Photodecomposition of Semiconductors Thermodynamics, Kinetics and Application to Solar Cells BY HEINZ GERISCHER Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D 1000 Berlin 33, West Germany Received 28th May, 1980 Photodecomposition of semiconductors is caused by reactions of electrons or holes at the surface. Thermodynamic criteria for such processes are derived. The thermodynamics and kinetics depend on the energy position of the band edges and the concentration of electrons and holes at the surface which can both vary under illumination. The role of competing redox reactions and the influence of surface states on the decomposition reactions are discussed. Consequences for photoelectro- chemical solar cells are outlined. Photodecomposition is a phenomenon common to all semiconducting electrodes in photoelectrochemical cells. It is the prominent obstacle to their application in liquid junction solar cells and it is therefore very important in understanding the conditions which lead to photodecomposition.This problem has already been discussed from thermodynamic and kinetic points of ~iew.l-~ Some earlier conclusions ' n 3 will be modified in this paper. 1. THERMODYNAMIC ASPECTS 1 . 1 . DECOMPOSITION POTENTIALS OF SEMICONDUCTORS Semiconductors in contact with an electrolyte can decompose in electrochemical reactions either by oxidation or reduction. It was found in the earliest stages of semi- conductor electrochemistry that oxidative decomposition is caused by reactions with hole^^-^ and reductive decomposition by reactions with electron~.'9~ In some cases, electrons and holes are involved in different steps of the overall reactions.In order to provide a general formulation of this process we shall consider the decomposition of a binary-compound semiconductor MA and describe this by the following reactions : MA + (z - x)h+ + soh $ Mz+ solv + A + xe- MA + (z - y)e- + solv + M + A': solv + yh+. (1) (2) It turns out that x and y in these equations are practically zero if the semiconductors have band-gaps > - 1 eV.' A combination of both processes can describe the electro- chemical mechanism of a neutral decomposition reaction. The above reactions have been formulated as reversible processes although they are in most cases irreversible, proceeding only in the direction from left to right.In this paragraph, however, we shall deal with the thermodynamics of these reactions and consider them as reversible. Combining reactions (1) or (2) with the electrode reaction of the reference system, e.g., the standard hydrogen electrode,138 PHOTODECOMPOSITION OF SEMICONDUCTORS one can formulate chemical reactions for which the free-energy difference may be available in thermodynamic tables. This gives for the oxidative process, MA + zH+ solv + M": solv + A +$H2 and for the reductive reaction, (4) Knowing the AGO values of reactions (4) and (5), one ultimately obtains the standard decomposition potentials co in the electrochemical scale, with reaction (3) as the refer- ence zero, from -- AGO - cOdecomp d 3 F where the plus sign is used for the anodic decomposition [reaction (l)] and the minus sign for the cathodic one [reaction (2)].The free energy of the electrons and the holes depends on the electrode potential and is therefore variable. The thermodynamic data of all the other reactants of eqn (1) and (2) are invariable for a given composition of the system. Knowing the decom- position potentials for a semiconductor one can predict its stability from the free energy, i.e., the redox potential of electrons and holes in the electrode. If the redox potential of holes is more positive than the anodic decomposition potential, p&decomp, decomposition can proceed; otherwise not. If the redox potential of electrons is more negative than the cathodic decomposition potential, ncdecomp, decomposition is possible.These thermodynamic conditions for decomposition, however, do not imply that decomposition really occurs if these limits are exceeded. Kinetics modify the real behaviour very much as we shall discuss later. 1.2. FREE ENERGY OF ELECTRONS AND HOLES AND THE ELECTROCHEMICAL SCALE OF REDOX POTENTIALS The free energy of electrons in a solid is described by the position of the Fermi level, EF, because electrons obey Fermi statistics.' The reference state for the elec- tron is either the vacuum level or, in the case of a semiconductor, one of the band edges which form the energy gap. The concentration of electrons in the conduction band, n, is related to the energy of the bottom of this band, E,, to the effective density of states, N,, in this band and the Fermi energy EF by EF - Ec n N T - exp (- -) kT * (7) This is an approximation in which the electrons are treated as if they were all species For referred to a potential-energy datum at the bottom of the conduction band.n << N,, a simpler approximation is Analogous equations describe the concentration of holes in the valence band within the same approximations :H. GERISCHER 139 i f p < Nv: EF = Ev - kTln __ (9 where p is the hole concentration in ~ m - ~ and Nv is the effective density of states in the valence band in cm3. At equilibrium, the concentrations of electrons and holes are coupled by the rela- tion n x p = (Nc - n)(NV - p ) exp (1 1) where Ec - Ev = AEgag, the width of the band gap. For n < Nc and p < N,, relation (1 1) reads n x p = N c N v e x p ( - E&EV). Eqn (7)-(10) demonstrate that the free energy of electrons and holes is strictly corre- lated to the energy position of the band edges, Ec and Ev.It is therefore very impor- tant to know these energies. They are related to the work functions (Ev) and to the electron affinity (Ec) of a semiconductor. However, since in electrochemistry elec- tron energies are measured as redox potentials uersus a standard electrode as the refer- ence, it is necessary to know the positions of Ec and Ev on such a scale. One obtains the correlation between the electrochemical scale and the vacuum level if one knows the Fermi energy of the reference system in relation to the vacuum level. For the standard hydrogen electrode, this would be the Fermi level of the electrons in the metal on which the electrode reaction (3) is in equilibrium.This value is not known exactly, but is in the range -4.5 to &0.2 eV.lO*ll The exact value is not important from the conceptual point of view. We shall use the correlation EF = -eoc + const (13) where the constant is ca. -4.5 eV. There are several ways of measuring the position of the band edges on the electro- chemical scale. The most reliable comes from capacity measurements in the potential range where a depletion layer is formed at the contact to the electr~lyte.l~-~~ Another convenient method is by observing the onset of a photoc~rrent.~~ The position of the band edges can vary if the electric charge on the surface varies with the potential applied. This can be caused by an excess of electric charge either in electronic surface states, or in form of adsorbed ions or by a very high concentration of electrons or holes at the surface (approaching degeneracy).The position of Ec and Ev relative to the reference electrode in the electrolyte is then altered by a varying potential drop in the Helmholtz double layer at the interface. Such a variation of the position of the band edges can also be a consequence of illumination as we shall discuss later. 1.3. QUASI-FERMI ENERGIES OF ELECTRONS AND HOLES UNDER ILLUMINATION In the illuminated region of a semiconductor, where light is absorbed and electron- hole pairs are generated, equilibrium between electrons and holes is no longer pre- served. Both charge carriers are in an excess to such an extent that, in the steady state, recombination and transport locally compensate the generation rate.However, since the dissipation of excess energy within the electron bands occurs very rapidly, one can still assume that the distribution of electrons and holes over the quantum140 PHOTODECOMPOSITION OF SEMICONDUCTORS states of their respective bands remains in thermal equilibrium. The increase in free energy can then be described by the excess concentrations, and the free energy of electrons and holes can locally be represented by their respective quasi-Fermi levels,16 .E: and pEz Denoting the excess concentrations by An* and Ap* we can write n* = n +An* p* = p 4- Ap* (16) where n and p may be the equilibrium concentrations according to eqn (12).One sees that drastic changes in free energy under illumination can only be expected for carriers with a low equilibrium concentration such that Ac* > c. These are the minor- ity carriers of a doped semiconductor. In an intrinsic or very low doped material, the deviation in free energy can be large for both types of electronic carriers. 1.4. STABILITY AGAINST PHOTODECOMPOSITION We have stated in section 1.1 that the decomposition in the anodic direction re- quires the redox potential of holes to be more anodic than the oxidative decomposi- tion potential. For decomposition in the cathodic direction it is necessary that the redox potential of the electrons is more cathodic than the reductive decomposition potential. The redox potentials of holes and electrons can then be replaced by their Fermi or quasi-Fermi energies and the decomposition potential by the equivalent Fermi energies for decomposition according to eqn (1 3), A decisive factor for the reactivity is the local free energy of electrons and holes at the surface.Consequently, stability against photodecomposition means where the index s means " surface ". In order to predict stability or instability we must get some idea of the E$,s values which will considerably differ from the bulk values if light is falling onto the electrode. 2. KINETIC ASPECTS 2 . 1 . RATE OF DECOMPOSITION REACTIONS It has been stated in section 1.1 that anodic decomposition of semiconductors with a wider-band gap occurs with holes as reactants and cathodic decomposition with elec- trons as reactants.It appears that the rate-determining step in most cases is the first or second one-electron transfer step in a series of consecutive oxidation or reduc- tion steps which are needed for the net reaction. The real process is much more com- plex since structural influences like surface orientation, structural defects, efc., have to be taken into a c c o ~ n t . l ~ - ~ ~ We shall, however, use here a very simplified model for the description of the reac- tion kinetics which is represented by fig. 1. This picture shows the bond breaking inH. GERISCHER 141 two steps. The first is induced by a hole and results in the formation of a new bond between a nucleophilic ligand and one of the previously connected surface atoms. The second step completes the bond-breaking by a second hole with the formation of a new bond between the other surface atom and a second ligand.We assume that g: X x x -.sol v g X + h++ X- - + s o l v @ X +h'+ X- R + h++ X - - f-- I - P FIG. 1.-Model for the two first steps of anodic decomposition of a semiconductor. one of these steps is rate-determining and the following reaction steps completing the removal of the kink site atom from the crystal lattice are fast. The kinetics of the two reaction steps of this scheme can be described by the fol- lowing equation: ps is the surface concentration of holes, [I] the concentration of the intermediate and AqH the potential drop in the Helmholtz double layer, a1 and cc2 are the charge-trans- fer coefficients for the attachment of the ligand X- to the surface atoms in step 1 and 2 where the charged ligand has to pass the Helmholtz double layer.* Dl = 1 - al.Applying the steady-state condition, v1 = v2, one gets for the rate of decomposi- tion, The two limiting cases are as follows: First step rate-determining, second step rate determining, 3 * If the ligands were uncharged, but lose an ion during their attachment, like HzO forming an OH- bond, the same type of equation would be valid.2142 PHOTODECOMPOSITION OF SEMICONDUCTORS The rate equations resulting from this simplified model are typical of all electrolytic decomposition reactions, although they will usually be even more complex. They show that it is not only the concentration of holes (or electrons in cathodic decompo- sition) which controls the rate but also the position of the band edges at the surface which varies with the voltage drop ApH in the Helmholtz double layer.Whether and how a change in ApH can be induced by illumination will be discussed in the next sec- ion. We see in these rate equations that p s and ApH are the important parameters influencing the rate of anodic decomposition. For cathodic decomposition this role is played by n, and AyH, To establish the connection with the thermodynamic treat- ment, we shall use eqn (7)-(lo), (14) and (15) in order to describe the surface concen- trations. 2.2, SEMICONDUCTOR/ELECTROLYTE CONTACT UNDER ILLUMINATION The electronic charge carriers which take part in photoreactions are overwhelmingly generated in the bulk. Transport from the bulk to the surface occurs either by dif- fusion or by migration in an electric field.The mean diffusion length of excess car- riers depends on their lifetime and can vary to a large extent. Electric migration is important in the space-charge layer, which has a considerable extension only under conditions where a depletion layer is formed. The combination of electron-hole pair generation by light absorption with diffusion, recombination and electric migration in an electric field, which itself is dependent on the distribution of the mobile charge carriers, makes the theoretical calculation of the real charge distribution in the sta- tionary state of illumination extremely complicated. Some solutions have been out- lined based on simplifying a s s ~ m p t i o n s . ~ ~ - ~ ~ In order to understand the principal features, we need not go into such detail.A qualitative representation of the situa- tion found in an illuminated boundary layer at a semiconductor electrolyte contact will be sufficient for this purpose. We consider first a blocking semiconductor electrolyte contact in order to show how much, and in what way, illumination can change the free energy of electrons and holes at the surface. We compare the situation in the dark and under illumination for different positions of the Fermi level in the bulk, i.e., for different voltages applied. Fig. 2 shows the course of the band edge positions and of the quasi-Fermi levels in the boundary layer of the semiconductor for three characteristic situations. Fig. 2 is constructed for an n-type semiconductor with the penetration depth of the light being larger than the extension of the space-charge layer under illumination.For a p-type semiconductor with equivalent properties, the figures would have to be inverted with the band edges and Fermi levels exchanged in order to represent the analogous situa- tions. The energy scale in fig. 2 is related to the flat-band energy, Efb, of the particular semiconductor. The illuminated case represents the steady state where all generated electron-hole pairs disappear by recombination. The Fermi level in the bulk is as- sumed to be held constant by an external voltage source. Fig. 2(a) shows the situation at the flat-band potential. The bands remain prac- tically flat under illumination (Dember voltages are neglected).The Fermi level of the majorities (electrons) is nearly unchanged, but the quasi-Fermi level of the minorities (holes) deviates in the illuminated layer largely from the equilibrium value and reaches its maximum deviation at the surface. At very high intensity, pEZ can approach Ev. Fig. 2(b) represents the depletion layer with a positive excess charge on the n-type semiconductor. The large band-bending in the dark indicates the presence of an elec-H . GERISCHER 143 tric field in the space-charge layer which, under illumination, separates electron- hole pairs if they are generated therein or reach this region by diffusion. This charge separation acts in opposition to the electric field present in the dark, and the band bend- ing decreases. With a fixed Fermi level in the bulk, the energy difference between the bulk and the electrolyte remains constant.This is only possible if the voltage drop lost in the space-charge layer is compensated by an equal voltage gain in the Helm- holtz double layer. In order to obtain this compensation, surface charge is needed. dark iII uminated E lbJ FIG. 2.-Energy diagrams of an n-type semiconductor electrode at three different electrode potentials in the absence of any electrode reaction. If surface states with donor character are available in the band gap at sufficient den- sity, they can perform this function. Otherwise, an accumulation of the minority carriers at the surface is needed, and an inversion layer is obtained. This is assumed in fig. 2(6). For completeness, fig.2(c) shows the situation where an accumulation layer is formed in the dark. This has the consequence of an increased recombination rate at the surface, as indicated in fig. 2(c) by the upward bending of &$ at the interface. With regard to stability we have to correlate the quasi-Fermi levels at the surface with the semiconductor decomposition potentials. This means that a current can pass the interface. We shall first discuss the case where decomposition reactions are the only144 PHOTODECOMPOSITION OF SEMICONDUCTORS possible redox reactions. Although this case is rather unrealistic, since redox reactions of the solvent are unavoidable, it provides some instructive information. Fig. 3 com- pares the situation of an n-type semiconductor in the dark and under illumination for three different positions of the decomposition potentials relative to the band edges.As in the dark situation, the flat-band potential is used. The three cases differ in the position of the decomposition potentials and in their distance from each other. dark iilu minat ed 1 la) \ E I - n E decornp - [fb -p 'decornp - € f b -n Edecom p p fdecomp - EV E - E l f c , s n decornp \ \ I b €",S 9- p ldecornp n Ed ecom p p ldecomp - p fdecom p FIG. 3.-n-Type semiconductor at the flat-band potential showing 3 different positions of the de- composition Fermi levels. In the absence of other redox reactions which could compensate the charge con- sumption of an electrochemical decomposition reaction, unidirectional photodecom- position cannot proceed in a steady state.Recombination controls the steady-state situation and may be catalysed by the intermediates of the decomposition process as indicated in fig. 3(a) and (b) by the dashed arrows. In case (a), the accumulation of electrons leads to an upward shift of the band edges until anodic decomposition is prevented by recombination. In case (b), cathodic decomposition is avoided by a depletion of electrons. Case (c) shows a situation where both decomposition reactions have Fermi ener- gies within the gap and can both proceed under illumination. How fast these occur is a question of reaction rates. This scheme represents the electrochemical mechanism of photodecomposition such as seems to occur with Cu,O, which disproportionates under illumination to Cu and C U O .~ ~H. GERISCHER 145 2.3. COMPETITION BETWEEN DECOMPOSITION AND REDOX REACTIONS We now proceed to the more realistic assumption that, besides decomposition reactions, redox reactions with species of the electrolyte are possible. Again, we shall discuss typical and interesting cases in terms of the position of the characteristic energy levels in the dark and under illumination. The cases to be discussed here cor- respond to the four types derived previously1g3 from a comparison between the posi- tion of the band edges and the decomposition potentials. Fig. 4 shows an n-type semiconductor which is stable against cathodic decomposi- i II urn ina ted dark - nE decomp - fredox - p Ed ec o rn p FIG. 4.-n-Type semiconductor in contact with a slightly oxidising redox system: (a) dark; (b) slow; (c) fast redox reaction.tion because ,,Edecomp>EC. The redox system has a redox Fermi level located in the band gap and electron exchange may be fast enough to establish equilibrium such that a depletion layer is formed [fig. 4(a)]. Two possible situations under illumination are shown in fig. 4(b) and (c). If the redox reaction is slow, as for example the oxidation of water due to the slow reaction steps involved, can pass pEdecomp as shown in fig. 4(b). It then depends on the kinetics of decomposition (cf. section 2.1) whether it occurs at a noticeable rate or not. If the redox reaction is very fast, the quasi-Fermi levels of both charge carriers will be held at the surface close to the redox Fermi level. A great deal of the recom- bination between electrons and holes occurs then via the anodic and cathodic current of the redox reaction which compensate each other.The decomposition Fermi level cannot be reached by the holes. This is depicted in fig. 4(c). The situation of fig. 5 is much less favourable. The redox system is so strongly dark i I lu m ina t e d fF - - - ---- - EV fr::: - redox - p [decamp ICl f ' - [redox - p Ed eco rn p FIG. 5.-n-Type semiconductor in contact with a strongly oxidising redox system: (a) dark, (b) slow, (c) fast redox reaction.146 PHOTODECOMPOSITION OF SEMICONDUCTORS oxidising that it can even inject holes in the dark, with the result that an inversion layer is formed at the contact. If the redox reaction is sluggish, ,,E$ will be shifted downwards at illumination, partly by a further increase inp, but mainly by a downward shift of Ev (increase in ApH) as shown in fig.5(b). This can accelerate decomposition according to section 2.1 to a considerable extent, as is indicated in this figure. If, however, the hole-exchange rate is high, the quasi-Fermi level of holes will remain closely pinned to the redox Fermi level in solution, and the decomposition rate will remain negligible under illumination as indicated in fig. 5(c). Fig. 6 shows the equivalent situations for a p-type semiconductor with respect to d a r k i l l u r n i n a t ed la/ Ibl /C/ P fF FIG. 6.-p-Type semiconductor in contact with a redox system forming a depletion layer: (a) dark, (6) slow, (c) fast redox reaction. cathodic decomposition.Now, the quasi-Fermi level of electrons plays the decisive role in decomposition. This is indicated in fig. 6(b) and (c), where (b) depicts the unfavourable situation with a slow redox reaction where an upward shift of the band edges occurs by an accumulation of electrons at the surface. The kinetic model discussed in section 2.1 has shown that the rate of a decomposi- tion reaction can be of higher order with respect to the surface concentration of holes. A competing one-electron transfer redox reaction will in such cases become less pro- tective with increasing illumination intensity. If the competing redox reaction is it- self complex, containing several steps, and the rate-determining step is not the first step to occur then its rate will also follow a higher order inp,.In such cases, increas- ing illumination intensity will not in every case favour decomposition in relative terms. However, each increase of p , or AyH will accelerate anodic decomposition in absolute terms, each increase of n, and - A q H will accelerate cathodic decomposition if these reactions are possible. Therefore, increasing light intensity will in all cases increase the risk of photodecomposition. A systematic investigation of the competi- tion between redox reactions and the anodic decomposition process has recently been conducted by go me^.'^ 2.4. ROLE OF SURFACE STATES Surface states can catalyse the rate of recombination and of redox reactions at a semiconductor s ~ r f a c e . ~ ~ ~ ~ ~ - * ~ They usually can exchange electrons rapidly with redox couples in solution if their energy levels are in the same range as those of the redox system.Electron exchange with the bulk of the semiconductor will be fast if the surface states have energy levels close to one of the band edges. Surface states too far away from the band edges will only pick up charge in the downhill directionH . GERISCHER 147 with respect to energy. That is to say, donor states can trap holes from the valence band but cannot inject electrons into the conduction band; acceptor states will pick up electrons from the conduction band but cannot inject holes into the valence band. Only with very highly doped semiconductors are the reverse processes possible via t~nnelling.~~ -31 A consequence of this picture is that surface states with energies in the band gap will have a different state of occupation under illumination.If they are present in considerable concentrations, this can contribute to the charge in the Helmholtz double layer and thus cause a corresponding shift of the band edge positions at the interface with all its consequences for the kinetics (cf. section 2.1). On the other hand, surface states catalyse recombination and can pin the quasi-Fermi level to this energy range either by fast recombination or, in the absence of recombination, by a rapid electron transfer to a redox system in solution. Fig. 7 shows these two functions of surface states with donor character at an n-type dark ill u rn inat e d FIG. 7.--n-Type semiconductor with surface states of donor character in contact with a redox elec- trolyte.semiconductor. They are neutral in the occupied state and positively charged if they are vacant. The left-hand side of fig. 7 represents a situation at equilibrium where the surface charge has shifted the band edges downwards compared with their position at the flat-band potential, where all surface states would be occupied. This is indicated by the arrow representing the energy drop in the Helmholtz double layer Under illumination, the positive charge will increase by hole capture from the valence band. This causes a further downward shift of the band edges at the interface, while in the bulk the band edges shift upwards because of the decreased space charge. This is depicted at the right-hand side of fig. 7. The amount of this shift depends on the illumination intensity, on the concentration of surface states and, most important, on the electron and hole capture rates by the surface states.If both rates are very fast, the shift will be small. If hole capture is the faster process, the downward shift will be large and pE: may pass the Fermi level for decomposition as assumed in fig. 7. If the hole capture is slow, pinning of pEg to the range of the surface-state energy will not occur. In this case will easily pass Edecomp and the surface-states have little effect on stability, or even worsen the situation by accumulating positive charge and shifting the band edges further downwards. Fig. 8 shows the analogous situation for an n-type semiconductor with surface states of acceptor character, which are negatively charged if occupied, and neutral if vacant.In this case, accumulation of charge in surface states can only cause an up- (-eoA%)-148 PHOTODECOMPOSITION OF SEMICONDUCTORS lifting of the band edges at the interface. This improves the stability against anodic photodecomposition. It may, however, cause cathodic decomposition if the uplift goes too far (somewhat farther than shown on the illuminated case of fig. 8). For p-type semiconductors, the situation is fully analogous, as one can easily derive in the same way. The general conclusion is that surface states can help prevent photo- decomposition by fast catalysis of surface recombination. They can, however, also I acceptor ‘dew rn p d a r k illurninat ed FIG. 8.-n-Type semiconductor with surface states of acceptor character in contact with a redox elec- trolyte. increase the tendency to photodecomposition if they accumulate charge of the same sign as that of the minority carriers and shift the band edges at the surface by a varia- tion of ApH in the direction of the minority band.3 . APPLICATION TO SOLAR CELLS Electrochemical solar cells are either of the regenerative or storage type.32-34 Both types are based on the formation of a Schottky barrier at the semiconductor-electrolyte interface. Optimal efficiency can be reached if the barrier height in the dark becomes identical to the band gap. This corresponds to a slight modification of fig. 4 and 5 with Eredox close to the valence band edge or to fig. 6 with &dox close to J!&.Under illumination, we have again very similar situations as in fig. 4-6 with the only difference being that the anodic current through the interface is not compensated by a cathodic current. The current of the majority carriers flows now into the bulk of the semi- ductor and from there via an external loop with resistance Rext to the counter-elec- trode. The result is a smaller upward or downward shift of the Fermi level in the bulk and, at the surface, a larger deviation of the quasi-Fermi level of the minority carriers from the Fermi level of the redox system. Fig. 9 shows this situation for an n-type semiconductor. With decreasing Rext one approaches the situations of fig. 2 with a fixed Fermi level in the bulk, while increasing Rext leads to the situations of fig.4-6. In the first case, the risk of photodecomposition is largest since the greatest deviation of E$ is then obtained for the minority carrier. With respect to the competition between a redox reaction and the decomposition process, the same situation is found as pointed out in sections 2.3 and 2.4. The case of a storage cell will be discussed for a redox battery with two different redox couples in the two compartments of the cell, separated by a membrane withH . GERISCHER 149 selective permeability. If one of the electrodes is a metal and the other a semiconduc- tor, the electrodes must be disconnected in the dark in order to prevent discharge. Direct contact between both electrodes (ReXt + 0) will pin the Fermi level in the bulk of the semiconductor electrode close to the Fermi level of the metallic counter-elec- trode, because the redox reaction there will have a much larger rate constant and pro- se mi condu ctor e I e c t ro l y t e m e t a I semiconductor electrolyte m e t a l d a r k i l l u m i n a t e d FIG.9.-Energy diagram of a regenerative photoelectrolytic cell with a slow redox reaction at the semiconductor electrode. ceed at a smaller overvoltage. In order to store energy, the quasi-Fermi level of the minority carriers must differ at the surface by more than the open-cell voltage of the battery system from the Fermi level in the bulk of the semiconductor. In the dark we therefore arrive at a situation similar to that shown in fig. 4(a), while the illuminated case corresponds to fig. 5(b) or (c).This is depicted in fig. 10. I I / i.F-t--- I I \ I I '\I,\ 1 \ \ r e d o x I r e d o x semiconductor electrolytelelectrolyte m e t a l s e m i - 1 redox I redox I conduct or electrolyte electrolyte metal FIG. 10.-Energy diagram of a photoelectrochemical storage cell with a slow (a) or fast (b) redox reaction at the semiconductor electrode. With respect to photodecomposition, the statements made in section 2.3 and 2.4 are valid. If the decomposition Fermi levels are not outside the band gap, it is a question of competing kinetics whether, and how fast, decomposition occurs. In contrast to the previous case of a regenerative cell, the danger that a shift of the band150 PHOTODECOMPOSITION OF SEMICONDUCTORS edges at the surface by an accumulation of surface charge increases the free energy of the minority carriers at the semiconductor surface too far is diminished in a storage cell.The reason is that the decrease of the free energy of the majority carriers in the bulk which would be connected with such a shift would cause the rate of the redox reaction at the counter electrode to decrease and finally fully to cancel the charging current. In summarising, the discussion in this paper has shown that in order to analyse the tendency to photodecomposition one has to take into account the possibility of a variation of the voltage drop in the Helmholtz double layer caused by the contact with the redox electrolyte or by illumination. This will often have an unfavourable in- fluence since it is more likely that this shift makes the minority carriers at the surface more reactive (downwards shift for holes or upwards shift for electrons).However, this effect can also lead to an improvement of stability if the added surface charge has the opposite sign from the minority carriers. To find such a system should be a chal- lenge for future research. For the electrochemical solar cells the previously derived criteria of ~tabilityl-~ can still be used if one relates the decomposition Fermi energies to the correct position of the band edges at the surface of the semiconductor under working conditions instead of to their position at the extrapolated flat-band potential in the dark. How fast decomposition really occurs even provided it is thermodyna- mically possible, cannot be predicted from general principles.This must be checked experimentally from case to case. All light absorbed would then be lost by recombination. H. Gerischer, J . Electroanalyt. Chem., 1977, 82, 133. A. J. Bard and M. S. Wrighton, J. Electrochem. SOC., 1977, 124, 1706. H. Gerischer, J . Vac. Sci. Technol., 1978, 15, 1422. W. H. Brattain and C. G. B. Garrett, BellSyst. Tech. J., 1955, 32, 1. F. Beck and H. Gerischer, Ber. Bunsenges. phys. Chem., 1959, 63, 500. R. Williams, J. Chem. Phys., 1960, 32, 1505. H. R. Schoeppel and H. Gerischer, Ber. Bunsenges. phys. Chem., 1971,75, 1237. W. Shockley, Electrons and Holes in Semiconductors (Van Nostrand, Princeton, 1950). S. Trasatti, Advances in Electrochemistry and Electrochemical Engineering, ed. H. Gerischer and C. W. Tobias (Wiley, New York, 1977), vol. 10, p. 213. New York, 1967). ' H. Gerischer and W. Mindt, Electrochim. Acta, 1968, 13, 1329. lo F. Lohmann, 2. Naturforsch., 1967, 22A, 813. l2 J. F. Dewald, Bell. Syst. Tech. J., 1960, 39, 615. l 3 cJ V. A. Myamlin and Yu. V. Pleskov, Electrochemistry o j Semiconductors (Plenum Press, l4 R. A. L. Van den Berghe, F. Cardon and W. P. Gomes, Surface Sci., 1973, 39, 368. l5 M. A. Butler, J . Appl. Phys., 1977, 48, 1914. l6 W. Shockley, Electrons and Holes in Semiconductors (Van Nostrand, Princeton, 1950), p. 302. e.g., H. Gerischer, F. Hein, M. Luebke, E. Meyer, B. Pettinger and B. Schoeppel, Ber. Bunsen- ges. phys. Chem., 1973, 77, 284. R. L. Meierhaage, F. Cardon and W. P. Gomes, Ber. Bunsenges. phys. Chem., 1979, 83,236. l 9 W. Kautek, H. Gerischer and H. Tributsch, Ber. Bunsenges. phys. Chenz., 1979, 83, 1000. 'OW. W. Gaertner, Phys. Rev., 1959, 116, 84. R. H. Wilson, J. Appl. Phys., 1977, 48, 4292. 22 H. Reiss, J. Electrochem. Sac., 1978, 125, 937. 23 J. Reichman, Appl. Phys. Letters, 1980, 36, 574. 24 K. Hauffe and K. Reinhold, Ber. Bunsenges. phys. Chem., 1972, 76, 616. 25 W. P. Gomes, lecture at the ACS-meeting in Houston, March 1980, in course of publication. 26 H. Gerischer, Surface Sci., 1969, 13, 265. 27 K. H. Beckmann and R. Memming, J . Electrochem. SOC., 1969, 116, 368. 29 P. J. Boddy, J. Electrochem. SOC., 1968, 115, 199. 30 F. Moellers and R. Memming, Ber. Bunsenges. phys. Chem., 1972, 76, 469, 475. 31 B. Pettinger, H. R. Schoeppel and H. Gerischer, Ber. Bunsenges. phys. Chem., 1974, 78, 450, S . N. Frank and A. J. Bard, J . Amer. Chem. SOC., 1975, 97, 7427. 1024.H . GERISCHER 151 32 cf. H. Gerischer in Solar Power and Fuels, Proc. 1st Int. Conf. Photochemical Conversion of 33 cf. Semiconductor Liquid-Junction Solar Cells, ed. A. Heller, Proceedings Vol. 77-3 (The Elec- 34 cf. H. Gerischer in Topics Appl. Phys., 1979, 31, 115. Solar Energy 1976, ed. J. R. Bolton (Academic Press, New York, 1977), p. 77. trochem. Society, Princeton, 1977).