KINETIC THEORY OF ADSORPTION AND DESORPTION OF GASES
ON SEMICONDUCTOR SURFACES
Vin-Jang Lee
ABSTRACT
In this report the rate equations for adsorption and
desorption of gases are derived on the basis of a charge transfer
model. The rate equations for adsorption on different types
of semiconductors are compared with-'da-ta fron the literature.
The observed changes..n electrical con'duotivity and work function
during adsorption are atIo explained squan.ti'tatI:velyo
This work has been supported by Texas Instruments, Inc.

CHAPTER 6
KINETIC THEORY OF ADSORPTION AND DESORPTION
OF GASES ON SEMICONDUCTOR SURFACES
INTRODUCTION
The rate processes of adsorption and!/or desorption of gases or
solids have been studied by both chemists and chemical engineers for
over three decades as a means towards the understanding of heterogeneous catalytic chemical reactions. With the advent of semiconductor
technology, a new field of research, namely the semiconductor surfaces,
was brought in with new vitality and new tools of experimentation. This
latter research not only has provided a good quantitative understanding of
the electrical properties of semiconductor surfacess, Abut alsd ihas- e-stablished
the gas-surface interaction via "charge transfer adsorption, " which
generates a space charge region, (S,. C. R.), in the semiconductor.
The simultaneous measurements of the rate of variation of
some electrical properties of a semiconductor surface, (e. g. the work
function or surface conductivity), and the rate of gas adsorption have
provided new insights to the understanding of the rate of adsorption on
semiconductor surfaces. Although the "charge transfer" hypothesis for
adsorption and/or desorption of gases on semiconductors has long been
postulated and considered by many authors, a quantitative check
which permits the direct association between the rate of change of
electric properties of semiconductor and that of gas adsorption has been
lacking until recently. At the 1960 Prague Conference of Semiconductor
(7)
Physics, Enikeev, Roginsky and Rufov reported detailed measurements
on the rate of change of work function, A th' and the rate of gas
adsorption, which can be summarized in the following statements.
For accumulation adsorption, i. e., an accumulation S. C. R.
is created during adsorption; e. g. oxygen (acceptor) on NiO (p-type
semiconductor):

Af th cc log t (6. 1)
AO cc tl/m (6.2)
AOth cc log A (6.3)
For depletion adsorption, i. e., a depletion S. C. R. is created
during adsorption, e. g. oxygen (acceptor) on ZnO (n-type), or MnO2
(n-type).
A th cc logt (6. 4)
Ae oc log t (6. 5)
A th cc AO (6.6)
where "t" is time, AO = e - 0O, 0 is the initial gas up-take
_ 0
which is dependent on the preparational procedure. These observations
(8) (9) (10)
agree with those of Barry and Stone, Linde, Sebenne and
Melnick, (who present both adsorption and electrical measurements,
(z)
but contradicts those of Engell and Hauffe, whose data contains only
adsorption measurements without substantiating electrical measurements.
The results presented by Enikeev et al are in complete accord
with our conclusions reached in Chapter 4, that the space charge region
adjacent to gas-solid phase boundary dominates the gas-surface interactions on semiconductors. At the same time these results can not be
(12)
explained by the heterogeneous surface model, the site generation or
annihilation models (13-15) or the simple dipole layer model. None
of these theories predict or even assume that the rate laws of gas adsorption are associated with the space charge region or the typeness of the
semiconductor catalyst upon which the adsorption process occurs.
However, in addition to the affirmation of the charge transfer theory of
chemisorption and catalysis, all these experimental results further indicate the inadequacy of the present-day "charge transfer" adsorption theories.
For example, equations (6. 1), (6. 2), (6. 4) and (6. 5)(7) have never been

satisfactorily derived nor completely understood on a monolithic basis of
the charge transfer theory gas-surface interactions and heterogeneous
catalysis on semiconductors.
In this chapter, we shall formulate the rate laws for adsorption
and desorption of charged particles. The related rate of change of electric
properties of the semiconductor surface will be discussed.
LITERATURE SURVEY
Rate "laws" for adsorption and desorption of gases on solid surfaces
(1)
have been critically reviewed by Low in 1960. These rate "laws"!', or
more correctly, rate expressions, resulted from either theoretical considerations or experimental observations. It is seen from these reviews
that theoretical works devoted to the explanation of adsorption kinetics
far outbalance those devoted to desorption kinetics.
For adsorption, two kinds of empirical rate laws are observed,
namely, the power rate law, 8 cc t/ (18) and the logarithmic rate law,
(19)
a cc log (t + to) So far there is no theory which can provide a mono0
lithic explanation for both of these observations.
In recent years, the logarithmic rate law has been in the limelight.
(1)
Many theoretical models have been proposed for its explanation. Perhaps
never before have so many people explained so little. Thus, Low wrote,
"It suffices for the present purposes to state that none of the models
appears to be satisfactory.... As a consequence of this, the use of a
particular chemisorption mechanism is almost a matter of personal preference
until much more experimental and theoretical work has been done and an
adequate model emerges. "
Among the models which are pertinent to the adsorption and/or
desorption of charged particles are the "charge transfer models" of
(2-6, 8 11)
chemisorption. The general development of this charge transfer
theory of chemisorption and catalysis on semiconductors has been reviewed
in Chapter 5. Several of these authors have considered the kinetics of
adsorption of charged particles (molecular ions or atomic ions). We

shall review these theoretical rate laws for the adsorption of ions, or
adsorption processes which include ions in one of the critical steps.
(2, 3)
Engell and Hauffe have postulated that "the rate-determining
step is the electron transfer between the adsorbent and the adsorbate,
the work function will be increased with increasing coverage of the
surface, since the energy barrier, to be overcome by the electrons moving
from the solids to the adsorbate, will be increased with increasing coverage
of the surface." With this assumption, a rate equation equivalent to the
following is obtained,
d KH exp.-q (UH - AOH)//kT (6. 7)
where qUH is the height of the energy barrier at the beginning of chemisorption ([ A-] = 0), and qa H is the "difference between the work
functions for a free surface and one occupied by adsorbed particles."
The pre-exponential factor, KH, is "-the frequency factor of the chemisorption, " which is proportional to the fraction of electrons that are in a
state of transition from a lower to a higher energy level, which was
assumed by Engell and Hauffe to be constant "at least for the start of
chemisorption".
With the above mentioned postulates, Engell and Hauffe derived
a rate law for the adsorption of oxygen on nickel oxide, NiO. Engell and
Hauffe evaluated AO H by solving Poisson's equation in one-dimensional
form for an accumulation space charge region; i. e., oxygen (acceptor)
on NiO (p-type semiconductor). However, due to their mathematical
difficulties, they did not obtain an explicit function of the diffusion
potential, VD, in terms of surface charge. Their VD can be shown to
be Y /q in the notation we have been using from Chapter 2. In addition
to the diffusion potential, they further assumed that there was a dipole
layer on the semiconductor, NiO. They gave I H in the following
equivalent form:
A~,s = - a~, 47.q.[ A-] - Vg (6.8)

where aH = constant. The diffusion potential was expressed as
V = kT$2I [ A [1 2 (6. 9)
D q E (p ) V
It is clear that they did not obtain an explicit function for VD
Equation (6. 8), as presented in reference (2) as Equation (11), is
correct; the same equation was presented in reference (3) as Equation (31),
but the negative sign before the first term was missing.
By substitution of Equation (6. 8) into Equation (6. 7), they
obtained the following equation, (again in equivalent form).
d = KH (E PB VD/Zr q) (1/[ A-] )
dt H BD
exp- (UH q E + 4+ q aq [ A-] )/EkT (6.10)
Equation (6. 10) is the correct form of Equation (33) in reference (3), where
the plus sign in the exponential term (UH qE + 4r q aH[ A-] ) is missing.
It is obvious that with Equation (6. 10), they could not obtain the
logarithmic rate law of chemisorption, which they claimed without justification, that VD in Equation (6. 10) could be replaced by a constant.
Granting that this could be done, Equation (6. 10) can be reduced to the
following form:
d [ A- (aH/[ A-] 2) exp (- PE [ A]) (6.10a)
dt H
where, H KH(E PB VD/2iZ q) exp (- UH q/kT)
2
PE = 4ir q aH/EkT (6. lOb)
Although Equation (6. 10a) can be integrated, Engell and Hauffe have not
shown the results of this integration. The present author has performed
the integration, the result of which is:
[A-] [A-] 2E [ A]+2Z expC7E [ A-]] aHPEt+2 (6.11)

Only under the condition that,
z >> PE [ A I 2,PE[ A-]
that is, when [A-] approaches zero, then Equation (6. 11) reduces to
the logarithmic rate expression which was presented by Engell and Hauffe
without the qualification that [ A-] must be small. Therefore
[A-] = (1/PE) In [ aH PE t/2 + 1] (6.13)
Equation (6. 13) could have been derived without even considering
the accumulation space charge region. This can be done by assuming
that the rate-limiting step is the charge transfer across the surface dipole
layer. Indeed this was assumed indirectly by Engell and Hauffe when they
stated that the PE term in the exponential part in Equation (6. 10a) above
dominates the relation between the rate of adsorption and surface concentration, [ A-]. In their original statement, "Die exponentiellen Glieder
werden auch hier wieder den cberwiegenden Einfluss auf die Beziehung
zwis chen Reaktionsge s chwindigkeit und Oberflchenkonzentration." In
regard to the surface dipole layer model, it has also been considered by
(16)
Higuchi, Ree and Eyring within the framework of the transient state
rate theory.
(7-10)
In view of the recent data and the experimental evidences
in Chapters 4 and 5, it is clear that the space charge region in a semiconductor generated by surface charges, the adions, is a dominating factor
in the phenomenon of gas-surface interaction on semiconductors. However,
for metals or at the initial stage of charge transfer adsorption on semiconductors, the surface dipole layer may be rate-limiting.
Weisz(4) has discussed the adsorption of negative adions, A (ads),
on n-type semiconductors. He expressed the rate of electron transfer
from the n-type semiconductor to surface acceptors by means of the following equation, (again in equivalent form):
dt =- (-n W + Ye)/kT (6. 14)

where Y' is surface potential in our notation, CW is a constant, "the
s w
frequency factor including the electron concentration and mobility" as
assumed by Weisz. He then expressed Y' in terms of A by the
s
relationship,' C [ A-]2 (6. 15)
Equation (6. 15) represents a special case relating surface potential as a
function of the surface charges, which has been pointed out in Chapter 2.
By combining Equations (6. 14) and (6. 15), the rate of adsorption
of A-] on an n-type semiconductor is:
d t = exp- (n B + C [ A-] 2)/kT (6. 16)
In deriving the equivalent of Equation (6. 16) Weisz assumed that
the rate-limiting step in the adsorption of adions is the "charge transfer
across-the space charge region"
In contrast to Engell and Hauffe, Weisz did not assume the
presence of a surface dipole layer. Equation (6. 16) was not integrated.
(5)
As a matter of fact, it was Germain who.wrote Equation (6. 16) by using
Weisz's original rate equation for electron transfer.
Assumptions similar to those of Weisz, which lead to Equation
(6) (11)
(6. 16), have been made by Morrison. Later, Melnick applied
Equations (6. 14) and (6. 15), but not Equation (6. 16) in his effort to
obtain a logarithmic rate law to explain his observations.
(8)
Barry and Stone have investigated the adsorption of oxygen
on zinc oxide. Their postulates were described by the schematic diagram,
F igure 10 of their paper, and stated the following:
"... at zero coverage there is an activation energy, qB' for
adsorption and a heat of adsorption (aB - 0 o B)' As adsorption progresses, each adsorbed particle acquiring one electron, a potential
barrier develops due to the depletion of electrons from a layer of the
semiconductor adjacent to the surface, increasing the activation energy
to (aB + VB) and decreasing the heat of adsorption to (C - ^ B - V)....

They gave the rate of adsorption for low surface concentration by
means of the following equation
d[ ] = AB exp (]B + VB) /k (6. 17)
dtB B B
where AB = constant
VB =[0] ( 2 kT) (6. 18)
= ----- (6. 18)
B,=[O-] 2as TE nB
"VB" was obtained by solving the one-dimensional PoissonBoltzmann equation for low surface ion concentration, i. e., qVB/kT < 1.
Except for a factor of Af, Equation (6. 18) was rewritten in the following
form,
d t = As exp{( B[O] 0 (6. 19)
Equation (6. 19) was discussed by saying: "it is interesting to
note that this is formally identical with the Roginsky-Zeldovich equation
which we found to be accurately obeyed for the rate of depletive chemisorption on ZnO "whereZ:-fnhO _is a sample of zinc oxide which has
1J' 1
the lowest excess Zn atom concentration, according to the authors.
In view of the above derivations and assumptions, Barry and
Stone's model is similar to that of Weisz, except for the low surface ion
concentration restriction.
(20)
More comprehensively, Garrett has made use of the Hall(22-24)
Shockley-Read model for trapping of carriers in a semiconductor
to write down the rate of charge transfer between the adsorbate and the
semiconductor. The adsorbed particles, donor or acceptor, are treated
as surface "impurity centers" or "trapping centers". This approach is
consistent with the Krusemeyer-Thomas paper(38) on charge-transfer
adsorption, which has been discussed in Chapter 5. However, Garrett
did not apply the rate equations of charge transfer to formulate the rate
equations for adsorption and desorption of charged particles, even though

such an approach is perhaps more logical than using it to treat unimolecular
reactions directly, as was done in his paper.
Garrett has also discussed the location of the donor or acceptor
energy level. He pointed out that "the potential energy of the atom, in
its neutral and in its ionized state, will be grossly affected by the
proximity of the surface". The Auger electron emission was cited by him
as qualitative evidence.
However, such a "proximity effect" of a solid surface can be
equally understood by considering that the dielectric constant in the
proximity of the solid surface might be increased. Consequently the
ionization energy or electron affinity of an adsorbed atom will be changed
(21)
accordingly.
From this brief survey, it is seen that a comprehensive treatment
of the kinetics of adsorption and desorption of charged particles is still
lacking. For the rate of charge transfer adsorption or unimolecular reactions,
the aforementioned works have the following points in common:
I. Charge transfer between the adsorbate and the solid adsorbent,
a semiconductor, is always assumed to be the rate-limiting step in
adsorption and/or desorption of gases.
II. The charge transfer process is activated, like that of thermionic emission of electrons. The wave mechanical tunneling process was
not postulated.
III. Poisson's equation in one-dimensional form has always
been applied to obtain the surface potential for a few special cases. The
surface potential acts either as a static potential to adjust the carrier
concentration at the surface, (Garrett), or as a potential energy barrier
to limit the charge transfer process.

DISCUSSION OF POSTULATES IN THE CHARGE TRANSFER THEORY
In the previous section, we have summarized the general approach
to the rate process of charge transfer adsorption and/or desorption in terms
of three postulates. We shall discuss the aforementioned postulates in
this section.
I. On the Charge-Transfer Rate-Limiting Hypothesis
The first postulate in the charge transfer theory of adsorption
and catalysis is that "charge transfer between the adsorbate and the
solid adsorbent, a semiconductor, is the rate-limiting step". Now our
first question: "Is this hypothesis plausible, or is it logically reasonable
in the light of the recent observations on the semiconductor surface during
adsorption? "
To answer this question, we shall consider the following adsorption of charged acceptors. Let An denote a molecule as it exists in gas
phase. The adion is A. In the process of adsorption as A, we can
visualize the following steps represented symbolically:
A (gas) A (ads) ) nA(ads) n( A + ne
n(1) n (2) (3)
(6. 20)
The last step represents the charge transfer step, which involves
the adatom A and an electron from the semiconductor adsorbent. Now
a priori any one of the three steps, namely, (1) the molecular adsorption
step, (2) the dissociation step, or (3) the ionization or charge transfer
step, can be rate-limiting. Now if step (1) or (2) is slow or the ratelimiting step, it will be difficult to understand why the rate laws of
adsorption are dependent on the typeness of semiconductor, since there
is no interaction with the semiconductors which involves the carrier
concentration. However, if step (3) is the rate-limiting step, the dependence of the rate laws of gas adsorption on the type of semiconductor can
be easily understood, since the carrier concentration of the semiconductor

is directly involved. Therefore, the charge transfer rate-limiting
hypothesis is qualitatively, or intuitively plausible.
II. On the Activated Charge Transfer between the Semiconductor
and the Adsorbaite
In the previous development of the charge transfer theory of
adsorption and catalysis, the charge transfer mechanism was always
assumed to be activated, like thermionic emission. The wave mechanical
tunneling process was not postulated. However, in semiconductor
surface research the charge transfer between the semiconductor and
slow surface states has also been postulated by the tunneling process
(25) (25)
by Kingston and others.Lax has pointed out the experimental
contradictions to such a postulate. The main argument for a tunneling
transfer process is that the slow changes in surface potential are
independent of temperature. In addition to the data cited by Lax )
(26) (27)
Morrison and, more clearly, Liashenko and Litovchenko have
reported the temperature dependence of the slow relaxation process.
In view of the above cited observations, the postulate of
activated or thermionic charge transfer is very plausible if not firmly
established.
III. On the Evaluation and Application of Surface Potential
by Poisson's Equation in One-Dimensional Form
The problem of using the solution of Poisson's equation in
one-dimensional form has been discussed in Chapter 5. Here the physical
situation is a different one. The difference arises from the fact that in
dealing with the "adsorption isotherm" the total charge in the space
charge region is time invariant. The space average diffusion potential,
(2 za)
Y(x), over the y-z plane at x, is equal to the time average in
the case of adsorption-desorption equilibrium. This can be seen by
considering the space average of the charged particle density p,
since at any point in the space charge region, the continuity equation is

presumed to hold
(p(x, Y, z)
v ~ j (x,y,z) = -q 6tp(x, z) (6. 21)
where the subscript "I " denotes a "local" point in the field, the space
charge region. If we average j, (x, y, z) over the y-z plane at x,
Equation (6.21) becomes
= -q (6. 22)
8x 8t
Now at adsorption-desorption equilibrium, the net charge transfer between
the semiconductor and the adsorbate is zero. That.s, j(O) = 0, similarly
j(x) = 0, and it follows that 6p(x)/6t = 0. Therefore, p(x), the space
average charged particle density at x is independent of time and the
problem is a static one as discussed in Chapter 5.
However, in treating the adsorption and/or desorption kinetics,
the net rate of charge transfer between the semiconductor and the gas
adscrbate is not zero. The left hand side of Equation (6. 22) is not zero.
This can be easily zeen by considering j(oo) = 0, but j(0) 0; i. e. the
net rate of charge transfer at the surface is not zero. Therefore j(x) varies
from the surface to the bulk, and 6j(x)/6x 0. Consequently p(x) is
a function of time, and we shall write p(x, t) from now on to denote the
time dependent space average charged particle density, to distinguish it
from the static case discussed in Chapter 5.
Now the question: "If the space average charge density, qp(x, t),
at any plane x is time dependent, is the surface potential, Y(0), obtained
by solving the static Poisson's equation applicable or sufficient to describe
the rate of charge transfer?"
The answer to the above question depends on the velocity of
electrons or holes transferred to or from the adsorbate, (or in other words,
the rate of charge transfer). If the velocity of the charged particle is non(28 b)
relativistic, it is sufficient to consider only the electric field,
defined by a scalar potential function, which satisfies Poisson's equation.

In general the field equation in place of Poisson's equation is
2 1 6V
2 - 2 = 4r q p~ (x,y, z,t)/E (6.23)
c 6t
m
where c = c/ V/', the velocity of the electromagnetic wave (i. e., light);
[L is the magnetic permeability of the medium (i. e., the semiconductor),
10
c is the ratio of e. m. u. to e. s. u. of charge, 2. 998 x 10
To appreciate why the rate of charge transfer has anything to do
with the velocity of light in a semiconductor, we shall consider the extreme;
that is c c co. Then Equation (6. 23) reduces to Poisson's equation of
m
an electrostatic field. One can also reach such a conclusion by a
consideration of the integrated result of Equation (6. 23), which is given
in standard text books, (29)
1 PgLx,y, z, (t - r/c)]
V (x',y',z',t) P= - dxdydz (6. 24)
$Y E r
where (x', y', z') is the field point, (x, y, z) is the source point; "r" =
[ (x - x') + (y - y') + (z - z') ] 1/2 The integration is to be carried
out with respect to (x, y, z).
The right hand of Equation (6. 24) is called the retarded potential.
That is, the contributions which the source makes to the potentials at a
point (x', y', z') in the field do not arrive till after a time, r/c. When
c - D>, Equation (6. 24) reduces to the solution of a static field. Now
what has this extreme case to do with our problem? To appreciate this,
-4
let us consider a cubic element with edge length, r = 10 cm, cut from
c
tile space charge region, with one face of the cube corresponding to the
original semiconductor surface. Then the longest linear dimension in the
-4
cube is 1/ v = 1. 7 x 10 cm. The face of the cube which is the surface
~c 2 -8 2
of the semiconductor has an area, r 10 cm. Assume that the area
c -8 ___-8 2 -15 2
of one unit of the surface square lattice is (3. 33 x 10 cm) = 10 cm.
Then the original surface face of this small cube has 10 lattice sites.
By assuming a monolayer coverage, the maximum ion density is that in

which all the acceptors on the surface are charged, as A, and, it takes
therefore 10 electrons. Since the saturation time is the order of minutes
(26, 33)
to hours, let us assume that it takes only one minute to fill the
monolayer with 10 electrons. That is, the rate of electron transfer
is -' 1. 7 x 10 electrons/sec., or on the average one electron is trans-6
ferred from the interior of the "cube" to its face in every 6 x 10 sec.
The maximum electron velocity across the space charge region is about
-4 -6
v = 10 cm/6 x 10 = 17 cm/sec.
e
Now assume that B~ = 1, E = 16, the magnetic wave velocity is,
then, c = (c/4) cm/sec. = 7. 5 x 10 cm/sec. Since the longest linear
m 4
dimension of the cube is 1. 7 x 10 cm, the magnetic wave created when
one electron is transferred from the space charge region to the surface
will reach every point in the cube in a time interval, At. less than
-14 -14
2. 3 x 10 sec. The time interval, 2. 3 x 10 sec., is the "time lag"
or "retarding time". If the magnetic wave velocity, c, is infinite
the "retarding time" would be zero. However, since a second electron
will not be transferred until 6 x 10 sec. later, which is 2. 6 x 10 times
-14
greater than the "time lag" of 2. 3 x 10 sec, the transfer of the second
electron is definitely affected by the electrostatic potential, i. e., the
diffusion potential, due to the previous electron transfer. The "time lag"
is inconsequential as far as the transfer of the second electron is
concerned. For the transfer of the second electron, the diffusion potential
can be obtained by the solution of the Poisson's equation using the charge
density before the second electron is transferred. Now let us inquire
further into a question: "Does the electron experience a field due to the
hole it left behind when the electron reaches the plane x = 0? "
To investigate this, we shall choose the field point (x'My', z')
to be a point on the face of the "cube", which was cut from the space
charge region. The face of the cube is on the plane x = 0o. Therefore
the field point is (0', y', z'), with y', z' on the face of the "cube"
Now let us imagine that one electron-hole pair was located at a distance

x from the surface, the electron is now moving toward the surface leaving
the hole behind. Since on the average the time interval for the electron
to travel from x to the surface bound by the face of the cube is 6 x 106
sec., ( = < xjv >), the magnetic wave will reach the field point at a time
interval less than (r + x ) / c < 2. 3 x 10 14 sec. Therefore the
c m
electron will also experience a field due to the hole it left behind as it
crosses the plane x = 0. Therefore we can take cm as infinitely large
so that the electric field is instantaneously adjusted as far as the charge
transfer to the surface is concerned. Consequently the second term on the
left hand side of Equation (6. 23) can be neglected. The resulting V 2V,
when the space average over the y-z plane at x is taken becomes
2 2
d V/dx. The result is Equation (6. 26).
Another numerical estimation based on a different concept(30)
will lead to the same result. For this analysis, Equation (6. 23) is
averaged over the y - x plane at x and t to obtain V (x, t),
2 2
2 V(x, t) - 2 2 V(x,t) = -(4Tr q/E) p(x, t) (6. 25)
2 2 2 P
6x c 6 t
m
(31)
By numerical analysis Equation (6.25) can be written as
V(x' + Ax, t) - 2V(x', t') + V(x' - x, t) (6. 25a)
(6. 25a)
(Ax)2
V(x',t' + At) - 2V(x',t') + V(x,t' - At) = -4rq/E) p(x,t')
2 2
c (at)
m
Now we shall choose x' = -L /2 and t' = At /2, ax = L /2 and
At = at /2 where L and at are the depth of the space charge region
and saturation time, respectively. Then since V(-Ls, At ) = 0 and
V(L /2, 0) = 0, Equation (6. 25a) becomes
V(O, at /2) - 2V(-L /2,t /2) V(-L /2, At ) - 2V(-L /2, At /2)
(L /2)z c Z(at /2)
= - (4r q/E) p(L /2, At/2) (6. Z25b)
5

Now since, V(0, At /2) V(0, At) and V(-L/2, At) < V(0, t )
the numerators of the two terms on the left hand side of Equation (6. 25b)
are about equal in magnitude, the relative magnitude of the two terms on
the left hand side of Equation (6. 25b) is determined by the magnitude of
the denominators of the two terms. If the second term is to be negligible,
we must have
(Ls /2) << c 2 (At / 2)
That is, L << c At (6. 25c)
s m s
Now since, L = 10 cm, c =7.5 x 10 cm/sec, and At = 60 sec.,
s m c
-4 11
we have, 0 -<< 4. 5 x 10. Therefore, the second term in Equation
(6. 25b) can be neglected. Since Equation (6. 25b) is the difference representation of Equation (6. 25), it follows that Equation (6. 25) can be
approximated by
d V(x,t) = - (4r q/E) p(x,t) (6. 26)
dx
Consequently it is concluded that the answer to the question
posed at the beginning of this discussion is affirmative. The solution of
Equation (6. 26) is sufficient for this rate process. Therefore the previous
treatments of the charge transfer problem by Garrett 2) Weisz and
others are sufficient for the problem under consideration.
STATEMENT OF MODEL FOR ADSORPTION AND DESORPTION
OF CHARGED PARTICLES
In the last section, we have discussed the plausibility of the basic
assumptions in the kinetic theory of adsorption and desorption of gases on
semiconductors. The assumption of a charge transfer rate-limiting
process implies that the rate process concerned in this theory is the
adsorption and desorption of charged particles. The model can best be

represented in the following generalized symbolic equations.
I. Adsorption of Charged Particle Before Dissociation
For acceptors:
A (gas). An (ads) > A (Ads) + e' A + (n-1)A
(6. 27a)
For donors:
D (gas) D (ad(a(ads) + e D + (n-1)D
(6. 27b)
II. Adsorption: of Charged Particle With Dissociation
For acceptors:
A (gas) ( A (ads) -- nA(Ads) - >nA + ne (6. 28a)
n n (ads)
For donors:
D (gas) ->D (ads) - nD(ads) > nD (ads) + ne
n n
(6. 28b)
III. Desorption of Molecular Ions
For acceptorsA (gas) "-' An(ads) - An (ads) + e (6. 29a)
n n n
For donors:
D (gas)' D (ads) <- Dn (ads) + e (6. 29b)
n n n
TV Desorption of Atomic Ions
For acceptors:
A (gas)' A (ads) = nA(ads) < nA (ads) + ne
(6. 30a)
For donors:
D (gas). D (ads). nD(ads)< nD (ads) + ne
(6. 30b)

where the symbol " _ represent fast steps, and the symbol "
represents the slow step or rate-limiting step. The implied assumption
in the "charge transfer rate determining" postulate is that the species
at either end of the symbol "'- I " are in equilibrium or "quasi-"
equilibrium with one another and with the gas phase. The charged
particles at the right end of the generalized symbolic equations are
not in equilibrium with the gas phase. They increase with time toward
the equilibrium surface concentration in an adsorption process or decrease
with time toward "another equilibrium" in a desorption process.
From this understanding, it is clear that the rate theory requires
that the physical situation be represented or approximately represented
by the above generalized symbolic equations. The theoretical model
requires the "presence" of the various uncharged particles adsorbed on
the semiconductor surface, and further requires that the uncharged particles
are in equilibrium or quasi-equilibrium with the gas phase. That is, the
adsorption process of charged particles is preceeded by a fast process of
adsorption of uncharged particles, which of course does not involve the
carrier concentration of the semiconductor adsorbent. This picture is quite
in accord with observations. Many authors( 3 reported observations
of initial fast adsorption, which precedes a slow adsorption. When gas
up-take and electrical conductivity of the sample are measured at the
same time, the "massive" initial gas up-take does not change the surface
(33,34)
conductance.,
The above statement combined with other postulates discussed in
the previous section will be used in the remainder of this chapter for the
formulation of the rate laws of adsorption and desorption of charged particles
on semiconductors.

ON THE RATE OF CHARGE TRANSFER IN ADSORPTION AND DESORPTION
OF CHARGED PARTICLES ON SEMICONDUCTORS
In the section on Literature Survey, we have discussed various
models conceived by different authors. The rate functions for charge
transfer across the surface "are most neatly and most generally written
down by making use of the Hall-Shockley-Read model for trapping in a
semiconductor", as stated and carried out by Garrett. Garrett's
Equations (4) and (5) can be written in the following form.
The rate of electron transfer from the semiconductor is the
sum of electron transfer from both the conduction band and the valence
band
R(') = Rc (4) + Rv(') (6. 31)
c n,A s ] n,A 1,A (6.32)
R (t) =[, A. - [A-] c, A s (6 33)
v pA1.A A[] p,AP (6.33)
Similarly the rate of electron transfer into the semiconductor can be written
as
R(4,) = R (~) + Rv(4') (6. 34)
c v
where
R (c) = [A-] cn Dnl D [A] cn D s (6. 35)
R ( = [A-] c DPS - [ A] cp, DP1 D (6. 36)
Equation (6. 31) is equivalent to Equation (5) in Garrett's paper,
which expresses the rate of electron transfer from the semiconductor to
the acceptor, A. The terms Rc (T) and R ("1) express respectively
the rate of electron transfer from the conduction band and valence band
to the acceptor. Equations (6. 32) and (6. 33) are written in a form which
is equivalent to Equations (3.8) and (3.9) in the Shockley-Read() paper.
it!s fairly obvious that Equation (6. 31) corresponds to the rate of adsorption of charged particles, A. Equation (6. 34) is equivalent to Equation

(4) in Garrett's paper. The terms R (L) and Rv($) express the rate of
electron transfer to the conduction and valence band, respectively. The
factors cA' p, A are constants; n,ps are the electron and hole
concentration at the surface; and nl A P1, A are defined by the following
equations:
n1,A =Nc exp(EA- E)/kT (6.37a)
PA = N exp(E - EA)/kT (6. 37b)
That is, nI A and P1 A are the respective electron and hole concentrations
when the Fermi level coincides with the acceptor level, EA.
The rate equation for charge transfer to and from donors can be
simply obtained by replacing [ A-] with [ D], [ A] with [ D 1, and
the acceptor level by the donor level, ED. Due to the similarity, we shall
treat the case of adsorption and desorption of acceptors only, the case of
adsorption and desorption donors should follow by analogy with that of
acceptors.
Now before we apply Equations (6. 31) to (6. 36) in treating the
kinetics of adsorption and desorption of charged particles, one more
inquiry has to be made. Namely, is the Shockley-Read model valid in
this case, since it was originally derived to express the rate of electron
and hole recombination via traps in the bulk. That is, the charge transfer
to and from the "trapping centers" was assumed to be in a three-dimensional space. In applying this theory to charge transfer between the semiconductor and the surface ad-particles, the charge transfer is only in one
direction. That is, only electrons which move in the x-direction and cross
the plane, x = 0 (the surface plane), can be trapped or emitted. Now the
question: "Does this unidirectional charge transfer affect the rate equations
for charge transfer as written down by Garrett, and reproduced as Equations
(6.32), (6.33), (6.35) and (6.36)?"
We shall show that the rate equations are not changed, i. e.
Garrett's rate equations are correct. To see this, we have to go back to
(23)
the original Shockley-Read model. Now let us follow the procedure

of the Shockley-Read paper, defining F(E) as the probability that a
quantum state of energy level E is occupied, and F (E) as the probability
that the state is empty. Therefore,
F(E) = 1/1+ exp(E -E)/kT?
F (E) = 1 - F(E) = F(E) exp (E - Ef)/kT.
p
E = E - Ys, the modified energy level in the space charge region.
v (E) = electron velocity in x-direction with energy, E.
a' (E) = capture cross section for electron with energy, E.
c
e (E) = emission cross section for electron with energy, E.
S(E)dE = number of quantum states per cm in (E, E + dE).
[ A] = number of unfilled traps per cm2
[ A] = number of filled traps per cm
Then, the gross rate of electron capture is,
gross electron capture rate = [ A] oc v S(E)F(E)dE
Rate of emission is,
gross electron emission rate = [ A- ] v S(E)F (E)dE
The net rate of electron capture from the conduction band is:
e F (E)
n P
dR(') = [ A] - [ A] c F() v (E)(E)E)dE (6.38)
c & c F (E) cx
n
where c = average of <v > <ac > for all E.
e = emission constant corresponding to c (see Shockley and
n n Read).
Equation (6. 38) corresponds to Equation (2. 8) of the ShockleyRead paper. Using the quasi-Fermi level concept as proposed by
Shockley and Read, Ef is written as Ef for the semiconductor and
E for the acceptor. At thermodynamic equilibrium,

Ef) = Eft) = Ef (6. 38a)
Furthermore, if we assume that the electron spin on [ A] is
uncompensated, the distribution function becomes
[A-]I
(6. 38b)
[ A] +[] 1 + (1/2) exp[ (EA - E f )/kT] (6.38b)
where E = E +Y
A A s
or
[ A] /[A-] = (1/2) exp[ (E - E )/kT] (6. 38c)
A f
When the electron transfer rate between EA and E is zero, then it
follows from Equation (6. 38) and the preceding definitions that
(e n [ A-] F (E) - (1/2) exp (EA E)/kT
(1/2) exp i (EA - E/kT <n (6. 38d)
Equation (6. 38d) is Shockley-Read's Equation (2. 9). Now substitute
Equation (6. 38d) into Equation (6. 38). At any condition we have
dR (') = i A] - (1/2) [ A-] exp [(EA - E (n) )/kT] o- v S(E)F(E)dE
(6. 38e)
Equation (6. 38e) is equivalent to Shockley-Read's Equation (2. 10), which
can be easily obtained by combining with Equation (6. 38b).
For a non-degenerate semiconductor Equation (6. 38e) can be
integrated following a procedure similar to that which was used in Equations
(4. 13) to (4. 18) of Chapter 4. For EA < E, the integration is from
v= O to v = oo. Then the result is
X X

R (1) = A[ A] - (1/2)[ A-] exp[ (EA - E()/kT]
C A fE
2 2
<~ > 4 k T exp - E - E )]kT (6 38f)
C L c f]Ik
where <a- > is average capture cross section for electrons from conduction
c
band.
Equation (6. 38f) can be written as,
A]= expl (B * -(n))/kT]4
c() = [ A] - (12) [ A exp (EA - E ))/kT]
* < a> (kT2ir mi) i N exp [E - E f(n )] /kT (6. 38g)
"1/2
Now (kT/ 2r m ) = <v >, the average electron velocity in x-direction.
x
If we write cn A = < c >-<vx >, Equation (6. 38g) can be written as
Rc() = [A] cnAs (1/2)[ A-] c N exp E E )/kT (6.39)
Since EA - EB = EA - E Equation (6. 39) reduces to
SineA C A c
R (1) = [ A] c An - (1/2)[ A-] cnA 1,A (6. 39a)
Equation (6. 39a) is the same as Equation (6. 32) except for the
factor 1/2, which takes account of the uncompensated spin on [ A-].
Therefore the Equations (6. 32), (6. 33), (6. 35) and (6. 36) should have the
following form
R ($) = [A] c n, - (1/2)[ A-] c n (6. 32a)
c,() [ n, A P1 A n,A A

R c (1/ )[ A-] cn Dn1 D [A]CnD s (6. 35a)
RV() = (/IZ)[ A-] cp DPs - [A] c D'P1 D (6. 36a)
For the remainder of this chapter Equations (6. 32a), (6. 33a),
(6. 35a) and (6. 36a) will be used to derive the rate equations of adsorption
and desorption of charged particles. Furthermore, for the adsorption or
desorption of molecular ions, [ A-] should be replaced by [ A], and
[ A] by [ An], etc. The final resulting rate equations can also be
obtained by the above replacement.
FORMULATION OF RATE EQUATIONS FOR ADSORPTION
OF CHARGED PARTICLES
In this section, the rate equations for adsorption of charged
particles will be derived. For convenience of presentation, space charge
regions are used to classify the subsections. The fundamental equations
for adsorption are:
dt[A] = R (~) + R (1) (6. 40a)
d [ D+] = Rc(4) + R () (6. 40b)
where R (t) and R (/') are given by (6.32a) and (6.33a); R (4.), R (4)
C v c v
are given by Equations (6. 35a) and (6. 36a) with [ A-] replaced by [ D]
and [ A] replaced by [ D+]
To save space, we shall treat the adsorption of acceptors only.
The counterpart, adsorption of donors, will be given without analysis.
Rate Laws Associated/With Accumulation Space Charge Regions
This subsection is further divided into adsorption on an intrinsic
semiconductor and adsorption on an extrinsic semiconductor.

Adsorption on an Intrinsic Semiconductor
We shall use Equation (6. 40) together with the following equations
from Chapter 2:
u = Y /kT = (L /n)/2[ D+] < 0.9 (2. 20)
s s m 1
u = Y'/kT = (L In.) /[ A] < 0. 9 (2. 20')
s s m 1
u YY /kT = In (L /ni)[D ] Z (2. 21)
u.s = Y'/kT = ln~(L /n)[A (2. 21')
For the convenience of presentation we shall divide this section
into two cases. The first case corresponds to u' represented by
Equation (2. 20') and is defined as the initial stage of adsorption. The
second case corresponds to Equation (2. 21') and is the high coverage
stagge.
In the initial stage, the reverse process, (i. e., desorption),
is negligible. Equation (6. 40a) can be written as
d [A-] =c [ A] n + c Pl,A (6. 41a)
dt nA s pA A L
Now let us consider the rate process a little more. As adsorption
starts, the surface charge [A-] increases. Equation (6. 26) says that
u s'(t) can be evaluated by [ A-] (t), therefore n (t) is a function of
[ A-] (t). Then Equation (6. 41a) can be written in terms of [ A-] from
Equation (2. 20'), which is a function of time.
dtA - = cn ni [A] exp {- (L /nI) I/2[A-+ ['A] pAP1A
(6. 41a')
where n, is the bulk hole or electron concentration. From our discussions
1
in the "Model" section, [ A] is a function of the gas pressure only.
Therefore in an isobaric process [A] is independent of time. In an

isosteric process [ A] is a function of time because the gas phase
pressure decreases with time, and Equation (6. 41a') can not be integrated.
It is rather unfortunate, because a large amount of reported data in the
literature were taken in an isosteric condition. Equation (6. 41a) is
miserable enough without experimentally introduced variations!
Now let us consider an isobaric process. The relative magnitude
of the two terms on the right hand side of Equation (6. 41a') determines
the form of rate law of adsorption. For example: if the first term is small,
the rate law is linear, i. e., [ A-] cc t. If the second term is small, the
rate law is logarithmic. The question becomes, "What determines the
relative magnitude of the two terms on the right hand side of Equation
(6. 41a')?" Of course, it is determined by the factors in the respective
terms!
Since c A and c A are the products of the average capture
cross section and the velocity, cn A is always larger than c A. For
n and P1 A' ni is determined by the bulk energy gap, E; P1 is
i' AA
determined by (EA - Ev) [ see Equation (6. 37b)]. That is, if EA is
close to Ef, ni will be close to P1 A' Therefore, when EA is close
to the middle of the energy gap, the first term on the right hand side of
Equation (6. 41a) is always larger than the second term, since c A is
in general much larger than cp A. Under this condition Equation (6. 41a)
can be approximated by
d [ A-] [ A] cn Ani exp 3 (Lm/ni) [ (6. 42a)
Equation (6. 42a) can be integrated under isobaric conditions in which
[A] = K (PA)l/n is independent of time.
aA
n
[A-] = (n/L ) /2ln + [A] cn (n Lm ) t (.41a')
1 rm n,A m j
For adsorption of donors on intrinsic semiconductors: the correspond<ing results are:

dt ] = (c n D/2) [ D]
n.,D lD
1/2 +b
+ (c ni/2) [D] exp- (Lm/n) / [ D+]. (6. 41b)
pD i mi
When R (1~) >> R (t), (the donor level is very deep), the integration of
V C
the exponential term gives
D+] (n,/)1/2 In + [ D] c (L n)1/ t/2'(6 41b')
1 m / pD m 1
In the high coverage stage u' = In(L /ni) [A] > 2,
and the general expression is obtained by making use of Equations
(6. 32a) and (6. 33a).
d[A- ] =c[A] c ni exp (- u') + c
dt n, A s p, A PlA
exp (u (6. 43a)
-jA] An cAnl A p+A ns'
In the case that R (1) >> Rc (l), i. e., the surface region is highly p-type,
Equation (6. 43a) can be approximated by
d A[A] =
-d[ A-3= CpAP1 A [ A] (cp,A/) [ (6. 44a)
Under isobaric conditions, where [ A] is independent of time,
Equation (6. 44a) can be integrated into the following series
+ 1 (L/2 A [ A] )[ A 3n+
n=O 3n1 +
[ A] cP,AP,At + const. (6.45a)

The integration constant arises from the fact that Equation (6. 45a)
is an approximation for u' > 2.
For donors on intrinsic semiconductors, the counterpart equations
can be obtained from Equations (6. 35a) and (6. 36a). These are
d[ D+]
cdt 2D] D [ D] c Pi exp (- u) + c nD
cdt 2 p,D 1 s nD I, D
-[ [I D~pP+c n + ni exp (u) (6. 43b)
p, D l, Dn, D s....
Under the condition that R ($) >> R (4,) an equation similar to Equation
c v
(6. 45a) can be obtained.
1 n
3n + 1 D D+] 3n+l
n=0 3n+L D
([ D] c n D 2)t + const. (6. 45b)
n, D lD
Adsorption on an Extrinsic Semiconductor
For the adsorption of acceptors on p-type semiconductors, the
electrons "trapped" by the surface acceptors are mainly from the valence
band. We can safely assume that Rv () >> Rc ('') at high surface coverage.
For the derivation of the rate laws, we shall make use of Equation
(6. 40a) together with the following equations:
u' = (L Ip )1/2 [ A-] 0.9 (2. 34a)
s mB
U = ln~(Lm/pB) [ A-] i> 2 (2.37a)
Therefore Equation (6. 40a) can be written as
dt p, A, p,A s (6.40a')

At the initial stage of adsorption the second term on the right hand side of
Equation (6. 40a') can be neglected. The rate, is, therefore, linear. For
high coverage, Equation (6. 40a') is combined with Equation (2. 37a),
and the derivation is similar to that of Equation (6. 45a). The result is
3n; zpm [A-] 3n+ [ A] c P t (6. 46a)
n=O 3n + 1 2p 1 AE A3 p, A l A
It should be noted that when n = 0, Equation (6. 46a) reduces to
the rate equations for low coverage or the initial stage of adsorption.
When donors on an n-type semiconductor are considered, the
result is
rn...1 2_ + 3n+l
zn= 3n + 1 i D] nlo L D [ ] ([ D] c n D/2) t
(6. 46b)
Rate Laws Associated with Depletion-Inversion
Space Charge Regions
The adsorption of acceptors on n-type semiconductors (or donors
on p-type semiconductors) will produce first a slight depletion-inversion
space region, and finally a strong inversion region. The classification
of these regions has been discussed in Chapter 2.
In the following analysis, we shall derive the rate laws for
adsorption of acceptors on an n-type semiconductor in detail. Only the
result for the adsorption of donors on a p-type semiconductor will be given.
Together with Equation (6. 40a), the following equations will be used:
u' = [L /(n +p )]l/2[A] 4 0.9
s m B B
u = m'(Ln)/ [A-] - b (5.71)

where u' in Equation (5. 71) must be:
B s B
UB- 1.< US'< (2uB+ 1)
where m' and b are given in Equations (5. 27) and (5. 27a) of Chapter 5.
For convenience of presentation, we shall divide this section
into three subsections, namely: the slight depletion region, the depletioninversion region, and the strong inversion region.
Slight Depletion Region
The slight depletion space charge region is defined by Equation
(2. 46). At this initial stage the electrons transferred to the acceptors are
from the conduction band; therefore, Rc(1) >> R (1). Then Equation
(6. 40a) can be written as,
dt [ A-] n A nB [ A] exp (- u c' A A"2) - (A. 47a)
dt n.A B s n,A l,A
Since [ A ] is very small, the reverse reaction can be neglected.
When this is done, and Equation: (6. 47a) is combined with Equation (2. 46),
the following equation results.
d [A-] = c n [ A] exp - [2L /(nB+ p)]/2 [A-] (6.48a)
dt n,B m B B
Under isobaric conditions, Equation (6. 48a) can be integrated:
[A-] = [ (nB + B)/Lm]/2 ln1 + [ A] c A nB [ (Lm/(n + 1/
(6. 48a')
For donors on p-type semiconductors the results are
dt P D P(c B/2) [ /[D] D B + p (6. 48b)
An equation similar to Equation (6. 48a) has been obtained by Barry and
Stone (see Literature Survey).

and
F (n +P) / L'
B n + [D] Lm
i Ln.' LBD] p It i (6.48b')
ZLm I p, D B I2 (n p)
Depletion-Inversion Region
For acceptors on n-type semiconductors, the general rate expression
is:
d [A] = A] c n + c P
dt n,A s p, A Pl, A
[A-] pc n + cp / 2 (6. 49a)
_ nA 1, A p, A sUnder the condition that RC () > Rv (1) and that the reverse reaction can
be neglected, Equation (6. 49a) in combination with Equation (5. 71) gives
[A] (cn A nB) [A] exp - B [A] (6. 50a)
dt n, AB n
where B = m' (L /n )/2 (5. 77)
n m B
and A = C exp (b) (6. 51a)
n,A n,A
Under isobaric conditions, Equation (6. 50a) can be integrated to
give
[ A-] = (1/B) ln1 + B c' n [A] t (6. 52a)
n n n,A
When B c' nB[ A] t >> 1, Equation (6. 52a) can be further
n n,A B
simplified to the following equation.
[A-] ~ (1/B) ln t + Z (6. 53a)
n n
where (1B) / n bIn [ A] Cn (6. 54a)
n n n n, Z 5
In general, if R (1k) can not be neglected, Equation (6. 49a) can
be written as

dt A-] c'nB [ A] exp- B [A-] + [A] c (6. 55a)
dt n,A B n p, A l, A
The integrated result: of Equation (6. 55a) gives
In 11+ pA 1,A exp (B [A-])
Cn. AnB n
=-B [A]cp AI1n AtA (6. 56a)
n p, A 1, A n, A B
Note that Equation (6. 56a) reduces to an equation of the form of
Equation (6. 53a) when the second term in the logarithm on the left hand
side is less than one.
For donors on p-type semiconductors the results are
d[ D+]
dt p,DB p
where c' = c Dexp (b)
p, D p,D
B = m'(L /pB) (5.75)
p m m
Integration gives
[ D+] - (1/Bp) ln1 + B D t/ 2 (6. 52b)
which can also be written as
[ D] (1/Bp) In t +Zp (6. 51b)
where, (/Bp) n DI c PB/2 (6. 53b)
P p D B'
When R ($) is not negligible:
d [D+] = (c' PBE D] /2) exp{- II D ]- +[D] n /2
dt ~~p,D p 9 n, D l,D

Integration gives
ln 1 + CnP lD Iexp (B [ D ]
c' PB P
= B [D] n Dnl Dt/2 - ln p, DPB D](6. 56b)
Strong Inversion Space Charge Region
The rate equations for this situation are exactly like those of
Equations (6. 46a) and (6. 46b). We shall omit the repetition.
FORMULATION OF RATE EQUATIONS
FOR DESORPTION OF CHARGED PARTICLES
The desorption process is the reverse of the adsorption process,
which has been treated in the last section. For the formulation of rate
laws of desorption of charged particles, the starting equations are:
For desorption of A
d [A] = R (,)+ (4,) (6. 57a)
dt c v
For desorption of D
dt D+] = Rm(1) + R (4) (6. 57b)
where R (R) and R (v4) are given by Equations (6.35a) and (6.36a);
R ('I) and R (') are given by Equations (6. 32a) and (6. 33a) with [ A]
replaced by [ D+, and [ A-] replaced by [ D]. Due to the similarity
for the desorption of positive adions, [ D+], and negative adions, [ A-], we
we shall treat the desorption of negative adions only. The rate laws for
the desorption of [ D ] will be given by analogy.

Rate Equations of Desorption of Adions
Associated with an Accumulation Space Charge Region
This section is further divided into desorption from an intrinsic
semiconductor, and desorption from an extrinsic semiconductor.
Desorption of Adions from an Intrinsic Semiconductor
The desorption process should tend to restore the straight band
condition by transferring the electrons back to the semiconductor. Now let
us imagine an intrinsic semiconductor with A ions adsorbed on its
surface. When the space surrounding the semiconductor surface is under
a high vacuum or when the temperature of the system is changed, the
uncharged ad-particles will be desorbed, first quickly to a new surface
concentration in equilibrium with the pressure at the new condition, then
more slowly toward the new equilibrium. Therefore, the initial stage of
desorption of adions corresponds to the high surface coverage of adions;
the final stage corresponds to the low surface coverage of adions.
For the formulation of the rate equations for desorption of adions,
[ A-], we shall make use of Equation (6. 57a) and Equation (2. 37a).
For simplifying the treatment, we shall assume that the new
condition is such that the surface of the semiconductor corresponds to a
"clean" surface, i. e., [ A] - 0. Consequently, the reverse reaction in
Equation (6. 57a) can be neglected.
At the initial stage of desorption Equation (6. 57a) can be written
as
d__ A-] - (c Lm/Z) [A-] 3 + (cn /2) [A] (6.58a)
dt p, D m n,D D
For the convenience of representation let,
d = c L /Z (6. 59a)
p p,D m
d =c n /2Z (6.60a)
n n,D l,D

Therefore, Equation (6. 58a) can be written as,
d d
dt [A-] -dp[A-] + d[A-] (6. 58a')
The integrated form of the equation is:
A-] (d A-] + d )
i0 p n 2d t (6 61a)
[A] (d [A-] 2 + d n
p 0 n
where the limits of integration have been chosen as [ A-] = [ A-]
when t = 0.
It is possible that at the beginning of desorption R (4.) >> R (J.),
and then Equation (6. 58a') can be simplified to,
dt A ] - d[ A-] (6. 62a)
By integrating Equation (6. 62a), the following equation is obtained.
[A-]
[A-] [ (6. 62a')
+[ A-] dpt}l/
It is interesting to note that Equation (6. 62a') is the Becquerel hyperbola.
For donors desorbing from intrinsic semiconductors, the results
are:
d D+ = (cn Am ] +cPAPlAD (6. 58b)
dt n,A m p,APl, A P 1
The integrated form of the equation is
[ D+] (d' [ D+] + d')
In n 2d' t (6. 61b.)
[ D+] (d [ D ] 2 + d')
p

where:
d' = c L (6. 59b)
n. nn,A m
d' = c,A (6. 60b)
In the case that R ('t) >> R (')
C V
d [ + d D+ 3 (6. 62b)
dt n
The integrated form is:
[ D+]
[ D ] 1/2 (6.62b')
For the final stage of desorption, the starting point of this
derivation is still Equation (6. 57a). If the reverse rate is still negligible,
we shall have
dt [ A-]' (cp n /2) [ A-] exp L /n) /2 [A-]
dt pDi Lm ]
+ (c n1 /2) [A-] (6. 63a)
nD,D
This equation is not easily integrated analytically in simple form.
Desorption of Adions from an Extrinsic Semiconductor
During the initial stage for the desorption of negative adions from
a p-type semiconductor the space charge region changes from strongly
p-type to moderately p-type in this case, and R (4,) >> R (J.). The rate
of desorption can be derived by applying Equations (6. 57a) and (2. 37a).
The differential rate equation is:
dt-[A- ] - (cp L /2) [A] = d [A]3 (6. 64a)
dt pD m p

Equation (6. 64a) is the same as Equation (6. 62a). The integrated
result will be the same as Equation (6. 62a').
For the desorption of positive adions from an n-type semiconductor,
the result. is given by Equations (6.62b) and (6.62b').
For the final stage of desorption of negative adions from p-type
semiconductors, the surface ion concentration is such that u' < 0. 9.
s
The rate equation can be written by making use of Equations (6. 57a) and
(2. 34a).
dt [A-] [A-] (pD PB/ ) exp Lm/PB)l/2 [A-]
(6. 65a)
Equation (6. 65a) can be integrated by expansion of the exponential.
The result is
n A-] + 1 (L ([ A] A- ]
[A-]o ncl n'n, B (
(Cp, DPB/ 2) (tt o) (6.66a)
where [ A ] = [ A-], when t = to, and u' < 0.9.
The first term approximation gives:
[A] - [A 10 exp (Cp DPB/2) (t - to) (6. 67a)
Note that Equation (6. 67a) is the exponential decay formula.
For desorption of positive adions from n-type semiconductors,
the results are
d + 1/2 +2
d [ D+] [ D c] cn AnB exp Lm /nB)B D (6. 65b)
Integration gives
ln ED.]ll C n I~n( LL/n 1n/2+ ([tD+)
EDn /] - [ D] E= c nB (t- to)
n=lJ nm
(6. 66b)

and the first term only is
[D -D exp n (t - t) (6. 67b)
Rate Equations of Desorption Associated
With a Depletion-Inversion Space Charge Region
For completeness, we shall assume that the desorption process
starts from an adion concentration such that a strongly inverted space
charge region is generated in the semiconductor.
Desorption from a Strong Inversion Space Charge Region
The rate equations for desorption of negative adions from n-type
semiconductors are the same as Equations (6. 64a) or (6. 62a) and (6. 62a').
The rate equations for desorption of positive adions from p-type
semiconductors are the same as Equations (6. 62b) and(6. 62b').
Desorption from a Moderate Depletion-Inversion Space Charge Region
For the desorption of negative adions from n-type semiconductors
Equation (6. 57a) can be written as,
dt [ A-] = (12)[ A] nlD + cpP (6.68a)
For the depletion-inversion region, u' is given by Equation (5. 71) where
2 uB + 1 > u' > uB - 1. Substituting u' into Equation (6. 68a) gives
s s
d[A] ([A] /2)n, Dnl, Dp, D +c exp (B [A-]) (6.69a)
dt nD lD DB n
where cD = c exp (- b)
Dhere p, D
B = m' (L /n )l/2 (5.77)
n m B

There are two extreme cases in Equation (6. 69a), namely,
(i) R ($) >> Rc(L) and (ii) Rc(,) >> RV().
For case (i),
d[A-] (c' p /2) [A] exp B [A (6.7 0a)
dt p,D n
Let [A-] = [A-] at t = 0. Equation (6. 70a) can be written,
d A-] (c', [A] ( rp )dt [A ] ( p,DPB [A-] exp n A]}
0 0
- (cp DPB/2) exp n A-] + B A-] (6. 70a')
If for all the time periods investigated the following relation holds,
B [ A-] >> In ([ A-] /[ A-]o) (6.71a)
then Equation (6. 70a') can be written as
dt [A-]3 (c p, DPB/ 2) exp n [A (6. 72a)
Equation (6. 72a) can be integrated to give the logarithmic equation of
desorption:
[A] = - (/Bn) l BncD A[-]o t/2 + exp (-Bn [A-] (6.73a)
For the case (ii), the differential equation is
dtA (cnD 1, D/ 2)[A-] (6. 74a)
dt n,D 1,D
Integration gives
[A-] A [A ] exp -cD, nl nt/ j (6.75a)

From these above extreme cases we see that the desorption rate
equation associated with an inversion-depletion space charge region,
Equation (6. 69a) can either be logarithmic or exponential depending on
the relative magnitudes of Rc (o) and R (4/).
For the desorption of positive adions, [ D+], from a p-type
semiconductor, the general results are:
d [ D] [ D] p APlA + cns0 (6. 68b)
which can also be written as
d[D+] _[D] cp + c' n exp (B [ D+] )
-dt - p, Al, A nA B p
(6. 69b)
where B = m' (L /pB)l/ (5. 75)
when R () >> R ({'), [ case (i)]
c v
D] (1/B) in B c' nB[ D+] t + exp (-BnL D ]op (6.73b)
-when R (t) << R (4), [ case (ii)]
C v
[ D+] = [ D]] exp (-cp AlA t) (6. 75b)
Rate Laws of Desorption Associated With
a Depletion Space Charge Region
For the desorption of negative adions from n-type semiconductors,
we shall discuss the case when u' < 0. 9. Under the condition of ultras
high vacuum, [ A] = 0, and the adsorption can be neglected. Then, the
situation will be the transfer of electrons mainly to the conduction band,
and R (4-) >> R (4-). Therefore the result will be the same as Equation
(6. 75a).

For the desorption of positive adions from p-type semiconductors,
then R ("') >> Rc(1), and the result is the same as Equation (6. 75b).
DISC USSION
In the last two sections, the rate equations for the adsorption
and the desorption of charged particles on semiconductor surfaces have
been derived. These equations were written in terms of atoms and atomic
ions. For the adsorption or desorption of molecular ions, the corresponding
rate equation can be obtained by the following replacements:
[ A-] becomes [ AT]
n
[A] becomes [A ]
n
[ D ] becomes [ D+]
[ D] becomes [ D ]
In the remainder of this section we shall point out the limitations
and the special features of the derived rate equations. The electrical
phenomena associated with the rate process of adsorption and desorption
of charged particles shall also be discussed.
The Limitations
(1) In the derivation of the rate equations, we have applied the formulas
for u' or u, which were obtained in Chapter 2 for the case of nons s
degenerate semiconductors. Consequently, the derived rate laws are
limited to the cases contemplated in Chapter 2; that is, homogeneous, nondegenerate semiconductors.
(2) The integrated rate equations for adsorption are applicable to isobaric
processes only. Otherwise only the differential rate equations should
be used.
(3) The integrated rate equations for desorption are to be used in case of
high vacuum or high temperature degassing. Otherwise only the differential
rate equations for desorption should be used.

The Special Features
(1) The rate equations for adsorption and desorption of adions on semiconductors are derived on the monolithic basis of charge transfer theory.
(2) The form of the derived rate equations for both adsorption and
desorption of charged particles are dependent on the space charge
regions, i. e., the typeness of the semiconductor adsorbent.
The logarithmic rate equations for adsorption are obtained for a
depletion or depletion-inversion space charge region on an extrinsic
semiconductor adsorbent and for the accumulation space charge region on
an intrinsic semiconductor with u j < 0. 9.
For an accumulation space charge region on an extrinsic
semiconductor or on an intrinsic semiconductor with I uS - > 2, a rate
equation in the form of an infinite series was obtained, e. g. Equations
(6. 45a, b) and (6. 46a, b), instead of the simple power rate equation such
as Equation (6. 2). We shall discuss this in the following paragraph.
The rate equation such as Equation (6. 46a) is an infinite series.
It converges when (Lm/ 2 lA L A] ) [A- 3 < 1; when it is equal to 1,
the rate of adsorption is zero, and the adsorption process attains dynamic
equilibrium. Therefore, at any time before equilibrium, when there is a
rate process, Equation (6.46a) always converges. Equation (6.46a)
can be written as,
[A]+ (1/4) (Lm /Plp ALA]) [A] 4 +.. = [A] c AP, At (6.76)
The first order approximation is therefore,
[A-] _ [A]c p At (6.77)
During the adsorption [ A-] increases with time. The terms with
higher order of [ A-] will be gradually important as [ A-] increases,
and the first order approximation will not be adequate. However, the
series on the left hand side of Equations (6. 76) can always be approximated by the form, Const [ A] m, for certain ranges of values of

[ A-] in the neighborhood of a median value, say, [ A-] To see
this, let g [ A-] - represent the series on the left hand side of the
Equation (6. 76), and kB[ A ] m be the approximation of the series in
the neighborhood of [ A-] 1
= kB [Am 1 (6. 78)
dg_=_rnkB 1
gi Kd[ [A])[ A-]'mk[A]ml (6. 79)
1l B 1[ A-] n-]
Therefore m gi [ A-]l/g (6. 80)
The constant kB can be determined by combining Equations (6. 80) and
(6. 78). The power rate equation, then, becomes:
kB [A-] m [A] c AP1l t (6. 81)
or
[ A- m [ A] BDt (6. 81a)
where BD - (p Pl,A/kB) (6.82)
D p_, A lA B
Equation (6. 80) brings out another point, namely, that the
exponent "m" is a function of the median value, [ A-] 1' in the neighborhood of which the approximation [ Equation (6. 81a)] is valid. Furthermore, m'" increases as [A ] increases. This has been borne out by
the papers of Bangham et ala ) Their data show that "m" equals
3 to 4 "initially" and 10 to 12 finally. (18b)
Electrical Phenomena Associated With the Rate
Process of Adsorption and Desorption of Charged Particles
Electrical phenomena such as surface conductance and work
function changes associated with surface charges due to adsorption have
been analyzed and discussed in Chapters 3 and 4. These relationships

can be used to check the rate equations derived in this chapter.
For example, in case of high surface ion concentration [ A-], on
a p-type semiconductor, it was shown in Chapter 3, that
An = q p [ A-] (3. 23)
In the case of adsorption at high coverage, [ A-] is related with
time through Equation (6. 81a), therefore,
A- =q~ i D[ ]3 (6. 82)
In the case of initial desorption of [ A-] from a p-type semiconductor, Equation (6. 62a) can be combined with Equation (3. 23) to
give
= O(6. 83)
s t1'+ Z[ A-] d t I/ 2
where (As)o = q p[A-]
Similarly in the case of work function, 0 th we can use the
relationships in Chapter 4. For example, in the case of acceptors on a
p-type semiconductor with u' > 2, we can use Equation (4. 48a) and
Equation (6. 81a) to obtain,
AOth = (2kT/m) In t + const. (6. 84)
For acceptors on an n-type semiconductor when a depletioninversion space charge region is generated, we can use Equations (5. 71)
and (6. 52a) or (6. 53a) to obtain
Ad 0 B kT(1/B ) lnt + Z
n n n
or
Ath g kT In t + const. (6.85)

Other equations relating AO th and time in the rate process of
adsorption and desorption can be similarly obtained.
COMPARISON WITH EXPERIMENTAL OBSERVATIONS
In this section, we shall compare the derived rate laws as well as
the change of the electric properties associated with gas adsorption or
desorption with observations reported in literature.
Data by Enikeev, Roginsky and Rufov
(7)
We shall first discuss the data presented by Enikeev et al,
which has been summarized by Equations (6. 1), (6. 2), and (6. 3) for
"accumulation adsorption", and by Equations (6. 4), (6. 5), and (6. 6) for
"depletion adsorption". The data are also represented by Figure 6. 1.
For accumulation adsorption, i. e., oxygen (acceptor) on NiO
(p-type), curve 2 in Figure 6.1 shows the oxygen adsorbed as a function
of time, and can be represented by the Equation (6. 81a), with m = 1.7.
Curve 1 in Figure 6. 1 shows the change in work function with time, and
can be represented by Equation (6. 84).
For depletion adsorption, i. e., oxygen (acceptor) on MnO2
(n-type), the observed data are represented by Curve 3 in Figure 6.1
for the amount of oxygen adsorbed as a function of time. It can be
explained by Equation (6. 53a). The work function change during
adsorption (as a function of time) was represented by Curve 4, in
Figure 6. 1. It bears out Equation (6. 85).
Enikeev et al do not report the temperature of their measurement,
but the slope of Curve 4 indicates that the temperature was approximately
3450K.
The fact that Curve 1 is essentially parallel to Curve 4 is at
first surprising. However, the slope of Curve 1 should be 2kT/m,
where m = 1. 7. The parallelicity of the curves then is expected as long
as the measurements were made in the same temperature range.

Data by Linde
(9)
Linde has reported investigations of adsorption of oxygen and
other gases on Co 04, Mn304, CoMn 04 and MnCo 04. However,
only the change of electrical conductivity of MnCo204 during the
adsorption of oxygen and CO have been studied. His data are represented
by Figures 6. 2 and 6. 3. He reported that MnCo204 is a p-type semiconductor with conductivity at 20 C of 1.5 x 10-4 mho/cm. Both oxygen
and carbon monoxide are acceptors on MnCo204 as a function of gas
up-take. Figure 6. 3 presents the rate for adsorption of oxygen (acceptor)
on MnCo2O4 (p-type). His data agree with those of Enikeev et al; that
is, for accumulation adsorption a power rate equation of the form of
Equation (6.81a) is obtained. The exponent "m" is 2. 4 in Linde's system.
Data by Sebenne
(10)
More recently Sebenne studied the adsorption of oxygen
(acceptor) on CdS (n-type) in a doctoral thesis in solid state physics at
the University of Paris. He reported that CdS is an n-type semiconductor
with E = 2. 42 ev., at 3000K and dielectric constant 11. 6. His data
g
are represented by Figures 6. 4 and 6. 5 in its original scale.
Since Figure 6. 4 shows clearly that Y' > kT, therefore his data
(8)
can not be explained by the theory of Barry and Stone for low surface
adion concentration, which assumed that u' < 0. 9. According to Equas
tion (6. 85) the slope of the straight line portion in Figure 6. 4 should be
about kT, (T = 300 K). The rate law is represented in Figure 6. 5. It
beautifully bears out Equation (6. 53a). The slope of the figure cannot be
checked against the theories here since the surface ion concentration is
not known.
Other Observations
Observations on the long time work function changes induced by
light and electrostatic field have been reported by Pratt and Kolm(35) for

germanium, silicon, aluminum, and gold. These authors did not measure
the rate of gas adsorption or desorption. They reported that the incremental work function induced by an electrostatic field in a gaseous ambient
atmosphere as measured by contact potential difference decays
logarithmically after the removal of the field. The slope of the 9th
vs log t plot varies between (1/2)kT and kT for all samples with
temperature range, 195 - 373 K. This can be explained on the same
basis as the above explanation for Sebenne's data. However, their data
on gold can not be explained on the same basis since gold probably does
not form a semiconducting surface oxide. Furthermore, we have no
assurance that the decay of work function is due to adsorption, nor of
the condition of the surface of their sample. Therefore, we shall not
emphasize their data.
Incremental conductivity due to field effect and subsequent relaxa(36)
tion has been reported by Lyashenko and Chernaya. They reported
that the current relaxation process associated with different ambients
during field effect measurements can be approximated by the Becquerel
hyperbolic equation. Such an equation is similar to Equation (6. 83).
However, these authors present no information to justify that the relaxation process is due to desorption of gases.
In a similar nature the earlier reported data on gas adsorption( 2)
and some of the data recently reported on gas adsorption and desorption, (37)
do not report the electrical properties of the solid adsorbent which was
used; therefore, they can not be used to check our theory.
CONCLUSION
For the rate equations of gas adsorption, and the associated
changes in the electrical properties of the semiconductor, the theory
presented in this chapter has been borne out. However, there is virtually
no data which could furnish enough information to check the derived rate
laws for gas desorption.

REFERENCES
1. Low, M. J. D., "Kinetics of Chemisorption", Chem. Reviews,
60, 267-312 (1960).
2. Engell, H. J., K. Hauffe, "Die Randschichttheorie der Chemisorption - Ein Beitrag Deutung Von Vorgangen an der Grenzflache
Fest Kbrper/Gas", Z. Electrochem. Bd., 57, 762-773 (1953).
3. Hauffe, K., "The Application of the Theory of Semiconductors
to Problems of Heterogeneous Catalysis", Adv. Catalysis, VII,
213-257 (1 955).
4. Weisz, P. B., "Effect of Electronic Charge Transfer Between
Adsorbate and Solid on Chemisorption and Catalysis", I. Chem.
Phys., 21, 1531-1538 (1953).
5. Germain, J. E., "Modele Cinetique de l'adsorption activee sur les
catalyseurs semi-conducteurs", Compt. rend., 238, 236-238 (1954).
6. Morrison,. S. R., "Surface Barrier Effects in Adsorption, Illustrated
by Zinc Oxide", Adv. in Catalysis. VII, 259-301 (1955).
7. Enikeev, E. Kh., C. Z. Roginsky, J. H. Rufov, "Study of the
Influence of the Adsorption of Gases on the Work-Function of
Semiconductors", Proc. Int. Conf. Semicond. Phys., Prague,
560-563 (1960).
8. Barry, T. I., F. S. Stone, "The Reaction of Oxygen at Dark and
Irradiated Zinc Oxide Surfaces", Proc. Roy. Soc. (London), AZ55,
1 24-144 (1 960).
9. Linde, V. R., "Study of the Adsorption Properties of Spinels CoMn204
and MnCo204 and Oxides Mn304 and Co304 " Doklady Akad.,
Nauk. SSSR.,, 127, 1249-1251 (1959).
10. Sebenne, C., "Contribution a l'etude des effect de surface dans le
sulfure de cadmium", Doctoral Thesis, Physical Science, L'Universit6 de Paris (1962).
11. Melnick, D. A., "Zinc Oxide Photo-Conduction, an Oxygen Adsorption Process", I. Chem. Phys., 26, 1136-1146 (1957).

12. Kubokawa, Y., I"An Investigation of the Elovich Equation for the
Rate of Chemisorption on the Basis of Surface Heterogeniety",
Bull.Chem. Soc. ap., 33 734-738 (1960).
13. Taylor, H. A., N. Thon, "Kinetics of Chemisorption", J. Am. Chem.
Soc.:, 74 4169-4173 (1952).
14. Landsberg, P. T., "On the Logarithmic Rate Law in Chemisorption
and Oxidation", J. Chem. Phys., 23, 1079-1087 (1955).
15. Bennett, M. J., F. C. Tompkins, "The Low-Temperature Oxidation:
of Germanium", Proc. Fourth Int'l. Sympos Reactiv. Solids,
Amsterdam, 1960, 154-161, Elsner Publishing Co., New York (1961).
16. Higuchi, I., T. Ree, H. Eyring, "Adsorption Kinetics 1. The System
of Alkali Atoms on Tungsten", J. Am. Chem. Soc., 77, 4969-4975
(1955).
(11)
17. An equation similar to this has been derived by Melnick, and
Barry and Stone. Melnick's derivation is incorrect (see Literature
Survey); the logically correct equation should be that of Germain. (5)
Barry and Stone's derivation is essentially correct for Y /kT < 1
18. The power rate law is referred to as Bangham's rate law in:
a) Bangham, D. H., E. P. Burt, "The Behavior of Gases in Contact
with Glass Surface", Proc. Roy. Soc. (London), A105, 481-488 (1924).
b) Bangham, D. H., W. Sever, "Experimental Investigation of the
Dynamical Equation of the Process of Gas-Sorption", London
Philosophical Magazine, Series 6, 49, 935-945 (1925).
19. This equation is referred to as the Roginsky-Zeldovich rate law.
See references (7, 8, and 14).
20. Garrett, C. G. B., "Quantitative Considerations Concerning Catalysis
at a Semiconductor Surface", J. Chem. Phys., 28, 966-979 (1960).
21. Mott, N. F., "Semiconducting Materials", University of Reading
(1950), Butterworth's Scientific Pub. Co. (1951). pp. 1-7.
22. Hall, R. N., Abstract of Am. Phys. Soc., Phys. Rev., 83, 228
(1951); ibid, 87, 387 (letter) (1952).
23. Shockley, W., W. T. Read, "Statistics of the Recombinations of
Holes and Electrons", Phys. Rev., 87, 835-842 (1952).

24. Mason, D. R., Semiconductor Theory and Technology, Chapter
10 (1963); to be published by McGraw-Hill Book Co., Inc., New
York (1964).
25. Lax, M., "Present Status of Semiconductor Surface Physics",
Proc. Int. Conf. on Semicond. Phys., Prague, 484-491 (1960).
26. Morrison, S. R., "Slow Relaxation Phenomena on the Germanium
Surface", Semiconductor Surface Physics, R. H. Kingston, Editor,
University of Pennsylvania Press, 169-197 (1957).
27. Liashenko, V. I., V. G. Litovchenko, "Effect of Adsorption of
Molecules on Work Function and Conductivity of Germanium, II.
Kinetics of the Process", T. Tech. Phys. (USSR), 28, 454, Eng.
Transl. 3, 429-433 (1958).
28. Landau, L. D., E. M. Lifshitz, Electrodynamics of Continuous
Media, Pergamon Press (1960); a) pp. 1-3; b) pp. 344, 349-359.
29. See for example: Panofsky, W. K. H., M. Phillips, Classical
E and M, pp. 242-244, Second Ed., Addison-Wesley Co., Reading
Mass. (1962).
30. Weinreich, G., private communication (1963).
31. For example, Hartree, D. R., Numerical Analysis, Oxford Press (1951).
32. Burshtein, R. Kh., L. A. Larin, "The Influence of Adsorbed Oxygen on
the Electronic Work Function of Germanium", Doklady Akad. (USSR),
130 (Eng. Transl.), 59-61 (1960).
33. Smith, A. W., "Adsorption and Semiconductivity-Oxygen on Cupric
Oxide", Actes du Deuxieme Congres International de Catalyse, Paris,
1960, Part A. Technip, Paris (1961), pp. 1711-1731.
34. Cimmo, A., E. Molinari, E. Cramarossa, G. Ghersini, "Hydrogen
Chemisorption and Electric Conductivity of ZnO Semiconductors",
J. Cat., 1, 275-292.(1962).
35. Pratt, G. W., Jr., H. H. Kolm, "Long Time Work Function Charges
Induced by Light and Electrostatic Fields", Semiconductor Surface
Physics, R. H. Kingston, Editor, University of Pennsylvania Press,
Philadelphia, 297-323 (1957).

36. Lyashenko, V. I., N. S. Chernaya, "On the Nature of Relaxation
Processes in the Field Effect", Soviet Physics, Solid State (Eng.
Transl,.), 1, 921-1066 (1959).
37. Sommerfeld, J. T., "Chemisorption of Oxygen on Ruthenian Dioxide",
Ph. D. Thesis, Ch. E., University of Michigan (1963).
38. Krusemeyer, I. J., D. G. Thomas, "Adsorption and Charge Transfer
on Semiconductor Surfaces", J. Phys. Chem. Solids, 14, 78-90
(1958).

FIGURES
Fig. 6.1 Work-function variation and rate of adsorption of oxygen on
NiO and MnOz (after Enikeev, Roginsky and Rufov).
1. Ah a log t
NiO X 2. log @ a log t
3. @ a log t
M 2 n 4O 2th A log t
Fig. 6. 2 Change in the electrical conductivity of MnCO204 (p-type)
caused by the adsorption of acceptors: oxygen (1), and
carbon monoxide (2), at 100 C (after Linde).
Fig. 6. 3 The rate of adsorption of oxygen (acceptor) on MnCOzO4
(p-type) at 100 C (after Linde).
Fig. 6. 4 Work-function variation during adsorption of oxygen (acceptor)
on CdS (n-type) at 300"K as measured by contact potential
difference (after Sebenne ).
Fig. 6. 5 The rate of adsorption of oxygen (acceptor) on CdS
(n-type, n = 5 x 1015/cm3) at 3000K (after Sebenne10).

.30
8
7
NiO
ea 6t- 15 3. 9 a log t
-4 4c:1
0) 14 I0.Mn 2
NiO
2. log G ca log t
3. 9 ca log t
MnO2. ~ th aY log t

n 2
0
r)
b 3.0 I I
< 0 10 20 30 40
ex o104 (cm3/m2)
Fig. 6.2 Change in the electrical conductivity of MnCO204
(p-type) caused by the adsorption of acceptors: oxygen (1),
and carbon monoxide (2), at 100 C (after Linde).

E I.0
x 0.5
o
0.5 1.0 1.5 2.0
log t (min.)
Fig. 6. 3 The rate of adsorption of oxygen (acceptor) on MnC0204
(p-type) at 1000C (after Linde).

)-. 0.20 P l"
C
IL
l l i l l l I I I l lll
I 10 100
Time in minutes)
Fig. 6. 4 Work-function variation during adsorption of oxygen
(acceptor) on CdS (n-type) at 300~K as measured by
contact potential difference (after Sebenne ).

X
E
(I
Q)
=E
0 I3
OC
Z)
0
x~ 2'10 100
Time (in sec.)
Fig. 6. 5 The rate of adsorption of oxygen (acceptor) on CdS
(n type5 /cm3) at 300K (ater Seenne).
(n-type, nB = 5 x l0 /c ) at 300 (after Sebenne