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III. SPECIFIC FEATURES OF THE STRUCTURE OF THE SEMICONDUCTOR/ELECTROLYTE INTERFACE

III. SPECIFIC FEATURES OF THE STRUCTURE OF THE SEMICONDUCTOR/ELECTROLYTE INTERFACE

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202



Yu. V. Pleskov and Yu. Ya. Gurevich



Figure 3 shows schematically (not to scale) the spatial distribution of the interphase potential drop (the Galvani potential) A^<£

at the semiconductor/electrolyte interface.

The semiconductor occupies the region to the right of the

vertical solid line representing the interface (x = 0). To the left of

it, there is the Helmholtz layer formed by ions attracted to the

electrode surface, and also by solvent molecules; its thickness, LH,

is the order of the size of an ion. The space-charge region in the

solution (the Gouy-Chapman layer) is adjacent to the Helmholtz

layer from the electrolyte side.

Let us denote the electric potential in the electrolyte solution

bulk (for x -» -oo) by el>b and in the semiconductor bulk (x -> oo)

by sc'b. The total potential drop across the interface A si* b =

sc>b - eKb i s t h e n



A £ U = Ae2ub<£ + tf + Mt:l

b



{2)



(22)



elb



Here &f' = - is the potential drop in the space-charge

region in the solution, i.e., between the solution bulk and the outer

("2") Helmholtz plane; this quantity is usually denoted by \fj'

("psi-prime" potential). The second term A2s = sc's - (2) is the

potential drop across the Helmholtz layer. Finally, the third term

Kl\b = sc'b ~ <£sc'5 i s the potential drop in the space-charge

region in the semiconductor. Below we shall omit, for the sake of

brevity, the index "sc" and use the notation A ^ ; ^ = A£<£.

We should note here the following circumstance, important in

methodological respects. In electrochemistry, the positive direction

of the electrode potential is conventionally the one for which

positive electrode charge grows. On the contrary, in the physics of

semiconductor surfaces the positive surface potential, which is

usually reckoned from scb, is characterized by the accumulation

of electrons in the space-charge region, i.e., the formation of a

negative space charge. All this directly follows from the Boltzmann

distribution determining the concentration of electrons ns and holes

ps near the surface:

ns = n o exp[e( sc ' s - sc ' b )//cr],

Equation (23) shows that if sc'5 > sc'fc, then ns > n0 and ps < p0.

Thus, the direction of the potential axis accepted in electrochemistry



Electrochemistry of Semiconductors: New Problems and Prospects



203



is opposite to that accepted in semiconductor physics! This is

reflected in the fact that the sign of potential drop in the semiconductor, (f>sc's - sc-b (which is equal to -AJ0) reckoned from the

potential in the bulk sc'\ is opposite to the sign of the last term

in expression (22) for the Galvani potential. This should always be

taken into account in order to avoid confusion in comparing results

concerned with the physics of semiconductor surfaces and

electrochemistry.

It is to be noted that the positive direction of the potential axis

in the semiconductor is in conformity with the direction chosen as

positive in the "physical" scale of energy (see Section 2.2). Indeed,

in formula (17), the terms characterizing the position of the Fermi

level and electrode potential have opposite signs.

When an electrode is polarized, i.e., the electrode potential is

varied by A
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 <—\n(no/po)

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 is nonzero, in particular, due to specific adsorption of ions

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 must be a linear function of solution pH. For a certain

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 at the interface

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 for a

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 change in the course of electrode



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 - kT/e)



(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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