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IV. QUASITHERMODYNAMIC APPROACH TO THE DESCRIPTION OF PHOTOELECTROCHEMICAL PROCESSES

IV. QUASITHERMODYNAMIC APPROACH TO THE DESCRIPTION OF PHOTOELECTROCHEMICAL PROCESSES

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Electrochemistry of Semiconductors: New Problems and Prospects



217



At the same time, another approach is quite efficient for qualitative

understanding and sometimes for quantitative interpretation; this

approach is quasithermodynamic rather than kinetic and is based

on the concept of "quasi-Fermi levels."

We recall that the concept of quasi-Fermi levels, first suggested

by Shockley,51 can be introduced in the following way. Suppose

that, in addition to thermal generation, charge carriers in a semiconductor are also generated because of certain external factors, say,

illumination. In the steady-state regime, a dynamic equilibrium

arises between generation and recombination of electron-hole pairs.

As a result, certain steady-state (but not equilibrium) concentrations

n* and /?* are established in the semiconductor under illumination.

Suppose, further, that the lifetimes of excited states are rather large.

Then, interaction with lattice vibrations (phonons) gives rise to

equilibrium distributions with the temperature of the lattice (the

phonon system) separately in electron and hole gases containing

the photogenerated particles. However, the electron and hole gases

may not, in general, be in equilibrium with respect to each other.

Under such conditions, each distribution (electron and hole) is

characterized by its own chemical and electrochemical potentials.

For electron and hole systems, the latter will be denoted by Fn and

Fp, respectively. Unlike the case of complete thermodynamic equilibrium where Fn = Fp = F, the quantities Fn and Fp, called the

quasi-Fermi levels and corresponding to a partial equilibrium, are

not equal to each other (Fig. 8).

Thus, in the quasi-thermodynamic approximation considered

here the occurrence of nonequilibrium electrons and holes in the

bands can be described as the "splitting" of the initial Fermi level

F into two quasi-levels Fn and Fp.

V/////////////////



///////////////////

-F



FP



(a)



â



(b)



Figure 8. Diagram illustrating the splitting of the Fermi level

into quasilevels of electrons and holes (a) in the dark (b)

under illumination of the semiconductor.



218



Yu. V. Pleskov and Yu. Ya. Gurevich



The quasi-equilibrium concentrations /i* and p* are given by

w J = n0 + An,



pt = p0 + Ap



(34)



and outside the space-charge region An = A/? because carrier photogeneration occurs in pairs.

Substitution of n* and p* into Eqs. (21a)-(21c) yields the

quasi-Fermi levels Fn and Fp. For example, in the case of an n-type

semiconductor, Eq. (21b) gives Fn ~ F, if the condition An « n0 is

satisfied. At the same time, since p0 « n0, the condition A/? » p0

can be satisfied simultaneously; for F - Fp we find then from

Eq.(21c):

F-Fp~kT\n^9



Ap»p0



(35)



Po



Similar relations hold for a p-type semiconductor.

Thus, Eq. (35) implies that a noticeable shift of the

electrochemical potential level under photogeneration can only take

place for minority carriers. For moderate illumination intensity, the

shifts of the quasi-levels, Fnj» are proportional to the logarithm of

the intensity; as it increases, further growth of the shifts slows down

due to enhancement of recombination processes. The ultimate shift

of Fnp with increasing illumination intensity, so long as Eq. (35)

(and a similar formula for a p-type semiconductor) is valid, is the

edge of the corresponding band.

2. Description of the Most Important Types of

Photoelectrochemical Reactions



Let us now turn, using the concept of quasi-Fermi levels, to the

description of qualitative peculiarities in the occurrence of photoelectrochemical reactions at an illuminated semiconductor/electrolyte interface.15'52

The quasithermodynamic approach employed below relies

upon the assumption that an electrode reaction is accelerated under

illumination due to the formation of quasi-levels Fn and Fp, which

are shifted relative to the equilibrium position F. Conditions (16a)

and (16b) should now be modified. Namely, for an anodic process

to occur with holes being involved, the following inequality should



Electrochemistry of Semicoajuctors: New Problems and Prospect!



219



be satisfied:

FP < f w



(36a)



and a cathodic process, with conduction-band electrons, requires

analogously the fulfillment of the inequality:

Fn > F redox



(36b)



Let us first consider a semiconductor electrode under open-circuit

conditions, an individual particle of a semiconductor suspension

in a conducting liquid being an example. Suppose that in a certain

potential range, electron transitions across the interface between

the semiconductor and solution do not take place in darkness, i.e.,

the semiconductor behaves as an ideally polarizable electrode. This

potential range has an upper and a lower limit, namely, the potential

of solvent decomposition and/or the potential of semiconductor

decomposition (corrosion). The stationary electrode potential in

the region of ideal polarizability is determined by chemisorption

processes (in aqueous solutions, it is most often chemisorption of

oxygen) or, which is the same in the language of the physics of

semiconductor surfaces, by charging of slow surface states. It is

these processes which determine steady-state band bending.

Figure 9 shows the energy diagram of a semiconductor, rc-type

as the example, in contact with the solution. Besides the energy

levels in the semiconductor, the bottom of the conduction band EC9

and the top of the valence band EV9 the figure depicts the

electrochemical potential levels for reactions of anodic dissolution

of the semiconductor, F dec p , and cathodic evolution of hydrogen,

FH 2 /H 2 O (We consider the case where semiconductor decomposition with involvement of holes, and water-to-hydrogen reduction,

with involvement of conduction-band electrons, are the most probable anodic and cathodic reactions, respectively).

Figure 9 corresponds to the case where a depletion layer is

formed in the near-surface region of the semiconductor. Lightgenerated electrons and holes move in opposite directions in the

depletion-layer electric field: holes toward the interface and electrons into the semiconductor bulk. The electric field, which arises

as a result of such charge separation, compensates, in part, for the

initial field. This is manifested in the decrease in band bending

eksb


220



r



Yu. V. Pleskov and Yu. Ya. Gurevich



H 2 /H 2 0



'decj



Electrolyte



Semiconductor



Figure 9. Energy diagram of the semiconductor/electrolyte junction: (a) in darkness

and (b) under illumination.



leads in turn to the change in the mutual position of other energy

levels in the system. Indeed, suppose for simplicity that the potential

drop across the Helmholtz layer does not change under illumination

(As = const), so that the position of the band edges at the surface,

Ecs and EVtS9 is fixed with respect to the reference electrode and,

therefore, to energy levels in the solution (band-edge pinning at

the surface; see Section III.2). At the same time, the position of

the electrochemical potential level of the semiconductor F (the

Fermi level) relative to band edges is strictly determined in the

semiconductor bulk. Thus, the bands unbend under illumination

and "pull" the Fermi level, so that it shifts with respect to its

position in the nonilluminated electrode, as is shown in Fig. 9. The

shift of the level F under illumination can be measured by a

reference electrode. It is this shift, AF, which is observed as the

photopotential
Let us consider the effects related to the formation of quasiFermi levels of electrons and holes. For majority carriers (electrons),

the shift of Fn with respect to F is very small, as was noted above,

and it is usually neglected; on the contrary, for minority carriers



Electrochemistry of Semiconductors: New Problems and Prospects



221



(holes) the quasilevel Fp can shift quite significantly with respect

to R

For a certain illumination intensity, the hole quasilevel Fp at

the semiconductor surface can reach the level of an anodic reaction

(reaction of semiconductor decomposition in Fig. 9). In turn, the

electron quasilevel Fn can reach, due to a shift of the Fermi level,

the level of a cathodic reaction (reaction of hydrogen evolution

from water in Fig. 9). Thus, both these reactions proceed simultaneously, which leads eventually to photocorrosion. Hence, nonequilibrium electrons and holes generated in a corroding semiconductor under its illumination are consumed in this case to accelerate

the corresponding partial reactions.

Simultaneous consumption of nonequilibrium electrons and

holes at the semiconductor surface in the course of photocorrosion

formally resembles surface recombination. Therefore, processes of

this type are referred to as "electrochemical recombination."53

In principle, another anodic reaction can take place instead

of semiconductor decomposition (dissolution), for example, oxidation of dissolved substance or oxygen evolution from water.

Apparently, in the latter case, the illumination of semiconductor

leads to photoelectrolysis of water with the formation of hydrogen

and oxygen, that is, conversion of the energy of light into chemical

energy of the photoelectrolysis products.

If the whole semiconductor/electrolyte interface is illuminated

uniformly, both conjugate reactions proceed at the same rate over

the same areas on the interface. The stationary potential of an

illuminated semiconductor is thus a mixed potential. If the surface

of a semiconductor, homogeneous in its composition and properties, is illuminated nonuniformly, in the illuminated and nonilluminated areas conditions will not be identical for electrochemical

reactions. Here the conjugate reactions appear to be spatially separated, so that we can speak about local anodes and cathodes. This

situation is deliberately created, for example, for selective lightsensitive etching of semiconductors (see Section V.2).

There is another way of spatially separating anodic and

cathodic reactions on an illuminated semiconductor, namely by

providing certain regions of the semiconductor surface with different electrochemical (in particular, electrocatalytic) properties. Such

regions act as local electrodes, and the entire system as a galvanic



222



Yu. V. Pleskov and Yu. Ya. Gurevich



couple. A suspension of platinized strontium titanate in an aqueous

solution may serve as an example of such microheterogeneous

systems. When it is illuminated, light-generated electrons and holes

are separated in the electric field of a depletion layer near the

surface (Fig. 10), the holes moving toward the semiconductor

surface and the electrons into the bulk where they are transferred

across the semiconductor/metal interface. Therefore, hydrogen is

evolved on the surface of the metal (platinum in this case) and

oxygen on the strontium titanate surface. Such microheterogeneous

systems have been widely used in recent years in view of their

applications for solar energy conversion.54"56

Finally, a natural extension of this approach would be the

creation of a "macroheterogeneous" system: for example, an

electrochemical short-circuited cell with a semiconductor photoelectrode and light-insensitive, say, metal, auxiliary electrode (Fig.

11). If a strontium titanate electrode in an aqueous solution is used,

illumination of such a cell leads to photoelectrolysis of water, with

the gaseous products, hydrogen and oxygen, being evolved on

different electrodes of the cell. Reliable and convenient separation

of photoreaction products, which is a direct consequence of the

separation of primary photogenerated charges, electrons and



Electrolyte

Figure 10. Scheme of water photoelectrolysis on a particle of

semiconductor (platinized SrTiO3) suspension in an aqueous

solution.



Electrochemistry of Semiconductors: New Problems and Prospects

ô0



Electrical



circuit



223



-*0



Diaphragm

Hz



|



0 2 E4



u

>\

- -ằằ

/

/



0

t



U3eV

i

f



Metal



H 2 0/0 2



Electrolyte



c 6F



1

1



i



Semiconductor



Figure 11. Energy diagram of an illuminated photocell with an

n-type semiconductor photoanode for water splitting.



holes—due to the space-charge field, is the most important advantage of semiconductor photoelectrochemical devices for converting

the energy of light into chemical energy.

The advantage of spatial separation of anodic and cathodic

partial reactions of the overall process, stimulated by the illumination of the semiconductor/electrolyte interface, is twofold. First,

nonequilibrium electrons and holes tend to recombine and the

energy of light stored in these particles is transformed into heat

and cannot be utilized again. By directing the carriers of opposite

sign, immediately after their formation, into different areas on the

surface where they participate in the corresponding reactions

(instead of offering them a possibility to react in the same area, as

is the case with uniform illumination of a homogeneous semiconductor; see previous text), we can radically reduce energy losses

due to recombination, thereby increasing the photocurrent quantum

yield and conversion efficiency. Second, the efficiency of photoelectrolysis is increased considerably if one of the two conjugate reactions, namely that proceeding with majority carriers involved, is

transferred to a separate auxiliary electrode. Indeed, in the case of

an n-type semiconductor considered here, the cathodic reaction,

in itself, is almost not accelerated due to illumination (because



224



Yu. V. Pleskov and Yu. Ya. Gurevich



Fn — F), so that the whole "acting force" of a photoelectrode is

concentrated on the anodic partial reaction taking place with minority carriers (holes) being involved. It is therefore convenient to

carry out the cathodic partial reaction (e.g., hydrogen evolution)

on a metal electrode, which possesses good electrocatalytic properties for this reaction.

Let us now turn to the case where an equilibrium is established

between the semiconductor and solution, even in darkness. This

usually takes place when the solution contains a well-reversible

redox couple. Then, the semiconductor attains the equilibrium

potential of this couple:


Considerations similar to those presented above show that

illumination of a semiconductor leads to a shift of both the Fermi

level and the quasi-levels of holes and electrons, and both the

forward and reverse reactions, proceeding according to Eq. (1), are

accelerated. In other words, the result of illumination is, above all,

the efficient increase of the exchange current in the redox couple57;

but this is not the only result. If a semiconductor under illumination

is an electrode in an electrochemical cell and is connected through

a load resistor with an auxiliary electrode, the cathodic and anodic

reactions become spatially separated, as in the case of water photoelectrolysis (Fig. 11) considered above. The reaction with the minority carriers involved proceeds on the semiconductor surface, and

that with the majority carriers involved, on the auxiliary electrode.

Thus, the illumination of a semiconductor electrode gives rise to

an electric current in the external circuit, so that some power can

be drawn from the load resistor. In other words, the energy of light

is converted into electricity. This is the way a photoelectrochemical

cell, called "the liquid junction solar cell," operates.

Consider in detail the performance of such a cell for a particular

case: n-type CdS/alkaline solution of S2~ + S^/metal cathode

(Fig. 12). In darkness, the equilibrium

Sf-+ 2


(37)



is established in the cell.

Both electrodes take the equilibrium potential of this redox

couple, so that the Fermi levels of the metal and CdS, and the level

^Vedox = ^V/s^" m the solution, become equal. Good separation of

light-generated electrons and holes requires that a depletion layer



Electrochemistry of Semiconductors: New Problems and Prospects

-0



225



-ô-â



'met



Metal



Semiconductor (CdS)



Figure 12. Energy diagram of an illuminated "liquid junction solar cell" with a CdS photoanode and a S2~/Sl~

electrolyte. F (dark) is the Fermi level in nonilluminated

CdS.



should be formed in the semiconductor and this, in turn, requires

that the equilibrium potential of the redox couple be more positive

than the flat-band potential of the semiconductor, i.e. (pQredox > .

When the electrode is illuminated, the bands unbend and the Fermi

level of the semiconductor F shifts (see Fig. 12), which is manifested

as a change in the electrode potential. It can be seen from Fig. 12

that this change in the electrode potential
electrode relative to the nonilluminated one divided by the electron

charge e. In the simplest case (which, as experiment shows, is rather

frequent in practice), the potential drop across the Helmholtz layer

A2s under illumination has the same value as in darkness;

moreover, it does not depend on (p°Tedox. In other words, the band

edges are pinned at the surface (see Section III.2). Under these

conditions, the maximal value of
open-circuit photopotential) is equal to the initial (dark) potential

drop across the space-charge layer, A£$, i.e., the difference |

that this difference be as large as possible.



226



Yu. V. Pleskov and Yu. Ya. Gurevich



Next, photogeneration of electron-hole pairs leads to the formation of quasi-levels of minority and majority carriers, Fp and

Fm as shown in Fig. 12. Since, at the surface, Fp < FS2-/S2- and

Fn > FS2-/S2-, illumination results in the acceleration of both forward and reverse reactions in a sulfide polysulfide couple. If the

circuit is closed on an external load R, the anodic and cathodic

reactions become separated: the holes are transferred from the

semiconductor photoanode to the solution, so that S2~ ions are

oxidized to S2 , and the electrons are transferred through the

external circuit to the metal counterelectrode (cathode) where they

reduce S2 to S2~. The potential difference across a photocell is

iphR, where iph is the photocurrent, and the power converted is

equal to ilhR.

In certain cases, however, the potential drop across the Helmholtz layer does not remain constant under illumination or when


redistributed and the photopotential becomes lower than |

certain redox couples. In other words, band-edge unpinning takes

place, which eventually goes over into Fermi-level pinning at the

semiconductor surface. This is manifested in the fact that, as the

redox couple potential
Figure 13. Dependence of the absolute value of

the open-circuit photopotential |^ ph | on the redox

couple equilibrium potential:58 WSe2 photoelectrode (solid line, p-type; dashed line, n-type) in

-1

acetonitrile solutions. Redox couple (figures in

parentheses are charge numbers of the ox and

red components): (1) anthracene (0/-1); (2)

phtalonitrile (0/ - 1); (3) nitrobenzene (0/ - 1);

(4) 2,2'-bipyridyl complex of ruthenium

(+2/+1); (5) azobenzene ( 0 / - 1 ) ; (6)

anthraquinone (0/ - 1); (7) benzoquinone (0/ 1); (8) methyl viologen ( + 2/ + 1); (9)

tetracyanoquinone-dimethane ( + 1/0); (10)

tetramethyl-p-phenylenediamine ( + 1/0); (11)

OM 0.8 \yph\V

tetraphenyl-/?-phenylenediamine ( + 1/0); (12)

I"/IJ; (13) Br7Br3'; (14) C1"/C1J; (15) thianthrene (+1/0); and (16) 2,2'-bipyridyl

complex of ruthenium (+3/+2). All the potentials are given against the saturated

calomel electrode. (Reprinted by permission of the publisher, The Electrochemical

Society, Inc.)



Electrochemistry of Semiconductors: New Problems and Prospects



227



photovoltage of the cell
The origins of this phenomenon, which restricts significantly

the characteristics of photoelectrochemical cells for solar energy

conversion into electricity, have not so far been understood completely. Possible reasons might be the following: (cf. Section III.2):

strong charging of a semiconductor electrode on approaching the

Fermi level to the band-gap edges, for example, in the formation

of an inversion layer in a semiconductor;37'59 high density of surface

states;35'36 and also the shift of the flat-band potential in redox

couple solutions because of partial oxidation (reduction) of the

semiconductor surface as a result of the chemical action of the

components of these couples, so that (p^ becomes dependent on


in favor of the latter.

One may believe that for WSe2 considered here (see Fig. 13)

(and similar relatively wide-band-gap semiconductors), the second

and third reasons seem to be the most probable (as far as the second

reason is concerned, the assumption that the density of surface

states increases on approaching the band-gap edges is quite reasonable). On the contrary, the formation of a developed inversion layer

in a sufficiently wide-band-gap semiconductor (hence, the bulk

concentration of minority carriers is rather low), when the limiting

current of minority carriers flows in it, seems to be less probable.

In fact, minority carriers are efficiently extracted from a semiconductor so that their concentration appears to be negligibly

low even within the space-charge region and, under such conditions, this region represents an exhaustion rather than an

inversion layer.1

The inversion layer is, in fact, formed in a relatively narrow-gap

semiconductor, germanium, in which the equilibrium bulk concentration of minority carriers is sufficiently high. But the main

reason for band-edge unpinning in germanium, which is observed

practically over the whole potential range accessible,61 is either a

high density of energy-distributed surface states or the change in

the dipole potential drop caused by adsorption of water molecules

on the electrode surface (for details, see Ref. 1).



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