PHILIPS LABORATORIES, INC. Irvington-on-Hudson, New York Research Laboratory TECHNICAL REPORT NO. 34 August 15, 1950 Case No. 4500 I. THERMIONIC EMISSION FROM OXIDE CATHODES; II. PHOTOCONDUCTIVITY IN SEMICONDUCTORS by E. S. R3fTNER Approved 0. S. Duffendrc Director of Research Approved for Distribution F. M. Vogel Manager, Patent Department August 15, 1950

i. PREFACE This report represents a supplement to Technical Report No. 25 entitled, "Concerning Sone Aspects of Solid State Theory." Section I of the present report supersedes section VIII B of the previous report, which passed into obsolescence about the time of printingp whereas section II contains new information not covered previously. The material of this report also represents substantially the content of five lectures delivered by the author during the week of August 7, 1950 at the Summer Electronics Symposium on Semiconductor Electronics sponsored by the University of Michigan.

ii. TABLE OF CONTENTS INTRODUCTION............... I. THERMIONIC EMISSION FROM OXIDE CATHODES.. 1. Facts........... 2. Early Explanations.......... 3. Simple Semiconductor Model...... 4. Quantitative Theory for Simple Model.. 5. Test of Simple Theory......... 6. Pore Conduction Hypothesis....... 7. Evidence for p-type Conductivity.... 8. Latest Theory............ 9. References............... Figs. 1 -9 and Table I II. PHOTOCONDUCTIVITY IN SEMICONDUCTORS..... 1. Introduction............... 2. Expectations from Band Scheme. * * * 3. Experimental Facts......... Thallous Sulfide Cell.... Lead Sulfide Cell............ Lead Selenide and Telluride Cells.... 4. Energy Level Diagram.......... Page * * * 0 * * 2 ~ * * * * ~ 17 ~ ~ ~ ~ ~ ~ ~ 17 ~ ~ 0 ~ ~ ~ ~ 24 0 0 ~. 0 0 ~~ 25....... 25 0....... 0 25 0 0 0 0 0.. 26 ~ ~ ~ ~ ~ 0 ~ 26.. 0 0 0 0.. 26 ~ ~ ~ ~ ~ 23 * - - 0 0 0 0 ~. 0 0 0 0 28 laterial... 29 5. Photoconductivity Theory for Unsensitized M 6. Photoconductivity Theory for Intrinsic Semiconductor Produced by Compensation of Impurities........ 34

iii. Page 7. n-p Barrier Picture................. 38 8. General Theory............ 39 9. References............ *........ 45 Figs. 1 - 15

1. INTRODUCTION It is the purpose of the present series of lectures to discuss two specific topics, namely thermionic emission from oxide cathodes and photoconductivity in semiconductors. Both subjects have something in common in the sense that although the original discoveries were made many decades ago, even at the present time a complete understanding of these phenomena are not yet at hand. For this reason our procedure will be to present a somewhat chronological account of the more important pictures that have been advanced up to the present time. I. THERMIONIC EMISSION FROM OKIDE CATHODES 1. Facts Oxide cathodes usually are comprised of alkaline earth oxides, notably BaO, and preferably BaO-SrO mixtures. The oxides are coated (by spraying or by cataphoresis, etc.) on metal bases (usually Ni) in the form of carbonates, which are subsequently decomposed to the oxides by heating in vacuo at high temperatures. In order to produce good electron emitters, a further process called "activation" is required. Before activation the resistance and work function are both quite high (megohms and a few e.v. respectively). Activation usually consists of further heat treatment in vacuo. It is accelerated by incorporating small amounts of electropositive metals in the base metal or by drawing emission current. In the latter case oxygen is evolved at a rate which

diminishes as activation proceeds. The activated cathode is seiiconducting and exhibits a low work function (iv 1 e.v.). It is, however, highly susceptible to poisoning by 02 or H20 vapor (but not by inert gases). 2. Early Explanation We shall skip hastily over the early pictures which were advanced to explain the behavior of oxide cathodes and summarize the situation as it existed in the mid-thirties (see de Boer1)). At that time it was thought that Ba atoms were adsorbed on active spots of surface of the cathode. The high electrostatic fields at these points were supposed to lower the ionization potential by a Stark effect so that the Baatoms could be thermally ionized at much lower temperatures than are required for free Ba atoms. Since this picture was not susceptible to a quantitative development, we shall not deal with it further here. 3. Simple Semiconductor Model With the development of wave mechanics and its applica& ion to solids followed by the further application of Fermi statistics, the situation became ripe for explaining the oxide cathode behavior in terms of a semiconductor picture and all the more recent explanations have been of this variety.* The qualitative idea is that activation removes *For a review of the situation as of 1939 and 1948 see references 2) and 3), respectively.

30 a sall quantity of ox-gen, leaving behind a stoichiomc tric excess of barti in the lattice. This is accelerated by contact with electropositive metals owing to their affinity for oxygen. (In fact interface oxide compounds have been found in many cases, but this is probably only a complicating but relatively unimportant feature.) Electron emission activates by electrolytic action, oxygen gas being evolved at the surface and free Ba being plated out at the metal base. A stoichiometric excess of Ba in the lattice represents a source of extra electrons which -an be freed more readily than normally bound electrons. The analogue i: an energy scheme is shown in the accompanying sketch. The quantity X (cal3ed the electron affinity of the crystal) represents the energy separation between the conduction band bottom of the conduction barnl and -. - (allowed localized energy states a poinW outside the solid. X Q.rises (Fe assoiated with (Fermi level) the excess Ba) from the attraction by the positive ions of the crystal for the free 3lect.c as and also from the presence of surface double layers. Since in the activation process an insulator allowed energy /// 7/// states for is converted to a semiconductor, normally bound electrons) this explains why the resistance and work function decrease so markedly.

40 4. Quatitative Theor for Simnle Mode The question then arises as to what success this picture has when put on a quantitative basis? There are two quantities we wish to calculate: I, the thermionic emission current density, and a, the electrical conductivity. We also Wish to know the dependence on temperature and activation of these quantities. A previous lecturer has already derived the general thermionic emission formila (see also Philips Technical Report No. 25, p. 277) I * A(l-r)T2e4A/kT = 2(rk ) r)T24/kT which is applicable here if 0 is taken to represent the energy separation between the Fermi level, -, and a point outside the cathode (i.e. B - X - O. With respect to cr, by definition o - neeb, the mobility b (drift velocity per unit fieldstrength in the field direction) is difficult to calculate, but since it is ne (the number of free electrons per unit volume in the material) which changes markedly with temperature and activation we shall focus attention on it. A previous lecturer has shown already that ne 2(2rmekT)3/2 e/kT e W and we shall also reprove this in a moment.

5. Thus, if we assme a semiconductor xbde. (incldlng a ralew of X ), we can determine the Fermi level position and in tus I and ne (whicb is proportional to a ). Consider the mdel x -. - - - At T " 0~K, let Nd nrbe of electrons/ in iirpity leve ml Then, since the space charge - O, u(L)f(B)dl - I (1) where n(e)dE is the niber of energy stats/'3 vlU en0ergiee between E and 1 + dl and f(e) - probability of ooeatiea a 1 Em *k 1 (2) for Fermi Dirac statistics integral into two regions. n(E) (see Seits), pp. 140-143). For E < 0 let n(E) at the 6-fOuntion (which apply to eleotros). Divide the For I > 0, assaing a free electron gas -,)3/2 1L/2 (3) impurity level be reprsented by a Dirao n(E) - IOd(E + A Cd) (4)

6, Substituting (3) and (4) into (1), Z(2me)3/2 / E1/2d d6(E + A Cd)dE % (5) 3 E/ + El/2 _ - + eS /kT + d The first term of eq. (5) cannot be directly integrated. However, if the Fermi level is several kT or more below the bottom of the conduction band, it is possible to neglect the 1 in the denominator, which is equivalent to the use of Boltzmann statistics. Taking out of the integral the constant quantity eQ/kT, defining a new variable x = E/kT (which yields (kT)3/2 outside the integral), we obtain an integral of the form Vx dx which has the known value T2. Thus, the integration ex of vq. (5) yields 4r (2me)3/2e/k.T(kT)3/2^.. + Nd I — 2 -e ( dc —- 2/- -Nd (6) or substituting P 2(2namekT)3/2 ~PeC^/kT~ -Ne/kT (7) Pe/kT = Nd (1 e-^cd/T + e/k Nde-4d/k * e-d/kT + e.T. e (8) *Note that from the following equations (a) ne = PeQ/kT (b) no = nee'/kT (Boltzmann eq.), where no = density of free electrons outside solid (c) (l-r)ne = I(2r/kT)'/2 (from kinetic theory) one can readily derive the general emission equation.

7. If the same procedure had been carried out with additional unfilled levels of density Na at a separation -A&a and a full batl at-., the following expression (needed later) would have been obtaineds (see reference 5) for complete details). d/kT Nde^Cd/ NaeC + Q (-/kT -A&/kT) e.Cd/kT + e/kT eAca/kT + e /kT J ne density of bound density of bound nh holes in donors electrons in acceptors I (9) where 2(27rmhkT)3/2 Q =. h3 Eq. (8sis a quadratic equation for e i, which is the quantity needed in the emission equation and in the equation for ne (and hence r ). The solution is e/kT = e'-(d/kT I + e^dT 1/2] 2 p (9a) There are now two interesting casest (a) (b) 4Nd acd/kT > > 1 Aed/kr (< I p In case (a) we have eCAT y e-Ard/2kT (10)

8. Substituting into the emission eq., I 2(2 e ) ( - r)T2. /i (2ne) / e(T)5 a eikI) N 1/2 J3/2 jlA 12 ( (aT) A//4 (1 - r) Nd/2 (- /2 +?)/kT'h3/2 (11) and also ne Pe = e^-A"d/2kT = /2 _ - 3/4 Ow~cd/2[t (12) In case (b) developing (1 + x) 1/2 1 + 1/2 x we have P efc/T = d Therefore I = 2(2.ek2) (1 - r)T2eh-AkT Ed2(2 h3) I3 2(2mNek3T)-V2 = (2)'l/2e(l - r)(kT)1/2 Nde' / and ne? ~Nd (complete ionization) The behavior of the Fermi level for this mdel may be seen in Fig. 1 which shows t vs. T for Acd = 0.2 e.v. below the conduction band, and for Nd a 1017, 3 x 1017, and 101/cm3. In the lower teperature.

9. region,case (a) is valid (Fermi level several kT's below conduction band and several kTts above donor level). At high temperatures where the Fermi level is well below the donor level, case (b) is valid. When the Fermi level is just at the donor position, the donors are fifty per cent ionized, as is iwanediately obvious from the definition 3f the Fermi level. Fig. 2 shows a plot of log ne against 104/T correpponding to the three Fermi level curves of Fig. 1. At low temperatures, in the validity range of case (a), eq. (12) is valid and the slope of the straight lines constitute a measure of A cd. At high temperatures where case (b) applies, complete ionization of the donors occurs, in accordance with eq. (14). 5. Test of SiDMle Theor In order to decide which of these equations to use and in order to apply them, it is necessary to know Nd, Acd, and X. These can only be obtained from experiment. Nd is determined by direct chemical analysis. Ba and n20 vapor - H2, which is measured volumetrically. In a well-activated cathode Nd is found to be 3 x'C17/cfm, which represents an excess of barium or about ten parts per million. If eq. (12) applies since b does not vary rapidly with T compared to Hn, then from a plot of log a vs. 1/T, one measures Acd. In early experiments log a' vs. 1/T plots gave single straight liles with a slope yielding a value for Acd of about 1.4 e." For these values of AC and Nd and over the normal operating temperature re, ige of the cathode, d e^d/kT > 106 P

11. and Kawamura6) and very detailed experimenrit by Hamnna, MacNair and White8' yield the results shown in Fig. 3 which implies that X is independent of activation. Thus, the simple semiconductor picture seems to have had marked svccess; it could account for the then observed temperature dependence of crand I and gave a not too unreasonable calculated value for I. It also implied X independent of activation, which is appealing because of its simplicity. It failed, however, to account for the gradual change in Richardson work function and apparent Acd with activation which has been generally observed (Mott's explanation of interaction between impurities seems unreasonable on the basis of the large interaction energy required (ca 1 e.v.) in view of the small magnitude of Nd), and it could not explain more recent data (that of Vink and Loosjes9)), and cf Wright-l) and Morgulis and Iagovdik2 ) to be discussed below. 6. Pore Conduction Hy3othesis The situation has been materially altered by the recent work of Vink and Loosjesd) who extensively investigated the conductivity over a wider temperature range than that employed previously. Their technique was to measure the conductivity of the configuration shown in the sketch by means of an A.C. Wheatstone Bridge, with a low applied voltage. Their results, which are shown in Fig. 4 as a plot of log resistance vs. 1/T, indicate three separate regionss I (between about 600 and 800~K) of lou slope, II (between about 800 and 10000~K) of steeper slope, and III a part of gradually diminishing slope (above about 1000~K). The slope in regions oxides?/e \ thermocou~pks

12. I and II decrease progressively with activation. (In region I the slope can be as low as 0.1 e.v.). Previous workers covered small temperature ranges and this data is generally in agreement with most previous published data. They further measured i-V characteristics up to ca 500 V/cm. In region I the i-V characteristics were found to be linear, in region II they were curved toward the voltage axis, and in region III they were linear again. It is clear that the simple semiconductor model outlined above will not explain this data. The explanation given by Vink and LooRjes of their data stems from a consideration oi the effect of pores. The cathodes studied by them arp typical of commercial cathode ray gun cathodes made by spraying and are very porous (50-60% porosity). It is orly to be expected that at higher temperatures the pores will be filled with an electron gas due to thermionic emission and that this gas can contribute to the conductivity. Thus, one expects two parallel conduction mechanisms, through the semiconducting grains and through the pores via the electron gas. The latter may become important at high temperature because the effective conduction area as well as the mean free path increase greatly for this process. The slope of log R vs. 1/T curves are in accord with the notion of two parallel conduction mechanisms. On correcting the slope in region II for conduction mechanism I, it is found that the corrected slopes agree with measured work functions for all stages of activation (see Fig. 4). The contribution of the pores to the total conductivity can be estimated in an elementary way: in any electron gas, in thermal equilibrium

13. in the absence of a field, the electrons have a mean velocity v in all directions. When a field F is applied, the electrons (of charge e and mass m) are subject to an acceleration a in the field direction during the time t which the electrons take to cover their mean free path. a -SeF (15) m The mean increase in velocity Av in the field direction during the time t is AVs S gt (16) If Av << v, which will be so for small fields across each pore (or generally so in solids), then t. - (17) and 2m At the end of the mean free path, this increase in velocity is destroyed by collision. Therefore Av represents the mean drift of the electrons in the field direction and therefore the current density, i = pAv = paiP (19) where p = mean space charge density in pore. Thus, for low fields (for which the above calculation iswvlid), Ohm's law is obeyed and o- = P- (20)

L4 The space charge density p may immediately be related to the saturated emission current density I by way of elementary kinetic theorys (l-r)p I(2rm/kT)1/2 (21) factually Vink and Loosjes performed a much more sophisticated calculation for p taking into account the potential maximum existing inside each pore due to space charge. The result is not appreciably different from eq. (21) in region II). Combining (20) and (21), r - I(2T*kT)1/2 e (22 2mv ( Taking I = 10 amperes/cm2 at 1000oK (pulsed value), 2 = 2/ (2 ~ pore diameter), v 2 x 107 cm/sec (thermal velocity), we find r = 2 x 10-2 Slem"t. Observed values of or at 10000K for well —activated cathodes vary between 3 x 103 and 7 x 10'3 (latter is Vink's highest value). Hence calculated a- is sufficient as to order of magnitude to explain experimental results. Also note that or - I for small fields so that this explains why the corrected slope ~ work function. With respect to the curved i-V characteristics in region II, this is to be expected on the basis of the pore picture as may be crudely shown as follows. Returning to (16), sr = A t 2m If v << EV (case of high fields in pore), in limit t A- (23)

15. -V eF (24) 4- v 1g n (25) i = pF0 (26) This accounts for the curved i-V characteristics in region II. At higher temperature the more exact calculation of Vink and Loosjes including the effect of space charge gives rise to a potential maximum inside the pore which increases rapidly with T (Fig. 5). This makes the mean space charge density smaller than would be given by simple kinetic theory and in region III, cr lags behind the straight line characteristic of region II. Also, if the internal field gets more important than the applied field, t becomes independent of F and we return to (17) ad (20). This may possibly explain the linearity in the i-V characteristics in region III. Thus, Vink and Loosjes make out quite a convincing case for pore conduction in the cathodes studied by them (which were essentially commercial cathode ray gun type cathodes. The concept of dominant pore conduction at high temperatures has not yet been universally accepted, the mefi dissenters being Hannay, MacNair and White8). They have presented a number of arguments designed to show that pore conduction, while present does not constitute the primary mechanism. Of these arguents, the following two are probably the most cogent; 1. Treatment with excess methane which deposits carbon over all surfaces (even making the interior of the cathode gray) kills the emission without materially affecting the conductivity at high temperature,

16. 2. The calculated value of - using eq. (22) (taking I 2.3 i because of 1 atm. of He introduced to set an upper limit on Q ) and the observed value of I for their cathode (20 ma/cn2 at 1000oK)is 6 x 10'5 %-1 cml whereas the observed value of r- for the same cathode was 5 x 10'4 C- cm 1. The reasons for the disparity in the data obtained by Vink and Loosjes on the one hand and by Hannay, MacNair and White on the other are not yet clear. It is to be noted, however, that the configuration and activation method employed by the latter group are both quite different from conventional commercial ones and that their cathode was thermionically far less active than well-activated commercial cathodes (20 ma/cm2 vs. 10 amperes/cm2). Further theoretical interpretation, to be given below, will be based on the data of Vink and Loosjes. One of the main consequences of the Vink-Loosjes model (see referencel0) is that it is the slope of log or vs. 1/T in sgion I which is related to an energy level diagram and not that in region II. Thus, Acd should be as low as 0.1 - 0.4 e.v. In this case strong ionization above 800~K occurs (for example, withAcd = 0.2 e.v. and T = 10000K, 4Nb e /v.08) and if we stick to a simple semiconductor model, we are now dealing with case (b) -- i.e. eqs. (13) and (14). Note that now 4ihh X - 1 e.v. The calculated value of Ilooo1 K Iamp/l2 compared to the experimentalval of 10 ampere which re ents not unreasonable agreement.

17. 7. Evidence for -tYpe Conductivity It is now necessary for completeness to mention recent data of Wrightl) and Morgulis and Iagovdik2). These data pertain to all measurementsl) and thermal e.m.f. measurementsl2) from which one can obtain the sign of the carrier and with proper interpretation in simple cases, the density of charge carriers as well. Both groups of workers have reported p-type conductivity at lower temperatures reverting to n-type conductivity at higher temperatures. These data unfortunately greatly complicate the picture and, moreover, these data have not yet been generally believed. Indeed Wrightll) has very recently retracted some of his previous conclusions by Rating that the p-type conduction was "definitely foreign to the Ba-SrO system." 8. Latest Theory 13) A theory has Just been advanced by du Pre, Hutner and Rittner which attempts to incorporate into a single consistent picture a more complicated semiconductor model and the Vink-Loosjes picture so as to permit an explanation of many of the important observations on oxide cathodes, including the change in work function and conduction slope with activation. The theory includes the semiconductor model shown in Fig. 6 as well as the Vink-mLoosjes picture of the pore conduction mechanism at higher temperatures. The semiconductor model comprises a full band, a conduction band (separation equal to 1.7 e.v.) donors 0.3 e.v. oelow the conduction band, acceptors 1 e.v. below the conduction band

18. and X = 1 e.v. It is assumed for simplicity that there is a fixed density of acceptors in the cathode (due perhaps to lattice de-ts) and the classical interpretation of activation as a gradual 4ncrease in donor concentration is retained. As long as Nd < Na,the cathode is poorly activated; when Nd > Na, the cathode becomes well activated. The choice of values was effected as follows, the work function varies between 2 and 1 e.v. on activation. The lower value was taken as X and the higher one as the energy separation between the acceptor levels and a point outside the cathode; the position of the donor level was chosen to give the required low slopes of Region I. The full band was taken to be 0.7 e.v. below the acceptor level in order to obtain the maximum slope observed by Vink in region I for poorly activated cathodes. This makes for a thermal band separation of only 1.7 ev.3, compared to an optical separation of 3.8 e.v. Originally this was not considered a difficulty. Maximum Nd was taken from chemical data to be 3 x 101 cn, whereas minimum Nd ( 1017) and fixed Na (1.5 x 1017) were chosen by trial to give the best fit of the data. Both values are entirely reasonable as to order of magnitude. The expression for the conductivity is - a neebe + nhebh (27) In the absence of data concerning the mobilities, we have taken b -= bh and have neglected the temperature dependence of these quantities, which is probably small compared to that of n and nh.

19. Thus, - r % (n + 0 ) P 1 n, + nh ne = pe /kT e * "petkT and n Qe </T -E/- T) Thus knowledge of 4 permits an estimate of the specific resistance vs. activation and temperature. Similarly, because of the general emission equation I - AT2(1 - r)e( X - )/kAT knowledge of C permits a calculation of the emission current density vs. activation and temperature. The Fermi level was calculated numerically from eq. (9) for several values of Nd and for varying temperatures between 0 and U000K, and from this information r- and I were determined. CONDUCTIVITY Fig. 7 shows calculated values of log [ ne + n^) plotted as a function of 104/T for different donor concentrations, and hence for different stages of activation. The graph indicates that the model presented here predicts decreasing slopes in region I with increasing activation, in agreement with Vinkts experimental results. (See also Table I). In fact, low slopes occur for most stages of activation except the very poor ones, which is also in accord with Vink's data. (In concordance with

20. the Vink-Loosjes concept that the conductivity above about 8000K is primarily determined by conduction through the electron gas in the pores, the curves of Fig. 7 have not been extended above 800~.) Furthermore, the type of conductivity in region I can be either n- or p-type, as is indicated in Fig. 7 and in Table Ig it is evident that the model predicts p-type conductivity for the more poorly activated cathodes. For these cathodes, however, the conductivity at higher temperatures may become n-type since in region II the effective cross section for the electron current increases enormously and in addition the mean mobility of the electrons becomes much greater than that of the holes. Thus, these cathodes may show a p-n transition at about the same temperature where the transition from region I to region II occurs. On the other band, well-activated cathodes should always show n-type conductivity. THERMIONIC EMISSION The thermionic emission current was calculated, in the tear perature range from 800~ to 1100~K, from the general emission equation using the values of C(T) determined from eq. (9). These calculated currents were then used to make Richardson plots (log I/T2 vs. /T), and straight lines were obtained. Thus, the calculated values of the current can also be represented by I RichT2 ex(-P icKT). (28) The quantities, ARich, %Rich, and ILOOOoK, as determined from these calculations for different stages of activation, i.e. for different

21. values of Nd, are shown in Table I. The magnitude of 4Rich varies from 2.1 to 0.93 e.v.-with increasing activation, in good agreement with experiment. Similarly, the corresponding values of i check reasonably well wita observations, as may be seen from the calculated values of I at 1000~K. Moreover, a semilogarithmic plot of ARich vs. Rich for different stages of activation is essentially a straight li (see Fig. 8) and in good agreement with Veenemans' datal4). We wish to emphasize that since ARiCh and ich are constants independent of temperature, ich f x - (T) and therefore (29) Rich A as may also be seen in Table I. Thus, the temperature independent work functions, %Rich, obtained from Richardson plots do not measure directly the energy difference between the Fermi level and a point Just outside the eathode. On the other hand, there is a different technique for determining work functions, namely contact p.d. measurements. The f c.p.d.'s so determined are temperature dependent and actually measure the position of the Fermi level, for according to theory, fc.p.d4. X - t () and therefore 0c.p.d. i 0Rich

22. A plot of the variation of the Fermi level with temperature is presented in Fig. 9. A comparison of the values of 0c.p.d. as read from this figure for Nd " 3 x 1017/c3 with the two values of 0c.p.d. measured by Huberl) is shown at the bottom of Table I. The absolute magnitude of the calculated $c.p.d. and its temperature variation agree remarkably well with Huberts values, although the excellence of the agreement is, no doubt, fortuitous. In Fig. 9 note that in the temperature range from 800~K to 1100~Kt (T) is closely approximated by a straight line and can be represented by the formula C e o - a kT (30) Inserting this in the general emission formula, we get I = AT2 exp(-( X - o + a kT)kT) = AeaT2 exp(-X- )/kT. (31) Thus ARich Aea and Rich X -4 (32) This last equation clearly shows that $Rich may also be obtained by extrapolating linearly to 0~K the high temperature part of each C curve. Numerical confirmation of this statement is shown by a comparison of the extrapolated ih values in Fig. 9 with the results in collmn 5 of Table I. It may also be seen from Fig. 9 that whereas in a wellmactivated

23. cathode ficp d > hRich' the model predicts for a cathode, so poorly activated as to be p-type in region I, that Oc.p.d. < %Rich. At the same American Physical Society meeting at which this theory was first expressed publicly, Apker presented some results of his electron emission technique for BaO, showing that the Fermi level is about 3.7 e.v. above the full band at room temperature. Thus, unless one assumes the operation of a most unusual selection rulg our 1.7 e.v. gap would seem to be much too small. Since there is reason for preferring Apker's results to those of Wright or of Morgulis and Iagovdik the dilemma can be resolved by lowering the full band to a position 3.8 e.v. below the conduction band while keeping all other features of the model unchanged. Since the full band contribution was negligible anyway in all cases in the preceding calculation save in those cases dealing with p-type conduction, all of the previous results still stand except those dealing with p-type conduction. Thus, the combination of the armended semiconductor model with the Vink-Loosjes concept of conduction by an electron gas in the pores appears to explain in a natural way many-of the accepted experimental facts pertaining to conduction and thermionic emission of commercial (Ba-Sr)O cathodes.

24 9. References 1) de Boer, "Electron Emission and Adsorption Phenomena," Cambridge University Press (1935). 2) Blewett, J. App. Physics JQ, 668, 831 (1939). 3) Eisenstein, "Advances in Electronics. I. Oxide Coated Cathodes, Academic Press, Inc., New York (1948). 4) Seitz, "Modern Theory of Solids," McGraw Hill Co., New York (1940). 5) Hutner, Rittner, du Pre, Philips Research Reports., 188 (1950). 6) Nishibori and Kawamura, Phys Math. Soc. Japan Proc. g 378(1940). 7) Bien, Technical Report No. 73, Research Lab. of Electronics, Mass. Inst. of Techn., June 1949. 8) Hannay, MacNair, and White, J. App. Phys. gQ, 669 (1949). 9) Vink and Loosjes, Philips Research Reports, 449 (1949). 10) Rittner, du Pre and Hutner, Phys. Rev. 2, 996 (1949). 11) Wright, Nature 16, 714 (1949); British, J. App. Physics 1,150 (1950). 12) Morgulis and iagovdik, Report of the USSR Academy of Science L_, 247 (1948). 13) du Pre, Hutner, Rittner, Phys. Rev. 28, 567 (1950). 14) Veenemans, Ned., Tijdschr. Natuurk. 12, 1 (19J4). 15) Huber, Thesis, Berlin (1941).

eV 0 -.02 -.04 -.06 -.08 -.10 -.12 -.14 -.16 -.18 -.20 -.22 -.24 -.26 -.28 -.30 -.32 -.34 -.36 -.38 -.40 -42 -M 4 a.." EmAGO / it' ///' // CO(JDUCTNYI - ~~_. ~ _. _. ~~~_ i i^ _ _~_1i..~~~~~~-~~i ___J___J_____//_ _/1i,/I n>7//_ T'' —----— =. =. - b 3r l..,. -........DOFILE I. A_,' - I_ \1n,-,ol", 0 100 200 300 400 500 600 700 T ~K TEMPERATURE DEPENDENCE OF FERMI LEVEL IN SIMPLE h-TYPE - EMIONUCT0R 800 900 FIG. I

T*K 10. 1017 to15 0 10 20 30 40 50 60 70t IO/T DENSITY OF FREE ELECTRONS IN SIWLE h-TYPE SEMICOId@CTOR FIG. 2

CONDUCTIVITY IN (OHM-1 CM'1) Conductivity and emission upon activation of the (Ba, Sr)O, for a typical tube. FIG. 3

5.2 4.8 4.4 4.0 36 32 2.8 2.4 2.0 1.6 1.2 0.8 9 10 II 12 13 10/T 14 15 16' 17 _Ilr~rrr ~rrrl 18 FIG. 4

~~~~~-0.10 --- 0.4 -Q~u- -~~ — 0.3 - -- - - - -~-I -aw —- -- - 0 f 2 3 4 5 59441 -f The electron density and the potential between infinite flat emitting surfaces. Is = 3$82.101 A/m2, T = 952 OK, distance d = 5 p.

+1.0 w outside I x / /' / /G 0 conduction bond /. - - ~ ~ ~ ~ ~ I~~ AOb _ 4_ 1B3 m 4m m at m m A I Ha 4. 0' - 4mhimmI~~~~~~~~~~~~~~~inmmu..mqiilii~~~~~~~~~~~~~~m.~ -- donor levels -- acceptor levels 77 full band -1.7 FIG. 6

.t C 0.,. O O4/ T FIG.7

T C (T) (f- ar hl_'0~ Ria Idh I hIPooo I Eop I. IT I t E.g.! I.. 1 x 17/ 6o l -.97e 197 1ow pg/ l os2 mp o).76 p 70 -.96 1.96 800 -.95 1.95 900 -.93 1.93 112.10 1,105..0288 1100 -.88 1.88 ) iloo I ss l os 1.5 x 107 600 -.67 1.67 (.58 a 700 -.70 1.70 800 -.73 1.73 900 -.76 1.76 1i.50. 18.115 1100 -.81 1.81 ) II,- m mm 1.6 x 1 017 600 -.49 1.49 700 -.56 1.56 11 800 -.64 1.64 900 -.71 1.71 1.21.211.17 o1100 -.80 1.80 3 l017 600 -.36 1.36.12 a 700 -.41 11 J 800 -.47 1047 900 -.53 1.53.93.049 1.01 1100 -.67 1.67 j I _ I m m m,, f,,,.d, (uber)'o!Ld. (Chaluated) -- - I -womwelme I U - 640 1.46 ow 1.38 1.45 rw 1.38 TABLE I

J c.ci 100 10 I 0.1.01 8 Io 12 1.41.6 1.8 2.0 22 Rich. FIG 8

t /^ j/ z //// //// \, O'tt$/y // // /= / / / 4 / / // / 0 [ - -- -- -n_,,: -- -- I-!-:t.___ —_. | I _ DO_._ _____ LEV. -- _g.... r i **__~~ _I __us _ IE Le l. 0 *0' -8- -- -' - o Ioo0 too0 3oV 4050 SoW tOO? oo 00 oo P0oo uO0 TOK

25. II. PHOTOCONDIUTIVIT IN SEMICONDIUTOR I. antroductio Historically, the first discovery of a photoeffect in solids was made by We Smith in 1873 who noted a change in the electrical resistance of metallic Se on illumination. The early comercial photocells consisted of thin films of "metallic" Se deposited over two interpenetrating electrodes. These cells in time were supplanted by photoemissive and photovoltaic cells which had certain important advantages in operating characteristics, notably improved linearity to light intensity and improved frequency response. In fact commercial photoconductive cells essentially disappeared from the scene until World War II when important improvements were made in photoconductive cells, improvements stimulated by military applicationss secret signalling and passive detection of "thermal" bodies. These applications were made possible by the fact that the sensitivity of some photoconductive semiconductors, notably T12S, PbS, PbSe, and PbTe extend appreciably into the infrared. Additional applications utilized since the war are the use of PbS cells for sound reproduction and astronomical detection amd the use of all the Pb cells for infrared spectroscopy. 2, Expectations from Band Scheme The phenomenon of photoconductivity is immediately to be expected on the basis of the band theory of solids. Absorption

26. radiation raises electrons from the full band to the conduction band, leaving behind positive holes. Both electrons and holes constitute free charge carriers which can contribute to an enhanced conductivity. The situation is similar for impurity semiconductors except that only one type of charge carrier is released and that the magnitude of the absorption is less. In fact the photoconductivity problem could be phrased: "Why are not all non-metallic substances photoconductive?" The answer to this question is that in most cases the charge carriers do not remain free for a sufficiently long period to materially increase the conductivity; they may disappear very rapidly into traps (which is the important process in insulators, such as crystal counters, not to be discussed here) or by recombination with each other or with an "ionized" impurity level (which is the important process in semiconductors). Before delving further into the theory, some of the important experimental facts about semiconductor photocells (T1oS, PbS, PbSe, PbTe) will first be recited. 3 Exerimental Facts Thllous,Sulfide Cell This cell was first discovered by Case in 1917 and was relatively recently developed into a radiation detector of extraordinary sensitivity by Cashman. Fig. 1 shows a typical cell and electrode structure. Pure T12S is vacuum evaporated over the electrodes to a thickness of about 0.5/u. At this stage the photosensitivity is negligible.

27. Photosensitization is then effected by admitting 02 at a low pressure and heating the layer to a few hundred degrees C. This process increases the dark resistance and the photoresponse (defined as A I/Id) and changes the conductivity from n- to p- type (see Fig. 2 and reference 1). Both the photocurrent (AI) and the dark current (Id) are linear functions of the applied voltage. However, the photoresponse is non-linear with intensity of illumination (see Fig. 3). At very low levels of illumination with nmodulated light, the cells exhibit essentially a single time constant the value of which varies from cell to cell between 4 x 104 and 4 x 10'2 sec. at room temperature (see Fig. 4). An increase in temperature decreases the time constant greatly (in a particular wae changing T from 27~ to 750C, produced a decrease in X by a factor of 40), but this is obtained only at a sacrifice in photoresponse (which falls by a factor of 7 in the same range for that particular cell ). The spectral response exhibits a cut off at 1.3/u and a maximum at about 0.9,A. (See Fig. 5.) The same data expressed as an apparent quantum yield show that many charge carriers may pass through the layer per incident quantum of radiation. Lead Sulfide Cell This cell is prepared usually in a similar manner to the T12S cell but it can also be prepared by chemical deposition of a PbS mirror. Its characteristics are generally similar to those of T12S cells. An interesting correlation has been found6) between sensitivity and resistivity (see Fig. 6). Because of the lower intrinsic resistance, the

28f, electrode arrangement is different from the T12S case and provision is sometimes also made for cooling (see Fig. 7). Their spectral response extends considerably farther into the infrared with a cut-off at about 3.4y at room temperature, the cut-off wavelength extending further into the infrared with a decrease in temperature2) (see Fig. 8). The dependence on illumination intensity has been found to be the same as that of T12S cells in some cases and quite different (linear) in others (see Fig. 9). Lead Selenide and Tellude e Cells These can be made in a manner similar to that described above or by sensitization with the electronegative constituent. The latter 3) type of preparation has been developed by Simpson, particularly for PbTe cells. It is necessary to cool the cells to observe appreciable sensitivity. The spectral response is similar in both cases and extends out to about 6/1 at low temperatures (see Fig. 10). Again the threshold shifts to longer wavelengths on cooling2). 4. Energy Level Diagram In the case of PbS a careful study of the conduction mechanism has been made by Hintenbergei4leading to the following conclusions. Heating a thin layer of PbS in vacua causes slight removal of sulfur producing an n-type semiconductor. Heating in sulfur vapor produces a p-type semiconductor. The presumed stoichiometric composition shows a minimum in conductivity, but the substance is still in the class of semiconductors.

29. From the slope of the conductivity vs. 1/T data at low temperatures, it appears that the impurity levels are extremely close to their respective bands. Thus, the energy level diagram applying to this case is 1 l _ / / n-type or p-type o.38e.v. at 25~C for PbS / I /I 71 77 From the electrical properties, there is reason for believing that a similar diagram applies to the other substances as well, the band separation decreasing in the orders T12S, PbS, tPbSe. Further support for ~PbTe this kind of diagram in all c ases is found in the optical absorption coefficients measured in the region where the cells are sensitive. In all cases the absorption coefficients are of the order of 0l to 105 crDwhich is so high as to inply that all the atoms of the material participate in the absorption process and not Just the impurity atoms. These data also imply that the photoconductivity is associated with optical transitions from the full band to the conduction band and not from one impurity level to a band (or vice versa). 5. Photoconductivity Theory for Unsensitied Material Let us now attempt to see why the semiconductor, before photosensitization, is not appreciably photoconductive. We shall consider only an n-type semiconductor: the argument is analogous for a p-type

30. semiconductor. For simplicity we shall make the following assumptions (a) complete ionization of donors (which is reasonable in view of the closeness of the donors to the conduction band); (b) the layer is so thin that the intensity of light is not a function of depth within the layer. The density of free electrons in the dark at temperature T, we designate ned; because of assumption (a) ned - Nd. The density of holes, nh, will be small compared to nd because of the general relation nednhd =PekTQe(-/ -AE/kT) PQe E/kT constant (1) For T12S at room temperature, nedhd 1022. If Nd 10 1/cm3 (a reasonable impurity content), nhd 104/cn3. The small free hole density nhd is maintained in the dark kinetically by continuous thermal ionization and recombination. In equilibrium the rates of formation and recombination are equal. The latter rate will be given by the bimolecular recombination law dnh, dnhd... = B h B 2 dt form. \ d / recomb. Bddnhd (2) where B is the recombination probability. Under steady illumination with intensity J, the rate of formation of holes (and electrons) increases by an amount cJ, where c = number of charge carrier pairs created per second per unit volume under unit illumination. In the steady state the rates of formation and recombination are equals Bnhne = BNdnhd + cJ (3)

31. where rn and nE. are. the new equilibrium co:centrati.n. under conCj;:-'...,n of illumination, Since A ne < Nd, as will be proved in a moment, ne= Nd Therefore, BNd(nh nhd) = cJ (4) Anh A- = Ane BNa as the light creates electrons and holes in equal numbers. The photosensitivity, expressed as A I/Id, is then = Arnhevh + A eveve A _ IN I h Id nhdevhd + nedeved Since the optical.y released charges lose their extra velocity vory rapidly (<10'11 sec. for example {100 mean free paths C 1C"'I: traversed at rate of 107 cm/sec } ) by interaction with the la.tic, for practically all of their lifetime the drift velocity of pho4toreleased carriers will be identical with that of the thermally released carriers, i.e. vt = vd. Since this is only an order of magnitudic calculation, we shall take ve = vh. Also, since nhd < ned N and A ne =Anh, = 2cJ 6) The constant c may be readily calculated from the number of effective quanta/sec absorbed in a layer of thickness 6 c 6c mj - -- for J in/u watts/c^On

where f C fraction of the incident radiation that is absorbed and P = efficiency factor for the creation of charge carrier pairs. For example for T12S, f = 0.75,p, 0.9, d 5 x 10-5 cm and assuming P = 1, c = 6 x106 cx 1 3 sec'1 watt1 cm The recombination probability B is much more difficult to estimate but it is possible to determine an upper limit by assuming that every collision between a hole and an electron leads to recombination. In that case Bmax Av (8) where A is the collision cross-section and v the thermal velocity of the carriers. A may be estimated to be of atomic dimensions, i.e. 10-15 cm2 and v = 107 cm/sec at 25~C. Hence BmaX 108 cm3 sec 1. B will tend to be less than Bmax because in the course of recombination energy must be given up to the lattice and this is usually not readily accomplished because the probability of the lattice accepting the excess energy as a large number of small vibrational quanta is very small. (In bulk Ge, experiments indicate that B/Bmax' 10'4.) The situation is different, however, for the non-symmetrical situation prevailing at surfaces as the excess energy can be imparted to the solid as a whole and therefore in a thin photocell layer Bma may possibly not exceed B by a great deal. Using the above values of Bmax and c, and for a reasonably high intensity of illumination (J 1000/u watts/cm2) and a value of Nd = 10/cmn3,

33. A I.2 x6x106 x 13. 1-e Id 10-8 (1018)2 (compared to experimental value of say 25 Note that Aue = c~ 10o is K4 NF BN one of the original assumptions, now proven. Even if the above calculation underestimated the photoresponse by several orders of magnitude, it is clear that an intrinsic semiconductor with appreciable impurity content will possess a negligible photosensitivity owing to the recombination of the optically released charges with the high density of thermally released charges. It is also of some interest to estimate the time constant for the recombination process. This may be done as followss dnh = t BNd (nhd - ) = - Bd Anh (9) (a differential equation expressing the rate of disappearance of charge in a transient state). Since Anh nh - nhd d(nh) = dnh dt dt Hence, the rate of disappearance with time of the excess holes produced by light will be adCh:.- BNdAnh dt

34r. Integreting, InAnh n(nnh) t - BfNdt or (nL Anh (nh) B6t an exponential decay witt a time constant BNd ( Using the above mentioned values, T = 10 sec. again showing that the recombination proceeds so quickly that the average lifetime of the photoreleased carriers is negligibly small. 6. Photoconductivity Theory for Intrinsic Semiconductor Produced by Compensation of Imourities It is clear from the above argument that in order to improve the photosensitivity, it is desirable to reduce the impurity content. Although it is possible to remove foreign impurities from materials to an extent of a few orders of magnitude better than Nd = 108/cm3 discussed above, stoichiometric deviations are unavoidable. In most cases chemically undetectable quantities of such "impurities" may destroy the photosensitivity. One might imagine that the introduction of oxygen is simply a trick for effectively removing the deleterious influence of the impurities. if into an n-type layer (produced by vacuum evaporation), p-type impurities (due say to 02) are introduced in exactly equivalent amount, the result is

35. to convert the material into essentially an intrinsic semiconductor, either by direct recombination or by virtue of the fact that the electrons fall spontaneously from the donors (which were near the conduction band) to the acceptors (which are close to the full band). In this instance the thermal charge density, which is so important for the recombination process, is reduced to its minimum value for the chemical system under consideration; i.e., the intrinsic value of ned nhd It is therefore of interest to consider the problem of photosensitivity in an intrinsic semiconductor in much the same manner as that employed above. Again for simplicity we assume a very thin layer such that J is taken independent of depth. In the dark the density of electrons ned = density of holes nhd = nd. In the steady state with an illumination J. the recombination rate will be equal to the formation rate, is. Bn2 Bnd2+ cJ (13) where n - equilibrium density of electrons and holes under illumination. n = 2B j n nd An -nd + n2 + n = - 1 1* + cJ I (14) nd Bna2 ]d Eq. (14) is precisely of the form observed experimentally in all T12S cells and in many PbS and PbTe cells. IMreover, we may again estimate the constant involved, c Bed

36. It will be recalled (eq. (1)) that in general ned^d pQe /k For an intrinsic semiconductor, ned " d =, eNE/2kT (E5) For T12S at room temperature, Ad 3 x o10/cm3 Hence taking c again = 6 x 106, B = Bmnx r 108 and the above value of nd, we find that c 6x1016 70 B2 c 1~0- x 9 x lW02 which is to be compared to experimental alues of the order of 5. In view of the crude approximations employed in the calculation (particularly J independent of depth), this is to be construed as reasonable agreement between theory and experiment. We could in the same manner as before compute the time constant for the recombination process from the differential equation expressing the rate of disappearance of charge SIB B (nd2 - n2) (16) The detailed calculation (to be found in von Hippel and Rittner)) is much more complicated in this instance, but for the case of very low illuinnation level, the resulting expression for the time constant is substantially the

37. same as before: X' BnL =r 2 x 104 sec. (17) 2 Bnd The order of magnitude of T is not unreasonable in view of the uncertainty in B and furthermore eq. (17) shows immediately why X decreases with increasing T, as 2d' p e-IA/2k It is also easy to see why in this picture the apparent quanta yield can exceed 1. Each incident quantum creates on the average fP free charge carrier pairs. During their average lifetime, r, the conductivity is enhanced such that L b. extra charge carriers can flow through the material, where b - mobility, F = field-strength and d = electrode separation. Thus, the apparent quantum yield, 7 f PL,,~ b (18) d It can also be shown that (18) is consistent with (14). Taking f = 0.75 again, P = 1, X = 4 x 10'3 (average experimental value), b = 1 cm/sec/volt/cm, F = 500 volts/cm d =.1 cm, we find rt = 15, in good agreement with experiment. Note that this picture also explains the observations that heating in 02 increases the dark resistance and the photoresponse, that the type of conductivity changes from n- to p- type (due to some excess 02), and that the photocurrents and dark current are linear functions of the applied voltage,.

38. In short the picture of a uniform "intrinsic" semiconductor produced by detailed balancing of n- and p- type impurities seems to have great success in accounting for the presently known properties of T12S photocells. A picture of essentially this type, but in less refined form, was proposed by von Hippel and Rittner5) several years ago for the case of T12S. 7. n-p Barrier Picture Quite a different explanation for the properties of PbS cells has been advanced by Sosnowski, Starkiewicz, and Simpson6), who have proposed that part of the grains of the layer are n-type whereas the remainder are p-type. The inter-crystalline contacts between the two different types of grain are considered to constitute the controlling influence in the resistance. The picture of barriers between n-p contacts has been further developed by James9), who has stressed that a homogeneous semiconductor produced by careful balance between n- and p- impurities will become split up into a large number of tiny n- and p- type regions owing to random fluctuations in impurity concentrations. We shall not discuss here the details of the pictures proposed by Somnowski et al and by James; a detailed discussion of n-p contacts will, however, be included in the more general theory to be presented below. The most direct experimental evidence for the presence of n-p barriers is twofolds a) on scanning a PbS layer with a small spot of light, photo-e.m.f. ls are observed which vary in sign and magnitude from point to point in the layer (see Fig. 11) (Sosnowski, Soole, Starkiewicz7)); (b) from measurements of impedance vs. frequency, it is found that the

39. parallel resistance decreases with frequency, ostensibly due to the eapacitative shunting of the barriers (Fig. 12) (ChasmarS)). 8. Geeral Theory The method of preparation and properties of T12S, PbS, PbSe, and PbTe photocells are so similar as to suggest that a single explanation should apply to this class of materials. It is apparent that the two pictures that have been proposeds a) intrinsic semiconductor, and (b) n-p barriers, are mutually exclusive and in fact as a general explanation of photoconductivity in semiconductors, each is subject to difficulties. The first picture fails to explain the two experiments on PbS cells Just discussed and also carries the extremely stringent requirement that n- and p- type impurities balance each other ou exactly chat the maximum net impurity concentration anywhere in the layer be less than the intrinsic density of charge carriers (1016 in PbS and 10 }cam in T12S at 3000K). The second picture will not account for the bimolecular recombination law that has been observed in T12S, PbS and PbTe photocells. A more general explanation has recently been advanced by RittnerlO), an explanation which follows naturally from one method of preparing the photocells and which reduces in limiting cases to essentially pictures (a) and (b) while avoiding the difficulty of the exact balancing of impurities. It is perhaps not unreasonable to assume that the following events occur in the course of fabricating photocells by vacuum evaporation and subsequent sensitization. During vacuum evaporation of the material

40. to form a thin layer, a slight loss of the electronegative constituent occurs, giving rise to an n-type semiconductor in which the photosensitivity is extremely small owing to the rapid recombination of the electrons and holes created optically with the thermally produced charges. Subsequent heat treatment in the presence of the electronegative constituent or oxygen converts portions of the surfaces of the grains into p-type material thus calling into existence randomly distributed local n-p transition regions. As the "oxidation" proceeds further, the n-type conducting paths become more and more disrupted by the p-type regions until a point is reached where all charge carriers travelling between electrodes have to pass through some of the n-p transition regions. With still further "oxidation," continuous threads of p-type material of negligible photosensitivity are formed and these grow progressively thicker, until in the limit the layer may become completely p-type. The properties of the photocell layer are determined mainly by those of the transition sgion which in turn depend upon the detail of the impurity distribution. Fig. 13 illustrates the sort of impurity distribution to be anticipated in the sensitization process outlined above, i.e. the interpenetration of an n-type region of relatively constant donor concentration with a p-type region in which the acceptor concentration tails off with distance. To the left of line 1 in Fig. 13 some of the electrons from the donors fall spontaneously into the acceptors, completely filling the latter*. Since the net donor concentration remains high, the material is n-type. To the right of line 2 all of the donors are emptied of electrons by spontaneous transitions to the acceptors,* but since the net *An alternative possibility, having essentially the same consequences, is the mutual annihilation of donors and acceptors by recombination.

41. acceptor concentration is high, the material is p-type. Between lines 1 and 2, the net impurity concentration is either zero or extremely small, and this transition region behaves essentially as an intrinsic semiconductor. The thickness of this quasi-intrinsic region increases with temperature because of the tendency of the Fermi level to merge with the intrinsic line at high temperatures (see Fig. 14). It is also larger the more gradually the concentration of p-type impurity varies with distance in the transition region. Thus, in general, a quasiintrinsic region is to be expected, the thickness of which may vary widely depending upon the chemical and heat treatments employed and upon the operating temperature of the photocell. Mbreover, the equilibrium condition that the Fermi level be everywhere the same requires transfer of electrons from the n-type region to the intrinsic region and from the intrinsic region to the p-type region. Thus, space charges are set up whicd correspond to potential barriers for the passage of charge carriers. The situation is illustrated by the energy level diagrams of Figs. 15 and 16 which show two limiting cases, one where the thickness of the quasi-intrinsic region is zero (a) (Fig. 15), and one where it is large (b) (Fig. 16), compared to the thickness of the space charge region. Although intermediate cases are of great interest we shall for simplicity discuss only these limiting ones. Case (a) - Sharm n-p Transition (Fig, 15) In a perfectly sharp contact between n- and p- type regions, the establishment of equilibrium requires that electrons be transferred from the n- to the p- type material in the neighborhood of the contact. This

42. creates a positive space charge iin the n-type region and a negative space charge in the p-type region, corresponding to a variation of potential which, in the present instance, is continuous across the plane of contact and which obeys Poissonts equation in boxh regions. The height of the (rectifying) potential barrier so created is equal to the difference in the Fermi level positions which would obtain if the n- and p- type regions were separated. This height can vary from zero (high temperatures, low impurity content) to about the energy separation between the bands (low temperatures, high impurity content) as may be seen from the calculated values of the Fermi level for PbS (Fig. 14). With reasonable impurity content (ca 1017 - 1019/cm3) the resistance of such a potential barrier can greatly exceed the resistance of an impurity semiconductor of comparable thickness. On exposure to steady illumination, electrons are excited from the full band to the conduction band everywhere throughout the material. In both the n- and p- type regions far from the plane of contact, the electrons ardpositive holes created optically disappear so rapidly by recombination with the thermally produced charges that the net increase in charge carrier density is extremely small. However, electrons and holes produced in the space charge region are rapidly separated by the strong electric field; electrons are drawn into the n-type region and partially neutralize the positive space charge, whereas the holes are drawn into the p-type region and partially neutralize the negative space charge. Consequently, the height of the space charge barrier and the corresponding D.C. resistance are lowered. It will be noted that for each pair of charge carriers created optically and separated in the space charge

43. region (photovoltaic effect) many charge carrier pairs can pass over the barrier (photoconductive effect). On removing the illumination, the system will spontaneously return to its equilibrium state in the dark with great rapidity by thermionic emission over the barrier of the excess charge. The following behavior is expected of a photocell which may be approximated by a large number of sharp barriers of the type Just described shunted by thin well-conducting threads of n- or p- type material. The D.C. resistance will appear to be ohmic and will be determined at high temperatures by the barriers and at low temperatures by the thin conducting threads. The D.C. resistance will be considerably higner than the A.C. resistance at high frequenciesg the former will be appreciably lowered by radiation but not the latter. The photoconductivity can be shown to be a linear function of the intensity of radiation up to very high levels for diode theory. The response time will probably be determined by the product of resistance and capacitance of the photocell. Case (b) - Gradual n-p Transition (Fig. 16) If the quasi-intrinsic region is much thicker than the space charge region, the potential barrier becomes split into two halves. Electrons and holes need only surmount the smaller barriers in order to recombine with each other. Uider these circumstances the barrier resistances may be negligible with respect to the resistance of the quasiintrinsic region in which case the properties of the latter will dominate The theory then reduces to that giveL above for an intrinsic semiconductor.

44. The following behavior is expected of a photocell which may be approximated by a large number of diffuse barriers of this type, shunted by thin threads of well-conducting material. The D.C. resistance and A.C. resistance at high frequencies will be the same and both will be equally affected by radiation. The resistance-temperature behavior will be similar to that of a homogeneous intrinsic semiconductor containing impurities. The photoconductivity will be a non-linear function of the intensity of radiation, following the bimolecular recombination law. The response time will be determined by either the recombination relaxation time or by the RC time constant, whichever is the longer. The preceding discussion has stressed the extreme differences in properties resulting in two limiting cases. Obviously all shades of intermediate behavior are possible in actual photocells, for example, appreciable barrier contribution to the D.C. resistance and non-linearity with radiation intensity. There is evidence (linearity with J, A.C. measurements of Chasmar) that some of the PbS cells which have been studied may approximate the sharp transition case. On the other hand, the ncrE-near response to radiation which has been observed in T12S and in other PbS and PbTe cells indicates more gradual n-p transitions in these layers. Independently of the thickness of the quasi-intrinsic region, the general picture outlined above is capable of explaining a number of additional observations which have been mentioned previously, for example, the sensitizing role of oxygen or of the electronegative constituent, the requirement for high photosensitivity that both n- and p- type impurities be present simultaneously, the change in sign of the thermal

45. e.m.f. coefficient with "oxidation," the correlation of nmaximu photosensitivity (expressed as I/Id) with minimun conductivity, increase in photosensitivity with a decrease in temperature, quantum yields exceeding unity and the occurence of photo-e.m.f.'s varying in magnitude and sign from point to point in the layer. 9. References 1) von Hippel et al, J. Chem. Phys. 4, 355 (1946). 2) Moss, Proc. Phys. Soc. 13, 62, 741 (1949). 3) Simpson, unpublished dissertation. 4) Hintenberger, Z. f. Physik,9 1 (1942). 5) von Hippel and Rittner, J. Chem. Phys. 4, 370 (1946). 6) Sosnowski, Starkiewicz, and Simpson, Nature 1_, 818 (1947). 7) Sosnowski, Soole, Starkiewicz, Nature 160, 471 (1947). 8) Chasmar, Nature 1, 281 (1948). 9) James, Science.10, 254 (1949). 10) Rittner, Science 11, 685 (1950). Technical Report No. 34 - Case No. 4500 7 ff?+-_ Written by: > V E. S. Rittner

30 MM NONEX GLASS TUBING \ 6MM NONEX GLASS TUBING AQUADAG GRIDWORK 4- ia- ----'I' -- FIG. I

TI (MUTS) OF HEATWN m OKVwC AT s00o A OEIXATI )a 0 19 19 _ ELATIVE bSE AT v25 C AT T.-Ca.ES RELATION BETWEEN DARK GCONDUCTIVTY, PHITORESPONS, AND THEMO-E.M.F. WITH IICEASNG COXIATION SAMPLE ^ I 2Ad I ( --- _ 1a _ I I _-A -A - _A A -.. O.10..t TiEOL. MLUVOJS,/),G A FIG. 2

I 16 I _ _ ^C ><^2.0 g 12 __X5 1o 1.0 8. M 0.5 0 10 20 30 40 50 60 70 4 1 l I I Microwatts/in. (color temp. = 2500 K) 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Illumination, microwatts/in2 (color temp. = 285(0 K) Photoresponse of Thallous Sulfide Cell as Function of Intensity of Radiation. v. Hippel, Chesley, Denmark, Ulin, and Rittner

~*unsuoa au}i aq}J jo sanleA Wuajaj!p joj Aauanbaij'sa asuodsai aA!WeaII *oD /SXImiOAO { 0AONIfO3 u aO OOfL O09 cO OOG w 00~ 00z 001

12 24 o 10 0 —-..-... l- 20 u} S~~~~~~~~~~~E _ _ _ _ __,^ __ —--— _ I II \ —----- 16 c E z 6 1 14 —--- A l8. -M --- Quantum yield ___ 2 o 1.5 microwatts 4 * 0.75 microwatt 0 1 0 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Wave length in microns Photocurrent and Quantunl Yield as Function of Wave Length for Twl Light Intensities (dark resistance 2.5 megohms; voltage 22.5 volts). v. Hipl)lx Chesley, Denmark, Ulin, and Rittner I I

6 5 C \ bI' I \ I I It A I I > \ -0- — 1 0 0-1 0-2 0-3'rhermoaelectromotive power (mV./~ C.) VAitIATION OF CONDUCTIVITY (FULL LINE) AND SENSITIVITY (Il1tOKFN 1.INE) WITHi THER.I0-ELECTRIC PO)WERt (HIOKEN~K LINIE) WITHI THERMIO-ELIECTKIC PO(WEH~ FIG. 6

II 11 I1 II Single-Walled and DoubleWalled Lead Sulfide Cells. Cashman FIG. 7

C I m 0 0 aV v:) 3 09 C X o c, t V)

3.2 2* 2.4 20 4 12 a. RESPONSE OF - i I COVER 2 CETROI.......... I.... i........... i.........I LEAD SULPHIDE CELLS TO ViS TO VISIBLE LIGH1 (color temperature * 2850 K ) r -i _ _ ____ i___ I I IDUAL CELLi DUAL CELL OI I CELL,701 I I I 3 CETRON CELL* m02' I. ~~~~~ — - —.. —— i' I I t t.I I t II I i I I ~ ~ ~~~~~~Ij Ir I I ~ ~~~~~~~~~ I i~~~ - -- ~- -~~ — ~ —-~~~ —---— ~~ -t~.j — ~ 1IIll r~~~~~~~~' i / I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:.. r ~~~~ ~..~..r.....i:~:...:.~ -........ ~si ~~ " i~-;S;','~i'.i ~ - t..'-".r... I-~;'~:'""'"" ~~~~.t~. o.~;- ~ t.. r. O ~-.~~~~~ _.... 4.:. ~I:,.10 2.0 3.0 40 5o 0 6.0 O 80...10 INCIDENT RAOIATION DENSITY. M1LLIWATTS/ CM' INCOiENT'RAOtATION' WENSITY. —" MII'WATt c/ M 11 12

LL 4', in arf~: -:r~.: ~

mnV 3 I 0 -I -2 SPOT 5SZE O0 mm. FIG. II

107 10. ------------------ -—. Isj I4 10 10' 0 10 20 30 40 50 60 Frequency (Mc./s.) Curves 1 and 2; 1945~ K., cellin darkness (1), iluminated (2).,, 4;2970 K.,,,,,,, (),,, (4). FIG. 12

n - TYPE REGION QUASI - INTRINSIC REGION1 p-TYPE REGION I I I C( ACCEPTOR )NCENTRATION I'DONOR CONCENTRATION I I I I I I I I I 2

l/il 7'0.k -0.12 -0.16 C,ev -0.20 -0.24 -0.28 -0.32 -0.36 -0.40 -0.44, 300 400 600 VARIATION OF FERMI LEVEL WITH TEMPERATURE AND IMPURITY CONTENT IN LEAD SULFIDE FIG. 14

SI'91. I I I I I I I I z __ C) 0 c 0 z >1C zr or B I II I I I I B

I l I a. C) I 0 t*A- I -o t~ s ~II C I I FIG. 16