ LS A 085(7) Second heating cycle w -0.4 0 185(7) First heating cycle * 185 (7) Second heating cycle 0 189 (4) First heating cycle -0.5 me_ measured by 0'Kane -0.5 -0.6 -200 -100 0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE, t, (~C) - Jn Figure 10.4. Seebeck Coefficient of CdIn2Se4.

126 electrical conductivity to 40 mho/cm for specimen No, 189(4) at 250 C, 2 mho/cm for specimen No. 185(7) at 2700C was followed by an electrical conductivity increase. Regardless of the way the electrical conductivity was changing, the Seebeck coefficient of the specimens, showing n-type conduction, increased in magnitude as the temperature increased, from 0. 1 mV/~K at 1000C to 0. 25 mV/~K at 630~C for specimen No. 185(7), and from 0. 5 mV/~K at 60~C to 0.25 mV/~K at 600~C for specimen No. 187(4). The change of the Seebeck coefficient of specimen No. 189(4) above 600 C may indicate that the compound is not stable above this temperature. The electrical conductivity of both specimens increased by the heat treatment of the first heating cycle, while the Seebeck effect decreased in magnitude. DISCUSSION OF RESULTS 1. The theoretical density of CdIn Se using published lattice o 3 parameter data (a = 5. 82 A ) is 5. 54 gm/cm. No density measurements were made on specimen No. 185(7). By assuming that the increase in density is attributable to excess interstitial Se, the compositions of the remaining specimens using the measured pycnometric densities are CdIn2Se4.00 (stoichiometric) for specimen No. 189(4), CdIn2Se4.03 for specimen No. 085(7), and CdIn Se 46 for specimen No. 083(2) (measured by O'Kane). Comparison of electrical conductivity data of these specimens (Figure 10.3) shows that the excess Se acts so as to suppress the donors in the material at room temperature. This conclusion conforms to that observed by Suzuki and Mori. Our conductivity curve for CdInZSe4. 0 ' No. 085(7), is substantially identical with that reported by Suzuki and Mori. However for the CdIn2Se4 06 composition, [ our No. 083(2)] their conductivity curve is considerably below ours, Since their samples were made by actually using excess Se, whereas ours were made by zone refining or zone leveling the

127 / stoichiometric composition, our samples undoubtedly also contain excess Cd and In in interstitial positions which act as donors. Therefore our samples probably approximate the composition CdIn Se4 0O with varying amounts of interstitial Cd, In and Se in the stoichiometric ratio. 2. The electrical conductivity of all specimens are substantially constant for the temperature below 1 50 C. This indicates that the temperature dependency of the electron concentration may just counterbalance the temperature dependency of mobility. Seebeck coefficient indicates that all specimens were still in the extrinsic region up to the highest measuring temperature. If the mobility of 25 cm /v-sec. is assumed for the compound, the carrier concentration of the specimens 18 3 19 3 19 3 will be about 6x10 cm, 6x10 /cm and 3.8x10 /cm for specimens No.185(7), No. 189(4), and No. 085(7) respectively. These values are at the same order to the concentration of the states at room temperature. 3. The electrical conductivity of specimens No. 185(7) and No. 189(4) which are measured without extra Se in the cocoons increased in the second heating cycle as a result of the heat treatment of the first heating cycle, while that of specimen No. 085(7) decreased after annealing in the Se atmosphere during the first heating cycle. This indicates that the specimens measured without extra Se in the cocoons loses some Se but gains Se in the other case. The excess Se suppresses some of the donors in the material. This result also suggests that a low impurity ingot may be obtained if the starting composition has small amounts of excess Se over the stoichiometric composition to compensate the Se loss during sample preparation. This agrees with the results (71) of Suzuki and Mori. ( 4. It has been shown that when N >> N and 128 N exp(E -E )/ d c c g d kT >> Nd, Equation (18) relates the Fermi level, donor energy level, donor concentration and the energy states. When Equation (18) is

128 substituted into Equation (58), an equation for Seebeck coefficient for an n-type extrinsic semiconductor is found to be a = - Ak/q - (E - E )/2qT + (k/2q) In (Nd/2N) n q d d c or -a q =Ak+ (E -Ed)/ZT - (k/2) In (Nd/2U) + (3k/4) In (m /m ) n g d d n o This equation indicates that the slope of -a q- (3k/4) In T versus 1/T n plot for an n-type extrinsic semiconductor is equal to (E -E )/2. Figure 10. 5 shows the plot of -a q - (3k/4) In T versus 1000/T for specimen No. 085(7). E - Ed estimated from the slope of this plot for the low g d temperature range is 0. 014 eV, for both the first and the second heating cycles. The carrier concentration of this specimen has been assumed 19 3 to be 3.8 x 10 donors/cm. When this value is substituted to Nd d between 900 to 130 K, where 0.014 eV donor level below the 18 conduction band id obtained, both N >> N 5 x 10 and d c 128 N exp (E -Ed)/ kT >> Nd are satisfied and the estimation is valid. c gd d The corresponding plots on the other specimens do not show this donor level as they were not measured at sufficiently low temperature.

129 TEMPERATURE, t, (~C) oO 727 227 60 -23 -73 -106 -130 -148 -162 Cd In2c A 085(7) A 085(7) Y-250 - - -- -- - 0 E C 4r A -350 i _____ ___ I 2 3 4 5 6 7 8 9 10 11 12 13 14 RECIPROCAL ABSOLUTE TEMPERATURE, I00/T, (~K-1) -a q- (3k/4) In T versus Reciprocal Absolute Temperature for CdIn2Se4. Figure 10.5.

CHAPTER 11 THE SEMICONDUCTING PROPERTIES OF Ag In 13Se 2o-8 ---13 INTRODUCTION A review will be given of the phase diagram of the Ag2Se-In2Se3 pseudo-binary system and the electrical properties of Ag In8Sel3o Electrical conductivity, Hall effect, and Seebeck coefficient measurements have been made with a cocoon arrangement. With extra Se sealed in the cocoon, it was possible to restore the original high electrical resistivity of a sample of Ag2In8Se 3 after it had exhibited a high electrical conductivity as a result of heat treatment caused by the first measuring cycle. The properties of both the high and low electrical conductivity forms of Ag2In8Sel3 have been carefully studied. The cause of the change of the electrical properties has been attributed to a solid-solid transformation. A preliminary examination on the photoconductive properties of Ag2In8Sel3 has also been made on the high resistivity material. A third form of this compound is also postulated. LITERATURE REVIEW (49) O'Kane made DTA measurements for 0, 10, 20, 40, 50, 60, 80 and 100 mole % of Ag2Se within the Ag2Se-In2Se3 pseudo-binary system and proposed a partial phase diagram. He found that AgIzn8Se13, i.e. 20 mole % Ag2Se and 80 mole % InZSe3 melts congruently, and made electrical conductivity, Hall effect, Seebeck coefficient, and thermal conductivity measurements on zone refined Ag2In8Se13 specimens. The energy gap of the compound was reported to be 1. 51 ~ 0. 02 eV for this material. During his measurements it was found that high resistivity material became highly conductive after being measured. It was proposed that the cause of the change is the loss of selenium by the heat treatment during the measurement. 130

131 EXPERIMENTAL RESULTS O'Kane and Kulwicki have made more DTA measurements within the Ag2Se-In2Se3 pseudo-binary system in this laboratory, and completed the phase diagram for this system as shown in Figure 1 i 1. The system contains three eutectics at about 24, 79, and 85 mole % In Se and 698~, 8000, and 8100C respectively, and three intermediate phases: the P-phase which decomposes in a peritectic reaction at 799 C and 50 mole % InZSe3, the y-phase which melts congruently at 815 C and 70 mole % InzSe3, and the 6-phase at 80 mole % In Se which melts congruently at 822 C. Crystalline transformations take place in the a-phase (Ag Se) at 134 C, the y-phase at 645~C, the 6-phase at 749~C and the E-phase (In Se ) at 2010C. 2 3 Powder form x-ray photographs have been taken for both the high conductivity (specimen No. 224) (Form I) and the low conductivity 2 (specimen No. 1517)(Form II) materials. Sin a values are listed in Appendix F. It is found that the high conductivity material (Form I) has a chalcopyrite (tetragonal) structure with lattice parameters a = o o 5. 676 A, c = 12. 50 A whereas the low conductivity material (Form II) crystallizes in a monoclinic structure with lattice parameter a = 5. 676 A, 0 o o b = 5. 903 A, c = 12.48 A, a = 74. The pycnometric density of the 3high ductivity material is 5. 542 gm/cm Chemical analyses made on zone refined specimen No, 741, using the Volhard method as described in Appendix E for determination of the silver content indicated that the material contained 10. 01 ~ 0. 002 wt. % Ag. If it is assumed that the final composition lies on the AgzSeIn2Se3 pseudo-binary line as seems most probable from DTA measurements made on each side of the pseudo-binary, the composition of the compound should be Ag2In8Se 3. The electrical properties were measured in two experimental arrangements, one using a cocoon with extra Se in the system, and

132 1 LIQUID 800 700 600:D F — Lli 4: I I I I / / / /3 y 30 a'+ / 134 MOLE FRACTION In2Se 2 3 Figure 11.1. Phase Diagram of the Ag2Se-In2Se3 Pseudo-Binary System.

133 the other using a two-furnace arrangement capable of controlling the sample temperature and the temperature of a Se source independently of one another. Figure 11. 2 shows the electrical conductivity of specimens 296(5B) and 741 (2A) measured by the cocoon arrangement, and 296(6) measured in the two-furnace arrangement for the initial run with the Se temperature maintained at 80 C. Figure 11.3 shows the electrical conductivity for specimen No. 296(5B) in the temperature range below room temperature. Five successive heating cycles to progressively higher temperatures and a sixth heating cycle up to 200 C have been made on specimen No, 296(5B). The only change observed on the first two heating cycles wherein the specimen was not heated above 324 C, was that the deep donor activation energy increased from 0. 92 eV to 1. 20 eV, which is approximately that observed by O'Kane (1. 2 ~ 0. 1 eV). In the third heating cycle, the deep donor activation energy of 0. 92 eV was observed instead of the 1. 19 eV energy, and the resistivity of room temperature was increased by a factor of ten. At 470 C, the electrical conductivity became unstable and the specimen was held at that temperature for four hours until it stabilized. During this period, the electrical conductivity increased -1 from 3 x 10 mho/cm to 3 mho/cm, after which the specimen was cooled to room temperature. The electrical conductivity remained high, and it was found that the cocoon had cracked. The specimen was sealed in a new cocoon with extra Se before the fourth heating cycle was made. The fourth measurement began from liquid nitrogen temperature. The electrical conductivity increased very slowly from 1.2 mho/cm at 196 C to 2. 2 mho/cm at 23 C; it then started to decrease, slowly, and much more rapidly above 110 C. The electrical conductivity rapidly decreased from 2 mho/cm at 110 C to 1.5 x 102 mho/cm at 317 C, a point just on the previously measured curve forthe high resistivity form of Ag2In8Sel3. Heating the specimen up to 454 C did not transform the specimen into the high conductivity form, and the specimen had an electrical conductivity of 5 x 10 mho/cm

134 TEMPERATURE, t, -C 727 560 414 352 282 227 181 143 III 84 60 39 21 4 100 1,0 _I *_' 1.49 eV 1 -0- ---- - 80 I. eth c d heating cycle cl 454 C yMaximum temperature on the -— 1.51 eV I-. -I z 164 119.5 *C10-5 =-, 296 (5B3) Ag,lnSe Se - _ A First heating cycle 10 A First cooling cycle ^ \ ~ o Second heating cycle \ \\~ * Second cooling cycle -1 o Third heating cycle \r * Third cooling cycle \ \ 0 Fourth heating cycle 9e\\ Fifth heating cycle \ l0 V Fifth cooling cycle -o Sixth heating cycle - \ 741 (2A) -0 First heating cycle ____ __ - Second heating cycle -- 296 (6) First heating cycle 0 * 296(6) After annealed in Se atm. 0.8 1.2 1.6 2D 2.4 2.8 3.2 I RECIPROCAL ABSOWLUTE TEMPERATURE, 1000/T, (K-1) Figure 1. 2. Logarithm of Electrical Conductivity versus Reciprocal Absolute Figure 1 1.2. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se13 C. 0 133

135 TEMPERATURE, t,(C) -106 -148 -173 ca 227 -23 -190 -202 5.0 4.0 3.0 o E 02.0 C> 2.0 0 3 0 1.0 0.15eV s,~0.1/ eV 296(5B) Ag2 In8 Se,3 0 Fourth heating cycle I _- _- I 0 2 4 6 8 10 12 RECIPROCAL ABSOLUTE TEMPERATURE, 1000/T, (~K-') 14 Figure 11.3. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se13 in Low T —lperature Region.

136 at 37 C after the fourth heating cycle indicating that the high resistivity form had been restored. On the fifth heating cycle the electrical conductivity of the specimen followed the curve of the high resistivity form up to about 470 C showing the activation energies of 1. 19 eV and 1.51 eV below and above 180 C respectively. A rapid increase of electrical conductivity was observed at about 500 C from 4 x 10 -mho/cm to 15 mho/cm. Further heating increased the electrical conductivity, but on cooling the high resistivity properties were not restored. No obvious crack was observed in the cocoon after it was cooled to room temperature, nor was any extra Se found remaining in the cocoon. Before making the sixth heating cycle which was made only up to 200 0C, the sample was removed from the cocoon, and the surfaces polished off, and new contacts were formed. The electrical conductivity of the specimen stayed at about 40 mho/cm for this cycle. Two measurements were made on specimen No. 741(2A) without excess Se in the cocoon, and the transformation from high resistivity to high conductivity was observed. For purposes of comparison and discussion, the electrical conductivity data of O'Kane are reproduced in Figures 11.4 and 11. 5. All the specimens measured in this work showed an n-type Hall 3/2 coefficient, and Figure 11.6 shows the logarithm of IRHT/ I1 vs. 1000/T plot. The high resistivity form gives E = 1.4 ~ 0.1 eV where the high g,0 conductivity form (low temperature range of the fourth heating cycle and sixth heating cycle) gives a negative slope, which has no significance on this plot. On the sixth cycle, RH was constant showing that all donors were ionized. For purposes of comparison, O'Kane's Hall data are reproduced in Figure 11.7. Although the plots of the logarithm of JRH IJ vs logarithm of absolute temperature for some of the runs shown in Figure 11.8 are rather scattered, other runs show clear trends. Except for the fourth run, mobilities of about 40 ' 90 cm /v-sec were obtained. O'Kane's

137 TEMPERATURE, ~C E o 0 _ - E b >: I() Q z 0 0 1 0 F0 LJ I w UJ 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 RECIPROCAL ABSOLUTE TEMPERATURE, IO /T,(~K') Figure 11.4. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se13 (by O'Kane).

138 TEMPERATURE, ~C 7 560 441 352 282 227 181 143 III 84 60 39 21 E U 0 E b II — 0 z 0 C-, w -J w Ag2 InB Se/3 A 211 (IA) x 2/ (/B) _o 21/ (38) o 2// (7) * /99(4) First Heating Cycle 1 /99(4)Second Heating Cycl 6-199(4) Third Heating Cycle 19,9 (5B) I I A P - - 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 ABSOLUTE TEMPERATURE, 103/T,(K-') RECIPROCAL Figure 11.5 Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature for Ag2In8Se13 (by O'Kane). Z&8S l 0 b O' Je)

139 TEMPERATURE, t, (~C) 352 227 143 1 Ii 977 560 84 39,I v 296(5B) Ag2ln8Se13 - 0 Second heating cycle ~ Second cooling cycle 0 Third heoting cycle * Third cooling cycle 0 Fourth heating cycle V Fifth heating cycle D Sixth heating cycle 741 (2A) -o- First heating cycle - Second heoting cycle 1010 109 108 I — x 7 r 10 rr I0 Ft IA -II 1.40 eV _ 7-1.35 eV= 3.5 e - I:.. ^^......... 10 104 0.8 1.2 1.6 2.0 2.4 2.8 32 _ RECIPROCAL ABSOLUTE TEMPERATURE, IOOO/T, (~K') 3.6 Figure 11.6. Logarithm of RHT | versus Reciprocal Absolute Temperature for AgIn8Se1 3

140 TEMPERATURE, ~C C-J K) H 1.2 1.4 1.6 1.8 2.0 2.2 2.4 RECIPROCAL ABSOLUTE TEMPERATURE, 10 /T,(~K-') 2.6 Figure 11.7. Logarithm of I RHT | versus Reciprocal Absolute Temperature for Ag2In8Se13 (by O'Kane).

141 300 200 0) (n - 90 b- 80 I - 70 60 ' 50 0 m 4 ' 40 I ABSOLUTE TEM PERATURE, T, ' K) Figure 11.8. Logarithm of |RH or versus Logarithm of Absolute Temperature for Ag2In8Se 13

142 -1.4 data is also reproduced on Figure 11.8. A T temperature dependency of mobility found by O'Kane is also observed. No Seebeck effect data was taken for the first, the second, and the third heating cycles. The Seebeck coefficient taken on the fourth, the fifth and the sixth heating cycles are shown in Figure 11. 9 along with O'Kane's data. The data on the lower range of the fourth heating cycle is characteristic of high conductivity forms while the fifth heating cycle represents that of the high resistivity form. O'Kane's data is confirmed by these results. The second measuring technique used two closely coupled horizontal furnaces. The sample was placed in one end of a fused quartz tube about 10 inches long, and Se was placed in the other end. The Se and sample temperatures could be varied independently, the Se temperature always being lower than the sample temperature. Only electrical conductivity measurements were made in this arrangement on two different specimens, No. 296(3) and 296(6). Figure 11.10 shows a plot of the logarithm of electrical conductivity versus reciprocal absolution temperature of both samples under constant Se temperature and Figure 11.11 shows the logarithm of electrical conductivity versus reciprocal absolute temperature of Se at constant sample temperature. The following is the chronological history of the measurements. For specimen 296(3) 1. Varied sample temperature with constant Se temperature at 2940C (Figure 11.10). 2. Sample temperature constant at 6120C and varied Se temperature (Figure 11.11). 3. Sample temperature constant at 691 C and varied Se temperature (Figure 11.11). 4. Varied sample temperature with Se temperature constant at 3010C (Figure 11.10).

0 I -200 0 E - 6 -.400 z w IlJ a -.600 wo 0 0 I.I m -800 wIJ bn O3 U.) -1.000 -1.200 O'Kane's data (49) 211(18).First heating cycle 211(3B) First heating cycle 225(A) First heating cycle 225(A) Second heating cycle 736 First heating cycle 0 100 200 300 400 500 600 700 800 900 ABSOLUTE TEMPERATURE, T, (~K) Figure 11.9. Seebeck Coefficient of Ag2In8Se13. 2I 0 1 3

TEMPERATURE, t, (DC) 560 527 496 U o 0 E b" -I O >:10 > o z o u._J -J o L I -I b. 1.10 1.15 1.20 1.25 1.30 1.35 1.40 RECIPROCAL ABSOLUTE TEMPERATURE OF SAMPLE, IOOO/T, (OK-') Figure 11.10. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature Measured Under Constant Se Temperature for Ag In8Se13.

(Log) PRESSURE OF Se, PT, (mmHg) 100 10 I 0.1 0.01 I 1 I I TEMPERATURE OF Se, t,(~C) 13 -23 -51 50 E u 0 o iE J 0 z 0 -J 0 -J J I 0.1 I-I cl RECIPROCAL ABSOLUTE TEMPERATURE OF Se, IOOO/TSe, (~K') Figure 11.11. Logarithm of Electrical Conductivity versus Reciprocal Absolute Temperature of Se Measured Under Constant Sample Temperature for Ag2In8Sel 3

146 5. Sample temperature constant at 535 C and varied Se temperature (Figure 11.11). 6. Varied sample temperature with Se temperature constant at 998~C (Figure 11.10). 7. Constant sample temperature at 693 C and changing Se temperature (Figures 11.10 and 11.11). For specimen 296(6) 1. Varied sample temperature with Se temperature constant at 8000 (Figure 11.10). 2. Constant sample temperature at 5650C and varied Se temperature (Figure 11.11). 3. Varied sample temperature with Se temperature constant at 360~C (Figure 11.10). 4. The Se temperature being changed and remained at 360 C and sample temperature varied (Figure 11.10). 5. Se temperature being changed to 138 C and kept there (Figure 11.10). 6. Se temperature being changed to 800C. 7. Power failure. 8. Varied sample temperature with Se temperature constant at 850C (Figure 11.10). 9, Sample temperature varied with the temperature of Se being held at -78~C (dry ice) (Figure 11.10). 10. Sample temperature varied with the temperature of Se held at 0~C (Figure 11.10). These data are summarized in Appendix I in chronological sequence. It is found that the energy gap of 1.3 eV and 2.0 eV appears many times. The experiments were also made on preparing Ag2In8Se13 with a small amount of excess or deficiency of Se. All specimens prepared by this way were highly conductive, however, after one zone refining

147 pass the electrical conductivity was changed significantly. Characteristic results are shown in Figure 11.12. A preliminary examination of the photoconductive properties for Ag2In8Se13 on a block of material about 0. 1 sq cm cross section and 2. 5 cm long indicated that the resistance of the specimen was 6 x 10 ohm in the dark and 0. 9 x 10 ohm in light at room temperature (R /R = 1/7), and 90 x 10 ohm in the dark and 5 x 103 ohm in light L D at liquid nitrogen temperature (R /R = 1/18, 000)o A lifetime measurement using a stroboscope indicated that the lifetime varied from 115 to 134 on different measurements. With a rotating mirror illuminator, the lifetime was found to be 115 microseconds after maximum conductivity and 140 microseconds at a time of 200 microseconds at a time after maximum conductivity, indicating the presence of multiple recombination centers. DISCUSSION (49) 1. O'Kane) has shown that the irreversible effect of Ag2In8Se13 obtained as the result of a heating treatment is not surface effect but a bulk property, and proposed that the cause of the change is a decomposition of the material (vaporization of Se) or contamination by copper. The cocoon arrangement is believed to be effective in controlling the decomposition and eliminating contamination. Yet, the irreversible properties were still observed, A calculation on the diffusion rate cf Se into the specimen indicated that the rate must be too high to be plausible, and it is concluded that the cause of the change is neither decomposition nor contamination. 2. The x-ray analyses in this work has proven that the high conductive material (Foim I) and the low conductivity material (Fosrm II) have different crystalline structures; chalcopyrite for high conductivity form and monoclinic for the low conductivity form. The possibility of recovering the high resistivity from the high conductive material by

148 100 tai z LLI cr cr LJ Ld Uf) ck U1) U) LUI z 0 10 I0 0.I 0.01 0.001 DISTANCE, d, (inches) Figure 11.12. Logarithm of Electrical Conductivity Character of Zone Refined Ingot for Ag2In8Se 13

149 annealing the sample in a Se atmosphere as performed in this experiment shows that the transformation of the crystalline structure depends on the selenium pressure and temperature. 3. The Hall mobility calculated according to [ H = RH for some of the runs on the specimen is rather scattered, from 25 to 90 cm /v-sec between 300 K to 700 K. However a T1 ~ to T a5 temperature dependence are estimated from some of the runs. Our experimental data for the high resistivity form (Form IT) of Ag In8Sel3 very well agree with O'Kane's results. However our mobility of the high conductivity form of Ag In Sel3, from 25 to 90 cm /v-sec are lower than that of O'Kane who reported it to be from 50 to 250 cm /v-sec. 4. It is found that the ratio of lattice parameters, b, of the high conductive form to that of the low conductive form is 0. 96 while that of c is 1.0. This fact indicates that the low conductivity form, the monoclinic structure is: obtained by a tilt in the structure of the high conductivity form, the chalcopyrite structure to an angle of 74 degrees, 5. The data obtained by the two furnace arrangement can not be very well understood with the data available currently. This may be because of the existence of a third form of this material, as mentioned subsequently. However, the activation energies of 1.3 eV and 2. 0 eV are considered to be real. A third electrical modification apparently exists for Ag2In8Se13, as seen from the plots of log conductivity versus 10 /TSe. At high selenium vapor pressures the conductivity of specimen No. 296(3) actually decreases with increasing sample temperature, with a negative Boltzmann activation energy of about 1.45 eV. 6. All specimens prepared by adding excess amounts of Se in the ingot had a high conductivity as prepared, indicating that the Se as incorporated on quenching gives the high conductivity form. After zone refining, however, and slow solidification, it appears that Sedeficient material has a high conductivity, and Se-rich material has

1 50 a low conductivity. The transformation from one form to the other is also a function of Se vapor pressure and temperature. 7. At high Se contents, the Se apparently kills donors, and at high Se vapor pressures, the saturation concentration of Se increases, giving rise to the lowering of conductivity observed having a 1. 5 eV Boltzmann activation energy. This may represent a third form (Form III) for this material, or merely a saturation manifestation of Form II. 8. The vapor pressure dependency of conductivity for Form II (high resistivity) can be explained on the following basis. Se enters the lattice interstitially and accepts two electrons from the conduction band to become doubly ionic -2 Se + 2e - Se (11.1) c Selenium exists both as Se2 and Se6 in the vapor phase. At high Se temperatures, the Se2 is a significant fraction of the total vapor, whereas at temperatures below the melting point of Se (222 C), the Se2 species is almost entirely absent. Assuming that the Se2 species dissociates, Se. - 2 Se (11.2) and that Se atoms interact with the surface of the lattice to produce the transition then the equilibrium constant for the above reaction is 1/2 2 PO n Se c = const (11.3) (Se-2) which can be solved for the conduction electron concentration. (const)l/Z (-2 )1/2 -1/4 n (const) (Se P (11.4) c Se2 thus strongly suggesting that at least part of the excess Se exists as -2 in this structure. Se in this structure.

151 9, At low pressures, the vapor pressure of Se can be expressed (81) approximately by the relationship(8 12 14, 3 Pe (mm Hg) = 10 exp- 1 (11.5) Hence substitution of this relationship into Equation (11. 5) shows that 3. 6 log n cc log cc kT (11. 6) c kT Hence observed activation energies near 3. 5 eV to 4. 0 eV accompanying the transition from high resistivity (Form II) to low resistivity (Form I) Ag In8Se 1 can be explained by the inverse of the reaction indicated by Equation (11.1) as Se is rejected by the sample. 10. Table 11.1 gives a summary of calculations made on the structure of Forms I and II of Ag2In8Sel3 along with the theoretical values for comparison. Both Forms I and II contain more Se than the theoretical amount, although Form II approaches the theoretical concentration of tetrahedral vacancies (1.70 vs. 1.85). By clustering of the tetrahedral vacancies, larger octahedral vacancies may be formed. The o maximum dimension of such a vacancy in Form I is only 3. 40 A, which is 0.86 times the size of a vacancy needed to accommodate a Se ion. In Form II, however, the maximum dimension is equal to the size required -2 to enclose a Se ion, thus again suggesting that the excess Se in Form II -2 exists as Se 11. It remains to account for the position of the excess Se in Form I. From geometric calculations from the structure data, the o distance between a corner Se atom and a tetrahedral interstice is 2. 55 A, o giving an effective average interstitial radius of 1.41 A. A summary of bonding radii for Ag, In, and Se are given in Table 11. 2 along with the bonding lengths for various bonds. The chalcopyrite structure of Form I 3 3 0 dictates either sp or sp (res) bonding, and the 1.41 A interstitial 0 3 position easily accommodates In atoms with r = 1.35 A in the sp bond

152 TABLE 11.1 SUMMARY OF CALCULATIONS ON STRUCTURE OF Ag2In8Se 3 mol. wt. AgzIn8Sel3 = 2160 Theoretical Form I Form I II Lattice Constants a b c a Unit cell volume Density mol. wt. /unit cell molecules / unit cell Se atoms/unit cell Total atoms/unit cell Tetrahedral Vacancies/ unit cell Octahedral Vacancy size, 2r r r max. max rSe-2 1.98 rseg 403 5. 465 1329 0.615 8 14.15 1.85 5.676 5. 676 12.50 900 404 5. 705 1395 0. 640 8.31 14.70 1.30 5. 676 5. 903 12.48 740 402 5. 542 1342 0. 621 8.07 14.30 1.70 0 A o A o A gm/cm 0 3.40 A 0.86 0 3.40 x 3.62 x 3.96 A 1.00

153 TABLE 11.2 BONDING RADII AND BONDING LENGTHS IN Ag, In. Se STRUCTURES Bond Type Radii Ag In Se Ionic Ag =1.26 + In = 1.32 +3 In =0. 81 -Se 2 Se =1.98 3 Sp3 1.52 1.44 (1.35) 1.14 Sp (res) 3 3 p p (res) atom 1.645 1.57 1.255 1.57 1.50 1.75 1.675 1.205 1.41 1.40 Bond Lengths Ag-Se 3.24 In-Se (+1)3.30 (+3) 2. 79 2.66 2.58 2.49 2.28 2.90 2. 825 2. 775 2. 705 3. 16 3. 085 Se-Se 3. 96 2. 51 2.41 2. 82 2.80

154 0 characteristic of In in Se and Te defect structures. The 1. 52 A Ag atoms undoubtedly account for the apparent bond stretching. The tetrahedral interstices are also sufficiently large to accommodate Se atoms, either in the sp state or the sp (res) state, and the octahedral o interstices (ra = 1.70A) are sufficiently large to accommodate Se in the p (res) state, the most probable states for Se to exist in the compound. However for the symmetry of structure to be maintained giving the tetragonal crystal modification of Form I, the Se undoubtedly goes into the tetrahedral interstices as Se with covalent bonds. In this case, the Se is converted from Se to Se with the liberation of four valence electrons/atom, each of which should have a characteristic activation energy. 12. The two shallow donor activation energies now can be interpreted. The four shallow donor levels expected for Se+ should follow a hydrogluic series having activation energies with ratios of 1/1, 4/1, 9/1, and 16/1. Hence the activation energies of 0.015 eV and 0. 01 eV are the last of this series, the others being at about 0. 004 and 0. 001 eV respectively. It would require measurements considerably below 77 K to observe these levels, and such measurements were not made in this work. 13. The transformation between Form I and Form II then represents a different ratio of Se atoms in octahedral positions and tetrahedral positions, the ratio being influenced by the vapor pressure of Se surrounding the crystal, and the temperature.

APPENDIX A 6F FERMI-DIRAC STATISTICS BASED ON = 0 6 ei Assuming that at equilibrium, the entropy of a system has a minimum value, it was shown that the Fermi-Dirac distribution function is expressed as f(E,) = (Al) 1f i) 1 +exp (Ei- E)/kT (A Equation (Al) is good for the adiabatic case. However when a constant volume or a constant pressure is considered, the derivation must be based on the assumption that at equilibrium, the free energy (Helmhotz free energy, F = E - TS, for constant volume and Gibbs free energy, G = H - TS, for constant pressure) has a minimum value. A Fermi distribution function is derived, based on this argument, and an expression for the electrical conductivity of intrinsic semiconductor is given. In deriving an expression for free energy, it is necessary to divide the total entropy into the configurational entropy, Scf and the thermal entropy, Sth. For a semiconductor, the configurational entropy of electrons is expressed by S = k n [ i (e) (q-e (A2) 1 1 1 where qi = total sites of E. energy state e. = occupied sites at E. energy state 1 1 And the free energy of a semiconductor thus can be expressed as i i i (qi): F(T) = e E - Tei S.- kT In I.. J (q (A3) i i ith,i Equation (A3) can be simplified by expanding the term inside the logarithm and applying the Stirling's approximation to form 155

156 i i i F(T) = 2 e.E, - T e. - kT [[ q. In qi- e. In e 11 i thi 1 - (qi - ei) In (qi - ei)] (A4) In order to find the equilibrium condition, the concept that at equilibrium, 6F/6 e. = 0 must be applied. One also notes that the total number of electrons in the specimen is constant regardless of the temperature change, and of the way of the configuration of the electrons. And the condition ] d (e.) = 0 must be combined with dF/d e, = 0 by using the method of undetermined multiplier A/kT, in such a way that A/kT is the same for every E.. Equation (A5) is the result of this process. i q e. TS - E - A [l n 1i 1 + —h] 1 0 (A5) e. kT Solving for the terms inside the braces, the Fermi distribution function is found to be e, 1 1 f(E.) =- 1(A6) 1 Ei q 1 + exp (A+ E.- TSS ),/kT (A6) i 1 thi The constant A can be evaluated by considering the condition of the quantum states at the Fermi level at the absolute zero of temperature. At this condition, the fraction of sites occupied by electrons is indeterminate A + E- TSth, f 0 ] i. e. I (A7) ikT 0 (A7) and A is found to be equal to -E. When this value is substituted into Equation (A6), the Fermi distribution is found to be f(E.) 1A, 1 s l+exp(E -TSh i Ef)/kT (A8) For semiconductors wherein Ei - TSth i- Ef in the conduction band is much larger than kT Boltzmann statistics can be used, and band is much larger than kT, Boltzmann statistics can be used, and

157 Equation (A8) can be approximated by f(E.) exp - (E - TS i- E)/kT (A9) i i S-th, i f It can be shown that when Equation (A9) is used for the electron distribution function for a semiconductor, the concentration of electrons in the conduction band is n = N exp - (E - TS - Ef)/kT (A10) c c g — th,g f and the concentration of holes in the valence band is p = N exp- (E - TSh )/kT (All) v v t th, v where Ser = the specific thermal entropy of the th, g electron at the bottom of the conduction band S = the specific thermal entropy of the th, v electron at the top of the valence band. The carrier concentration of an intrinsic semiconductor can be found by substituting Equations (A10) and (All) into Equation (10). n. = (N N ) exp- (E - T S h)/kT (Al2) 1 c v g -th where A Sh = S - St -h — th, g th, v = the specific entropy difference of electrons between the bottom of the conduction band and the top of the valence band. Noting that the thermal energy is 3kT/2, it is reasonable to assume that A S is very small, If this is correct, and if Equation (35) is th assumed, the slope of the logarithm of the carrier concentration versus 1000/T is E /2ko g,o

158 Shockley ) in discussing the ionic diffusion, applied the relation d(AS)/ dT = (1/T) dE/dT (Al3) for his diffusion equation which is similar to Equation (A12) and proved that d In ni/d(l/T) always gives the value of E /2k regardless of how the activation energy is dependent on temperature. This argument is incorrect since AS in Equation (A13) should be the total entropy while ASth in Equation (A12) is the thermal entropy. th

APPENDIX B THE MINIMUM VALUE OF F(T) = 128 N exp (E -E )/kT c r d When the definition of N is substituted, F(T) can be expressed C as F(T) = 128 x 2U(m /m )/ T2 exp (E - E )/kT (B1) n 0 g d And the Temperature at which F(T) has a minimum value can be easily found by solving d F(T)/d(T) = 0 E -E 256U (m I/m) L3 (3/2)T 12 exp (E -Ed)/kT- ( - d) T 1/2exp(E -E )/kT = 0 T = 2(E - E )/3k (B2) g d When the value of T in Equation (B2) is substituted into Equation (B1), the minimum value of F(T) is obtained. F(T)] i = 128 x 4.83 x 1015 (m i /m)3/[ (E -Ed)/3k] 3/ exp (3/2) min n g d 1l8 [ ] 3/2 1.53 x 1018 m (E -E )/m k] 3/2 n g d o where E E in eV, and k = 8.6 x 10 g d 159

APPENDIX C PREPARATION OF SAMPLES AND ZONE REFINING Sample Preparation Two general classes of samples were prepared: those for differential thermal analysis and those for zone refining. The differential thermal analysis samples were prepared by adding the stoichiometric quantities of the pure elements, usually a total of 18 grams, to a 10 mm inside diameter quartz tube which was then -5 sealed off at a pressure of 5 x 10 mm. Hg or lower. The mixture was heated using a programmed cycle that avoided explosions in most cases. The digital temperature programming unit used is (28) described by Hozak, Cook, and Mason. The compositions were heated about 200 C above the liquidus temperature and then water quenched. The material was removed from the sealed tube and ground to a powder before adding to a differential thermal analysis tube. This tube was made of 10 mm. quartz with a concentric well (4 mm. inside diameter) in the bottom to accommodate the thermocouple. The tube was sealed off at a pressure of 5 x 10 mm. Hg or lower with an over-all length of about 4 inches. The amount of free space above the sample was kept to a minimum. Before making the differential thermal analysis measurements, the sample was usually annealed one week in the region of 6000C, depending on the phase diagram being investigated. Samples for zone refining were prepared in one of three ways. For compositions which had a low heat of reaction during the fusion of the elements, 70 grams of the elements were placed in a 10 mm. -5 inside diameter quartz tube and sealed off at a pressure of 5 x 10 mm. Hg or below so that the length was approximately 12 inches. Heating was carried out at a rate of a few hundred degrees centigrade per hour until the material was about 200 C above the melting point of the compound. The tube was then transferred as a liquid to the 160

161 zone refining furnace. For InSe and In2Se3, the compounds were sealed in an evacuated 10 mm. inside diameter quartz tube which was then sealed in an evacuated 16 mm, inside diameter quartz tube. For compositions which liberated a high heat of reaction during the furion of the elements, such as Ag2In8Se13, the sample size was reduced to 35 grams and two fusion samples were made using a slow heating rate. These were then combined to provide one zone refining samples. Zone Refining The zone refining furnaces, which resemble submarines in appearance, had six independently heated zones. The liquid zone of the sample could be observed through a pyrex window mounted six inches above the center region of the furnace. Before inserting the samples, the furnace was balanced so that the center zone was about 15 C above the melting point of the congruently melting compound. The solid sections of the ingot were usually 60 C below the melting point. The liquid zone moved at a rate of 3/4 inches per hour for normal zone refining by moving the sample tubes through the stationary furnaces. The liquid zone was usually 1-1/2 inches long and the length of the sample about 12 inches. Zone leveling of the peritectic compounds was carried out at 0. 3 inches per hour and in some cases at 0, 16 inches per hour. The application of zone leveling to peritectic compounds is described by Mason and Cook.(9) compounds is described by Mason and Cook.

APPENDIX D DIFFERENTIAL THERMAL ANALYSIS Differential thermal analysis (DTA) measurements were made on a sample from the binary and the pseudo-binary system with a reference material, such as indium. It was possible to detect solidliquid transitions as well as solid-solid transformations which liberated sufficient heat to cause a temperature difference of about 0. 50C between the sample and reference. A continuous recording of the sample temperature and the differential temperature between the sample and the reference material could be obtained from room temperature up to as high as 1300 C. The measuring system is shown schematically in Figure D. 1. The thermocouple mounted in the bottom of the sample tube was connected through an ice-water reference junction to the Y scale of a Leeds and Northrup Model G. Speedomax X-Y Recorder. The differential temperature signal was amplified with a Leeds and Northrup D. C. amplifier and fed to the X-scale of the recorder. The range was 0-10 my. in each direction on chart paper 10 inches wide. The differential emf was shifted to read zero at mid-scale by providing a 5 my. auxiliary emf in series with the output from the D. C. amplifier. When the output from the sample temperature thermocouple reacher 10 my., a Leeds and Northrup precision portable potentiometer was used to buck out 10 my. At the same time, the chart paper on the X-Y recorder was reset so that the next 10 mv. of the temperature scale was recorded on a new section of chart paper. With chromel-alumel thermocouples, a chart about 40 inches long would be obtained for measurements on a sample between 25 C and 1000 C. The Kanthal resistance heated furnace, which had an automatic program control, provided essentially linear heating rates of about 2-1/2 C per minute. 162

I SAMPMirLt RE EETNCE | CAM I ~ ~~~~PRECISION PLUG ~~TEMOCOUPLE q__ y A.1 1 r — -- -- -- -- -I I CE llov1 c3^_-10 V TcI *. -@ - I~________________ _Pt S-l 1 PULSE GENERA rOR +60_ + _ L N x - SPEEDOMAX D.C. AMPLIFIER {o STRIPCHART o RECORDER S MV 0-10 MV vs TIME D.CE or 10 MV s 10 MV FIGURE D. 1. BLOCK DIAGRAM SHOWING OPERATION OF DTA EQUIPMENT a N

APPENDIX E CHEMICAL ANALYSIS Cu-In-Te System In particular, the investigation was centered on analyzing the composition of CuInTeZ. The development of a quantitative chemical analysis scheme for this system was complicated by co-precipitation of the elements and interference of the agent used in the analysis. The procedure was started from the reduction of tellurium ions to metallic tellurium with sulfur dioxide and hydrazine solution in a strong acidic solution. Two methods for analysis of indium were evaluated: precipitation of indium ions with hydroxide and titration with ethylenediaminetetra acetic acid (EDTA). Both methods had almost the same accuracy, but the precipitation method was more time consuming, hence the titration method was used. Three methods for the analysis of copper were evaluated: precipitation with a complex salt, electrolysis of copper, and titration with EDTA. The first method did not allow consistent results and the second method gave a low recovery. Therefore the third method was used. Tellurium Analysis The analysis is begun by weighing out about a 1. 5-gram sample and dissolving it in 20 ml. aqua regia solution. a known sample made by weighing the stoichiometric amount of elements should be analyzed along with the unknown sample for the determination of the accuracy. Because nitric acid interferes with the precipitation of Te, it should be removed from the solution before the reducing agents are introduced. After the samples are all dissolved, 3 g. of NaCl are added to each sample and the solution is diluted to 150 ml with 2N hydrochloric acid. The solution is then heated in a water bath until the volume reduces to about 20 ml. Then 100 ml. of 1:1 hydrochloric acid is added and the evaporation of nitric acid is repeated until the volume is reduced to 164

165 20 ml, again. To each solution, 80 ml. of 1:1 HCL solution is added, When it has been heated to the boiling point, 80 ml. of freshly prepared SO2 saturated solution is added. A black precipitate is formed. Then an addition of 70 ml of 15% hydrazine solution is followed by an addition of 100 ml of freshly prepared SO2 saturated solution. The solution is then heated to boil for about four minutes until the precipitate of tellurium changes to an easily filtrated form. After settling for one-half to one hour, the precipitate is filtrated into a clean glass crucible of known weight with the water vacuum connection in operation. The precipitate is then washed with hot de-ionized water (DI-water) until free of C1. Water adhering to the precipitate is then extracted by washing the precipitate with methanol. This procedure removes most of the water from the cake of tellurium. Three washings or more are required. The precipitate is then dried under vacuum at a temperature of about 50 C until it reaches constant weight. The drying process will require 30 hours or more. The precipitats is weighed as metallic tellurium. The error in the known sample will not exceed 0. 1%. The filtrate from the tellurium reduction step is then processed for titrametric chemical analysis for the copper and indium content. Each filtrate section, consisting of approximately 200 ml. of solution, is diluted to a volume of 500 cc after the addition of 50-80 cc of concentrated nitric acid. The acid is added to completely oxidize the copper from the +1 oxidation state to the +2 oxidation state to facilitate the titration. For a typical initial sample of 1. 5 grams, aliquots of 25 ml. are used for the titrametric analysis. The titration is executed in a basic medium (ph 7-8) using a NH4Cl-NH OH buffer solution (ph 10-11). The titrant is EDTA disodium salt which has been standardized by titrating with a known amount of indium and copper solution. The indicator is a 0. 1 weight o solution of 1-(2-Pyridylozo)-2-naphthol (PAN). The solution is adjusted to the desired ph range by additions of

166 the NH4C1-NH4OH buffer solution and acetic acid. Indium Analysis To the 25 ml. aliquot is added 25 ml. of de-ionized water, 1 gram Rochelle salt (potassium-sodium tartrate), 5 grams of sodium acetate and enough potassium cyanide (KCN) to complex the copper present (approximately 0.3 grams for a typical sample). With the copper complexed, it is possible to titrate directly for the sole indium content of the sample. The Rochelle salt is used to prevent the indium from precipitating down as In(OH)3 in the required basic medium. Seven to eight drops of the indicator solution are employed and the end point is a gradual change from red-orange to fluffy yellow. The accuracy observed was fairly consistent at 1. 5% too high on the known samples. Copper Analysis To the 25 ml. aliquot is added 25 ml. of de-ionized water, 1 gram of Rochelle salt, and 5 grams of sodium acetate. Here, no KCN is added so that the titration results in the total indium and copper content of the sample. Knowing the exact indium content, the copper content is found by difference. The sodium acetate was added in both analyses to aid in the end point color change. Six to eight drops of the indicator solution are employed and the end point is from red-purple to lime green. It was observed that, when titrating a cold solution, the end point was somewhat nebulous. It was found that the best procedure to follow is to titrate cold to the approximate end-point then titrate the heated solution to the exact end point indicated by the holding of the lime green color upon near-boiding. The accuracy observed again was fairly consistent at 1.4-1. 6%o too high on known samples.

167 Ag2In8Se 1 3 The Volhard method, described in standard texts was used to determine the silver content of the sample. The silver analysis together with the assumption that the composition lies on the Ag2Se-In Se3 pseudo-binary line gives the exact composition of the compound. The silver analysis is a little bit complicated in this system by the fact that the presence of indium and/or selenium causes a greenish color which obscures the end point color change from a very light brown tinge or yellow-green to light brownish-green. It is best that standardization of the titration agent KCNS proceeds with a weighed amount of Ag together with amounts of In and Se to simulate the unknown to be analyzed. The end points of the standards should be saved and used in helping obtain the proper end point in the unknown titration. About 0. 2 to 0. 4 ml. before the end point, the Ag CNS precipitate settles nicely leaving a nearly clear solution. There may be a very faintly perceptible brown coloring. Addition of slightly more KCNS will not at first increase the faint hint of a brown coloring significantly. Immediately prior to the end point and over a narrow range, so that it might not be observed, there occurs a yellow-green color. Further addition of KCNS causes a very definite increase in the intensity of the tinges of brown coloring. This is the end point. Further addition causes only gradual increase in the intensity of the brown color. The analysis for Ag in the zone refined Ag In Se3, Sample No. 741, gave reproducible results of 10.01 ~ 0.2% Ag, which indicated that the compound is Ag2In8Sel3. 2 8 13~

APPENDIX F X-RAY ANALYSIS This section contains the results of a detailed x-ray study of five alloys from the Indium-Selenium, Indium-Tellurium systems and a ternary compound. The alloys investigated were InTe, In2Te3, In3Te5, InSe, InzSe3 (high temperature or p-form) and AgzIn8Sel3. All the alloys were zone refined samples. Experimental Method In each case, a small section of the sample was ground into a fine, powdered form using an agate mortor and pestle. Finely ground, high purity germanium was added to each sample (about 1 mg. Ge to a one-gram sample) in order to produce standard Ge lines in the subsequent photograph thus allowing for corrections of the observed sample lines from the standard Ge lines. X-ray powder photographs were taken using o o copper radiations Cu Ka (X ) = 1.54051 A, (K2) = 1.54433 A, o Kcrl Ka'2 (XK ) = 1. 54178 A], or Cr Ka, with the appropriate filter. in a Kac mean Debye-Sherrer camera of 11.46 cm diameter with the film mounted in an unsymmetrical fashion using Straumanis' method. In each case, the sample exposure time was 6.0 hours. The x-ray photograph was measured with an accuracy of 0.01 mm. including the correction for the observed sample lines from the standard Ge lines. The line intensity was evaluated on a nine-point scale with the higher numbers corresponding to the brighter lines and the observed data was computationally 2 converted to sin a values for each specimen. Experimental Results 2 Table F. 1 contains the observed line intensities and sin a values for the alloys studied. The experimental results for InSe indicate o o that the compound has a hexagonal structure with a = 4. 03 A, c = 25. 04 A and c/a = 6. 213. These results agree quite favorably with those reported 168

i69 TABLE F. 1 LINE INTENSITIES AND Sin a VALUES OF X-RAY RESULTS In3Te [ Ingot No. 156] High Temperature Form_ Low Temperature Form Intensity Sina + Intensity Sin a Inensity Sin a 2.0386 10.0468 5.3747 7. 0470 5.0526 1.4213 1.0523 7.0608 1.4384 2.1015 1.0757 2.4772 1.1215 2.0973 3.5487 10.1249 2.1020 2.6258 1.1414 2.1171 1.6753 1.1672 9.1244 1.7034 7.1719 1.1438 1.7301 1.2427 9.1715 1.7437 3.2448 2.1763 1.7601 1.2885 1.2269 2.7989 1.3048 1.2503 1.8528 2.3637 2.2686 1.8680 5.3755 1.2851 1.8751 1.4079 1.3135 1.8802 1.4217 2.3309 1.9211 2.5297 2 =5:474 * Annealed at 615 C and quenched 2.6048 | * Annealed at 425~C and quenched 2. 6240 + Cu-Ka radiation ~2 o6240o0 ~2.7717 ~X = 15418 A 2 ~o7717 2.8484 1.8755 Result- Hexagonal O o a = 13.27 A, c = 3,56 A

170 TABLE F.1 (Cont.) In Te [ Specimen 1212(1B)J 2 + Intensity Sin a 5 0. 0466 2 0.0694 7 0. 1254 7 0.1724 2 0.1870 3 0.2502 7 0.3752 3 0.4216 3 0. 5467 3 0. 6246 2 0.6720 3 0.8734 2 0.9214 Result: Cubic a = 6163 A a= 6.163 A In2Se3 [ Specimen 1221(3)] 2 + Intensity Sin a 7 0.0263 3 0.0502 6 0.0611 3 0.0852 4 0.1225 4 0.1369 2 0.1628 3 0.1741 3 0.1911 2 0.2318 2 0. 2588 2 0.2673 2 0. 2832 2 0.3089 2 0.3166 1 0.3782 3 0. 4284 7 0. 4662 2 0. 4848 2 0. 5880 2 0. 6735 3 0.7488 Result: Hexagonal o a = 7.04 A o c = 19.00 A + Cu-Ka radiation o X = 1.5418 A.I.

171 TABLE F. 1 (Cont.) InSe [ Specimen 1200(2A)] InTe [ Specimen 248(5)] Intens ity 7 3 1 1 3 4 1 2 4 1 4 3 3 3 3 3 3 2 3 3 2 + Sin a 0.0345 0. 0495 0.0778 0.1380 0.1448 0.1826 0. 2060 0.2861 0.3105 0.3470 0. 4575 0. 5957 0. 6973 0.7416 0. 7524 0. 7966 0. 8894 0. 9000 0. 9492 Intensity 7 6 4 3 2 1 2 3 3 1 2 3 3 4 2 2 Sin a 0.0694 0. 0829 0.1566 0.1694 0.1822 0.1976 0. 2142 0. 2481 0.2541 0.2674 0. 2834 0.3012 0.3308 0.3812 0. 4342 0.4566 2+ Intensity Sin a 1 0.4799 1 0. 4858 2 0.5552 1 0.5691 2 0.5817 1 0. 6024 1 0. 7034 1 0.7396 3 0.7550 2 0.8378 2 0.8561 2 0.8796 2 0.8826 2 0.9156 3 0.9499 Result: Tetragonal 0 a = 8.44 A c = 7.o3 A c = 7.13 A Result: Hexagonal 0 a = 4.03 A o c = 25.04 A + Cu-Ka radiation o X = 1.5418 A * indicates diffuse line

172 TABLE F. (Cont.) Ag2In8Se13 High Resistivity Form (Ingot No. 1.517) Intensity Sin a 10.0537 2.0718 4.0894 4.0989 4.1069 2.1162 10.1419 8.1457 4.1596 2.1770 10.1942 2.2470 6.2821 2.3176 8.3339 8.4215 8.4743 4.5092 5.5609 8.6054 8.6999 6.7535 2.7707 2.7868 2.8037 6.8412 6.8945 Result: Monoclinic o o a = 5. 676A, b= 5. 903 A, c = 12.48 A Low Resistivity Form (Ingot No. 224) Intensity Sin a 2.0523 8.0548 9.1037 10.1249 8.1451 7.1976 3.2053 5.2861 5.3400 1.3536 5.4284 8.4372 2.4752 3.4824 1.5016 2.5703 2.6230 2.6490 5.7116 2.7656 2.7949 1.8883 2.9057 Result: Chalcopyrite 0 a = 5.676 A, c/a = 2.222 + Cu - Ka radiation o X = 1.5418A

173 TABLE F. 1 (Cont.) Ag2In8Se 3 High Resistivity Form Intensity 5 6 2 1 1 Sin azt.0524.1400.1926.3339.4213 Result: Monoclinic o a = 5,676 A 0o b = 5.903 A c c = 12.48 A ++ Made with Cr-Ka and converted to Cu-Ka values. 0o X = 2. 2909 A Cr X = 1.5418 A Cu

174 by Semiletov.() The observed sin a values also agree with those (66, 67) reported by Slavnova and Eliseev. The observed data for the high-temperature or p-form of In Se indicate that the material has 2 3o o a hexagonal structure with a = 7.04 A, c = 19.00 A and c/a = 2.702. These results do not seem to agree with the published results of //,\ o (61) 0 Semiletov which indicate a hexagonal structure with a = 7. 11 A, o 2 c = 19.3 A and c/a = 271. Nor do the observed sin a values agree completely with those reported by Slavnova and Eliseev. ( ) The experimental results for InTe indicate that the compound o o has a tetragonal structure with a = 8. 44 A, c = 7. 13 A, and c/a = 0. 845. (59) These results agree well with the values reported by Schubert. The experimental data for In2Te suggest the material has a cubic structure o 2 with a = 6. 163 A. The results confirm a past x-ray investigation of the compound in our laboratory. Indexing Method In the case of the In2Te sample, the line indexing was done 2Te3 sample, t 2 using an available Hull-Davey chart in which sin a values are graphed against the c/a axial ratio for the tetragonal system. The observed lines were plotted on the chart as explained in Cullity. For the remaining samples, an arithmetic indexing method was employed (48) as suggested by Nordman which is exemplified in detail in the following section. As an example of the indexing of the non-cubic powder patterns5 o consider the data for the compound InTe (X = 1. 54178 A). A portion of the data from Table F 1 is listed below with the eventual correlation.

175 2 Sin a 0. 0829. 1566 0. 1694 0.1822 0. 1976 0.2142 0. 2481 0.2541 0. 2834 0. 3012 0. 3308 Tentative Multiples q 2q 3q 4q Correlation 1OA= 0.0838 13A+ 4B = 0.1559 20A= 0.1682 16A+ 4B = 0.1815 18A + 4B = 0.1978 13A+ 9B = 0.2143 17A + 9B = 0.2483 8A+ 16B = 0.2543 34A = 0. 2838 A+ 25B = 0.3010 34A + 4B = 0. 3308 Using a trial and error method, we observe that some sin a values are multiples of others. Observed multiples may help to prescribe the proper crystal system to the data being indexed. For example, p, 4p could stand for (100) and (200) in any crystal system while q, 2q, 4q could be the tetragonal planes (100) (110) (200) or (110) (200) (220) or even (200) (220) (400). For the tetragonal system, sin2a = L X/4aZ](h+k) + [ X2/4c2] (12) or sin2 = A(h2 + k2) + B(12) where A 2 2 A = \ /4a and B = /4c and B = X /4c Clearly, if we choose A and B very small and (hkl) very large, we can essentially fit any set of sin a values. Hence, the sound approach is to choose A and B as large as possible in order to avoid pitfalls and to find the smallest possible unit cell. Of course, the coefficients of A and B, for any given value of sin a, can only assume certain values depending on the crystal system. In this particular case, for the tetragonal system, A = 1, 2, 4, 5, 8, 9, 10, etc. while B = 1, 4, 9, 16, etc. The procedure is then to assume the

176 simplest assignments of the coefficients of A and B for the two lowest angle sin a values and then, using the subsequent values of A and B (you have two equations, two unknowns), index all of the observed lines as allowed linear combinations of A and B (see the example). If a given A and B do not fit all of the lines with a reasonable accuracy, a new trial must be made. After the correct values of A and B are obtained, a least squares value of A and B gives the desired lattice parameters for the assumed structure.

APPENDIX G MEASUREMENTS OF HALL EFFECT, ELECTRICAL CONDUCTIVITY, AND SEEBECK COEFFICIENT Electrical Circuit Electrical conductivity and Hall effect measurements were carried out by the conventional direct current techniques described by (38) Lindberg. The direct current was supplied by a Lambda Model 65M power supply. The current was filtered to reduce ripple by use of an 8. 5 henry choke in series with a 40 L f capacitor. The desired current level through the sample was attained by placing resistors in series with the sample and in parallel with the capacitor. Switches were available for reversing the polarity of the current, the Hall probes, and the electrical conductivity probes. The potential readings were taken with a Leeds and Northrup K-2 potentiometer. A schematic diagram of the above circuitry is given in Figure G. 1. The magnetic field used in the Hall effect measurements was obtained from a 2100 gauss permanent magnet. This magnet had a pole face diameter of 2-1/2 inches and a 2-3/4 inch gap. To facilitate reversing the magnetic field, the magnet was mounted on a large roller bearing, and could be rotated exactly 180 degrees without moving the sample. The Seebeck coefficient was obtained from the differential temperature across the ends of the sample and the Seebeck voltage between the same points. The signal from the chromel-alumel differential thermocouple was fed to a Leeds and Northrup DC amplifier and then to a Leeds and Northrup Speedomax Recorder. A switching circuit was used to record the amplified Seebeck voltage across the ends of the sample and the sample temperature immediately after the recording of the temperature differential. 177

178 CHOKE 8.5H L.8N N. K-2 i- -- DPDT ^- P DSWITCH POTENTIOMETER D PDT H L. 8a N. K-2 -o-~ —o SWITCH, POTENTIOMETER I I ICE BATH REFERENCE THERMOCOUPLE HALL EFFECT PROBES BUCKING POTENTIAL TEMPERATURE MEASUREMENTS DPDT SEEBECK COEFFICIENT DPDT REVERSING SWITCH DPDT SWITCH DIFFERENTIAL TEMPERATURE Figure G. 1. Electrical Circuit Used for Measuring the Electrical Conductivity, Hall Effect, and Seebeck Coefficient of the Semiconducting Compounds.

179 Sample Holder and Container The sample holder was machined from Lava (hydrous aluminum silicate, American Lava Corporation, Chattanooga 5, Tennessee) and baked at 1000 C. Electrical contact was made to the sample by fusing hot 30 or 32 gauge platinum wire to the surface, A 30 gauge chromelalumel differential thermocouple was placed at the ends of the sample. The sample holder was mounted on a fired Lava (Lavite) platform with stainless steel screws. Directly over the center of the sample was a molybdenum tube containing a 30 gauge chromel-alumel thermocouple. This was used to provide a continuous recording of the sample temperature. A 2-1/2 inch long copper shield was placed over the sample holder while a solid copper rod with a heater mounted on it was connected to the lower end of this shield. The heater was made of a threaded piece of lavite which was wrapped with 28 gauge chromel heating wire. The large mass of copper was used to damp out temperature fluctuations. Connected to the top end of the copper shield was a 1/2-inch copper tube with a copper spacer and a lavite heater similar to the lower heater. A lavite spacer prevents heat conduction up the copper tube. A vycor tube encloses the sample and supporting apparatus. This tube was wrapped with Pyrex wool to reduce heat losses. The open end of the Vycor tube was sealed by means of "O" ring seals to a mounting coupling. The 1/2-inch copper tube passes through this coupling by means of seals which allow the vertical positioning of the sample directly between the poles of the magnet. An outlet from the coupling leads to a pressure gauge, a vacuum system, and the hydrogen and argon supply. The samples were measured under either a hydrogen or argon (99. 995%) atmosphere. Oxygen is removed from the hydrogen by passing it through a "Deoxo" catalyst. The water vapor in the hydrogen was removed with molecular sieves in the earlier

180 measurements and with a liquid nitrogen cold trap for the later measurements. The argon is passed through a dry ice cold trap before entering the measuring system. Measuring Procedures Hall Effect. The direct current method of measuring the Hall effect requires four readings. The order of measurements is: (1) positive current and positive field directions; (2) negative current and positive field directions; (3) positive current and negative field directions; (4) negative current and negative field directions. The four readings usually required 90 seconds. The current was kept in the positive direction except for the short interval when readings (2) and (4) were taken. This stabilized the contribution from Peltier heating so that its effect can be eliminated in the calculations. A continuous reading of the sample temperature was obtained on a Speedomax recorder during the time the Hall data were taken. The temperature variation was less than 0. 30C. If the voltage readings are designated as V(I+, H+), where the first term in the parentheses indicates the positive direction for the current and the second term is the magnetic field in the positive direction, then the Hall voltage is V = V(I+, H+) - V(I+, H-) + V(I-, H-) - V(I-, H+) H 4 (38) Lindberg shows that this method eliminates all the thermomagnetic effects except the Ettingshausen effect, which is usually small and can be neglected. Electrical Conductivity and Seebeck Coefficient. The sample holder must be moved out of the magnetic field for the electrical conductivity and Seebeck coefficient readings. The electrical conductivity is measured in the positive and negative ticurrent directions at each temperature. By averaging the two values, the Seebeck potential

181 caused by a temperature gradient along the sample is eliminated. The Seebeck coefficient is measured after stabilizing the temperature differential between the ends of the sample at about 20C. Type of Current Carrier. The carrier type of the semiconducting compounds was checked in at least one of three wayso For materials with an electrical conductivity greater than about 0. 01 mho/cm., the standard hot probe method was used at room temperature. When thermoelectric measurements were made, the type of carriers was determined simultaneously. Hall effect measurements also provided information on the carrier type. Sample Calculations Calculation of the Hall Coefficient. The Hall coefficient is calculated from the formula R - - t r V(I+. H+) - V(I+, H-) + V(I-, H-) - V(-, H+) j H -8 4 H 10 IH 3 where R is the Hall coefficient in cm /coulomb, t is the sample H thickness in cm., I is the sample current in milliamperes, H is the magnetic field strength in gauss, and V(I+, H+), V(I+, H-), V(I-, H- ), and V(I-, H+) are the Hall voltage readings in millivolts. The calculation is illustrated with the data from the first heating cycle of InSe, sample No. 1200(3), at 57.0 C. I = 771.0 La V(I+,H+) = -8.0265 mVo t = 0.267 cm V(I+,H-) = -5.7654 mV. H = 5480 gauss V(I-, H-) = 5. 9319 mV. V(I-, H+) = 8.2453 mV. R _ 0. 267 cm [ -8. 0265 - (-5. 7654) + 5. 9319 - 8. 2453] mV. ~~H ~10 (0.771 ma)(5480 gauss) (4) R = 7223 cm /coulomb H

182 The IBM 7090 computer was used to calculate the Hall coefficient, 3/2 the reciprocal absolute temperature, and RT. The energy gap obtained 3/2 from the RT/ vs. 1/T data was calculated by a least squares analysis. Calculation of the Electrical Conductivity. The electrical conductivity, cr, was computed by means of the formula L 2 wt V++ V where I is the current in milliamperes, f is the distance between the conductivity probes, w is the sample width, t is the sample thickness, and V and V are the potential drops in millivolts across the probes with the current in the positive and negative directions, respectively The calculation is illustrated with the data from the first heating cycle of InSe, sample No. 1200(3), at 57.0~C. I = 0. 771 ma V = 267.1 mV. w = 0.450 cm. V = 267.0 mV. t = 0. 267 cm. = 1.333 cm. (0.771 ma) (1.333 cm.) 2 1 (0.450 cm.) (0.267 cm.) 267.1 + 267.0 mV. r = 0 0321 mho/cm. The IBM 7090 computer was used to calculate the electrical conductivity, the natural logarithm of the electrical conductivity, and the reciprocal absolute temperature. These results were then used to plot the temperature dependence of the electrical conductivity and to determine the energy gap by a least squares analysis. Calculation of the Seebeck Coefficient. The Seebeck coefficient, a, was calculated from the measurements of the potential difference across the ends of the sample and the temperature difference which

183 was obtained with a chromel-alumel differential thermocouple. The following measurements were made on the first heating cycle of InSe, sample No. 1200(3), at 57.0C. Temperature difference = 0. 160 mV. = 3.91~C potential difference Seebeck coefficient 1900 tL v. -1.900 (mV.)= 098 mV/ C. 3.91 ( C)

APPENDIX H THE ORIGINAL EQUIPMENT The direct current was supplied by a Lambda Model 65M power supply. The current was filtered to reduce ripple by use of an 8. 5 henry choke in series with 40 pf capacitor. The desired current level through the specimen was attained by placing resistors in series with the specimen and in parallel with the capacitor. Switches were available for reversing the polarity of the current, The potential difference of the resistance probes was read with a Leeds and Northrup K-2 potentiometer. Again, switches were installed for reversing the polarity and selection of the probes, The magnetic field used in the Hall effect measurements was obtained from a 2100 gauss permanent magnet, The Seebeck coefficient was obtained from the differential temperature across the ends of the sample in conjunction with a Seebect voltage measurement between the same two points. The signal from a 30-gauge chromel-alumel differential thermocouple was fed to a Leeds and Northrup Speedomax Recorder through a Leeds and Northrup D.Co amplifier, A switch was installed to change the input into the Do C. amplifier from the differential temperature emf to the Seebeck emf, thus allowing both potentials to be measured with the same equipment. The sample holder was machined from Lava (hydrous aluminum silicate, American Lava Corp., Chattanooga 5, Tennessee) and baked at 1000 C. This sample holder was mounted on a fired lava (Lavite) platform with stainless steel screws. Directly over the center of the sample was a molybdenum tube containing a 30-gauge chromelalumel thermocouple. This was used to provide a continuous recording of the sample temperature into a Leeds and Northrup Speedomax recorder. A Leeds and Northrup potentiometer was used to buck out a finite number of voltage when the signal of the thermocouple was higher than 10 my. A copper shield was placed over the sample holder while 184

185 a solid copper rod with a heater mounted on it was connected to the lower end of this shield, The heater was made of a threaded piece of Lavite which was wrapped with 28 gauge chromel heating wire, Connected to the top end of the copper shield was a. 1/2 inch tube with a copper spacer and a Lavite heater similar to the lower heater, A Lavite spacer prevented heat from conducting up the copper tube, A Vycor tube enclosed the sample and supporting apparatus. The open end of the Vycor tube was sealed by means of an "O" ring seal to a mounting coupling. The 1/2 inch copper tube passed through this coupling by means of seals which allowed the vertical positioning of the sample directly between the poles of the magnet. An outlet from the coupling leads to a pressure gauge, a vacuum system, and the hydrogen or argon supply. The samples were measured under hydrogen, argon (99, 995 %) or helium (99. 995%) atmosphere. Oxygen was removed from the hydrogen by passing it through a "Deoxo" catalyst. The water vapor in hydrogen was removed with a liquid nitrogen cold trap. The argon is passed through a dry ice cold trap before entering the measuring system,

APPENDIX I EXPERIMENTAL DATA HALL COEFFICIENT HALL COEFFICIENT FOR SPECIMEN NO. 207(2A) In3Te5 TEMPERATURE (DEG.C) (DEG.K) 137.3 410o5 137.3 410.5 166.8 440.0 166.8 440.0 194*3 467.5 194.3 467.5 220.5 493.7 246.5 519.7 246.5 519.7 270.8 544.0 270,8 544,0 295*0 568.2 295.0 568.2 HALL COEF. (CC/COUL) 7.9826E 02 8.0360E 02 6.5114E 02 6 7292E 02 4.3732E 02 5 6073E 02 4.8306E 02 4 7556E 02 3,1308E 02 4.8515E 02 3.1685E 02 3 8559E 02 3 3897E 02 TEMPERATURE (DEG.C) (DEG.K) 280.5 553.7 280,5 553.7 318*0 591.2 318.0 591.2 356.5 629.7 356.5 629.7 395.0 668.2 395.0 668.2 435,8 709.0 435*8 709.0 475.8 749.0 475.8 749.0 HALL COEF. (CC/COUL) 2.2918E 02 2.3229E 02 1.4381E 02 1.4588E 02 2.0604E 01 4.3401E 01 9.4569E 01 8.5155E 01 1.0344E 02 1.1153E 02 3.7875E 00 8.8376E 00 HALL COEFFICIENT FOR SPECIMEN NO. 207(3) In3Te5 TEMPERATURE (DEG.C) (DEG.K) 134.8 408,0 134.8 408.0 170,8 444,0 170.8 444.0 206.3 479.5 206.3 479.5 245.0 518.2 245.0 518.2 296.8 570.0 296.8 570.0 296.8 570.0 346.0 619.2 346.0 619.2 418.3 691.5 418.3 691.5 120.0 393.2 12000 393.2 HALL COEF. (CC/COUL) 1,1433E 03 1.1610E 03 8.4661E 02 8.6611E 02 7.2521E 02 6.3989E 02 4.5335E 02 4*8169E 02 2*5245E 02 3,8623E 02 2.8386E 02 9,2479E 00 4.1615E 01 1.5759E 02 1.6372E 02 1,4710E 03 1.6396E 03 TEMPERATURE (DEG.C) (DEG.K) 177.8 451.0 177.8 451.0 217.8 491.0 217.8 491.0 255 0 528.2 255.0 528.2 297 5 570.7 297.5 570.7 3'29.5 602.7 329.5 602 7 392.0 665.2 392.0 665.2 425.0 698.2 425.0 698.2 495.0 768.2 495.0 768.2 HALL COEF. (CC/COUL) 9 4804E 02 9.8706E 02 7,0615E 02 7,2956E 02 4*9499E 02 5.0873E 02 3.2734E 02 3 5990E 02 1*5001E 02 1 6789E 02 1 8163E 02 1.7279E 02 1 6852E 02 1,7244E 02 3 8853E 00 3 8853E 00 186

187 / A L > C 0 F Fj t 4, T F, P I fI F, N I. 2 7 ( 4 In3Te5 iEM P<. "i- i, ';:....:: 4* 3 3 27. 5 71,5 3? * i 03-, 3 i, '2 123.3 396.5 122.0 395.2 ]94.3 467,5 94 i 3 ' 467 b 5 224.3 497.5 224.3 497.5 24 9 8.523 2''49.86 523.0 266.5 539.7 2 e 6 It s: 4 qr - ' 26,. 6 5 9,J 7 iA C i ( "F i (CC/'COt.Ji l) 2 8 6 6i E03 i.,34 03 i,3334E 03 7* 3 6 0 2 20 6 7420 0 ()2 6.6.35E 02 5.3299E 02 4W097 2El 02 5.6389E 02 3.8197E 02 4.1i226L 02.2 35 E 02 D.'?,. " 3,'9 0 9*2' 2 384.8 63587'9 40U... /u 439.0 7 12.2 439.0 712.2 3 0 6 293,3-5 472,5 ( 1.. C '/ ' OO E 8 i7 0 2 2.55E 0 2 3 36 L 5. 0 i.2496L 02 3.43 '31E 02 Li8329)E 01 6.5460E 0O 1 3675E 02 1.7843E 02 I.4912E 02 1.5690E 02 1.2278E 02 1 1115E 02 9 38 8 4 E -. 0 HAtLL COEFFICIENT FOR SPECIMEN NO 1212 1(2) In Te3 TEMPETRA URE (DEG.C) (DEG.K) 2 4 0 ( 50 2 274,0 54/.2 214.0 54-1/.2 274.0 541,2 312.0 586.2 3 13 3 6 " 6,5 353.3 626 5 ( c:,,::) 5. 3 9 9 e 6 I7 2 7 399.5 6"72.7 438.0 711.2 43 8.0 1: ' i1 2,:; 136.0 409.2 136.0 409.2: 74.2 447*,4 HALL COEF. (CC/COUL) 1. 380bE - 1,3685E 04 4.1857E 03 4, 3 1 C)5E 0 '3 4. 3 I f ~ i:? i.8563E 03 i.8406E 03 8.i198E 02 7.. 8 2 I"') E, 02 3.1026E 02 3.7606E 02 1.4430E 02 2.2868E 02 3.0842E 05 2.9057E 05 6.9205E- 04 TEMiPERA IURE i(D fG C) (DEG.K) 1i 4 44. 4 223.0 496.2 223.0 496.2 2 (:.; t, ( } 5 - q. ' ~ 265.0 538.2 304.8 578.0 304.8 578.0 'j)? 0, 0 6Z.:5 350U0 623.2 392.0 665.2 3922.0 665,2 436*0 '709.2 436.0 709.2 481.2 754.4 481. 2 154.4 HALL COEF. (CC/C OU i.. ) 73 386 E 04 1.5484E 04 1.8044E 04 6;) 2 0i. 6 03 6.1494E 03 2,2579E 03 2,2588E 03 * 264o ' 02 6.8825E 02 3.0385E 02 3.0201E 02 1.4256E 02 1.3369E 02 7,9005E 01 7.5817E 01

188 HALL COEFFICIENT FOR SPECIMEN NO. 1212(3 In Te3 TEMPERATURE (DEG.C) (DEG.K) 164.0 437*2 164.0 437.2 194.5 467.7 194.5 467.7 238.5 511.7 238.5 511.7 278.0 55162 278.0 551,2 320.0 593.2 320.0 593.2 357.2 630.4 357.2 630.4 392.0 665.2 392.0 665.2 431.0 704.2 431.0 704.2 470.5 743.7 470,5 743.7 511.0 784.2 511,0 784.2 78.8 352.0 78,8 352a0 91*3 364.5 91.3 364.5 HALL COEF (CC/COUL) 1.2369E 05 1.2206E 05 4.4746E 04 4.6270E 04 1.2453E 04 1.2255E 04 4.4899E 03 4.2986E 03 1.5825E 03 1.5484E 03 7.9422E 02 7.6554E 02 3.9156E 02 4.0558E 02 2.0074E 02 2.0648E 02 1.3028E 02 1.2167E 02 6.4073E 01 6.2926E 01 2.3452E 06 2.3454E 06 1.2385E 06 1.2261E 06 TEMPERATURE (DEG.C) (DEG*K) 118,8 392.0 118,8 392.0 148.8 422.0 148*8 422.0 103.3 376.5 103.3 376.5 138*5 411.7 138.5 411,7 171.8 44560 171.8 445.0 204.2 477.4 204.2 477.4 290.0 563.2 290*0 563.2 338 5 611.7 338.5 611.7 415.0 688.2 415.0 688.2 458.8 732,0 458.8 732.0 492.0 765.2 492.0 765.2 538.0 811.2 538.0 811*2 HALL COEF. (CC/COUL) 4.1172E 05 4.2739E 05 1 6312E 05 1.4245E 05 2.1693E 05 1 9430E 05 5.1983E 04 5,1900E 04 3.6845E 04 3 7014E 04 1 5872E 04 1 5764E 04 2.1482E 03 201079E 03 7 6480E 02 7 7380E 02 1 9727E 02 1 9727E 02 1.0033E 02 160062E 02 8.4132E 01 7.3900E 01 3.4676E 01 3.4278E 01 HALL COEFFICIENT FOR SPECIMEN NO* 1224(2) TEMPERATURE (DEC DEGCDEGK) 137.5 410.7 137 5 410.7 178.5 451.7 178,5 451.7 221.8 495.0 221.8 495.0 261,5 534.7 261.5 534.7 316,5 589.7 316,5 589,7 386.0 659.2 386.0 659.2 426.0 699.2 426*0 699.2 473.2 746*4 473.2 746,4 514.0 787o2 HALL COEF. (CC/COUL) 2.4063E 05 2.5045E 05 8.1773E 04 7.3930E 04 2.3310E 04 2.3420E 04 8.9603E 03 8.8178E 03 2.5369E 03 2.5495E 03 6.8257E 02 7.1407E 02 4.2915E 02 5.2661E 02 2.2512E 02 2.2305E 02 1.2320E 02 TEMPERATURE (DEG.C) 514,0 173.0 173.0 210*5 210.5 260*0 260.0 312 8 312 8 367.0 367.0 414.3 414.3 460.4 460.4 506 0 506.0 (DEG.K) 787.2 446.2 446.2 483.7 483.7 533*2 533.2 586.0 586*0 640*2 640.2 687.5 687,5 733.6 733*6 779.2 779 2 HALL COEF. (CC/COUL) 1.1628E 02 1.2622E 05 1.4274E 05 3,8502E 04 3.7829E 04 9.8872E 03 9.6812E 03 2.6922E 03 2 6829E 03 7.1945E 02 7.6616E 02 2.8803E 02 2.8012E 02 1,2840E 02 1.2444E 02 6.2590E 01 5.9368E 01

189 HALL COEFFICIENT FOR SPECIMEN NO. 1224(3 ) In Te3 TEMPERATURE (DEG.C) (DEG.K) 112.3 385.5 112*3 385.5 140.5 413.7 140.5 4 13 174*8 448.0 174,8 448.0 2C4,3 477,5 204.3 477.5 234.5 507.7 234.5 507.7 270.0 543.2 270.0 543,2 292.5 565.7 292.5 565.7 328*0 601.2 328,0 601,2 363.0 636.2 407.0 680,2 4C7.0 680,2 HALL COEF. (CC/COUL ) 3.2205E 05 3.2703E 05 1.3376E 05 1.4371E 05 5*7781E 04 5.8095E 04 2.6494E 04 2.7565E 04 1*1565E 04 1.3762E 04 5*3432E 03 5.2104E 03 3.2894E 03 3.3613E 03 1.5517E 03 1.6231E 03 8.4710E 02 4.2631E 02 4.0527E 02 TEMPERATURE (DEG.C) (DEG*K) 157,0 430.2 157.0 430.2 195.0 468,2 195,0 468,2 213.5 546.7 273.5 546.7 309.5 582.7 309,5 582 7 359.8 633.0 359.8 633.0 410.0 683.2 410.0 683.2 449.5 722*7 449*5 722.7 492.0 765.2 492.0 765.2 543.5 816.7 543.5 816-7 HALL COEF (CC/COUL) 1.6621E 05 1.3014E 05 4.8171E 04 4,3832E 04 6.0846E 03 5.7938E 03 2.3769E 03 2.3314E 03 4.8219E 02 6.9214E 02 2.1537E 02 2.2724E 02 1.1606E 02 1.2210E 02 5.0875E 01 6.7833E 01 2.8829E 01 2.8829E 01 HALL COEFFICIENT FOR SPECIMEN NO. 12i5 In Se3 TEMPERATURE (DEG.C) (DEG.K) 222,0 495.2 222.0 495.2 258.5 531.7 258.5 531*7 3C5,0 578,2 HALL COEF. (CC/COUL) 2.9684E 06 3.1562E 06 1.3004E 06 1.3128E 06 1.3858E 05 TEMPERATURE (DEG.C) (DEG.K) 357.5 630.7 464 0 737.2 464 0 737.2 518,0 791,2 518.0 791.2 HALL COEF. (CC/COUL) 1,9908E 05 3*1215E 03 2*6372E 03 4,4826E 02 4*2135E 02 HALL COEFFICIENT FOR SPECIMEN NO* 1200(2B) InSe TEMPERATURE (DEG.C) (DEG.K) 123.5 396.7 123.5 396.7 187.0 460.2 187.0 460.2 214.0 487.2 214.0 487.2 256.0 529.2 256,0 529,2 306.0 579.2 3C6.0 579.2 HALL COEF. (CC/COUL) 1 3920E 04 1 3926E 04 5 7057E 03 5 7248E 03 3 6216E 03 3 6487E 03 2*1916E 03 2 1963E 03 1 3336E 03 1.3385E 03 TEMPERATURE (DEG.C) (DEGK) 424*0 697*2 424.0 697,2 464*0 737.2 464*0 737,2 506.0 779.2 506 0 779.2 541.3 814*5 541*3 814*5 569 5 842 7 569.5 842 7 HALL COEF. (CC/COUL) 3,7761E 02 3 7551E 02 2 8826E 02 2 8339E 02 1 8935E 02 1 8928E 02 1 2898E 02 1.2840E 02 9 2322E 01 9.4811E 01

190 341.5 341 * 5 368,0 368.0 397.0 397.0 421.5 42 1 * 5 451.0 451.0 138.5 138.5 172.0 172.0 225.5 225.5 281,0 261.0 367.0 391.0 3 91.0 614.7 614.7 641 2 641.2 6 70 2 670.2 694.7 694.7 724.2 724*2 411.7 411.7 445*2 445.2 498 7 498 7 554.2 554.2 640.2 640.2 664.2 664.2 8.7642E 02 8.7074E 02 5.9418E 02 5.9104E 02 4.9650E 02 4.9022E 02 4.0135E 02 3.9722E 02 3.1432E 02 3.1395E 02 5.1069E 03 5.0146E 03 3.7850E 03 3.7154E 03 1.9089E 03 1.9423E 03 1.1452E 03 1.1476E 03 5.5436E 02 5.4900E 02 4.8010E 02 4.7645E 02 602.0 602.0 176.8 176 8 261 0 261.0 276.0 276. 0 324,0 324.0 364.0 364.0 401.5 401 5 443.0 443.0 491.5 491 5 529,5 529.5 563 5 563.5 875.2 875.2 450.0 450.0 534.2 534.2 549.2 549.2 597.2 597.2 637.2 637.2 674.7 674.7 716.2 716.2 764.7 764.7 802.7 802.7 836.7 836.7 6.4049E 01 6.4867E 01 5 0375E 03 5 0663E 03 1 6547E 03 1 7471E 03 1 4949E 03 1.5097E 03 9.8176E 02 9.8599E 02 7.0907E 02 7.0907E 02 5 1235 E 02 5 1210E 02 3*4181E 02 3*3882E 02 1.9721E 02 1 9783E 02 1.2208E 02 1.1797E 02 8 8331E 01 8 8331E 01 HALL COEFFICIENT FOR SPECIMEN NO. 1200(3 ) InSe TEMPERATURE (DEG.C) (DEG.K) 23.5 296.7 57.0 330,2 57.0 330.2 84.8 358.0 84.8 358.0 111.0 384,2 1110o 384.2 159.5 432,7 159.5 432.7 198.5 471.7 198.5 471.7 238.0 511.2 238.0 511.2 288.0 561.2 288.0 561.2 334.0 607.2 334.0 607.2 379,0 652.2 379.0 652.2 440*5 713.7 440.5 713.7 471*0 744,2 471.0 744.2 501.0 774.2 50o10 774.2 HALL COEF. (CC/COUL) 7.3753E 03 7.2231E 03 7.2016E 03 6.0139E 03 6.2233E 03 4.8801E 03 4.7327E 03 3.8100E 03 3.9218E 03 2.6717E 03 2.7376E 03 1.7764E 03 1.7827E 03 1.3167E 03 1.3269E 03 9.5679E 02 9.3816E 02 5.5595E 02 5.5265E 02 2.5025E 02 2.4957E 02 1.6583E 02 1.6322E 02 1.1036E 02 1.1090E 02 TEMPERATURE (DEG.C) (DEGK) 527 3 800.5 527,3 800.5 564,3 837,5 564.3 837e5 590.5 863,7 590,5 863.7 412.0 685,2 412.0 685.2 336.0 609.2 336.0 609,2 266.0 539.2 266.0 539.2 89.5 362.7 89,5 362.7 205.5 478,7 205.5 478.7 283.0 556.2 283,0 556,2 366.0 639,2 366.0 639.2 434,5 707,7 434.5 707,7 492.0 765.2 492.0 765.2 HALL COEF. (CC/COUL) 7.8286E 01 7.7263E 01 4,7381E 01 4.7576E 01 3.2855E 01 3.2709E 01 3.4435E 02 3.4388E 02 8.4974E 02 8,5607E 02 1 7922E 03 1.8411E 03 2.7629E 04 2.7608E 04 4.2825E 03 4.3438E 03 1.5977E 03 1.5990E 03 6,6111E 02 6.9201E 02 4.6439E 02 4.5972E 02 1.1811E 02 1.1830E 02

191;^A c I FT- O CFCT F NT Cro SPFCr MFN N8,;:.,~, ~:'::.,,.... ~, > n o) r, *.-', -. - - I InSe TEMPERA' URE <DEG*C) (DEG.K) 19.5 292*7 19.5 292,7 51.J 0 324 2 51.0 324.2 81.0 354,2 81. 0 354.2 139.'5 '42.7 139 4, 412 7 182,0 455.2 182.0 455.2 214.0 487,2 214.0 487.2 255.5 528.7 255.5 528,7 305.0 578.2 3C5.0 578.2 340.5 613.7 3 0.5 613. 396.5 669 7 3c6*5 669.7 440 5 713.7 440.5 713.7 462.0 735,2 462.0 735.2 5C3.0 776.2 503.0 776,2 542.5 815.7 542.5 815.7 183.0 456.2 HALL COEF (CC/COUL) 3.4999E 04 3.8522E 04 2.3406E 04 2,5780E 04 2*0412E 04 1.9932E 04 9,6400E 03 1.0820E 04 5.6531E 03.*6531E 03 3.4633E 03 3.3859E 03 2.0237E 03 2*0403E 03 12183E 03 1.2244E 03 7.4979E 02 7.8631E 02 3.9568E 02 4.0217E 02 2.3741E 02 2.3773E 02 1.7119E 02 1.8180E 02 1.1694E 02 i10835E 02 5.9245E 01 6.3237E 01 3.1515E 03 TEMPERA R-' R (DEG C) 183.0 224,0 224.0 319 0 319.0 263 5 263.5 309,5 309.5 357 5 357.5 400.0 400*0 434.0 434.0 464 0 200.5 200.5 355 0 355.0 454, 0 454 0 478 3 478.3 518.5 518 5 545.0 545 0 579.0 DEG. K) 456 2 497,2 497.2 592.2 592.2 536.7 536,7 582.7 582 7 630*7 630.7 673. 2 673.2 70 7 2 70 * 2 737,2 473 7 473.7 628.2 628.2 727 ~ 2 727.2 751.5 751.5 791.7 791.7 818.2 818.2 852.2 HALL C'OE F ( CC /COl 3.1475E 03 1,9375E 03 1.8097E 03 9.6175E 02 96175E 02 1.2264E 03 1.2807E 03 8.9581E 02 8.8991E 02 5.8663E 02 5.8092E 02 3.9222E 02 3.9019E 02 2.6778E 02 2.6822E 02 1 7684E 02 2.2101E 03 2 252 7E 03 5.8425E 02 5.7161E 02 2.0560E 02 2.1052E 02.5220E 02 1.5302E 02 8.8212E 01 8.7008E 01 6.2978E 01 6.9764E 01 4.4084E 01 HALL COEFFICIENT FOR SPECIMEN NO. 1201 (A) InSe TEMPERATURE (DEG.C) (DEG*K) 320,0 593,2 386,0 659,2 386.0 659*2 417.0 690.2 417.0 690,2 447.5 720,7 447.5 720.7 477,0 750.2 477~0 750*2 508. 781*7 5C8. 781*7 545. ( 818,2 54.0 818.2 579,0 852 * 579 0 852. * 213*0 48602 213.0 486.2 245*0 518*2 245.0 518,2 of..r. 0 59.2 HALL COEF. (CC/COUL) 2.6273E 03 1 9846E 03 1 9390E 03 1.3082E 03 1*2915E 03 8.4738E 02 8.4769E 02 5.5380E 02 5.5380E 02 3.2043E 02 3.1877E 02 1.7870E 02 1.7870E 02 1.2671E 02 1 2708E 02 9.0758E 03 1.0192E 04 9.1949E 03 1.0596E 04 8.0779E 03 TEMPERATURE (DEG.C) 286.0 332.5 332,5 370.5 370.5 440. 5 440.5 397.5 397* 5 478,0 478,0 511*0 511.0 547.0 547.0 588 0 588.0 586,0 586,0 (DEG.K) 559,2 605.7 605,7 643,7 643*,7 713.7 713,7 670,7 670 7 751,2 751,2 784, 2 784. 2 820,2 820 2 861 2 861,2 859 2 859.2 HALL COEF. (CC/COUL) 8,7711E 03 5.5915E 03 5 9474E 03 3 8821E 03 3 7980E 03 1.040E 03 1.4040E 03 2 3099E 03 2,3991E 03 7 7125E 02 7,6348E 02 4,5382E 02 4.6451E 02 1 9024E 02 2 4907E 02 1 4999E 02 12047E 02 1.3222E 02 1*2409E 02

192 HALL COEFFICIENT FOR SPECIMEN NO. 120 (B) InSe TEMPERATURE (DEG.C) (DEG.K) 312.0 585.2 312.0 585.2 354.0 627.2 354.0 627.2 392.0 665.2 392*0 665.2 421.0 694.2 421,0 694,2 442.0 715.2 442.0 715o2 478.0 751,2 478.0 751.2 C508,0 781.2 5C800 781.2 535.0 80802 535.0 808.2 312,0 585.2 HALL COEF. (CC/COUL) 1.4561E 03 1 5974E 03 1 4817E 03 1.5328E 03 1.1060E 03 1 2145E 03 7.8558E 02 8.0400E 02 5.9312E 02 5 9907E 02 3,3191E 02 3.3096E 02 2.0094E 02 2.0212E 02 1.3320E 02 1.3414E 02 5.5602E 03 TEMPERATURE (DEG.C) (DEG.K) 312.0 585.2 341.0 614.2 341*0 614.2 376.5 649.7 376.5 649.7 444.0 717.2 444.0 717 2 481.5 754.7 481.5 754,7 510.5 783.7 510.5 78307 555.0 828.2 555.0 828.2 581.0 854.2 581.0 854.2 610.0 883.2 610.0 883.2 HALL COEF. (CC/COUL) 5.3339E 03 3 8960E 03 3.7012E 03 2 5733E 03 2 3618E 03 8 4289E 02 8 2620E 02 4 0758E 02 4.0758E 02 2. 3893E 02 2.3040E 02 1.0482E 02 1 0436E 02 8,5658E 01 7.8963E 01 6,5202E 01 6.4879E 01 HALL COEFFICIENT FOR SPECIMEN NO. 1208(3) InSe TEMPERATURE DEGt.C) (DEG.K) 2C3.0 476~2 2C3.0 476.2 239 0 512,2 239 0 512,2 276,0 549.2 276.0 549.2 324.0 597.2 324,0 597.2 351.5 624.7 351.5 624.7 388.0 661,2 388.0 6:61.2 416.5 689.7 416,5 689,7 450*0 723.2 450.0 723,2 470,0 743,2 470.0 743.2 HALL COEF. (CC/COUL) 2.7144E 03 2.8805E 03 2.2827E 03 2.3949E 03 1.9675E 03 1.9636E 03 1.3261E 03 1 3123E 03 1,0412E 03 1.0231E 03 7.3389E 02 7,1618E 02 5.2415E 02 5.2809E 02 3.5749E 02 3 6205E 02 2 6198E 02 2.6198E 02 TEMPERATURE (DEG.C) (DEG.K) 512,0 785,2 512,0 785.2 548.0 821.2 548,0 821.2 586.0 859.2 586*0 859.2 344*. 617.2 344,0 61702 38600 659 2 386*0 659.2 421.5 694~7 421.5 694,7 451,0 724.2 451*0 724,2 545,0 818,2 545.0 818,2 595.0 868,2 595,0 868,2 HALL COEF. (CC/COUL) 1*4771E 02 1,5348E 02 9.6495E 01 908926E 01 6.8382E 01 6.7319E 01 7 3055E 02 6 9947E 02 5 6540E 02 5.6579E 02 4*4533E 02 4.4066E 02 3*4531E 02 3,4174E 02 9,7743E 01 9.7885E 01 5 1576E 01 5*2510E 01

193 *2 J N ['.., i. - 6,. t., ^ \ Ag2In8Se13 '!, i>,.C i i.' E(.. ) i.',* i.,, * o ) 5 '-' ' Ko:.... '-... jv" 9 ': ',,! < }2 5..3..* 4. * 3:.,,7- ( * _i 4.' 5 i ',:,. ~ r 5t4, i ~5 <* J- ~ * j3 9 i /p 3i 3 - 0 666 e fr (i A.: C: L j C! U 8. ~.;. '.. 1,, $ * 4' LI j I 3* I,31 ) 33 3 ~ 5 a 8a: i.r f. 0 ':! ).1 7, r i 0. I.,. 9 3. -' 0 4.-? '(i; "r..'; — 5 L-, 3,ft, 03 4,8. F 2 5 E 0 fi ', 1. *0 6 2: 3 E.' t)." 5,20980:: 5 S'4 7 -:i t, 9. 2 %~,: i:3 () ':.14 5 60 - 3 *, 7 9 ( / 2 i3. I, t,., r ':- -: () -.i- ~", 2 -'..b;.:.!.', * ' _' t * 5 0'9 '-::,' 9 2:. ' - 00. 3 ' i " 3 6, 0 0 630.: "' 3 b 0, * 213 4' ' 5 ()'5, / W.,,;i ) 6 ' 4 3 r *0 a, 6 7 8: 2 r.A... O ^ -,; "!.,: -J } i, j,.- '; vi... i.1 *. (, / 0.. i C' {' 3 ^ i ' 733) " i t o ' 9 E 0 i. ~ '6 6 3.i j 1. B:. * b55. 301 3,'7./31 E (;3,:.t. 1 5 77..: 3 ^. * 1 1 7.-;

194 SEEBECK COEFFICIENT SEEBECK COEFFICIENT FOR SPECIMEN NO. 121212) In Te 2 3 TEMP. (DEGK) 586 2 626 5 672 7 711*.2 758.2 758 2 757.4 SEEBECK (MV/ K) -~555,-.~. 5 O0 -.567 -.456 -- 40 l o~321 -.,235 TEMP. (DEG*K) 757.4 798,2 833.2 872*0 449*2 496.2 538.2 SEEBECK (MV/ K) - 228 - 2283.'229 - 244 -, 886 -.791 - 645 TEMP, (DEG K) 578.0 623.2 661.2 665.2 709.2 753 2 SEEBECK COEFFICIENT FOR SPECIMEN NO. 1212(3) In2 TEMP. (DEG.K) 437.2 467.7 511.7 551.2 593,2 630.4 665. 2 703.7 74 37 784.2 465.0 SEEBECK (MV/ K) -1 083 -o903 t- 825 - 756 -,664 -*606:,625 - 640 = 572 - 344 e 630 TEMP. (DEG.K) 492.2 523*7 555.2 580.7 607.2 651 7 411,7 458,7 451*2 445,0 478,7 SEEBECK (MV/ K) - 550 - 445 - 4 95.-460 -,500 - 490 -.468 -.730 - 838 -,800 - 697 TEMP. (DEG.K) 519 7 565.7 563,2 611o7 654*4 688 2 732.0 766.9 766,9 765 2 856.7 SEEBECK (MV/ K) -.465 -*471 -*570 -*539 — 473 -*415 re e3 SEEBECK (MV/ K) - 716, 687 - 523 -.550 -.440 -,560 -,570 -.447 -,409 - 352 - 388?e3 SEEBECK (MV/ K) -.517 -.469 -426 e3 SEEBECK (MV/ K). 404 -.354 -,325 - 252 2 5 Z SEEBECK COEFFICIENT FOR SPECIMEN NO 1224(2) TEMP. (DEG.K) 450.2 495.0 534.7 659.2 746.4 SEEBECK (MV/ K) -> 530 -.470 -o 460, 505 - 358 -.378 TEMP. (DEG.K) 787.2 826.2 861.2 447.2 533*2 586.0 SEEBECK (MV/ K) - 303 -*224 -207 1-927 -*750 In T TEMP. (DEG.K) 640.7 689.9 732.5 780 7 SEEBECK COEFFICIENT FOR SPECIMEN NO. 1224(3) TEMP * ",OFcG. K 477, 5 507.2 532.2 543.2 56 5. 599, 7 SEEBECK (MV/ K) o-478 -.516 -~,435 -.'544 ~.494 -.418 TEMP. ('DEG.K) 680,2 767.2 809 2 468,2 508 0 546 7 SEEBECK (MV/ K) -*440 '*283 -.209 -*725 -*595 -.466 In2T TEMP * (DEG.K) 683.2 722*7 702.2 816.7

1.95 SEEBECK COEFFICIENT FOR SPECIMEN N6. i200(iB~ InSe TEMP (DEG.K) 397.7 42 8 7 461.2 489 2 529.2 580,2 614.5 642, 2 SEEBECK (MV/ K).*080 -..161 —.176 -- 344 -.258 "- 302 -.392 -.393 TEMP. (DEG.K) 670.7 694.7 724.2 386.0 411.7 446*2 498.7 554*2 SEEBECK (MV/ K) -.394 -.388 -.437 -.160 -.131 -*.312 -.260 -*5258 TEMP. (DEG.K) 594.7 640.2 664 2 698.2 737.2 779.2 814.5 843.2 SEEBECK (MV/ K) -. 295 -.354 -.314 -.354 -.413 -.346 -.235 -.207 SEEBECK COEFFICIENT FOR SPECIMEN NO. 1200(3) InSe TEMP SEEBECK (DEG.K) (MV/ K) 324.5 -413 330*2 - 498 330.2 - 463 384.2 -.536 432.5 -. 635 472.2 4.450 511.2 o. 431 SEEBECK COEFFICIENT TEMP. SEEBECK (DEG.K) (MV/ K) 361.2 -,674 359.2 -665 411.7 -.776 455.7 -.787 487.2 -.790 576.7 —.793 613.2 _.759 666.2 -.687 713.2 -2.775 713.7 -.750 735.2 -.723 775.7 -.657 814.2 -.640 843.2 -.601 858.5 —.589 TEMP. (DEG.K) 561.2 607.5 654*2 745.2 744.2 751.2 680.7 SEEBECK (MV/ K) -,490 -, 546 - 442 -- 437 - 465 -,347 -- 372 TEMP (DEG, K) 610.2 399.2 480.2 555.7 639.2 707.7 766 0 SEEBECK (MV/ K) - 521 - 756 - 722 - 620 -.441 -.402 - 183 FOR SPECIMEN NO. 1200(4A) InSe TEMP. (DEG.K) 859.2 370.4 383.7 420.2 457.2 497.2 534.2 592.2 389.2 455.2 536.7 582.7 673.2 737.2 472.2 SEEBECK (MV/ K) -,570 -.441 -*556 -.644 -.660 -.672 -*688 -o740 -.589 -.698 -.729 -.746 -* 715 -*652 -,700 TEMP. (DEG.K) 628.2 727.2 791.2 852 2 322 7 341,7 356.7 367.2 388,7 411.2 430.2 456.2 472 * 5 SEEBECK (MV/ K) -.694 -.665 -.533 -.426 -.114 -.481 - 551 -.592 -.632 -.668 -.681 -.669 -.533

196 SEEBECK COEFFICIENT FOR SPECIMEN NO. 1.208(3) InSe TEMP. SEEBECK TEMP. SEEBECK TEMP. SEEBECK (DEGoK) (MV/ K) (DEG.K) (MV/ K) (DEG.K) (MV/ K) 343.2 - 272 661*2 -,351 617,2 -.435 409*2 - 391 689,7 -*386 659*2 -.415 435.7 - 385 723 2 327694*7 -*303 514.7 -400 743.2 -.324 724.2 -.252 549,2 7 368 761 2 -*300 818.2 -.262 597,7 7 324 821 2 - 288 840.2 -.290 625.7 -*428 540 2 -.425 868.2 —.294 SEEBECK COEFFICIENT FOR SPECIMEN NO. 248(2) InTe TEMP. SEEBECK TEMP. SEEBECK TEMP. SEEBECK (DEG.K) (t'V/ K) (DEG.K) (MV/ K) (DEG.K) (MV/ K) 323.2.107 737.2.139 637.7.140 34-9.5 112 765.2 *097 668.7.133 375.7.118 816*7 *102 694.7.138 392.2 ~117 841.2.086 720.7.140 427.2.127 869.7 *040 756.2 ~133 475.2 123 345.2.060 780.2 131 5C9.7.134 383.5.127 812.2.062 549*2.127 433.0.140 842*8.097 582,7.122 477.2.141 868,2.090 613.2 121 523 2 134 896.2 *093 64-6.2 114 568.2.138 70C82.117 607.2.152 SEEBECK COEFFICIENT FOR SPECIMEN NO. 738(5A) InTe TEMP. SEEBECK TEMP. SEEBECK TEMP. SEEBECK (DFG.K) (MV/ K) (DEG.K) (MV/ K) (DEGK) (MV/ K) 310.7 -.101 681,2 -o183 553.7 -.172 325,2 -.l06 709*2 * 138 581.7 -.173 342,5 -.104 735.7 7 215 6355 -.188 373,2 -.112 759,0 -o221 690*7 -.200 400.2 -.123 795,7 -.231 664.7 -.121 412.5 -.152 324*2 -.093 716.2 -.176 46 1 2 - 153 348.7 7 - 102 786.2 -.212 496.0 -- 1 37 364.0 - 106 786.2 -.212 523z2 i 155 394.5 -.114 811.5 -.205 553,2 -.142 4150 -. i28 833.2 -.209 588 0 - 158 445*0 -. 133 854.2 -.208 648.5 -,171 518.2 - 158 885.0 -.307

197 SEEBECK TEMP. (DEG.K) 316*7 342.2 397.7 693.2 715,7 736.2 76 32 79 47 COEFFICIENT FOR SPECIMEN NO. 738(6) InTe SEEBECK (MV/ K) - 09 4 -6101 - 127 -.233 -,260 -,280 -.383 -*275 TEMP. (DEG.K) 814*7 859.7 321.2 356.7 380.7 412.5 442.2 469,5 SEEBECK (MV/ K) -*280 -,288 -,081 -,093 -,098 -, 115 - 128 - 160 TEMP. (DEG.K) 531.7 594.7 698.7 725.7 749.2 782.2 839.2 868.2 SEEBECK (MV/ K) -.177 -.254 -.254 -.260 -.262 -.372 -.280 -.275 SEEBECK COEFFICIENT FOR SPECIMEN NO. 182(6) Cu7InTe17 TEMP. (DEG.K) 356.2 425.2 5C2 2 573.2 624 2 SEEBECK (MV/ K),140.179,156,242 *260 TEMP. (DEG.K) 676.0 735.2 810.2 866.2 914*2 SEEBECK (MV/ K).297 *331.342.398.478 TEMP (DEG.K) 966,2 981.7 996.2 1009.2 SEEBECK (MV/ K).416.462.438.430 SEEBECK COEFFICIENT FOR SPECIMEN NO. 232(2B) Cu7InTe17 TEMP. (DEG.K) 123.2 160,5 199.7 250.9 318.5 352.5 388.4 SEEBECK (MV/ K).071.095.133.204.270.281.300 TEMP. (DEG.K) 425.2 455,2 488.2 524.5 565 7 598,5 645,2 SEEBECK (MV/ K).333.352.386,422,426,450,482 TEMP. (DEG.K) 680.2 725 7 760.7 834.5 890.2 SEEBECK (MV/ K).520.557 *558.580.533 SEEBECK COEFFICIENT FOR SPECIMEN NO. 276(2B) Cu7InTe17 TEMP. (DEG.K) 3514 7 400,2 386.5 413.5 440,7 467 5 501.2 524,0 5 24 7* 2 547.2 574 2 601.7 SEEBECK (MV/ K),054,067 *058 *067.073,071.091.111.115.125 *135 TEMP. (DEG.K) 628.7 668.2 704 2 740.5 775*2 806 2 739.2 738*7 738.7 738*7 738,7 SEEBECK (MV/ K).145.141.133 *133,168.166,I1 6.6 *147 6159.164 ii57 *i52 TEMP. (DEG.K) 390 2 460*2 516 2 575 2 635,2 710.7 776.2 819 2 840.2 SEEBECK (MV/ K) 127 132 131 171.169.156.170 A167,160

t93 SEEBECK COEFFICIENT FOR SPECIMEN NO. 854( Bi Cu7In9Te7 TEMP (DEG.K) 3714 5 400.2 429 7 48 8.2 46 5 2 5C9.7 542.2 578.5 611.5 649 7 649,7 682 7 SEEBECK (MV/ K).087 100,112,137 134.125.143.159 *177.172,172.182 156 TEMP. (DEG.K) 722.0 754*7 786*2 786.2 786.2 826*5 329.5 356.0 379.2 412.7 439.2 472.0 502.2 SEEBECK (MV/ K) ~162.i80 *138 *153 * 164 145,144.154,171.200 *210.225,230 TEMP. (DEG.K) 524.5 538.0 646.5 674.0 716.2 751.2 784.0 811.2 845.2 866.2 866.2 887.2 SEEBECK (MV/ K).223.218,270.239 *280,295.319.287 *255.252.260 *222 SEEBECK COEFFICIENT FOR SPECIMEN NO. 855(2A) Cu7InTe17 TEMP (DEG.K) 97.7 108.7 118.2 154.7 179.7 218.7 391.7 391.0 SEEBECK (MV/ K) *022.029 *032.042.051 *068.171.163 TEMP. (DEG.K) 451.2 484.5 515.2 559.2 425.2 516.5 625,2 652.5 SEEBECK (MV/ K).183.196 *210.236.182,237.278,264 TEMP. (DEG.K) 687.7 639.2 700.0 733.2 777.2 833.2 SEEBECK (MV/ K).306.258.290.301 *301.360 SEEBECK COEFFICIENT FOR SPECIMEN NO. 1033(3) CuIn9Te17 TEMP. (DEG. K) 364.2 363.7 384.7 408.7 4415 * 5 473.7 5C6 05 573.2 59 1 2 619.2 SEEBECK (MV/ K).292.294.318.351.363.367.380.387 *392.394.392 o420.429 TEMP. (DEG.K) 644.2 670.5 696.2 730.2 756.0 783.7 810.0 833.2 852.2 343.5 397.7 454.7 503.7 SEEBECK (MV/ K).443,458.470 *460.475 *457.434.415.418.240.268 *291 *311 TEMP. (DEG.K) 553.7 593.2 642.5 678.0 706.5 734.7 763.2 793.2 815.0 849.7 871.7 893.7 SEEBECK (MV/ K).326 *348.361.374.383.405 *416.430 *417.419.410 *411

199 SrFBECK COEFFICIENT FOR SPECIMEN NO. 12 0(0) Cu7InTe17 TEMP (DEG.K) 327.2 366.7 481.2 514.7 547 * 7 SEEBECK (MV/ K).169.175,23k.238.220.227 TEMP. (DEG.K) 581.0 668,2 695,7 720.2 798.2 881 2 SEEBECK (MV/ K).215 *220.251 *280.290.327 TEMP. (DEG.K) 910.2 965.2 977,2 1000.7 SEEBECK (MV/ K).285.258.119.072 SEEBECK COEFFICIENT FOR SPECIMEN NO. 85(7) CdInSe4 4 TEMP. (DEG.K) 95.9 105.2 136.0 147.0 158.8 169.2 182.9 184.2 202.6 215.9 229.6 240.9 249.7 258.2 286 9 2 2 602 299~2 318.7 356.7 424.2 4 2 4 2 SEEBECK (MV/ K) '-.015 -.013 -.014 -.014 -.015 -.018 -.020 -.022 -.022 -.024 -.028 -.029 -.031 -.035 -.042 -.040 -,042 -.043 -.046 -o051 —, 059 TEMP. (DEG.K) 447.5 472.5 497.5 609.5 609.5 609,5 611*4 95 2 99.6 103.6 121.2 136.0 151.5 169.2 187.2 210.1 246 9 264.2 273.2 3112 327*7 SEEBECK (MV/ K) -*060 -. 064 -.067 -,095 -,096 -,095 -.096 - 014 -.015 -.011 -.019 -.013 -*013 -.018 -.022 -.036 I.038 -,044 -.047 -*051 TEMP. (DEG.K) 352.2 374.9 395.9 427.0 458.2 484.2 515.2 541.6 572.3 608.7 640.2 670.2 743.4 785.7 845.2 870.2 906.2 91 8 2 918.2 SEEBECK (MV/ K) -.055 -.059 -.062 -.069 "-074 -.080 '-.085 -.088 -,095 -.099 -.113 -.116 -.142 -.164 -.190 -.186 -.186 - 168 -*170 SEEBECK COEFFICIENT FOR SPECIMEN NO* 185(7) CdIn2Se4 TEMP (DEG.K) 369.7 405 2 435.7 462.2 5C2.2 53 9.2 564.0 SEEBECK (MV/ K) -,100 - 110 -. 126 -.134 -o154 - 166 - 177 TEMP. (DEG. K) 603.2 643.2 680.2 723.2 739.2 784.2 810.2 SEEBECK (MV/ K) -*192 -.200 -.213 -*226 -.239 -.244 -.250 TEMP. (DEG. K) 887.2 373.2 438.2 495.2 533.2 587.7 673.2 SEEBECK (MV/ K) -.255 -.060 -.073 -.092 -.102 —. 121 -.149

SEL.;,.i c- FT-t-ICEN OR S C....ML' N'O.* 89 -4 CdIr ~ r S1-1. 'A 1 -, s 4, -4 "- E l.' 3c DEG,.:, 3 34 * 2 3 -EiS 8 * 378.2 4.'" 3 ) '519l7,F F l - 4;.- K M V, K *.08 - ~0.Sa -.. * 09"? - 0 109 590C61 r- 6 u4 61 9. t2-1,C ') 4-?2 r s, 4,; SELBECK.*MV^ *<. i.-*141. I -,:!96 -- s... -._42 -7 --- ^ 2r 7 E 4F '-. DEG. k;" 809.9 865.2 '920, -7 107 L,, 4 927 * SEEBECK (MV/ K ' —.256 -.300 --- 5 36 -. 345 * — 29 -1 c4 SFEBECK COEFFfCIENT FOR SPECTMEN NO, 296i5bB, Aq 2In Se 3 89 i 2,!'.02 l08,2,..,,, 1 2.; 2 ';92~2 2 ':?34^ a ":"i,'.~ ~ 7 S EEBE C K {MV/ K) - c1 I 61. — 151 -.237 — o22 - 239 -~252 -.285 --.,301 -.. 330 --- 366 --- o 3) ~ 6 T~M" * (DEG, K ) 378,2 428.7 *4 8 * 2 590, 633*,2 682,2 502,2 580,2 676,0 680.2 813.2 877.7 Sf EBECK (MV/ K) -*393 -.415 - 9 7 1 Q - o 6 6 0 -~710 -o660 -—. 555 -1 220 - 107'5 --._ 770 — _890 -- 439 -* 24, iTEMPo IDEGK i 726,7 584,2 538,2 378.2 339, 378,2 415 *2 46 It 4 SEEBECK ItMV/ K) -- * 93 -.296 -. 240 - * 197 -.292 -.119 -.126 -—. 146 -- 166 —. 199

201 ELECTRICAL CONDUCTIVITY OF Ag2In8Se13 HE:-t0 LOW:iNGE E LEC A rOt4A. t )NDCVL vT DA A CW i tI 3 W: ' AI'EO U$S;G t WO-FURNACE,RRANUELML.NT WHICH Ai.LO..[D INOt.fDCNTo CON-;ROLN.NG OF 'HEAL SAMtr AND f itSE L.- iL M l-MPERAURES E -C ' R; ICA. CONDUC' V Y T' FO1R SPE Cri N N iMBER 293 Ag Tn Se..- 6 13 DATA NO, 2 3 4 - 9 nJ 1 i 9 11 12 i s L 6 C.0 7 30 2%. 7 30 38 39 SAMPL ' " o.000 82.0 1220 "~' 'J1. 190 398 i ~ 1 113: 3 ' 3 7 i 39 I!.1.029 P18991*-002 889 125 882, 'L*134 884 i.131 966 1035 967 033 959,0 3 059 1*0~3 965 1,036?59 9 * 043 19612 1 039 ^?65 1*037 962 1*039 966 1,035?65 * i 036 S DE - M FO A, '. 6.7 'i, 7oo, ' 7 * 7 63 5 1'7; i 6 3 1 '; e.. 7,'7 6 3 267- i.763 3 56i 1*76i3 515- 'i. 94 5. 5 1,9 41 598 1,672 598 6i 6 677 i47 7 - 2 1 * ' 1 4 ' 9 ~, 3'. 75 i i ~.3 3 i 657 1,521 513 i, 6'3 3 589 1i 6 9 559 1 788 5.25 i *904 574 i. 742 61i7 1.620 678 1 475 72 2 1 383 7-3 1 2'92 E cLC N D 8' MHO.CM) ',* ~ 301 ---. * 9o (- - t 6 3 5 L -1- 8 38. -.1 21 i': 00. ~80c- 00.- ~ O '.: O 3 * 94.0 C 3*90E0O 9, 40F O0, 0 E — 1 -3 85 - 1 3 94600L 3^50L i 3 50E — 1 5 3 [:7 E- i 7 iO-L -i 3.65 -1 2,90E -1 2*75E1 EQ.TIME (H4R M IN) 17 10 28 15 36 1 48 20 20 18 20 20 50 30 h 20 2 00 2 01 8 40 jO 20: 50 7 40 58 00 7 00 7 30 2,,0 10 15 5 25 8 1.5 3 00 15 35 6 20 11 20 2:50 11 25 14 45 11 15 8.,O 13 00

202 (<ont. DATA NO. 40 41 42 43 44 45 46 47 48 49 5s 51i 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 SA MPLE t EM:P DEG K} (1000/T) 965 1 036 963 lo 038 937 lo067 840 1 190 863 1 158 846 1 182 816 1 225 790 1 266 7'95 1 2:57 86,o t1241 8133 23 6 B1:5 2'3-6 809 1.236 807 1239 807 1.239 801 1.248 803 1 245 802 1.247 802 1.247 809 236 802 1.247 831 1 203 868 1. 15 909 i 1000 961 1.040 998 1,002 955 '1 047 907 1.103 967 1 034 966 1 * 035 SE TEMPERATURE (bEG.K <} 1000/T; 633 1579 574 1 742 574 1. 74 574 1 742 574 1*742 574 1*742 574 1,742 574 1.742 753 ' 1.328 753 L. 328 716 i4396:7i16 i 396 678 1 4:75 678 1 475 64:4 1. 552 581 1.721 635 1. 574. 694 1 441 3 7 1 35 7 689 1.451 571 1*751 571 1 75 1 571 1 75 571 I~751 571 1*751 571 1 751 657l 1.755 687 1.455 ELE. CO.ND*. MHO/CM5 4 25E-1 25 30E- 1 4. 10E-1 4.15E-1 4*05E-1 4,.30E-1 4,05E -- 2.80E.-1.960L-i 2*436E 1 2*43E 1 2 37E- 1 2:45E-1 2.10E-1 2. 19E-1 1.?7E-i i.80E-I 1.80E-1 2.40E-1 2 68 E-1 2 *88E-1 4*33t-i 6* 5 9 E- 3*40E-1 6,* iE-1 2 * 20E -1 EQ rIME (HRMIN 6 06 19 25 20 1 40 1 45 25 33 20 6 27 231 9 57 8 1 16 31 1 45 12 24 9 10 4 00 26 12 16 26 10 44 37 45 28 46 I6 1 8 22 24 48

203 E LEC 'RICA. CONDUT ' VTY FO -. -' P i',N NU IMB. 2c.;6 e, AcIn 8Se 3 ATA NOo 8 10 2 21 15 17 19 28 27 B8 29 3 cJ 36 37 40 45 46 49 50 31 '2 3 DF.', ) ( i l00 / D ' )ElJ, '/ ':000 ' t72 3?;68 7 838. 37 2 2,665 35:. 83: 16 2 405 7 ~ ~5 2.2 ~ 10 3. 5^6 e 900 3 2 2,83? 5356 1 798 33 )3 2 8' 59.2 1 o68 353 832 5 46 1 '48 35 83 696 1-,. 3 '3 2 28 738.354 3 3 2 832 787 1, 2 70 3.3 2 83 8 7 224 5 _ 2 8 844 1 185 353 2 832 8.38 1* 93 6 9 213 3 938 1 193 548 1.8?5 838 1,1. 93 60 / '.*,64'; 838 1 193 680,70 838 193o 502. 990 338 1*193 359 Z780 938 l 1 19 4a62:e 16 838 1l193 568 4760 838 l1e93 642 1r556 838 ~ 1.93 587 1 702 838 1 193 526 1.900 838 1 193 641 1.50 3 17 ~ 22 3 33 1 5 7,386 1e.269 633 15 79 764 e1310 633 1*5 9 7-2 1 * 348 6 3 3 1579 -7 Ob 1 1233 1}.7) 7:75 i ~ 29 ' 6 33 l 5 9;r' '3 803 1" 246 633 3 1 *7 8 0 3 #246 6- P 1 a7 828 1i208 633 1.579 828 1 20836 363 275 0 806 l2373 4111 2, 32 -)11I 0 31 4 1 2*4 3 -73 i ~1^03 411 2 4~32 731 15368 411 2 4-32 755 1.22'5 4!l 2,9432 9',", i. r 2 i52 i L 2 2 432 826 I l2.i0 41L: 2.32 82c ~ i 2l0 35 03 2.832 8C. 1o?48 353 2Z832 "; iL 17?95 35 3 2 32 ' '. 1g44 -53 24832 1t 8 392 33 32832,3 42 2 I 4 '3 i '32 ';-, E W ~.R FA I UfRE:' HERE' ~'..'; *.' OND. (MHO CM ",6 3E-' 8 F2 i 6 8.3 --, ~ 63t _-'. O O. -— 4 24.5E- i 6, 00 - 182ES00 1, 60E'00 1.l93EO0 4. 9 851 E 00 3 * 6 5 E O" 3 *60FO(t' 9,40F00 I. 07CO1 t,08Etl 920E00 3, 76E00 628EOO0 9*90E00 1? sbOEO ', i 0 t.00 00 '. " 1>"i,-.,; r v (5 L -i 3,80E -1 6:!} 0. ',, 0 L. 0 0, ~ i 6.:0,90100 48Ct -. 1.3 * 90 '-3 0L- k EQ.;'MI. ~HRMIN)

204 (cont.) DATA N0O 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 2'2 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 SAMPLE TEMP* (t6E*.K) (iOOO/T) 512 ~ 9-50 541 1.848 567 1.763 594 1*684 620 1*613 663 1.508 694 1441 7.20 1*389 775 1*342 769 1.300 798 1 *253 711 1*406 752 1.*326 775 1*290 798 1*253 812 1.23 1 816 1*225 824 1*2'14 845 1*183 856 1168 853 1. 172 855 1*169 855 1*167 869 1 151 897 1.115 909 1*100 924 1*082 937 1067 952 1~ 050 931 1*074 891 1122 864 1*157 829 1*206 809 1 236 785 1.274 849 1*177 902 1.108 973 1*028 990 1 010 990 1010 1000 1*000 977 1.*023 942 1.061 912 1,096 888 1 1126 888 1 126 888 1. 126 888 1.126 888 1.126 867 1.1.53 840 1.190 808 1*237 789 1 267 SE TEMPERATURE ( DEG.*K 1000/ T) 358 2.792 3:58 2*7 92 358 2 792 358 2.792 358 2*792 75'8 2 792 35.8 2 * 92 35'8 2.792 358 2.792 35.8 2*792 358 2 792 195 5*128 195 5 128 195 5 128 195 5.1:28 195 5*128 195 5,128 195 5*128 195 5*128 195 5 1"2'8 303 3.299 303 3.299 195 5*128 1 95 5 128 195 5.128 195 5 1:28 195 5.1 28 195 5*128 195 5*128 195 5*128 195 5 128 195 5* 128 195 5.128 195 5.128 19.5 5*128 195 5.128 195 5*128 195 5.128 19 5 5 12.8 195 5 128 195 5*128 1955 5. 128 195- 5. 128 195 5*.128 195 5 1.28 304 3 288 273 3 66'1 273 3*661 27 3 3*66-1 273 3*661 2'73 3 661 273 3 66'1 2-73 3.661 ELEC*COND* (MHO/CM 5 *40E-2 5 80E-2 56 80E-2 6*80.E-2 8.70E-2 1.84E-1 2.32E-1 3,01E-1 4,.16E-1 5*82E-1 1 *.18E00 2 80EOO 5 70E-1 1 01EOO *67EOO 3. 01EOO 3*55EOO 3, 5.55 E 0 4. 12EOO 4.93E00 6 50E0 8 OOEOO 8 lOEOO 9.10EOO 7.90E00 3., 11EO1 1 41E01 1 *70E01 2 06E01 2 53E01 3. 14E01 2. 30E01 1 14E01 7 90EO0 4.59E00 2 91E00 1 o95E00 5 90EO0 1 *55E01 3 28E01 3 55E01 3070E01 3 50E01 3 38E01 1 98E01 i 1*.4EO 1 8.30EO0 8 70EOO 8 40tEOO 8 OOEOO 5. OOEOO 3 36E00 2 18EOO 1 *52EOO 1 * 13EOO EQ.TIME (HR.MiN' 2 18 9 58 15 00 7 09 8 17 27 40 13 13 23 12 59 49 53 39

205 A b C E a Ed E g E g, o Ef Ei 1 E v AE e, 1 q qi h I k M APPENDIX J NOMENCLATURE Seebeck factor, a constant dependent on scattering mechanism. = the temperature dependence of the energy gap, (eV/ K). = l /lp, the ratio of electron mobility to hole mobility. 10 = velocity of light 3 x 10 cm/sec. = acceptor energy level, eV. = donor energy level, eV. = energy gap of a semiconductor, eV. = energy gap at 0 K, eV. = Fermi energy level with reference point of zero energy at the top of the valence band, eV. th = i energy level with the reference zero energy same as Ef, eV. = energy level at the top of the valence band, equal zero when taken as the reference level, eV, = energy difference between impurity level to the nearer band. = occupied sites at energy state E.. -19 = electron charge, 1. 602 x 10 coulomb/electron. = total sites of energy state E,. -27 = Planck's constant, 6.62 x 10 erg. sec. = h/2T. = electric current, amp = Boltzmann's constant, 1,38 x 101 erg/~K = 8. 64 x 10-5 eV/~K, = effective mass ratio m /m P n

206 m = effective mass of an electron, gm. n m = mass of an electron, gm. 0 m =mean effective mass, = Vm m, gm. o p pm = effective mass of a hole, gm p N = acceptor concentration, (cm)a N = ionized acceptors a -3 = concentration of holes in valence band due to acceptors, (cm) * 3/2 -3 N = density of state in conduction band = 2U(m T/m ) / (cm) c n o -3 N = concentration of donors, (cm) N = ionized donors = concentration of conduction electrons from the donors, (cm) *' 3/2 -3 N = density of state in the valence band = 2U(mp T/m ), (cm) n. = intrinsic carrier concentration, (cm)3 3 n = concentration of electrons in the conduction band, (cm) c RH m3 P = concentration of holes in the valence band, (cm)0 R = Hall coefficient, cm /coulomb. H T = absolute temperature, K o 2 3/2_4.83 15 U = a constant = (2rm /h)3 = x 10 O 2 V = gap potential for semiconductor, volt cg V = Imref potential for n-type semiconductor, volt n V = Imref potential for p-type semiconductor, volt * p a = Seebeck coefficient, volt/O K an = n-type Seebeck coefficient, volt/ K. n

207 ap = p-type Seebeck coefficient, volt/ K. = ratio of the Hall mobility to drift mobility y = mobility scattering exponent. 2 J H, n= Hall mobility for electrons, cm /v-sec. H, n 2 H == Hall mobility for holes, cm /v-sec. yH, p 2 - = drift mobility of electrons, cm /volt-sec. 2 = drift mobility of holes, cm /volt-sec. C- = electrical conductivity, mho/cm. ~()R ^- = electrical conductivity at Hall inversion temperature, H mho/cm. = the portion of electrical conductivity contributed by the holes due to the ionized acceptors, mho/cm.

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