and, generally, all its three components also change. But in solutions
of not very low concentration (>0.1 M), which are, as a rule, used
in electrochemical experiments, the quantity Alhb(/> = \jj' (and hence
its change) is negligibly small. Precisely this case is considered
below. Thus
A
(24)
Besides charge carriers, dipoles at the interface also contribute
to the formation of the double layer. Here we mean first of all the
dipole moments, which arise in the formation of polar bonds
between the semiconductor surface and atoms adsorbed from the
solution, and also oriented adsorbed solvent molecules.
The distribution of the dipoles does not contribute to the net
electrode charge, but gives rise to a certain additional potential
drop included into the quantity k2s(j>. Experiment shows that this
dipole drop Adip may vary relatively little when the electrode
potential changes, but it is usually rather sensitive to preliminary
treatment of the electrode surface and to the composition of the
surrounding medium.
Variation of the potential
semiconductor is equivalent, within the framework of the band
model, to energy-band bending. The bands are bent downwards if
AJ0 < 0 and upwards if Asb4> > 0. In the latter case, which corresponds to depletion of the near-surface region with electrons, a
204
Yu. V. Pleskov and Yu. Ya. Gurevich
depletion layer (the Mott-Schottky layer) is formed in n-type
semiconductors if the following inequality is satisfied:
kT
kT/e < M
e
(25a)
The space charge in this layer is mainly produced by ionized donor
impurities of concentration ND — n0. Similarly, in p-type semiconductors, the charge of the depletion layer, which arises in downward
band bending in the potential range
kT
kT
- — \n(po/no) < M <
e
e
(25b)
is mainly produced by an acceptor impurity (that captured an
electron) of concentration NA — p0.
The case where a depletion layer is formed is of most importance in practical respects, since in wide-gap doped semiconductors,
which are used very extensively in modern electrochemistry of
semiconductors, the potential range given by Eqs. (25a) and (25b)
is rather large.
If Ab = 0, the bands remain unbent ("flat") up to the interface, and the space charge in the semiconductor is zero. Under this
condition, the potential
against a certain reference electrode, is called as the flat-band
potential,
of semiconductors is equivalent to the zero-charge potential (the
potential of the zero free charge, to be exact31) in the electrochemistry of metals and plays an important role in the kinetics
of electrochemical processes occurring on semiconductor
electrodes.
It should be noted that at
= 0, the quantity
A2s
from solution. For example, in the case of oxide semiconductors
(TiO2, ZnO, etc.) and also semiconductors whose surface is oxidized
in aqueous solutions (say, Ge), the concentrations of OH~ and H+
ions chemisorbed on the surface are not equal to each other, which
necessarily gives rise to a contribution to A£$. AS follows from the
conditions of thermodynamic equilibrium between ions adsorbed
on the surface and present in the solution bulk, the above contribu-
Electrochemistry of Semiconductors: New Problems and Prospects
205
tion to A2b
pH value, dependent on the nature of a semiconductor electrode,
the total charge of adsorbed ions appears to be equal to zero. This
pH value (or a similar quantity in the case of adsorption of ions
of another kind) is characterized by the "point of zero zeta potential" (PZZP, which is sometimes called the isoelectric point) or,
according to terminology accepted in Reference 31, by the "potential of zero total charge." At the same time, even at PZZP, A 2 ^
may, in general, be different from zero because of adsorption of
solvent dipole molecules at the interface and also (in the case of
oxide semiconductors) because of the dipole character of the bond
between a semiconductor atom and oxygen.
In the study of specific features of the semiconductor/electrolyte interface we have to consider surface electron states. (In
this case it would be more correct to speak about interface states,
rather than surface states; in what follows, the conventional term
"surface states" is used to mean "interface states".) These states
can be rather important just in semiconductor electrodes, unlike
metal ones where they are of no significance because of the
enormous number of "free" electrons.
Surface electron states, which exist on atomically pure (ideal)
crystal surfaces, are usually called intrinsic. In recent years,
considerable progress has been made both in theoretical and
experimental methods of studying intrinsic surface states (see, e.g.,
Refs. 32-34).
Under ordinary conditions, in particular when the electrode
material is in contact with an electrolyte solution, adsorbed atoms
or even layers are present on the surface; moreover, real surfaces
may contain structural defects. They all can exchange electrons
with the semiconductor bulk to give rise to surface electron states
of kinds and properties other than those inherent to intrinsic surface
states. The former play an important role in adsorption and catalysis
processes.
Thus, a real semiconductor surface contains various types of
surface electron levels, which are characterized by a complicated
energy spectrum and may be both donor and acceptor in function.
Their concentration depends on the way the surface is treated and
may reach values of 1014-1015 cm"2, which approximately coincides
with the number of lattice sites per unit surface area of a solid.
206
Yu. V. Pleskov and Yu. Ya. Gurevich
Nonstationary methods of investigation reveal both "fast"
and "slow" surface states and enable their characteristic relaxation
times to be estimated. In most cases, a set of states with different
characteristic relaxation times exists on the surface.
The existence of surface energy levels leads to two very important effects. First, electrons and holes can be trapped at the surface
to form a surface electric charge layer and thereby induce an
opposite charge in the bulk. In particular, the influence of the
surface on equilibrium properties of semiconductors is related
precisely to this effect. Second, surface energy levels can change
significantly the kinetics of processes with electrons and holes
involved: on the one hand, they produce additional centers of
recombination and generation of charge carriers; on the other hand,
they can act as intermediate energy levels in processes of charge
transfer across the interface.
It is the existence of surface states that can lead to a considerable change in various electrochemical properties of semiconductors in the course of treatment of their surfaces.
Finally, surface states of a special type arise under conditions
of strong band bending. If, for example, A£<£ < 0, so that the bands
are bent downwards, a potential well for electrons is formed at the
surface. If this well is sufficiently deep, bound states can arise in
it, and electrons in these states are localized near the surface. The
occurrence of such states is one of the manifestations of the surface
quantization effect.
All that has been said above is, obviously, valid for holes, with
the only exception that in this case a potential well is formed when
the bands are bent upwards.
2. Potential Distribution: "Pinning" of Band Edges and/or
the Fermi Level at the Surface
Consider now how the total potential drop A si;bb
is distributed between its components A2s and A£$. According to
the well-known electrostatic conditions, the following relation
eH%H
= 4TTQ S S - ssc%sc
(26)
must hold at the interface. Here %H and g sc are the values of electric
field strength near the interface from the side of the Helmholtz
Electrochemistry of Semiconductors: New Problems and Prospects
207
layer and semiconductor, respectively; eH and esc are the static
dielectric permittivities, and Qss is the charge density at surface
levels which depends onAJ; the sign "minus" in the second term
of Eq. (26) accounts for the difference in the directions of potential
axes mentioned above. For estimates, we can assume that \%H\~
\&2b(t>\/LH and |» s c | - |A*|/LSC, where LH and Lsc are the thicknesses of the Helmholtz layer and the space-charge region in the
semiconductor, respectively. They are related to the corresponding
capacities by CH = 4rreH/ LH and C sc = 4iresJ Lsc, and depend, in
general, on A£ and A*<£. If the charge associated with surface
states is not too large, then, according to Eq. (26), | A ^ | « |Afo0|,
provided
eacLH/fHLac«
1
(27)
It is a simple matter to verify that condition (27) is satisfied
for reasonable values of the parameters esc and sH. At the same
time, for heavily doped semiconductors when the concentration n0
(or po) is sufficiently high, and also for large |Ab|, the quantity
L sc may become so small that inequality (27) will not hold true.
In order to estimate the effect of surface states on the potential
distribution, we have to calculate their capacity Css = dQss/d(Asb
This calculation appears to be rather simple in the monoenergy
model where all surface electron levels are assumed to have the
same energy Ess. It can easily be demonstrated (see, e.g., Ref. 7)
that if
Nss> eHkT/7re2LH
(28)
where Nss is the number of surface levels per unit area of the
interface, then | A ( A ^ ) | > |A(Ab)|. In other words, if condition
(28) is satisfied, the variation of the electrode potential gives rise
to a potential change in the Helmholtz layer, which is larger than
the corresponding potential change in the space-charge layer. The
critical value of Nss (to an order of magnitude), at which inequality
(27) becomes equality, is 10 13 -10 14 cm~ 2 .
Thus, since usually LH « Lsc, then |A£| » |A£|, and therefore in electrolyte solutions of not very low concentration, Ab
constitutes, as a rule, the main portion of the interphase potential
drop Asc,b<£. If we take into account the above considerations,
however, we see that this statement does not hold true in the
208
Yu. V. Pleskov and Yu. Ya. Gurevich
following cases:
1. For very strong charging of an electrode when the Fermi
level at the surface is in close proximity to the edge of the
conduction or valence band ("metalization" of the
surface).
2. For high concentration of surface states: the change in the
degree of their occupation (charging) leads to a considerable charge and potential redistribution, and can increase
noticeably the contribution of the component A2s
fixed value of A^.
3. For heavily doped semiconductors, for which the Fermi
level in the bulk lies near the majority-carrier band edge
(or, as in metals, even lies inside this band).
All that has been said is valid for potential distribution across
the interface both under equilibrium conditions and under electrode
polarization with the aid of an external voltage source.
Consider now two important extreme cases35"37:.
1. Suppose that |A(AJ<£)| » |A(A^)| when the electrode
potential varies. This inequality means that the potential drop across
the Helmholtz layer remains practically unchanged (A
under electrode polarization. Therefore, the positions of all energy
levels at the surface and, in particular, of band edges ECtS and EVjS,
remain the same with respect to the position of energy levels in the
electrolyte solution and reference electrode (Figs. 4a and 4b). In
this case, the band edges are said to be "pinned" at the surface.
Band-edge pinning is eventually related to the fact that, as was
already noted, the potential drop across the Helmholtz layer, A*,
is solely determined by the chemical interaction between the semiconductor and solution, and does not depend, to any significant
extent, on such external factors as polarization and illumination.
Therefore, the band edges Ecs and EVtS have the same position at
the surface for all samples of a given semiconducting material,
which are in contact with a given redox couple, irrespective of the
type and value of conductivity because the chemical nature of the
material remains practically unchanged through doping. Experimental determination of Ecs and Evs for several semiconducting
materials (see, e.g., Ref. 38) confirms this conclusion.
2. Suppose, on the contrary, that in electrode polarization
)| » |A(A£0)| for one reason or another (mentioned above),
Electrochemistry of Semiconductors: New Problems and Prospects
209
El
Reference
*
electrode
Electrolyte
Semiconductor
(a)
(b)
(c)
Figure 4. Energy diagram of the interface with an external voltage applied illustrating the band-edge pinning (transition from a to b) or the Fermi-level pinning
(transition from a to c) at the surface of a semiconductor electrode. The flatband
case is chosen as the initial state.
i.e., it is the potential drop across the Helmholtz layer which mainly
changes. Under these conditions (see Figs. 4a and 4c) the energy
levels at the surface shift relative to those in the solution by A
A(A^) but relative to the Fermi level in the semiconductor, the
band edges Ecs and EVtS retain the positions they had prior to the
change in the electrode potential since the quantity A£ does not
vary. In order to stress the difference between this case and the
preceding one, it is said that the bands are "unpinned" from the
surface (this effect is sometimes called, though not quite adequately,
pinning of the Fermi level with respect to band edges).
Fermi-level pinning leads to the situation that the level F can
reach the level Fredox even for systems characterized by a rather
positive or negative value of the equilibrium potential when the
level Fredox is beyond the semiconductor band gap. Thus, in the
case of Fermi-level pinning, conditions (16a) and (16b) are satisfied,
which permit electrochemical reactions to proceed at a semiconductor electrode, while in the case of band-edge pinning these
conditions are "unattainable."
In real systems, an intermediate case often arises, namely, both
potential drops A£ and L2h
210
Yu. V. Pleskov and Yu. Ya. Gurevich
polarization, so that neither the band edges nor the Fermi level are
actually pinned.
Experimental investigation of potential distribution across the
double layer on semiconductor electrodes is most frequently performed by differential capacity (see the next section) and photocurrent
measurement techniques. A survey of experimental results obtained
in this field is beyond the scope of the present review. Certain data
illustrating the pinning and more detailed discussion of its origins
will be presented in Section IV.2.
3. Determination of the Flat-Band Potential
The flat-band potential, as was already pointed out, is one of the
most important physicochemical characteristics of a semiconductor
electrode. In the electrochemistry of semiconductors this concept
has become even more important than the concept of the zerocharge potential in the electrochemistry of metal electrodes. The
quantity cp^, appears to be quite essential in the quantitative description of the double-layer structure and the kinetics of electrochemical
reactions at semiconductor electrodes. This is especially true for
the photoelectrochemistry of semiconductors because considerable
photocurrents can only be obtained under efficient separation of
light-generated electrons and holes in the space-charge region (for
details, see Section IV.2). This separation occurs reliably only for
electrode potentials that are more positive (in the case of n-type
photoelectrodes) or more negative (in the case of p-type photoeleetrodes) than the flat-band potential cpn, of a semiconductor (though
this condition of charge separation, as such, is not sufficient for
the occurrence of photocurrent).
The capacity of the space-charge region in a semiconductor
Csc, under the formation of a depletion layer, is related to the
potential drop in this region A£ by1
C;c2 = -^—
(M
(29)
eNDesc
(we consider, for specificity, an n-type semiconductor). Relation
(29) implies that a plot of C~c2 vs. Ash(f> should become a straight
line (the so-called Mott-Schottky plot—see Fig. 5). If we assume
that only the component A£ varies with the changing electrode
Electrochemistry of Semiconductors: New Problems and Prospects
Figure 5. The Mott-Schottky plot for a zinc oxide
electrode
(conductivity = 0.59 ft"1 cm"1)
in
1 N KC1 (pH = 8.5).39 The dashed line is calculated
by Eq. (29).
-0,5
211
0
0.5
potential cp and the semiconductor/electrolyte junction capacity C
coincides with Csc, the slope of the Mott-Schottky plot gives the
concentration of ionized donors and its intercept with the potential
axis—the flat-band potential (p^.
This method has widely been used in electrochemical measurements. It should be stressed, however, that direct application of
Eq. (29) to experimental determination of
assumptions (often accepted without proof) concerning the properties of the semiconductor/electrolyte junction. These assumptions
have been analyzed, for example, in Reference 38). Here we
formulate the most important of these assumptions:
1. It is assumed that the capacity measured, C, is not distorted
due to the leakage effect at the interface, a finite value of the ohmic
resistance of the electrode and electrolyte, etc. A correct allowance
for these obstacles is an individual problem, which is usually solved
by using an equivalent electrical circuit of an electrode where the
quantity in question, Csc, appears explicitly. Several measurement
techniques and methods of processing experimental data have been
suggested to find the equivalent circuit and its elements (see, e.g.,
Ref. 40).
2. It is assumed that donors (acceptors) in the semiconductor
are, first, completely ionized at the temperature of measurements
and, second, uniformly distributed in the sample, at least within
the space-charge region. (A non-uniformity whose scale is large in
comparison with the space-charge region thickness can be determined by a special method; see Section V.4). If the concentrations
212
Yu. V. Pleskov and Yu. Ya. Gurevich
ND and NA depend on the coordinate, more complicated relations
for the dependence of Csc on A£ are obtained instead of Eq. (29)
(see, e.g., Ref. 41). Deviations from Eq. (29) are also observed in
the presence of deep donors (acceptors), which are not ionized in
the semiconductor bulk at the temperature of measurements, but
become ionized in the space-charge electric field, thereby contributing to the capacity.42
3. The capacity measured is assumed to represent only the
capacity of the space-charge region in the semiconductor and not
to include, for example, the capacity of surface states, adsorption
capacity, etc. In certain cases, this condition is satisfied, for example,
on a zinc oxide electrode39; but more frequent is the situation where
the contribution of the capacity of surface states is considerable.
4. It is assumed that the electrode capacity measured, C, is
not affected by the Helmholtz-layer capacity, CH. If the dependence
of the measured capacity C on the electrode potential (p becomes
a straight line in the coordinates C2 -
interpreted, in accordance with Eq. (29) and the relation C"1 =
C^1 + C^1, as a proof that the following conditions are satisfied:
CSC«CH;
|A(AS6<£)| » |A(A^)|
(30)
In other words, it is supposed that: (1) the electrode capacity
measured is entirely determined by the capacity of the space-charge
region in the semiconductor; and (2) a change in the electrode
potential leads only to a change in the potential drop in the semiconductor, while the potential drop across the Helmholtz layer remains
constant.
A more detailed consideration43 shows, however, that the effect
of CH is a rather subtle problem which requires thorough analysis.
If the change in the potential drop across the Helmholtz layer
A(Ab<£) in the course of electrode polarization is not neglected and
nor is the contribution of the capacity CH to C, we obtain, with
due account of Eq. (29), the following relation between C and
C~2 = CH2 + - ^ - («p - ?fb - kT/e)
(31)
eNDesc
This expression shows that C'2 depends linearly on
the same manner as [according to Eq. (29)] C~2 depends on A£<£
[or C~c on
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III. SPECIFIC FEATURES OF THE STRUCTURE OF THE SEMICONDUCTOR/ELECTROLYTE INTERFACE