J. Phys. Chem. 1996, 100, 13061-13078
13061
Physical Chemistry of Semiconductor-Liquid Interfaces Arthur J. Nozik* National Renewable Energy Laboratory, 1617 Cole BlVd., Golden, Colorado 80401
Ru1 diger Memming* Institut fu¨ r Solarenergie-forschung GmbH HannoVer, Sokelantstrasse 5, D-30165 HannoVer, Germany ReceiVed: December 13, 1995; In Final Form: April 17, 1996X
The science describing semiconductor-liquid interfaces is highly interdisciplinary, broad in scope, interesting, and of importance to various emerging technologies. We present a review of the basic physicochemical principles of semiconductor-liquid interfaces, including their historical development, and describe the major technological applications that are based on these scientific principles.
I. Introduction The phenomenology of semiconductor-liquid interfaces represents a very interesting and important area of science and technology. The science is highly interdisciplinary, involving principles of physical chemistry (electrochemistry, photochemistry, interfacial charge transfer, and surface science) and semiconductor physics (electronic band structure, solid state charge transport, optoelectronic effects, and materials science). The applications, present and future, are also highly varied and include the following: liquid junction solar cells, photoelectrolysis cells for photolytic water splitting, heterogeneous photocatalysis for photooxidation of organic compounds and pollutants; recovery of precious metals, semiconductor processing technology, and sensor technology. The earliest scientific investigation of a semiconductor-liquid interface was undertaken by E. Becquerel in 1839:1 a silver chloride electrode in an electrochemical cell exhibited a photovoltaic effect when it was illuminated. This result, termed the “Becquerel effect”, represented the first reported photovoltaic device. The understanding of this phenomenon was not achieved until about 1954, when researchers2 at Bell Laboratories showed how chemical reactions occurring at the surface of Ge could be influenced by controlling the semiconducting properties of Ge, as well as by exposing the Ge to light. This development occurred as one component of the great advances that were occurring at that time in the field of semiconductor solid state physics; these advances included the discovery of the extraordinary electrical and optical properties of semiconductor materials that could be controlled by controlling their impurity content, the creation of novel optical and electronic semiconductor structures and devices, and the blossoming of solid state theory. The Becquerel effect was found to be caused by photoinduced charge separation at the AgCl-liquid interface; silver halides behave as semiconductors, and electric fields produced at the semiconductor-liquid interface lead to a large photovoltaic effect. The pioneering work on the photoelectrochemistry of germanium was rapidly followed up between 1954 and 1970 with studies of other semiconductor electrodes such as Si, CdS, ZnS, CdSe, ZnSe, ZnTe, GaAs, GaP, ZnO, KTaO3, Ta2O5, SrTiO3, and TiO2.3-11 These early fundamental studies established the first models for the semiconductor-electrolyte junction including the kinetics and energetics of electron transfer across semiconductor-electrolyte junctions and the nature of the charge X
Abstract published in AdVance ACS Abstracts, June 15, 1996.
S0022-3654(95)03720-8 CCC: $12.00
distribution at the semiconductor-electrolyte interface; many reviews of this early work are available.12-19 Whereas virtually all of the work in photoelectrochemistry prior to 1970 was of a rather fundamental nature, beginning about 1970 the potential application of photoelectrochemical systems for solar energy conversion and storage was recognized.20-22 Illumination of n-type semiconducting titanium dioxide anodes showed that the oxidation of water to oxygen could be achieved at significantly more negative potentials compared to the standard redox potential of the H2O/O2 redox couple; the implication was that it might be possible to use sunlight to split water into hydrogen and oxygen. This process is now generally known as photoelectrolysis. Photoelectrolysis of water using sunlight is extremely attractive for several reasons. First, this type of solar energy conversion alleviates the energy storage problem, since hydrogen can be stored more easily than either electricity or heat. Second, hydrogen is valuable as a potential fuel and energy carrier; it is nonpolluting, renewable, inexhaustible, and very flexible with respect to conversion to other forms of energy (heat via combustion or electricity via fuel cells). Finally, hydrogen is valuable in its own right as a basic chemical feedstock used in large quantities for ammonia synthesis and petroleum refining. Since the current primary source of hydrogen is the steam reforming of natural gas, a new process based on water and sunlight would be a very important development. During photoelectrolysis, radiant energy is converted into chemical free energy in the form of high-energy chemical products; that is, the chemical free energy change in the liquid phase is positive. The chemical reactions in the liquid could also have a negative free energy change; in this case the reaction is driven downhill in energy, and the process could be termed photocatalysis. Several important applications of photocatalysis based on semiconductor-liquid interfaces have also been developed in recent years. In addition to driving exoergic or endoergic chemical reactions, semiconductor-liquid interfaces can also be used to generate electricity from light. Photoelectrochemical cells operating in this mode, a general aspect of the Becquerel effect, are now called electrochemical photovoltaic cells, liquid-junction solar cells, or photochemical solar cells. In the latter case, photoexcited dye molecules adsorbed on semiconductor surfaces inject charge into the semiconductor to produce the photovoltaic response. © 1996 American Chemical Society
13062 J. Phys. Chem., Vol. 100, No. 31, 1996
Nozik and Memming obtains at equilibrium
(
n0p0 ) NcNv exp
Figure 1. Energy levels of semiconductor bands and energy distribution of the occupied and unoccupied states of the redox acceptor.
Accompanying the prospects for important applications of semiconductor-liquid interfaces are many equally alluring scientific issues and challenges related to their physical chemistry. In this article, we will describe the fundamental scientific principles and issues of semiconductor-liquid interfaces, and we will also discuss the status and prognosis for various applications of these interfaces. Several reviews and texts covering the science and application of semiconductor-liquid interfaces are available.23-40 II. Fundamental Principles 1. Energy Levels in Semiconductors and Liquids. The quantum theory of solids presents a complete description of the energy levels in a semiconductor, the nature of charge carriers and of laws governing their motion.41,42 The filled energy states correspond to the valence band (its upper edge denoted as Ev) and the empty states to the conduction band (its lower edge at Ec). The energy bands are separated by the band gap EG as illustrated on the left side of Figure 1a. In solid state physics, the vacuum level is taken as the zero energy reference. The density of energy states within the energy bands increases with the square root of energy above the conduction band or below the valence band edge and is given by
Nc )
8x2π (me*)3/2(E - Ec)1/2 3 h
(1a)
8x2π (mh*)3/2(E - Ev)1/2 h3
(1b)
for the valence band, in which h is Planck’s constant and me* and mh* are the effective masses of electrons and holes, respectively. The electron and hole densities in the conduction and valence band, respectively, are related to the corresponding Fermi levels EF,n and EF,p by
( (
n ) Nc exp -
) )
Ec - EF,n kT
Ev - EF,p p ) Nv exp kT
(2a) (2b)
in which Nc and Nv are given by eqs 1a and 1b. At equilibrium, the Fermi levels of electrons and holes are identical, i.e., EF,n ) EF,p ) EF, and n ) n0 and p ) p0. Inserting these values into eqs 2a and 2b and multiplying these two equations, one
(3)
ni2 is a material constant which decreases exponentially with increasing band gap. The relative position of the Fermi level EF depends on the electron and hole concentration, i.e., on the doping of the semiconductor. The equilibrium carrier densities in the conduction and valence band, n0 and p0, can be calculated using eqs 2a and 2b. Typical carrier densities in semiconductors range from 1015 to 1019 cm-3; this corresponds to a range of Fermi levels, EF, of 0.04-0.25 eV with respect to one of the energy bands. Thus, only a small portion of the energy states at the edges are occupied. It should be emphasized that the Fermi level is actually the electrochemical potential of electrons in the solid. In electrochemistrystaking a simple redox couple as an examplesthe electrochemical potential of electrons is given by
( )
µ j e,redox ) µ°redox + kT ln
cox cred
(4)
in which cox and cred are the concentrations of the oxidized and reduced species of the redox system, respectively. Usually, the corresponding redox potentials are given in a conventional scale, using the normal hydrogen electrode (NHE) or the saturated calomel electrode (SCE) as a reference electrode. In this case the electrochemical potential of electrons in a redox system is equivalent to the Fermi level EF,redox; i.e.
j e,redox EF,redox ) µ
(5)
on the absolute scale.33 The electrochemical potential of a redox system is usually given with respect to the normal hydrogen electrode (NHE). Using an absolute energy scale, the energy of a redox couple is given by
EF,redox ) Eref - eUredox
(6)
in which Uredox is the redox potential vs NHE and Eref is the energy of the reference electrode versus the vacuum level. The determination of Eref has been subject of various calculations.43,44 The data derived by various authors scatter from 4.3 to 4.7 eV. Usually, an average value of Eref ) 4.5 eV for NHE is used, so that eq 6 yields
EF,redox ) -4.5 eV - eUredox
for the conduction band and
Nv )
)
Ec - Ev ) ni2 kT
(7)
with respect to the vacuum level. The relationship between the various energy scales for the solid and liquid phases is shown in Figure 1b. The earliest model of the semiconductor-liquid interface was developed in 1960.3,4,12,13,45 Besides the Fermi level of the redox system, this model introduced the existence of occupied and empty energy states corresponding to the reduced and the oxidized species of the redox system, respectively. The model leads to a Gaussian distribution of the redox states versus electron energy as illustrated on the right side of Figure 1. The distribution functions for the states are given by
[ [
] ]
(E - EF,redox - λ)2 Dox ) exp 4kTλ
(8a)
(E - EF,redox + λ)2 Dred ) exp 4kTλ
(8b)
in which λ is the well-known reorganization energy of electron
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Figure 2. Band bending in n-type (left side) and p-type (right side) semiconductor electrodes upon equilibration of the Fermi levels of the semiconductor with the redox species.
Figure 4. (a) Photocurrent-potential curve for n-type WSe2 semiconductor electrode. (b) Mott-Schottky plots for n-type WSe2 electrode in 2 M HCl in the dark and under various intensities of illumination. Figure 3. Potential distribution across semiconductor-electrolyte interface.
transfer theory.36 λ is generally in the range 0.5-2 eV, depending on the interaction of the redox molecule with the solvent. The Gaussian type of distribution is a consequence of the assumption that the fluctuation of the solvation shell corresponds to harmonic oscillation. Further details of the model can be found in several review articles.3,4,23,33,45 When a semiconductor comes into contact with an electrolyte containing a redox system, equilibrium is achieved if the electrochemical potential is constant throughout the whole system; i.e., the Fermi levels of the semiconductor and the redox system must be equal on both sides of the interface
EF ) EF,redox
(9)
To achieve equilibrium, charges cross the interface until a corresponding potential difference occurs; i.e., the energy bands are bent upward or downward by an energy of eφsc depending on the doping as illustrated in Figure 2. 2. Potential Distribution. At the interface between a semiconductor and an electrolyte a double layer of charge exists, as for metal-liquid junctions. This layer can be formed either by adsorption of ions or molecules, by oriented dipoles, or by the formation of surface bonds between the solid and the species in solution. A potential difference φH develops between the two phases (Figure 3). In very dilute solutions (low ion concentration), there is also a diffuse double layer in the electrolyte (Gouy layer); however, with sufficiently high ion concentration it can be neglected. The countercharges in the semiconductor (electrons, holes, or ionized donor and acceptor states) are not only located at the interface, as in a metal, but are also distributed over a finite distance below the surface; this is because the carrier density (usually in the range 10151019 cm-3) is much smaller than in metals (ca. 1023 cm-3). The region in the semiconductor where this charge is distributed is called the space charge layer, and a corresponding potential difference φsc is developed across this space charge layer. Thus, the total potential difference across the interface is given by
UE ) φsc + φH + C
(10)
where UE is the electrode potential as measured between an
ohmic contact on the backside of the semiconductor electrode and a reference electrode (see Figure 3). The constant C is unknown and depends on the nature of the reference electrode. The potential difference φsc appears as a bending of the energy bands as indicated in Figure 2. Since the potential across the Helmholtz double layer is unknown, it is impossible to theoretically predict φsc just from energy considerations made in the previous section; i.e., the potential distribution has to be measured. Experimental information can be obtained by capacity measurements. The differential capacity of the space charge layer below the semiconductor surface can be derived quantitatively by solving the Poisson equation. For doped semiconductors one obtains the so-called Mott-Schottky equation
(
)
1 2kT eφsc ) -1 2 Csc 0n0e2 kT
(11)
in which is the dielectric constant of the semiconductor and 0 the permittivity of free space. This equation is only valid for a space charge region where the majority carrier density is depleted with respect to the bulk density; in this case the space charge layer is called a depletion layer. The thickness of the space charge layer, defined as dsc ) ee0/Csc, decreases with increasing doping. For a typical carrier density of n0 ) 1017 cm-3 and a band bending of φsc ) 0.5 V, one obtains dsc = 10-5 cm. Since the space charge capacity Csc is usually much smaller than the capacity CH of the Helmholtz double layer, it can easily be determined experimentally. One representative example of 1/Csc2 vs electrode potential UE is given in Figure 4b (“dark” curve). Since this Mott-Schottky plot is a straight line and its slope is identical to the theoretical value given by eq 11, it must be concluded that the potential across the Helmholtz layer remains constant. An extrapolation of the Mott-Schottky plot to 1/Csc2 ) 0 yields the electrode potential at which the potential across the space charge layer becomes nearly zero (φsc f 0). Accordingly, we have
at 1/Csc2 ) 0, φsc ) 0, and UE ) Ufb
(12)
Ufb is called the flat-band potential. In the above discussion, the energy bands are pinned at the surface, and any variation of the electrode potential leads to a change of the band banding
13064 J. Phys. Chem., Vol. 100, No. 31, 1996
Nozik and Memming published.3,4,16,45,60-62 In an ideal semiconductor-electrolyte interface without surface or interface states, charge transfer can only occur via the two energy bands, and the two processes have to be treated separately. The anodic current, due to an electron transfer from the redox system into the conduction band, is given by12,13
j+ c ) ekc,oxNccred
(13)
in which Nc is the density of states at the bottom of the conduction band as given by eq 1a and cred is the concentration of the reduced component of the redox couple, also given in cm-3. Thus, the rate constant kc,ox has units of cm4 s-1. In terms of the Gerischer model the latter is given by max Dred(Ec) kc,ox ) kc,ox
Figure 5. Equilibration of Fermi levels across semiconductor-liquid interface showing band bending in the semiconductor space charge (depletion) layer when the band edges are pinned.
as illustrated in Figure 5. Investigations of many semiconductor electrodes have shown that the positions of the energy bands are independent of the doping; i.e., the energy bands of n- and p-type electrodes have the same position at the surface, as shown in Figure 1. As previously mentioned, in aqueous solutions the potential across the Helmholtz double layer is entirely determined by the interaction of the semiconductor with the solvent. The energy positions at the surface for several semiconductors in contact with aqueous solutions are given in Figure 6. In many cases the flat-band potential, Ufb, and consequently the position of the energy bands, varies with the pH of the solution because of protonation and deprotonation of surface hydroxyl groups, as especially found with oxide semiconductors, germanium, and some III-V compounds (for detailed information see for example review articles23,33,34,46-50). If the energy band edges are pinned, they do not shift upon changing the redox system. Only a change in band bending occurs to maintain equal Fermi levels on both sides of the interface. However, there are many cases where the energy bands are not pinned, but rather the Fermi level of the semiconductor is pinned.51-54 In this situation, changes in the Fermi level of the system, by either changes in the redox system or changes in applied potential, will shift the energy bands. Thus, for example, the energy band positions at the surface of GaAs contacting acetonitrile or methanol depends strongly on the redox system added to the solution.55 This result was interpreted as Fermi level pinning by surface states (see also section II.4), as frequently occurs in semiconductor-metal systems. In 1980 it was reported that the Mott-Schottky curve measured with p-GaAs in aqueous solutions was shifted upon illumination of the semiconductor.56 This effect has also been found with many other semiconductors;35 an example is shown in Figure 4.57 This shift of the flat-band potential is due to an unpinning of energy bands. This effect can be caused by trapping of photogenerated minority carriers in surface states or by a very low rate of minority carrier transfer (as found with n-WSe257 and n-RuS258). In both cases minority carriers are accumulated at the surface which leads to change of the potential across the Helmholtz double layer, i.e., ∆Ufb ) φH. Band edge unpinning can also occur if carrier inversion develops at the semiconductor electrode surface.59 3. Charge Transfer Processes. Net charge transfer from semiconductors to redox species can occur via majority charge carriers in dark processes and via minority charge carrier under illumination. During the past 30 years a number of theories on heterogeneous charge transfer processes have been
(14)
in which Dred is the density of occupied states of the redox system as given by eq 8b. Inserting Dred(E) into eq 14, one obtains
kc,ox )
max kc,ox
[
]
(Ec - EF,redox - λ)2 exp 4kTλ
(15)
Since the conduction band remains fixed with respect to EF,redox during polarization, the rate constant and consequently the anodic current j+ c are independent of the potential. The cathodic current is thus given by
jc ) ekc,rednscox
(16)
in which ns is the electron density at the surface, defined by eq 2, cox is the concentration of the oxidized species of the redox system, and kc,red is defined by
[
max max Dox(Ec) ) kc,red exp kc,red - kc,red
]
(Ec - EF,redox + λ)2 4kTλ
(17) According to this model, electron transfer (ET) occurs at the energy of the conduction band edge without any loss of energy (Franck-Condon principle). The rate constant is therefore essentially determined by the relative position of energy states on both sides of the interface. Analogous expressions are obtained for the valence band processes. The resulting currentpotential curve is illustrated for an n-type semiconductor in Figure 4a. According to eq 16, the cathodic current is proportional to ns and cox. Provided that any potential variation occurs across the space charge region, the cathodic current at an n-type electrode is expected to increase by 1 order of magnitude if the electrode is varied by 60 mV. In many cases the current was found to increase exponentially with the electrode potential, but the slope did not meet the theoretical requirements; values much larger than 60 mV per decade were frequently found. In addition, the cathodic current did not increase with concentration. This behavior has been tentatively interpreted as being caused by an electron transfer via surface states (see also section IV). These deviations from the theory are still not sufficiently understood. There are actually only very few examples where slopes of 60 mV have been observed.33,34,63 Even for materials which have a rather perfect surface because of its layered structure, the current-potential dependence exhibits slopes larger than 60 mV. In recent years theoretical64-66 and experimental67-70 investigations have been conducted to determine the absolute values of the ET rate constants across semiconductor-liquid interfaces;
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Figure 6. Position of energy bands of various semiconductors in the dark (d) and in light (l) with respect to the electrochemical scale.
a recent review of this work is available.71 In one theoretical approach66 a model for ET across liquid-liquid interfaces72,73 was modified and applied to semiconductor-liquid interfaces. This latter model66 estimated the maximum possible value of the second-order ET rate constant (kc,red or kc,ox) for outer-sphere redox acceptors to be about 10-16-10-17 cm4/s. However, the validity of describing ET across semiconductor-liquid interfaces in terms of classical electronic particles has been challenged,65 and quantum mechanical models based on the interaction of the full electronic structure of the semiconductor with that of the redox species in solution have been published.64 At the present time there are relatively few experimental determinations of the ET rate constant, and the reported values vary over many orders of magnitude.71 Thus, for example, for photoinduced ET to the dimethylferrocene/dimethylferricenium redox couple, the reported value for kc,red is
