Surfaces for photoelectrochemical cells

Surface Scicncc 0 North-llolland

86 (1979) 462 483 Publishing Company

SURFACES FOR P~OTOELECTROC~E~ICAL

CELLS

1. introduction For a solar energy conversion method to be able to make a substantial contribution to man’s energy needs, it must be suited to large area low cost fab~ic~iti(~t~.At present the only luw cost methods arc concerned with collection of heat, the lowest form of- energy. For higher forms, such as electricity, fairly exj>ensive technology has so far been needed either for direct conversion of sunlight or for generation from solar heat. In the case of j’hotoelectroci~erliicai methods, interest sterns fi-tm their potential for producing electricity and in some cases hydrogen, a storable fuel, using relatively low cost technology. The main factor is that the semiconductor, which forms the basis of the method, has its front contact provided by an optically transparent liquid. This avoids expensive and troublesome provision ot‘ applied ohmic finger contacts, as in photovoltsic cells. In addition the complete surface coverage by the liquid relaxes to a significant degree the requirement for long tliffusion tengtlis of carriers in order to reach otherwise distant contacts. Hence lower cjuaiity semiconductor material can be used, in particular expensive single crystals do not have such an advantage over cheajm polycrystalline films. Lastly there is the possibility of producing fuel gas from tlic electrolyte - to date mostly hydropeu has been considered.

D. Hanernan

2. Fundamental

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cells

There have been various accounts of the processes in photoelectrochemical cells but an apparent misappreciation of some factors has led to incorrect or misleading energy level diagrams in the few cases where complete schemes have been produced (e.g. Nozik [I], Butler and Ginley [2]). In fact the PEC system is very complex in that it contains three different materials and includes a metal-electrolyte interface and semiconductor-electrolyte interface (sometimes two). While the physics of the semiconductor is well understood, the situation in the liquid electrolyte is not as thoroughly known. There have been various treatments in detail of the processes at solid-electrolyte interfaces but many problems remain, not excluding experimental reproducibility. In addition to practical features such as surface inhomogeneities even in single crystal studies, it is hard to obtain sufficient double layer (surface dipole layer) information to permit proper double layer corrections in kinetic studies. It is thus difficult for theoretical treatments to take into account fully the dynamic properties of the electrode--solution interface. particularly with respect to absorption. Of great importance is the development of a quantitative understanding of the factors which influence the interface charge transfer and rate constants and dissolutions mechanisms. Since a proper evaluation of the PEC energy diagram is a first step in order to decide on desirable parameters for the surfaces involved, we commence with a discussion of energy levels. It is desirable to adopt a uniform description for both semiconductor and electrolyte. Unfortunately different schemes have been used for the semiconductor on one hand and the electrolyte on the other. We shall use the language and concepts of semiconductor physics throughout as there appears to be some tendency for this to become the preferred framework. The emphasis will be on bringing out the fundamental physical concepts. The first point to appreciate is that the PEC system consists of three components and the energy equilibration is determined by all three, including the electrolyte, and not just by the anode and cathode. To illustrate how to achieve this three component equilibration, we briefly review the formation of a metal semiconductor contact.

3. The metal-semiconductor

connection

Fig. 1 shows the Fermi energy level and external surface potential barrier for a metal and n type semiconductor (without surface states) prior to contact. In these kinds of diagram the vertical scale represents the energy of a single electron. The top of the valence band F, is the highest energy state of the so called valence band which itself is a distribution of electron states corresponding to valence electrons in a molecule of the material. The quantity E, is the bottom of the conduction band, being the lowest state of the distribution of states derived from the next highest

I

F-

I (0)

Kg. 1. Electron

energy tevels for 0. Metal work function (a) greater conduction state distribution for conduction state distribution for

E “C

/

j

(b)

n type senliconductor and metal. relative to vacuum level V = than and (b) less than that of semiconductor. E, is bottom of semiconductor, Er;. is Fermi level, L<,, is bottom of valence/ metal.

state above the valence state in a section of the material. These valence and conduction state distributions (we henceforth refer to each as a distribution rather than the restrictive term “band”) arise because of overlap of orbitals of electrons when the solid is formed. They do not require that there be long range periodic symmetry. If there is long range translational symmetry as in a single crystal or polycrystalline semiconductor or metal, then a new quantum vector k may be defined and one-electron energy dependence on k can be calculated to give so called energy bands. However for the material to be a semiconductor or electronic insulator in general it is sufficient only that there be a significant energy gap between the valence and conduction state distributions, and that the Fermi level EF lie in this gap and not too close (20.1 eV) to 6’” or E,. The Fermi level in equilibrium is the energy of the electron state whose occupation probability is one half - there is no requirement that such a state actually exist (be “allowed”) for a given material. At the surface, an eIectron is in an asymmetric environment and can be removed to infinity if the attraction of the positive ion cores can be overcome. We define the energy of an electron at in~~lity as zero, and call this the vacuum level Y. We shall refer all energies to this fixed zero. The shape of the potential curve outside the solid is determined by the nature and packing of the ion cores and their shielding by electrons, it is shown schematic~ly in fig. 1. It is necessary to be careful about the concepts of work function and electron affinity. The work function W is not in general the energy interval between E,- and the vacuum level as sometimes loosely asserted - it is the interval between Er: and a point outside the solid. In practical cases, namely solids connected to others (or isolated solids with different surfaces exposed) this point is approximately the knee in the potential barrier prof3e as in fig .2. It can be specified as the point where the straight and curved portions of the energy profde in fig . 2 meet. Similarly the elec-

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cells

-._

-\-_ \

/

wscXI I

_-

r

\

I

%A

EF--L-lt

l-1--E

E”

\

EC

I

Y

F

Eve

(b)

Fig. 2. Same as fig. 1, but after electrical connection and equilibrium has been established. Note state distribution (band) edges are affected by surface region charges. The field penetration in metal is about 1 P. but in most semiconductors is of order microns.

tron affinity x of the semiconductor is the energy interval between E, and this same point. The importance of this is seen when an electrical connection (not contact) is established between the materials as in fig. 2. From thermodynamic arguments, once the electron distributions in the two materials come to equilibrium they must have the same Fermi level. This comes about by electrons flowing from the material of low work function to that of high since the latter has a deeper potential well, or stronger pull for electrons. Flow occurs until the Fermi levels equalise. In the example in fig. 2b, the metal had a lower work function W, than the n type semiconductor W,,. The extra electrons that the metal loses to the latter leave a net positive charge which has to reside on its exterior since the electron concentration is sufficiently high and mobile in a metal to prevent any field (or excess charge) penetration below about one atomic layer. However the corresponding electron excess in the semiconductor, which has a lower conductivity, is accommodated over a finite distance. Hence an electric field penetrates the material to a depth determined by the electron density and dielectric constant. The changes are illustrated in fig. 2 and it is important to note: (a) The new joint Fermi level is distant from L’ by an amount intermediate between the original amounts for the separated Fermi levels. The actual value depends on the electron densities and sizes (surface and volume) of the two materials, (b) The work functions as defined above have hardly changed (hence the value of the definition, since a work function that depends on the nature of connections is not a useful quantity). (c) The surface exterior potential barrier for the high work function material actually rises above the zero level V’,i.e. a distant electron is repelled from the material. This feature (which the author has not seen explicitly pointed out elsewhere) arises because the negative charge on the surface of the material has a relatively long range

repulsion compared with the strong but short Irange attl-action of the ion cores (a surface charge density 0 on an infinite sheet exerts an electric field I:’ = (i/co where E” is the fret space permittivity. This expression does not reduce at all with distance. For distances small with respect to the surface dimeiisions the Ihi-nida applies approximately, i.e. the field will reduce very slowly, whereas the ion core attraction r-educes rapidly with distance). (d) The electron affinity as defined above has, like the work function. hardly changed. However . (ej The distance off:‘, at the surface fmn the vacuum level c’will change in genel-al, contrary to frequent assumptions that it is constant. The reason it must change is that there is now charge, not only within the sennicollductor but also in a sheet outside it. Hence the energy required to remove an electron from ICCat the surface to V is altered since it must traverse the sheet of charge. (f) There is now an internal surface barrier in the semiconductor caused by the graclient in extra charge coming in from the surface. In fig. ?a the situation is described by saying the bands turn up and in fig. 21~.the bands tul-11down. (The most general statement would be that the energy gap edges turn up or down respectively.) This surface barrier is of vital importance to the operation of the PEC cell. (g) The extra charge on the materials is ~tccolllmotlatetl partly in internal states, partly in surface states if they exist, and partly in states external to the surface. These states ar-ise from a solution of the wave equation for the solid with cutru charge on il. We name them “outer surface states” and distinguish theni from the normal surface states which arise from a solution 01‘the wave equation for the surface region \viflmrt extra charge on the solid. The above description has not assumed an appreciable density of surface states. If these arc present to a considerable degree on the scniiconductor hcfim connection with the metal then the gap edges i:‘, and I:‘, will turn up in the (n type) sc with a result IIIII~I~ as shown in fig. ?a. This however is because electrons fl-on1 the SC interior accumulate on the surface in tlic special (gap) states allowed there i.e. SuTface states. leaving a coiresponding deficiency in the adjoining interior. (In ttlc cast in fig. 2a the interior semiconductor electrons also flowed out, but to the sui-face of the metal). When contact is made with the metal, electrons will still flow accot-ding to the work functions. If W,, < IV’,, then electrons Ilow to the SC. They will be partly accoiiiinodated in the interior as before. partly in the surface states, and partly in a sheet extei-nal to the surface. the “outc~ surface states”. The tendency oi this flow to cause the bands to turn down 3s iii fig. 21~ is opposed by the upward band bending assumed to pre-exist due to the surface states in the energy r-augc n(3:11 Inid gap and above. The net effect depends on the relative magnitudes of the two factors. For materials such as Ge and Si with high surface state densities, (of ordei IO’” --lo” per cm’) the surface barrier is very little affected by connection with other materials. When the metal and SC arc brought into SUI$XY~corltmt the extra charges on each al-e trapped at the interface. However the proximity of atoms from both mate-

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rials will lead in general to the appearance of different surface states, now called interface states. Assuming imperfect contact at some points the outer surface states, which continue to exist in these small gaps in the contact, would also be modified by the close presence of the other surfaces.

4. The metal-electrolyte-semiconductor

connection

We now consider the effect of an electrolyte. When two materials have come to equilibrium with a common Fermi level, they may for some purposes be regarded as one and when a third material is added, electron flow between the latter and former will still occur depending upon which Fermi level is deeper with respect to I/. To continue the discussion with the same concepts, we consider the electrolyte as an electronic insulator which contains mobile ions. It has no long range translational symmetry but as described before, this does not prevent it having valence and conduction state distributions for the electrons with upper edge & and lower edge E, respectively. (Electric conduction occurs mainly by the movement of ions rather than the flow of electrons. These can be regarded as in a narrow distribution of states (at T = O).) The electrolyte being liquid, the molecules at room temperature are in kinetic motion. This broadens the electron distribution and the broadening is temperature dependent but at a given temperature the distribution edges can be depicted schematically as in fig. 3. It is then necessary to specify the Fermi level for electrons. This is usually referred to as electrochemical potential by chemists but we will mainly use the term Fermi level. In the absence of any impurities in an aqueous medium the Fermi level will be close to the middle of the energy gap by arguments analogous to those used

--+--

v=o +

Fig. 3. Energy gap edges for electrons shown schematically for electrolyte in equilibrium with metal and semiconductor. Note gap edges show effect of surface charges at interfaces, arising from (a) charge transfer between solid and liquid to cqualise electron Fermi level and from (b) mobile ion adsorption and aggregation at surfaces. These effects are not independent. T\VO redox levels are shown.

for intrinsic seiiiiconductors. In the latter, electrons are excited into the conilucti~~n bud from the valence band by thernnal agitation. This occurs also in the liquid but the number is very snd! due to the large ener g1f gap. (A iiiore important el’lcct iii an aqueous liquid is that a fraction of t I20 ~i~olecules ;ire tleconiposcd 134then rlial agitation to yield II’- -lt20 and OH-- t120 conlplcxes.) When impurities arc present in ;I seniicoiitluctor (e.g. I’ in Si). the IYe~-miIcvel is drastically affected if the impurities 21-e ionised at troom tt‘mperature. Similarly ii) tile electrolyte, the presence of electron transferring iinput-ilics afl‘ects the t’et-mi level. Some of these “impurities” exchange electrons with tlie solid and (his is described in terms of so called retlox co~~ples. It is customary to t11ww an energy level wlluse significance must be clear-ly understood conlp~~retl with tht 01‘ the usual energy level of an electron inside a solid. The redo* level, which we draw dashed in fig. 3 is for cei-tain simple cases the average eiiergq at which ;III t’lecrrori must be supplied in order for- a I-wctioll to proceed. Thus the line labclled I l’,il I2 nieuis that if an electron is supplied 3t that energy then I I’ + c- -+ II or 71I’ f 2~. + H, t. Sometimes the level refers to ;I more cuinplex t-eaction such as the one O2 + 3li’ + 4e--f 1H20 indicating ;I possible reaction that wcurs in the prcscnce ot‘dissolved oxygen when electrons are supplird at the energy in question. This is somctimes (inconsistently) indicated by a line labelled 02/11,0. We discuss rdox levels in more detail below. The energy equilibration situation in the electrolyte is complicated by t11eprescncc of more thun one kind of charge carrier. The Fermi level hr clectr-oils may 1~ defined as above but the ions can he regarded as clifl’erent particles with their owu elcctrodlemicd potential or Fermi level. The two arc I-elated as sl~owu helow. The electrocllemical potential U is the Gibbs Cr-eewergy pt’r pal-tide. Considcltwo phases a and 3 which join at an iiiterl‘ace pcriiieable to the 2oni111oii constitucrit .Y (clcctrons). The mass transport of s across the interl‘acu is proportional to UC: potciiti;ll 01‘ pIi:w a I’oI- particles 01‘ type .Y. @ \\~llCIC 1 ‘y: is tlicv electrocll3iiical Tr3nspol-t CC:ISCSwhen U: = U< (i.e. the Izcrmi levels Imx~~ne quaI). C’onsidcr ttlc plr:isc Q (t‘lectrolyte) ;ind the situation where tllt‘re is ec~uilil~rititn under tllc i~licrnic;lI lreactiuil between species Ai and I$ of stoicliionit‘tric iiuiiilwrs II 1, and 11lj, aspect ivcly. Tllw

I‘I-om tlic i-cquit-cment that the Gibbs free energy (; be ;I minimum. For if 0tlP considers the change in free energy ii{; accompanying a dcparturc l‘roin ec~uilil~riuiii 171 3 single reactioii \‘JI,,.A~ I --f l;rrQp then

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For example equilibrium under the dissociation M + M*+ + 2e- implies r/c = U$z+ + 2lJz-. A detailed discussion of these effects in the adsorbed layer at a metal- electrolyte interface has been given by Barlow [3]. When the electrolyte contacts the metal-semiconductor combination the Fermi level for electrons will equilibrate with that of the combination and electrons will flow from the material of low to high work function, as shown in fig. 2. Hence we conclude that the surface barrier established or affected in the semiconductor bg connection with the metal can be firrtlrer affected by electron transfer between it and the electrolyte. Moreover, since the surfaces are in contact, the original surface state distribution on the semiconductor will be affected by the intimate overlap of surface orbitals with those of the liquid. Hence the initial semiconductor surface states rlluy hc /~&iji’ed by the contact. The semiconductor surface barrier will then be affected by the two factors when contacting the electrolyte: (a) surface states can be altered by intimate contact due to wave function overlaps; (b) charge transfer with the electrolyte takes place to equilibrate the Fermi levels. Estimates of the first factor are very difficult. It is only recently that any detailed treatments have been carried through for interface states, and these were for ideal solid-solid faces with specified matching of the atoms on the two sides 01 the interface. Some recent treatments are by Herman [4], and Pickett and coworkers [5]. However the contact between a real surface and a liquid involves details on the atomic scale that are not well known so that there are considerable uncertainties in this case even before a calculation can be commenced. The second factor, which has usually been overlooked, requires for its evaluation a knowledge of the Fermi level in the electrolyte. The above thermodynamic consideration, eq. (l), could be applied if the various ions and electrons could all be regarded as distinct species. However the number of ions and the number of valence and conduction electrons are mutually related so that a precise treatment is complex. However note that it is the electrons that are the species that pass across the interfaces and thus the Fermi level for electrons is the quantity of interest. At present theic is very little information on the Fermi level for electrons in a free liquid (without impurities).

5. Redox couples In many electrolytes there are ions present which can accept electrons from a solid; these, together with the products, form so-called redox couples. It is usually assumed that the energy of the state into which the electron can pass is higher than the energy of the electron once it is in the state, as shown in fig. 4a. The upper state distribution is labelled oxidation (electron acceptor) and the lower, reduction (electron donor). See, e.g., Gerischer [6] and Morrison [7]. This concept must be looked at carefully. In the first place, when a species accepts an electron, the energy of the electrons is increased, not decreased. There-

470

l’ig. 4. (a) Usual picture of oxidation and reduction states of redo\ couple of standard potenlial EK and “reorganisation cncrgy” A. Width trf’ distribution is due IO fluctuating field caused by agitation of polar nmlecules surrounding redox n:olcculcs at surface. (b) Actual sequoncc; 1, oxidation states; 2, increased electron encqy after capture of clcctron from a high state; 3, 3, new energies after hydration effects and possible changes in surt’a-acc sites. There may be several such. (c) Charge transfer for cast of n type (upper figure) dnd p type (lower figure) aemiconductors. Transfer may bc isocncrg~tic at owrlap of wdos statcc and hulk or surfxx states (later shown in upper figure). Ait~rnatively a rnctai;tahlc state may Ix* involved (lower figure) with probably lower rate.

fore, prior to any other effects, the reduction states cannot be lower than the oxidation states. Depending on the size and nature of the species accepting the electron, the increase can be very small (large number of electrons on species) or substantial (few electrons on species). This effect is well known in solid state theory, and arises from the increased repulsion energy of the electron due to the additioml electron. Hence a correct representation is as show~t in fig. 41). So far we have assumed the Franck-Condon principle, where the electron redistribution takes place before nuclear motions become significant. After the electron effects have occurred, further changes can take place. Firstly the state of hydration of the species can be allcrecl due to its new charge, with water molecules bonding differently to it and per-haps in different numbers. This can lower the energy. Secondly and sometirues nlure importantly, the species cm change the site which it has occupied on the surface. since it now carries extra charge and may be able to migrate to a site or sites of lower energy. Hence if suclt sites exist the final energy of the reduction state may indeed be lower than that 01 the oxidation state. This is depicted in fig. 4b. flowever there is no general reason why such surface sites should exist, not- wxcl hydration effects be large enough to reduce the reduction state energy appreciably. thence it is important to real& that the situation shown in fig. 4a is not a general case for a redox couple but is a result of specia1 effects which may or may not occur to any appreciable extent. It is quite conceivable that the final reduction state has a higher energy -. if both it and the

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oxidation state are below the Fermi level of the solid to which the species are attached, then equilibrium will occur with most species in the reduced state, but a finite number in the oxidised state at all times since the occupation probability (Fermi factor) is less than unity. The above discussion on redox couples is important because it is customary to draw a line midway (approximately) between the oxidation and reduction states (each broadened by thermal agitation and other non uniformities into a distribution) and treat it as the electrochemical potential lYR of the couple. It is related to the midpoint E, by E, = I?‘:‘R - kT ln(R/O) where R and 0 are the concentrations of the reduced and oxidised species, 0 + e + R. This EK is then assumed, under equilibrium conditions, to equilibrate with the Fermi level of the solid. If there are several redox couples present then the final positions of the respective ER levels with respect to Ep for the solid depend on the relative concentrations. The assumption that I:‘, for the case of one redox couple only, equilibrates with E,, is not strictly tenable. As discussed earlier, the Fermi level for the solid equilibrates with the Fermi level for electrons in the electrolyte, which itself is a chemical solution including all impurities, redox couples etc. At the interface various ions, neutrals and aqueous species attach to the solud surface. Hence the region of the electrolyte near the interface has a different (graded) composition from that away from the interface, and hence a different Fermi level (levels). These levels must equilibrate with that of the solid (metal-semiconductor connection) and with that of the rest of the electrolyte as well. Hence the true situation is very complex and depends on concentrations and compositions in the adsorbed and other layers. Measurements can be made for specific systems e.g. on Ge (Gerischer [6], his table 1). The information given is the standard potential of the redox couple (e.g. 0.64 V for Fe2’/Fe3+ in IN HC104, where H+/H2 in 1N H2S04 is 0). However such information should include the average concentration of the couples and the nature of all other electrodes. The finish of the surfaces is important because the concentration of the adsorbed redox couples can vary considerably. It should not be expected a priori that standard potentials depend only on the chemical formula of the solid. Hence tables of redox potentials should be treated as a rough guide only unless the exact surface orientation (or polycrystalline composition) and finish are reproduced. For many semiconductors in aqueous solutions, H’ and OH- are the dominant adsorbed species. Hence changes in pH affect the Helmholtz layer potential drop and the semiconductor surface barrier in a systematic way. If the change is close to the theoretical 0.059 eV per pH unit one may deduce from this that the primary adsorbed ions are 0’ and OH-. 6. Semiconductor

surface

barrier

and action

of light

Having considered in a qualitative way some of the important factors that determine the Fermi level in the semiconductor with respect to the vacuum level T/, we

I.‘ig.5. Light e.xcitation of hole electron pair in n type semiconductor surface region, showing separation of carriers by surface field. I’1, is band bcndinp, I’ is potential with respect to a refcrence electrode and is called “flat band potential” when it is sufficient to discharge surface excess charge and hence allow “flat bands”; ~1 is \vidth of band bcntlintz, defined in tc\t.

now discuss briefly the semiconductor surface barrier. This is the heart of I’EC (ad also photovoltaic) cells because this is the Iregion where the incident light is absorbed. Electrons are excited from the valence into the conduction band, leaving empty states called “holes ” in the valence band. The holes behave like positive charges with a mass generally similar to that of electrons. (For a periodic structure, precise “effective mass” formulae can be derived for holes and conduction band elctrons). Because of the inbuilt electric field in the surface region, shown schematically in fig. 2, electrons and holes drift in opposite directions, i.e. the electron hole pairs are separated. (For light energies slightly less than the bandgap, electron---hole bound pairs, called excitons, are formed but these usually play a minor role.) To be specific, for an n type semiconductor shown in fig. S where the bands turn up at the surface, photoexcited electrons in the conduction band drift away from the surface whereas the photogenerated holes drift towards it. Before we discuss the interface effects, we discuss the internal properties of the semiconductor. Any light absorbed beyond the surface barrier results in electron hole pairs not subject to a drift field. Hence they will recombine and be wasted except for those that diffuse into the surface field region and there become separated. Furthermore even within the barrier the efficiency of pair separation depends on the steepness of the barrier (strength of electric field) and the diffusion length and recombination time of the carriers. The presence of many defects such as grain boundaries causes rapid recombination, hence the surface barrier should be of short extent in such cases. But this requires a strong light absorption in the thin surface layer which will be of order 3 micron. This can only be achieved with so-called direct gap semiconductors where, in periodic materials, the valence band maximum and conduction band mini~nutn occur at the same value of k (wave vector). Both Ge and Si are indirect gap materials (peaks at different k values) so that the absorption edge is not steep because considerable absorption takes place by phonon participation at wavelength longer than those capable of directly exciting electrons

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across the band gap. (These matters are discussed in solid state texts.) Hence the absorption coefficient is at first lower, and significant light absorption takes place up to about 50-100 pm, which should be free of defects. Thus higher quality material is required than for direct gap semiconductors such as GaAs or TiOz. Furthermore, the deeper light absorption means a deeper barrier region is required, necessitating both a higher surface barrier and higher semiconductor bulk resistivity. The latter however is undesirable as it increases resistive losses in the semiconductor. The above discussion gives a qualitative feeling for properties needed in semiconductor barriers. Fortunately the solid situation, being atomically homogeneous, is more amenable to accurate quantitative treatment than the electrolyte boundary and many solutions have been obtained (e.g., Many, Goldstein and Grover [8], Frank1 [9]). A recent theoretical account with simplifying assumptions by Butler [lo], gives some usefully simple expressions for the current. Without repeating the steps in the derivation, the resulting equation for the total current induced at an n type semiconductor surface barrier of height L’,, and width w (fig. 5) is approximately i y 400 11 ~ [exp(-cu~~)l/(l

+ aL,)> ,

(2)

where y is the electron charge, @0 is the photon flux, cy the optical absorption,& the hole (minority carrier) diffusion length and w is the surface barrier region depletion layer) “width”. This quantity must be carefully defined since the barrier decays exponentially into the interior and is thus of infinite “width”. Since the separation of hole electron pairs depends on the surface field and is appreciable only when this is sufficiently high, one may compromise a number of variables and make the sufficient simple approximation that )

\v = Mj”(T/ ~ ,r)l’z

(3)

where wg is the depletion layer width when a potential V of 1 V more than the flat band potential is applied, with respect to some reference electrode. The quantity Vr is the so-called flat band potential applied with respect to the same reference electrode, being the potential at which the barrier height would become zero (“flat bands”). (This definition of \z10differs somewhat from that of Butler). Recombination losses of photo-generated carriers in the depletion layer and at the interface have been ignored in the above expression but could be readily included. One can make a further approximation wo = (2E/CIN,YZ

,

(4)

where ND is the donor density and E the dielectric constant. It is assumed that thermally or optically excited carrier concentrations are negligible with respect to ND. (This assumption is not justified under appleciable illumination.) A further simple expression can be obtained for the optical absorption coefficient CL Although its dependence for a crystalline material is affected by details of the band structure, in many cases the initial absorption is in the region of wave vector k = 0. In such cases

one may approximate

wlrere j’is the frequency. II, is the band gap, A is :I constant and II is I I.oI- dil-ect (no k change) or 4 for indirect transitions. Tile above n~odel has been tested by Butler and co-workers [ 10 12 / a~~1li)u~ld to give :I useful description for W03 [ 101, FeTiO,, t:ezTi03, I:c21’iO;, [ I 11 ;IIICI YFe03 [ 121. (liowever the iron coi~qx~u~ids sl~~wed clectroclieniical leaching 01‘ iron atom from the surface.) We define the quantum efficiency q as 71= j/qf&, The~l l’or the cast: of the pllcllorespomc near the absorption edge. where a is small aid ~YNJ~~ < I. one ot,tairis approximalely ??/l.f’~- (I, I) t ii’,) (I’

L’fy]

A(hj

/:g”‘2

1

(6 )

assuniing cd,,, -< 1. If II = 4 (indirect transitions). llicil ;I plot 01‘(q/r,/)’ ’ vcislis i/i sl1ou1J yield the hand gap. This procetlurc gave failI\. slraight lines arid I-~asoirahlc hnrl gaps for all the materials mcntioriccl. even at L\avclciigtlis ;IW:I\’ 1.1~oiii Il~c ahsorption dge. Ilowcver the mca~urement ol‘the Cfl’ect oI‘;i fw vc)lts bias I’or lhc c;isc of W0.3 showed ii significant shift in dctlticd hamI gap ivliicli was c.\plainctl ;IS clue to ;I tieId induced crystallographic distortion [lOI. This cI‘lScct bleeds III 112 exaiiiinecl more widely iii order- to confirm the rreli;lbilit> 01‘llie mprcssiori. llsing cq. (5) iii ccl. (6) and takin g the case of I,,, mall with respect to II‘, oiic derives approximately

\vhcnce the Ilat band potential could be Jecluccd 1‘1om ;I ~)lot 01‘ pllotocur-rcllt sc~u:iiml, versus potential with respect to ;t suitable ~rct‘erence eleclroilc. Near LIic absorption edge, such plots gave straight lines for some m:l~cri;ds, fig. 6, and yielded ;I value 01‘ l’f for W03 similar to that from the full cqliation. In generd however it‘ /,,, is small with respect to the barrier width n’. one would expect significant 1~2coiiibiriatic)ll losses in the barrier region, which \todd inoclify eq. (2). In all the above we have considered oiily the pi-opedies of the seniiconiluctoi and not taken into account the effects of changes in the aclsurl,ecl layer-s ill the clcctrolyte. This is 3 more difficult region to treat in ;I simple quantitative fashion (see e.g., hckris [I _3]). lfowever for the larger hand gap s~luicoiitlt:clors the cvideiice :Ippears to indicate that at least foi- sonit‘ cotifiguratioii~ the scnniconrluctoi ch:ir:icteristics and not the electrode kinetics arc donlinanr it1 determining the pllc’toi-espouse. ,2 usef~il general approach would be to use t’*pi-c5sioiis 2s in Iliis section ;I\; 2 I‘irst triai in a systcin and then, if tile fit is poor. consider the et‘fecl 01‘ elecl~oilc imclions. If the photocurrent is propoi-tional to light inlensily ovei- ;I certain range. tlicn this is ;I good iiitlication that carrier generation iii the scmicoliiliictoi is tile rate limiting step and clectrocle i-cactioils 211-cnot domiiiant. At suffici~~rt light

D. Hanemarz / Sltrfhces for pllotoelectrocherllical

cells

415

2oOi FeTi03 /

Pofent~al

VS

SCE

(Volts)

I:ig. 6. Plot of photocurrent squared, versus potential for various semiconductors showing straight lines obtained by Butler and co-workers [IO- 121, in accord with eq. (7). For W03, the numbers refer to wavelength in A, showing agreement for x axis intercept even at wavelengths away from excitation threshold. Intercept is flat band potential.

intensities however, electrode trol the current.

effects would become important

and eventually

con-

7. Surface chemical reactions and light We consider electron transfers across the interfaces in the presence of light, assuming the surfaces are not subjected to chemical attack in the dark. The operation of the PEC cell requires electron travel around the circuit as mentioned earlier. In an aqeous solution there are several possible reactions shown in table 1 depending on whether the solution is acid or alkaline and whether dissolved oxygen is present. In the case ofthe alkaline solution (taking NaOH, in order to be specific)we have written partial reactions involving Na’ ions for the cathode. Although the involve-

02 + 4 II+ + 3c --L 2 t120 7 1120 + 41’ -Lo?

+ 4 IIt

-k t 411 -+ 0

nnent of these is not proven it seems difficult to envisage :I reaction without them in highly basic solution where their concentration exceeds that of II’ ions by many orders of magnitude. However the net reaction does not involve the cation solute. We have written all reactions with four electrons or holes. This does not ot course imply that 4 are needed simultaneously ~~presumably one ion, and one hole or electron from the surface, interact 2nd the product survives l01lg enough fol- four such to aggregate. There is ;I significant difference in the cell action depending 011 whether- or not dissolved oxygen is present as first made clear by Mavroides and co-workers [14]. As seen in table 1, if no dissolved oxygen is present it is possible for hydrogen and oxygen to be produced by the decomposition of water if a suitable semicontluctoi is LISA. This has been called the photoelectrolysis mode and arises because two rcdox systems are effective, leadin, 0 to a net chemical change in the electrolyte. Ilowever if adequate dissolved oxygen is present then only one retlox couple (02/ H20) is effective. the photoanode reaction bein, 0 reversed at the carliotlc with no nel chemical change in the electrolyte. This has been called the photogalvanic mode [ 141 and appears to describe the situation for Ti02 and SrTi0,3 among others. In fig. 7 WC attempt to show very schematically the possible structure of a hydrated O2 -Na’ or O,--11’ complex in a11 alkaline or acidic solution respectively. pl-iol- to acceptance of 311 electron from the cathode. II‘ the solulion is initially fret ofouyge11 then one must pay attention to the physical arrangement 01‘electrodes so that

D. Ilanernan

/ Surfaces

for photoelectrochemical

cells

I+

o_o~H+~<;~+ + ,Ha+ L+

OEofNa0,

H2

l:ig. 7. Schematic picture of partially hydrated oxygen molecule -II+ (or Na+) complex at cathode surface. The symbol 3’ on the hydrogen of the water molecule is not precise but merely indicates some polarisation. I;&. 8. Change in n type semiconductor energy levels under illumination. The drift of photoexcited holes to surface tends to neutralise excess surface negative charge, causing reduction of band bending (to l’hl) and raising of bulk l:crmi level from Erb to EM. New levels sho\vn with heavy dots over lines. The flow of current reduces the effect somewhat but not entirely. Current also causes potential drop through bulk of semiconductor, illustrated schematically, so that measured photovoltage I’ph is less than surface voltage C’,. The values of the band edges at surface, 6,s and 6,,, are changed slightly due to modification of charge in interPace states outside semiconductor surface, caused by change in I:ermi level and consequent charge redistribution.

the photogenerated oxygen does not dissolve in the solution and convert the operation mode to photogalvanic. The above are possible reactions but the degree to which they occur depends upon the positions of energy levels under illumination. We have already discussed the energy levels and the factors that influence them in equilibrium. Upon illumination of the semiconductor anode, the number of electrons and holes in the irradiated surface region increases, the electronic effects being much as though this region were preferentially and substantially heated except that the ion core vibrations hardly increase. For n type material as in fig. 8, the holes flow to the surface and tend to neutralise the excess negative charge trapped here. This both lowers the barrier height and raises the bulk Fermi level. (For p type material the barrier also reduces but since positive surface charge is neutralised the Fermi level drops). When current flows these effects are reduced but not removed. See fig. 8 and caption. Note that the resistive potential drop in the semiconductor bulk reduces the external measured photovoltage I/,,, - this effect is shown by a slope in the semiconductor bulk Fermi level in fig. 8. If a current i flows through the bulk resistance R,, and through the surface resistance K, then the measured photovoltage

478

D. Hanemarr / Surfaces

for I~hotoelcctroclle~~,ical

cells

where V, is the difference between the Fermi levels in the metal and the semiconductor surface. More accurately, the quasi Fermi levels slmultl be used but we give this approximate expression to illustrate the ot-igin 01‘ the effects. From fig. 8 we can deduce that the barrier height under illumination

where the subscripts s and b refer to surface and bulk respectively. An additional effect of illumination that must not be overlooked involves the changes induced in the electrolyte. These changes arise from two sources. Firstly direct absorption of light by solvent and or solute molecules changes the molecule energy levels. Secondly, the light-induced changes in Fermi level in the solids. then affect the Fermi levels in the contacting electrolyte. Of particular importance is the effect upon the energy levels of molecules and ions which exchange electrons with the solids. When the Fermi level in the n type semiconductor moves with respect to the vacuum level V, its former equilibrium (not necessarily equality) with redox couples in solution (fig. 4) is disturbed. Accordin, ‘7 to our discussion of fundamentals earlier, the standard redox potentials will readjust according to the new Fermi levels in the solids. being higher in this case (nearer v). This will tend to populate the oxidation states, i.e. decrease the number of molecules in reduced states. If in addition, the electron in the reduced state can be optically excited and injected into the conduction band, then the concentration of oxidation states will increase again. The quantitative evaluation of these effects is a difficult nlatter which we do not attempt to treat because of uncertainties about tile composition of the Hetmholtz layer. Usually however the latter effect is small due to the low optical cr-ass section of the thin adsorbed layer. Any theory would be specific to a system for which the necessary detailed assumptions about the surt’ace adsorbed layers, would be most nearly appropriate. The electrode surface composition and topography (smoothness) as well as precise composition of electrolyte need to be specified.

8. Surface dissolution,

corrosion, and practical systems

One of the problems of PEC cells compared with photovoltaic cells is that photoassisted chemical dissolution of the photoanode can occur. A valence hole present at the surface means that a surface atom has a weakened bond which might be overpowered by the forces of attraction to molecules in the electrolyte. Experience shows that photo assisted dissolution is quite common for semiconductors 01 band gap less than about 3 eV. This rough gcneralisation is possible because of the correlation between band gap and bond strength. For quantitative analysis the strength of bonding of a surface atom to its neighbours needs to be known this is not simply the bond dissociation energy since surface fol-ces differ from hulk ones. Furthermore it is likely that atoms in kink sites mcl step edges, where the number of neighbours is reduced, arc bonded least strongly and parameters for these are the

Il.

ifatwmarr

/ Surfaces

for pkotoele~trocl~cn~ical

cells

479

appropriate ones. Therefore there are simple a priori reasons for using smooth surfaces to reduce chemical dissolution. Another problem, pat-~i~ttlarly with Gc and Si, is corrosion in the sense of build up of chemical layers due lo chemical interaction with the electrolyte. These layers, if they are insulating, inhibit electron transfer across the interface. This problem can be solved by choosing an electrolyte which either does not interact chentically, or else which dissolves any layer that tends to occur, thus providing an equilibrium surface which is nearly clean. An example is the ferrocene based solution used successfulfy with Si by Legg and co-workers [IS] _ In solutions such as NaOH, Si is rapidly oxidised and becomes ineffective. The problem of dissociation is severe because the solar spectrum at sea level consists of photons of energy less than about 3 eV. Hence semiconductors which can utilise reasonable fractions of this solar spectrum have bandgaps less than 3 eV and arc thus of necessity more weakly bonded. The first successful ~letlt~)ns~ratioli of a solar-surface EC cell by T~u~is~iit~ta and Honda [ 161 used TiOz with a bandgap of apprc~ximately 3 eV which is stable in alkaline solution. However it is activated by only 3% of the solar spectrum. Hence the overall solar conversion efficiency is quite low by optimising the electrolyte strength and area, and position of the countet electrode, overall solar e’fficiencies as high as 026% for electricity production have been reported [ 17] but usually this material gives much lower electricity output. Solar conversion efficiencies in the several percent range have been reported for 1’1.C cells based on GaAs [ 181 and several cadmium chalcogenides, all semiconductors being n type. The problems of corrosion in these systems were partly solved by choice of redox couples which compete with the dissociation reaction. A kinetic description of corrosion prevention is in tertns of the strong adsorption of the ions onto the surface. Cottsidering as a specific example Cd& and the redox couple S/S’ [ 191, the Se *- of CdSe is oxidised by holes to Se in atomic ot- molecular Tot-m. flowever, before further anodic dissolution occurs, its place is taken by a sulphide ion. On this theory one expects that part of the CdSe surface would be converted to CdS during illumination, and this seemed to have been confit-mcd by X-ray photoelectron spectroscopy methods which showed about 100 ,&depth converted to CdS, with a reducing ~rop~~rti~)n detectable to a depth of about 350 i! [ 191. (Tlte XI’S technique is useful in studying foreign penetration of I’EC surfaces, e.g. [ZO].) An energy level model of electrode stability has been presented by Gerischet 1211, Bard and Wrighton [z?] and quantitative studies made by hlemming [23]. The redox potentials of the oxidative and reductive decomposition reactions, 5; and A.:, are calculated and displayed on an energy level scale as in fig. 9b. The relative positions of Eg and Ef: are rthen compared with those of the desired redox reactions in the electrolyte and with the positions of the semiconductor band edges. Stability of the electrode is enhanced the more that f:‘fi lies below I:‘, and the more that I!z‘): lies above EC_ However such conditions do not occur in any cases studied to date and usually one or both of the Et, 1eveIs lie within the band gap.

making decomposition thermodynamically possible. Electrode stability then is determined by competition between the decomposition reactions and redox reactions, which is governed both by energy levels and by kinetics of the two kinds 01 reaction. If the redox level R supplying an electron to a valence band hole is substantially above E,, the transition may be slow, allowing corrosion to proceed. The rate can be increased if the transition is isoenergetic, which could occur if surface states range from I& to R SO that the hole is opposite R (fig. 4~). Another possible method is to arrange for other redox levels M to lie lower than R, and attached to the surface in a so called “derivatizing reagent layer” [24]. The electron then may make a fast transition to M which is close to l:‘“, allowing a second fast step (fig. 9b). A compilation of band edges and redox potentials has been prepared by Memming [23], shown in fig. 9, and by Noc.ik [ 11. These values are not however firm since the semiconductor band edges do not have a fixed potential as implied by the figure, but depend on the nature of the counter electrode, the face orientation and also the nature of the electrolyte as discussed at length in sections 3 and 4. Similarly the redox potentials are not fixed quantities but are affected by the two electrodes. Thus the relative energy levels in fig. 9 may have quite different values from those shown. This is doubtless one reason for some of the anomalous effects discussed by Memming [33]. To date the best solar conversion efficiencies have been obtained from materials which are also useful as solid photovoltaic cells. The high solal- efficiencies (9%) lot GaAs PEC cells [18] were obtained from single crystals, and these do not appeal suited for large area low cost fabrication. However the cadmium chalcogenides look interesting in this regard since films can be used and solar efficiencies up to 8% have been reported [?S] for the case of CdSe with an S2 -/S i redox couple to stabilise against dissolution. An extensive literature bibliography on work on these and other materials is given by Nozik [I]. It should be noted that some of the efficiency 01’ the CdSe cell may be due to the presence of a heterojunction between the bulk CdSe and the thin CdS surface layer induced by interaction with the redos couple. (In the case of solid CdS photovoltaic cells, the principal action is due to a hetelojunction between the CdS and cuprous sulphide, e.g. ref. [26].) Interesting possibilities exist if the metal cathode is replaced by a semiconduclol of smaller bandgap and opposite conductivity type from the other semiconductor. Action can be enhanced if light that passes through the first material can be used 11~ the second. However in practice this imposes difficulties in the disposition of the electrodes and the gain may not offset the establishment cost. To date little attention has been paid to the problem of large arca operation of’ PEC cells. A system of order 0.3 m2 has however been prepared [27] based on conducting TiO, films on glass. Although the efficiency is low the TiOz films arc vet-y robust and have survived several months of occasional overheating, drying out 01‘ the electrolyte and contamination by insects. An artist‘s impression of a large sys-

D. Haneman /Surfaces

for photoelectrochemical

cells

481

EA

Sic t

GaAsP

GaP 1 (n,p)

dSe (n)

dS n)

,

T (1

Mf/M

t 3.0

1

(a)

(b)

Igig_ 9. (a) Band edges for various semiconductors versus redos potentials at pH 1, from Memming [23]. I:igures in band gaps indicate gap widths in eV. The symbols CN and Ru on right hand scale refer to [I:e(CN),] 3-‘4- and Ru(bipy)2’/-s+ respectively. The left hand scale is labelled electron affinity but actual values may differ from those shown depending on surfxe finish, counter electrode and precise composition of electrolyte as discussed in test. (b) Semiconductor surface (n type SK’ to be specific) approximately to scale with (a), showing schematic decomposition potential Eb, redox couple B’/B in electrolyte and mediation system M+/M in layer on surface, called “derivatised layer” [24]. The capture of hole in valence band by M creates M+ which can then osidisc B. Decomposition of semiconductor is reduced by rapid capture of hole, facilitated by M. This has role somewhat similar to that of surface states shown in fig. 4c.

tern is shown in fig. 10, with provision for extraction of electricity, hydrogen and heat from the solar heated electrolyte. There is also a possibility of operating the system for desalination purposes in areas where this is important. The initial interest in hydrogen production has decreased somewhat with the realisation that the H’/H, level is above the Fermi level for many semiconductor

E .

systems. Exceptions are SrTi03 (3.4). BaTiO? (3.3). FeTiO,> (2.X), KTaO.> (3.5), Ta20s (4.0), and Zr02 (5.0). The hand gaps in CV a~-e shower in bl-ackcts and all at-c unii~rtuiiately rather large. For uthct- cases the cathode must he hiasml negatively to raise its Fermi level above the i1+/t-i, level, OT else irnmersecl in acid solution

separated

sucll

:I> agar

from

bias of‘ 0.059

the alkaline solution a~-ountl the pl~otoanodc by ;I pa~titiml fl-it. This has the same effect as ;I hias by providing an et‘i’ective eV per pI-1 number. In either case some enct-gy loss in involved during

cell operation

(electric

01 glass

power- or chennical

neutralisation).

tiowevcr

it is still possible

D. tlaneman /Surfaces

for photoelectrochemical

cells

483

to run the system at a net energy profit. The additional costs of collecting the hydrogen would also have to be considered, as well as the need to keep oxygen out of the electrolyte which would otherwise capture the electrons rather than H’, see table 1. Hence the potential advantage of producing storable fuel requires some work to capitalise on it effectively and economically.

9. Thermodynamics The key to action in PEC and PV cells is the potential barrier in the semiconductor which separates the photoexcited electrons from the holes. In this way electricity is produced from solar energy. However an alternative method is to solar heat a gas which then does work in a generator, producing electricity. In the latter case the maximum efficiency is known to be (T, - r,)/r, where T, is the high temperature (K) of heat input and T1 the low temperature of heat rejection, as originally worked out by Carnot. One may ask whether the PV and PEC cells are also subject to a Carnot limitation or whether this has been bypassed. We show that the PV action is subject to the Carnot limitation in the following way. The effect of light on the illuminated region is to excite the electrons into higher energy states. If the solid has no inbuilt electric field, the electrons decay into their initial states by the emission of radiation and excitation of lattice vibration, in other words the bulk solid becomes hot. If however this decay can be prevented or minimised, then one has a “hot” electron gas. In effect some of the (solar) spectrum has been used to increase the temperature of the electrons without increasing that of the ion cores. Hence the electron gas attains a much higher temperature T2 than it would otherwise. After the excited electrons flow around the circuit they return to their ground states, at temperature T1. Therefore work has been done by the electron gas and the Carnot principle applies to the system, the maximum efficiency being given by (T, -- T,)/T, . However T2 may be very high for the electron gas even though the ion core temperature remains low, so that the theoretical maximum efficiency can be 70% (T2 = 1000 K) or more. The value of T2 is not obtained in a simple way since the energy distribution of the excited electrons depends on the density of available states in the solid, and is in general not a Maxwell-Boltzmann distribution. In a quantitative discussion, the distribution may be considered as an appropriate sum of Maxwellian distributions, each with its temperature T,, To, etc. Then the maximum efficiency is

77 =

E

tZi(Ti - T1 j/Ti s

i=l

(10)

where ni hot electrons are in a Maxwellian distribution of temperature Ti, and C Ili = N, the total number of photoexcited electrons. The total number of

Maxwellian groups into which the electrons al-e distributed is hl.A value for q call be calculated from eq. (10) for any particular semiconductor, given a knowledge of the density of states in the conduction and valence bands and the transition probabilities and photoexcitation cross sections. It appears that practical limitations in the rest of the circuit reduce the theoretical Carnot efficiency from eq. (IO), which would be in the region of 70% and more, to values of about 21% for Si and 25% fotGaAs PV cells. These values for solar irradiation also take into account the fact that only a portion of the solar spectrum has energies greater than the band gap. Further, electrons excited into higher states decay to the bottom of the conduction band so that their excess energy is degraded into raising the ion core temper-ature. Clearly, a series of semiconductors each of which absorbs photons of energy just sufficient to excite electrons across the gap would be best, but this is not a practical possibility at this stage.

10. Conclusions Some of the main principles of I’K cells have become, and arc becoming. cleal-. Based on this understanding, solar energy conversion systems tllat are practical and economic are being developed. Conversion efficiencies in the few percent range (electricity production) have been already obtained from inexpensive films in systems which inhibit surface attack. As the presently used and new semiconductors are employed, attention to surface finish, the nature of the adsorbed layer, the electrolyte, redox couples and the counter electrode, will all enable improvements in performance and life. The inter-relation between these quantities is complex and considerable scope for innovation and optimisation is still available in a developing research and applications effort.

Acknowledgements The author has benefited from discussions with Dr. S.R. Morrison (Stanfold Research Institute) and Dr. D.J. Miller. This work has been supported by the Australian Research Grants Committee, and by tlffem Foods I’ty Ltd.

References [ 11 A.J. NoTik, Ann. Kcv. l’hyx. C’henl. (1 978). [2] M.A. ISutler and D.S.
D. Haneman / Surfaces for photoelectrochemical

cells

[ 71 S.R. Morrison, The Chemical Physics of Surfaces (Plenum, New York, 1977). [S] A. Many, T. Goldstein and N.B. Grover, Semiconductor Surfaces (Intersciencc, New York, 1965). [9] D.R. l:rankl, blcctrical Properties of Semiconductor Surfaces (Pergamon, London, 1967). [lOI MA. Butler, J. Appl. Phys. 48 (1977) 1914. [ 111 D.S. Finley and M.A. Butler, J. Appl. Phys. 48 (1977) 2019. [ 121 MA. Butler. D.S. Ginley and M. Fibschutz, J. Appl. Phys. 48 (1977) 3070. [ 131 J. O’M. Bockris, Ed.. Modern Aspects of Electrochemistry (Buttcrworths, London, 1964). [ 141 J.G. Mavroides, D.I. Tchernev, J.A. Kafalas and D.1:. Kolesar, Mater. Res. Bull. 10 (1975) 1023. ]lS] K.D. Lcgg, A.B. t-his, J.M. Bolts and M.S. Wrighton, Proc. Natl. Acad. Sci. LISA 74 (1977) 4116. [ 161 A. l~tr,jishima and K. ltonda, Nature 238 (1972) 37. [17] W. Gissler, in: Proc. Intern. Conf. on Hehotechnique, M.A. Kettari and J.L-I. Soussou, Eds., Development Analysis Assoc., Cambridge, MA (1976) p. 708. [ 181 K.C. Chang, A. lleller, B. Schwartz, S. Menezes and B. Miller, Science 196 (1977) 1097. [ 191 J. Manasscn, G. Hodes and D. Cahen, Proc. Electrochem. Sot. (1977). [ 201 D. Hancman and I;. Steenbecke, J. Electrochem. Sot. 124 (1977) 86 1. [2l] H. Gerischcr, J. Electroanal. Chem. 82 (1977) 133. [22] A.J. Bard and MS. Wrighton, J. Electrochem. Sot. 124 (1977) 1706. [23] R. Mcmminp, J. Elcctrochem. Sot. 125 (1978) 117. [24] M.S. Wrighton, J.M. Bolts, A.B. Bocarsly, M.C. Palazotto and E.G. Walton, J. Vacuum Sci. Technol. I5 (1978) 1429. [25] B. Miller, A. Hcller, M. Robbins, S. Menezes, K.C. Chang, J. Thomson, J. Electrochem. Sot. 124 (1977) 1019. [26] K.W. Boer, Phys. Status Solidi (a) 40 (1977) 355. [27] D. Haneman and P. llolmes, Solar L’nergy Mater. 1 (1979) 233.

485