J. E;lrcrrourtaf. Chem., 199 (1986) 126 Elsevter Sequota S.A.. Lausanne  Printed
SURFACE
RECOMBINATION
in The Netherlands
AT SEMICONDUCTOR
ELECTRODES
PART IV. STEADYSTATE AND INTENSITY MODULATED PHOTOCURRENTS AT nGaAs ELECTRODES
J. LI * and L.M. PETER ~~p~~trn~~t of C’hemut?, (Received
2nd August
The Ukversrty.
~o~r~~rnpto~ SO9 SNH (Great Brazm)
1985; in revised form 7th October
1985)
ABSTRACT The photoelectrochemtcal behavtour of nGaAs m alkaline solution is discussed with particular reference to the influence of surface recombination on steady state and periodtc behaviour. Intenstty modulated photocurrents have been analysed m order to obtain information about the ktnettcs of surface recombjnation processes, and the theoretical response expected for different types of surface potential distribution are derived and compared with expertmental results. It is shown that the surface potential of nGaAs depends on pretreatment and that surface heterogeneity can exert an important mfhtenee on the frequency response under modulated illumination.
(I) iNTRGDUCTION
electrochemical reactions at semiconductor electrodes are usually described within the framework of the band model which allows a distinction to be made between valence and conduction band electron transfer. However, the interaction of atoms in the surface of the semiconductor with components of an electrolyte solution will influence the electron energy levels, so that the band model is not an appropriate local description for electronic levels at the surface. The deviations from ideal behaviour that result from different types of interaction at the phase boundary in semiconductor junctions have been treated by the surface state formalism. In the case of the semiconductorelectrolyte junction, the term surface state has been used to describe experimental situations ranging from adsorption to surface phase formation and multistep lattice dissolution 111. In most cases, the chemical and physical identity of surface states has remained obscure, but their density and location within the energy gap of the semiconductor are more easily accessible to measurement. Theoretical treatments of the semiconductorelectrolyte junction have been extended to take account of recombination in the spacecharge region [2,3] and at the
* Present
address:
Department
of Chemtstry,
University
of Utah, Salt Lake City, UT 84122, U.S.A.
2
surface [461. It is difficult, however, to distinguish between the two types of recombination on the basis of steadystate photocurrent voltage curves. and nonsteadystate methods are more useful for this purpose. We have shown elsewhere [6.7] that the response of the junction to interrupted illumination gives information about the recombination of minority carriers via surface states, and an experimental study of pGap has shown that the surface states generated by illumination are due to hydrogen which diffuses into the near surface region of the semiconductor [7]. The theoretical treatment has been extended subsequently to allow for electron exchange between surface states and redox species in solution, and the response to intensity modulated illumination has been derived [S]. Although it is clear that the analysis of photocurrent response in the frequency domain offers a new and powerful approach to the study of semiconductor electrodes, there appear to have been no applications of intensity modulation to the study of semiconductor electrodes apart from the work of Albery and Bartlett [9] and of Kamieniecki [lo]. The alternative approach of combining steadystate illumination with ac potential modulation has been used more widely [1113], but the inte~retation of the photocurrent response under these conditions is less straightforward. The present paper develops further the theoretical description of intensity modulated ac photocurrents in order to take into account the effects of surface heterogeneity and uncompensated resistance. The utility of the method is then demonstrated as part of a study of the photoelectrochemistry of nGaAs. It is shown that the method provides strong evidence that the surface composition of the semiconductor depends on electrode potential, solution composition and illumination intensity. it is shown that two different types of surface coexist at low values of band bending, giving rise to differing rates of surface recombination at a given electrode potential. (II) EXTENSIONS
TO THE THEORY
OF INTENSITY
MODULATED
PHOTOCURRENTS
(II.1) First order ac response The theory outlined in the previous paper in this series [8] shows that the recombination of minority carriers via surface states gives rise to a characteristic firstorder frequency response of the intensity modulated ac photocurrent which can be represented as a semicircle in the complex plane. In order to simplify the discussions here, it is assumed that ~nority carrier transfer to the electrolyte occurs predominantly via surface states. The real and imaginary components of the photocurrent then become Ke( Jphoto/C)
= 1  /+r,,/( &r;2 + 1)
(1)
= &r:/(
(2)
and Im( Yrhoto/d) where
w”r;? + 1)
3
and (4)
P=k,,(n5+n,)
Here 6 is the ac component of the minority carrier flux into the surface from the illuminated bulk of the semiconductor, k,, is the rate constant for electron capture by surface states, n, is the density of electrons (majority carriers} at the surface and nt is the value of n, when the Fermi level in the semiconductor is coincident with the energy of the surface state. In this approximation, the potential dependence of the firstorder frequency response is seen to be a consequence of the variation of n, with bandbending. The photocurrent response predicted for representative values of 7, and /3 is
1.0
0. 5
0 &ml
1. 0
CJoc/Gocl
Fig. 1. Complex plane plots of the modulated phot~urrent response calculated for a set of surface recombinatton centres (centred 0.5 eV below the conduction band) that can exchange electrons wtth solution redox species. (1) Band bendmg 0.2 eV (/3 = 3.36~10~ s‘. I, = 2.93~ 10m5 s). (2) Band bending0.3 eV (p=6.25~10~~‘, r~=8.47~10~ s). Density of surface states 10” cm‘. Ared,,% 1.5 performed with exact forms of eqns (3) and (4) (see ref. 8). eV. e,&,,, lob5 mol cmm3. Calculations
4
illustrated in Fig. 1. The zero frequency follow5 from eqn. (1) as
(‘&h<,k&)
___o
=
intercept
of the semicircle
on the real axis
1  P?
It is evident that the semicircle will pass through the origin for the particular case that no electron transfer to the redox species occurs since under steadystate conditions all minority carriers must recombine at the surface. The theory outlined above is readily extended to more complicated situations. Experimental response curves are found to deviate from the simple form shown in Fig. 1, and the most obvious reason for such behaviour is that the surface of the semiconductor is not homogeneous. In anticipation of the experimental results, we therefore discuss at this point extensions of the original theory. (11.2) Two relaxation
time constants for mitwri(t~ carrier processes
The simplest case of surface heterogeneity arises if two distinguishable states of the surface coexist at one potential. These states may differ either in their composition or m their coverage with some adsorbed species. In either case, the differing dipole potential contributions to the Galvani potential difference between the semiconductor and the solution give rise to differing surface potentials, provided that individual patches are large compared with the wrdth of the space charge region (typically 100 nm). If the distribution of surface potentials resulting from this type of surface heterogeneity is approximated by two discrete values of the surface potential, E, and ET. the ac photocurrent can be obtained by weighting the contributions from the different types of area according to their relative surface coverages, 8, and 1  8,. The complex photocurrent response is then given by
where 8, is the surface coverage of type 1. Figure 2 illustrates the ac ~hotocurrent behaviour to be expected if the two time constants are distinguishable. Since to a first approximation the time constants depend exponentially on the surface potential, relatively small differences in surface potential suffice to give obvious deviations from semicircular response in the complex plane and two distinct maxima in the phase angle. (Zf.3) Frequency dls~ersl~~ due to a normal distrib~t~~~ of surface potenttat It is well known that the presence of a distribution of relaxation times about a mean value gives rise to the flattening of impedance semicircles; the work of Cole and Cole [14] on dielectric relaxation is the classical example. Frequency dispersion in MOS junctions has also been studied for some years [15], and Nicollian and Goetzberger [16] have developed a model of surface charge heterogeneity which
1
0.
75
0. 5
Ret C.Tac/Gad
Fig. 2. (a) Complex plane plot for the modulated photocurrent response calculated for two constants associated wtth local band bending values of 0.2 and 0.3 eV respectively. variables as in Fig. 1. (b) The corresponding Bode plots of the modulated photocurrent that the two time constants give rise to characteristic peaks in the phase angle. (0) Log phase angle.
relaxation time 0, = 0.5. Other response. Note magnitude. (v)
6
explains the broadening of the conductancefrequency spectrum under depletion conditions. In the case of the ac photocurrent response, we have cafcufated the effect of a normal distribution of surface potential on the complex plane and Bode diagrams. The photocurrent response takes the form
(7b) where P(E), the normal distribution function, describes the probability surface potential has the value E. The composite frequency dependence
that the of the ac
Fig. 3. The effect of a distributton of surface potential IS to produce a flattenmg of the semicircular plot in the complex plane. Curve,1 is calculated for the same conditions as Fig. 1 (plot 1). and corresponds to a single valued surface potential. Curve 2 corresponds to a distribution of surface potential centred on the same mean value as curve 1, but with a variance 0’ of 0.04.
photocurrent can then be obtained by numerical integration of eqns. (7a) and (7b) (the lower limit of integration is chosen to exclude the accumulation regime). Figure 3 shows that a broadening of the distribution gives rise to a flattening and distortion of the semicircular plots. (11.4) Limitations
of high frequency
response by series resistance
Under conditions where surface and bulk recombination are negligible, the semiconductorelectrolyte junction behaves as an ideal current source driving into a parallel RC network composed of the space charge capacitance and the series resistance, and at high frequencies the spacecharge capacitance begins to shunt the series resistance in the external circuit so that the ac photocurrent is attenuated. The most important contributions to the series resistance in a potentiostatic experiment arise from the ohmic contact and from the solution resistance. Figure 4 shows how the series resistance introduces a phase shift in a direction opposite to that due to
0. 5
0. 2s
3 B 28 ? @ 5 e .d
0
t 0. 2:1
0. 5
t
0
Fig. 4. Complex plane plot of modulated photocurrent response showing the addttlonal results from the combination of the spacecharge capacitance C,, and the solution T\ = 5 x 10e4 s. R,JZ,~ = lo’ s. Frequencies (in Hz) are shown.
semiclrcie resistance
which R,,.
8 surface recombination, so that the semicircle crosses into the lower quadrants with a high frequency intercept of zero. These calculations emphasise the need to minimise series resistance by careful design of contacts and electrodes. (III) EXPERIMENTAL
DETAILS
Intensity modulated light was produced from a 5 mW heliumneon laser source by a lead molybdate optoacoustic modulator (Isomet 1250C) driven via an r.f. modulator by a frequency response analyser (Solartron 1250). The light signal was monitored by a fast PIN silicon photodiode which was used to provide the reference signal for the frequency response analyser. The bandwidth of the optical system was limited by the ac generator to 65 kHz. A constant time delay in the optical signal was observed as the result of the acoustic propagation delay in the modulator crystal, but this had no effect on the performance of the system since the reference signal was obtained from the photodiode. The Solartron 1250 was operated under software control from a BBC model B microcomputer via an IEEE 488 bus, and data analysis was performed on line by the microcomputer. Measurements at high frequencies required the construction of a fast potentiostat with optimised phase performance. A lownoise battery operated potentiostat with positive feedback iR compensation was constructed using OP 17 broadband operational amplifiers. The measurement cell was mounted directly onto the potentiostat in order to minimise stray capacitance, and the cell itself was constructed with the same aim in mind. The performance of the potentiostat and iR compensation system was tested using a PIN diode with a series resistor to replace the electrochemical cell, and satisfactory performance (negligible phase shift and attenuation) was obtained for frequencies of up to 40 kHz. The nGaAs electrodes were cut from tin doped crystal wafers provided by Metals Research in the (100) orientation with a donor density of 1.3 x 10” cm ‘. Ohmic contacts to both sides of the semiconductor were prepared with indium solder. and the I/V characteristics of each sample were checked to ensure minimum series resistance. The contact was then removed from one side of the crystal and the sample was ground and polished to form a 2 mm diameter cylinder which was mounted in a glass tube with epoxy cement. The exposed front of the semiconductor was prepared by mechanical polishing on alumina followed by etching in bromine/~ethanol. The completed electrode was mounted on a 4 mm plug which was inserted directly into the potentiostat case. The glass tube formed a ground glass joint which fitted into the base of the cell so that the distance between the working electrode and control amplifier was limited to 5 cm. Miniature reference electrodes (either Hg/HgO or Hg/HgS) were prepared and fitted to a Luggin capillary probe. The potentials of these reference electrodes were checked against a saturated calomel electrode before and after each measurement. Solutions were prepared from AnalaR grade chemicals with triply distilled water and purged with oxygenfree nitrogen. All measurements were carried out at room temperature in a screened dark box. Steadystate and transient photocurrents were
measured at different wavelengths using lockin and signal recovery techniques that ave been described elsewhere [7]. Impedance measurements were made using the olartron 1250 frequency response analyser. V) RESULTS
AND
DISCUSSION
‘K 1) Shifts in the band edges of nGaAs The inte~retation of the photocurr~ntvoltage behaviour of nGaAs is comlicated by the shifts in the position of the band edges that occur both in the dark nd under illumination [17]. These effects are illustrated in the Mottottchottky plots I Fig. 5. Firstly, it is evident that the apparent value of the flatband potential epends on the prepolarisation of the electrode. At a sweep rate of 20 mV s’ a ifference of over 200 mV is observed in the intercepts, indicating that the changes :sponsible for the shift in the band edges occur rather slowly, at least in the dark. imilar, although smaller shifts in acid solution have been reported recently by chroder and Memming [lS]. The second conclusion that can be drawn from Fig. 5
lg. 5. MottSchottky plots for nGaAs in 0.1 mol dm’ KOH. (v) In the dark, measured from  1.6 V ) more posttive potentials. (0) in the dark. measured from 0 V ta more negattve potenttals. (0) Under Iuminatlon. measured from 0 V to more negative potentials. Sweep rate 20 mV sl. Electrode area 0.22 XI’. Frequency 500 Hz. Saturation photocurrent 1.5 x low4 A cm?.
10
is that the hysteresis between the forward and reverse sweeps is reduced considerably under illumination, although the flatband potential is more positive than in the dark. Impedance measurements carried out on solutions containing sulphide (TO’ mol dmj) gave results that were essentially identical to those in Fig. 5, supporting the conclusion of Savodogo and Deschanvres [19] that sulphide is not adsorbed to an appreciable extent at GaAs. The influence of surface states on the potential distribution at the semiconductorelectrolyte interface has been discussed elsewhere [1,6]. An order of magnitude calculation shows that a surfacestate density of about 1O’j cm2 would be needed to bring about the shift of 200 mV in the MottSchottky plots which is observed experimentally. However, it is important to realise that the dipole contribution to the Galvani potential difference at the semiconductorelectrolyte interface may also depend on prepolarisation as the result of changes in surface composition. Since impedance measurements [20] show that the density of surface states is not strongly dependent on prepolarisation in the dark, it is likely that the shift in flatband potential reflects changes in the surface dipole potential as the result of a chemical transformation of the surface. The shift in flatband potential under illumination suggests that the transformation involves an oxidation process. Allongue et al. [17] have reported a similar shift in flatband potential and shown that it saturates rapidly with increasing illumination intensity. Further evidence for the shift of E, under illumination has been obtained by electroreflectance measurements which confirm that the flatband potential in 0.1 mol dm”” KOH is  1.75 V vs. SCE [21]. (I V.2) The equilibrium potentialpH
diagram
for GaAs
Since there is strong evidence that the surface composition of GaAs depends on prepolarisation, it is useful to consider the range of thermodynamic stability of GaAs as a function of pH and of electrode potential. Calculations of the equilibrium potentialpH diagram have been reported by Park and Barber [22] but since their results differ substantially from our own, Fig. 6a displays the potentialpH diagram derived from the equilibrium data for arsenic and gallium [23]. The value of  77.4 kJ mol’ used for the Gibbs energy of formation of GaAs is based on the data recommended for IIIV compounds by Siroto [24]. The diagram shows that GaAs will be thermodynamically stable at pH 13 in the potential range  1.0 to  1.5 V, whereas at more positive potentials it will be oxidised according to one of the following reactions (written in terms of holes): GaAs + 3 H,O + 3 h+= GaO:E/V
+ As + 6 H+
(8)
= 0.468  0.1182 pH + 0.00197 log [GaOl]
G~s+5H~O+6~+=GaO~~+AsO~+lOH’ E/V
= 0.390  0.0985 pH + 0.00985 log{ [GaO:1
(9) [AsO
]>
11
By contrast, at negative tally possible: GaAs + 3 IIs + 3 e= E/V
= 0.874
In the region
1
potentials
of GaAs
becomes
thermodynami
Ga + ASH,
(10)
 0.0591 pH + 0.0197 log PAsw, of thermodynamic
s
stability
of GaAs,
the semiconductor
is in equi
Ga+ AsH3
20 0
the reduction
;
I
I
I
/
i
I,
2
3
I
5
6
7
/ 8
9
t 10
I
/
,
II
12
13
;
(a)
PH
Fig. 6. (a) ~quilib~um potentialpH diagram for the GaAsiH,O system at 25°C. The hydrolysis eqmhbria for GaAs (eqn. 11) have not been included in the figure. Note the regions in which As(O) coexists with Ga(III). (b) Solubihty of As(II1) and Ga(III) species as a function of pH.
12
librium with ASH, and hydrolysis reaction is GaAs + 3 H,O + GaO:
soluble
Ga(II1)
species.
+ ASH, + 3 H+
At pH
13, for
example,
the
(II)
but since the solubility product calculated for this reaction is lO_“, the equilibrium has not been included in Fig. 6a. The formation of surface phases on GaAs can be considered with the help of Fig. 6b, which shows the solubility of Ga(II1) and As(II1) species as a function of pH. Whereas As,O, is appreciably soluble over the entire pH range, Ga(OH), is expected to form a surface film at intermediate pH values. At pH 13, however, both Ga(III) and As(III) are sufficiently soluble that surface oxide formation can be excluded. Although the limitations of thermodynamic calculations of this kind are clear, Fig. 6a can be interpreted to suggest that the surface stoichiometry of GaAs will tend to change outside the region of stability in such a way that a galliumrich surface forms at very negative potentials. whereas arsenic will accumulate at more positive potentials before As(II1) dissolution becomes possible. It therefore seems reasonable to relate the shifts in flatband potential to changes in the surface atom ratio or to the formation of surface metal adatoms rather than to the formation of surface oxide or hydride phases suggested by Schroder and Memming [18]. Further evidence for changes in surface composition comes from the intensity modulated photocurrent results discussed in Section (IVS). (I V.3) Steadystate
photocurrent
voltage curves
As we have pointed out in the previous paper in this series [8], phhocurrent voltage curves obtained with chopped illumination may differ appreciably from the dc characteristics as the result of the timedependent relaxation of minority carriers via surface states. We begin, therefore, with currentvoltage curves measured under steadystate illumination. Figure 7a illustrates the behaviour of nGaAs in alkaline solutions containing polysulphide. Appreciable hysteresis between the forward and reverse sweeps is observed, both in the dark and under illumination. The direction and magnitude of the shifts are similar to those evident in the MottSchottky plots in Fig. 5. but the photocurrent onset potential is some 400 mV positive of the flatband potential measured under illumination. Figure 7b demonstrates that the considerable improvement in the shape of the photocurrent voltage curve brought about by ruthenium treatment is achieved at the expense of an increased cathodic dark current near the flatband potential. It has been shown that the ruthenium treatment of pGap introduces states which are able to capture electrons from the conduction band and transfer them to solution species [7], and we therefore conclude that the adsorption of ruthenium ions on nGaAs simultaneously removes preexisting recombination centres and introduces a new set of levels situated near the conduction band. Since the hole capture cross section of adsorbed ruthenium is evidently small [7], the surface recombination rate is expected
13
Frg. 7. Photocurrentvoltage curves for nGaAs m 0.1 mol dm’ KOH contammg 0.1 moi drnj Na,S+O.l mol dms S. (a} Freshly etched nGaAs electrode (b) Same electrode after dtppmg rn RuCl,/HNO,. Illumination (HeNe laser) 50 PW EIectrode area 0.22 cm’.
to be lower than for a neutral surface state. (The effect of ruthenium treatment MottSchottky plots has been discussed by Allongue and Cachet [17].)
on
(IV.41 Photocurrent behaviour under interrupted illunwmtron Figure 8 illustrates the pronounced relaxation effects that are observed in the photocurrent onset region. Similar effects at the pGap electrode have been studied in detail and attributed to surface recombination via photoinduced “near surface”
!
10 A
Y
ad 15
05
E/Y vs SCE
Fig. 8. Photocurrentvoltage curve measured under the same condrttons as the curve in Fig. 7a, except that interrupted illummatton was used. Pronounced relaxation effects can be seen m the photocurrent onset regton where the photocurrent appears superimposed on an apprectable cathodtc dark current,
14
levels. and transient photocurrents have also been observed in many other systems. Typical relaxation transients recorded in the onset region showed decay time constants of the order of milliseconds. Close examination of the decay transient showed small but significant deviations from the exponential form expected for simple first order recombination; typically two linear regions could be resolved in semilogarithmic currenttime plots. These effects are more readily resolved using intensity modulated ac photocurrent analysis over a wide range of frequencies. On the other hand, measurements using lockin techniques and chopped illumination must be interpreted with caution since the relaxation effects give rise to an apparent phase shift in the photocurrent response, and the photocurrentvoltage curves depend on the chopper frequency.
15
1 E/V
1.5
“s
D
05
0
05
0
SCE
LO E/V “f
1.5
10
05
SCE
Fzg. 9. A set of ph~t~urrentvoltage curves for nGaAs in 0.1 mol dm’ KOH+O.l mol dmNa,S+O.l mol dm” S, obtained by the lockin method (chopping frequency 37 Hz). At low hght mtensitles (a) the photocurrent onset occurs close to the flatband potential. but considerable hysteresis between the forward and reverse sweeps 1s observed. As the hght intensity is Increased, the hysteresrs is reduced, but the photocurrent onset 1s displaced to more posmve potentials (b) and (cf.
15
Figure 9 compares a set of photocurrentvoltage curves obtained by the lockin method for different light intensities. Two trends can be seen in these results. Firstly, the potential at which the photocurrent rises steeply towards its saturation value appears to move away from the flatband potential as the light intensity is increased. This effect is not expected if the delayed photocurrent onset is due to recombination at the surface [6,8] or in the spacecharge region [2,3]. Secondly, the hysteresis between the forward and reverse sweeps decreases with increasing light intensity. until at the highest intensity it is almost absent. In all cases, however, a significant photocurrent is seen to extend down to the flatband potential, and comparison with
,/,
’
I
I
15
10 05 EI" SCE
0
“5
fb)
c
dI
Cl3pA
_J
15
10 E/V
05
0
15
10
05
0
"S S‘E
Fig. 10. A set of phot~urrentvoltage curves obtained under stmilar condmons to those given in Fig. 9, except that the electrode was treated with ruthenium. A constderable mcrease in phot~urrent IS observed at low mtensities (a,) but this Improvement IS lost on continued potenttal cychng (a, .  ). At higher intensities the improvement m response becomes progressively less evident (b) and (c).
16
Fig. 8 identifies this region as the range where transient relaxation effects are important. By contrast, much lower steadystate photocurrents are observed in this region. Figure 10 presents by way of comparison a set of photocurrent curves obtained with a ruthenium treated GaAs electrode. The treatment clearly improves the photocurrent response at low light intensities, but it is evident that the effect becomes smaller as the light intensity is increased. If recombination takes place via a constant density of surface states, an increase m illumination intensity is expected to displace the photocurrent onset towards the flatband potential but the opposite effect is observed in the present case. If. on the other hand, the surface state density is increased by illumination as the result of minority carrier reactions, the photocurrent onset can be displaced in the opposite direction. A similar displacement in the case of pGap is known to be due to the incorporation of photogenerated hydrogen into the surface of the semiconductor. In the case of nGaAs, hole reactions at the surface will produce intermediate species which may act as recombination centres as part of the multistep process leading eventually to lattice decomposition [25,26]. (IV.5) Intensity
modulated
ac photocurrent
response
A set of complex plane plots of the normalised ac photocurrent obtained at different potentials for nGaAs in 0.1 mol dmm3 KOH is shown in Fig. lla; the corresponding Bode plots are given in Fig. lib. The gross features expected for surface recombination are seen in the experimental plots, and in particular wellformed semicircles are obtained close to the flatband potential. At more positive potentials, however, the complex plane plots become flatter and lose their initial symmetry. Instead of forming a nest of semicircles of decreasing diameter, the plots flatten progressively and show some evidence of two overlapping semicircles. The same trends are apparent in the Bode plots which exhibit a progressive broadening of the phase angle curves as the potential is made more positive. Clearly the recombination processes in this system are more complex than those considered in the derivation of the first order ac response, but this is not surprising since the minority carrier reaction leads to lattice decomposition via a multistep pathway rather than to the oxidation of a solution species. The most detailed recent study of the photodissolution kinetics of nGaAs has been reported by Allongue and Cachet [27] who have used the treatment proposed by Frese et al. [28] to show that the surface concentration of intermediate radical species depends on the surface hole concentration. Recombination in this simple scheme is identified with eqns. (12a) and (12b) in the process A:B+h++A.B A.B+e+A:B A.B+h+
k,
(12a)
k1
(12b) + products kz
(12c)
17
jxc
I
05
05
i
piyyq 0
05
yzG_ 05
‘,;,_l~
:
100
10
05 ~~ 0
pq
I
u
05
t
1
2
z
El 2 E
I
!
1
11
,
1
05
0
103
v
% E 05
0.5
,J.L.q :~ OS
0
1
1 098

1
v
t 05
0
05 red
Fig. lla. (a) A famtly of complex plane photocurrent plots obtamed for nGaAs m 0.1 mol dm 3 KOH for modulation frequencies between 1 and 6.5 X lo4 Hz. Note m particular the well formed semlclrcular response observed close to the flatband potential (e.g. at  1 68 V vs. SCE)
Such a scheme would, however, give rise to a single time constant due to minority carrier recombination, whereas a very broad response is observed experimentally. It therefore seems probable that recombination may involve electron capture by more than one intermediate in the lattice decomposition reaction. Further interpretation is difficult, however, since the surface composition is likely to be changed considerably as the result of photocorrosion, so that the local electron density at the surface will be subject to spatial fluctuations that broaden the ac response.
18 90
Cl
1
0
1
0 2
3
L
_I
90
0
1
2
L
3
1
0
0
90
5
0
tw
90
0
5
0:
lh‘
s
0 *0
0
1 Li zl
0
I
2
3
5
0
0
I______ 1
1 i
0 0
1 0
1
2 tog
3 f/Hz
I
5
90
0
0
1
I
1
/
2
3
0
.‘
L
5
90
log fith
Fig. 11 b. The corresponding set of Bode plots tllustratmg the changes in the magnitude of the photocurrent (solid lines) and in the phase angie (broken Imes). The phase angle plots are particularly sensitive to the presence of more than one ttme constant, and at 1.03 V, for example, two drstinct maxima can be seen. (100%modulation. Laser irradrance 3.5 mW cm‘.)
Figure 12 presents a contrasting set of measurements in which sufphide was added to the solution in order to provide a reactant for minority carriers. The overall behaviour is now seen to correspond more closely to that predicted for recombination in competition with charge transfer to a redox species. In particular the complex plane plots (Fig. 12a) largely retain their semicircular form as they collapse towards unity with increasing bandbending. The plots show that at least two time constants
19 1 122
v
05
'O?QL loo*/ '_r 0
l
1
05
1 112 v
t
z?
0
05
1
:!
05
0
0.5
1
0.5
I
u
0
05
10 1
1
05
0
real
Fig. 12a. A family of complex plane photocurrent plots obtamed for nGaAs tn 0.1 mol dm ’ KOH tO.1 mol dm’ Na,S+O.l mol dm” S. In the presence of S’, the plots correspond more closely to those predicted theoretIcally, and in parttcular at  1.32 V two semicircles can be resolved clearly. Note also that the diameter of the semicircles collapses to zero as the photocurrent approaches the saturatton region where recombination effects are negligible.
are involved in the recombination process at intermediate potentials where the complex plane data resolve into two overlapping semicircles. The two time constants differ by over an order of magnitude as can be seen from the two distinct maxima in the phase anglefrequency plots in Fig. 12b.
20
1
;___,___::.:,.
,. I ,I0
1
2
3
90;
$ 01111
0
‘\
I
,
/
\
. .. ’
1 0
1
2
3
(IOg f/Hz)
\
\
\
.
i
I
,___T___I_Z‘L
I.
so
1
2
90
1 07 v
Ii
,
so
L
{
3
L
so
(103 f/Hz)
Fig. 12b. The corresponding set of Bode plots. Note here the appearance of two distinct maxima in the phase angle plots (  ) at  1.32 V. This result suggests that two types of surface can coexist at potentials m this region. (100% modulation. Laser lrradiance 3.5 mW cm2.)
The discussion of surface heterogeneity in Section (11.2) demonstrated that relatively small differences in surface potential suffice to give rise to two semicircles in the ac photocurrent response. Although the theoretical treatment approximates the distribution of surface potential by two delta functions, an additional broadening of the distribution about the two values of surface potential will simply cause a flattening of the semicircles as shown in Section (11.3). The existence of variable surface composition is demonstrated by the MottSchottky plots in Fig. 5 which
21
show that the apparent flatband potential shifts by more than 200 mV, depending on the prepolarisation and illumination level. The ac photocurrent response provides proof that two types of surface coexist at low values of band bending. The recombination time constants associated with these two types of surface differ by a factor of 20, and since T? is related via the electron density to the surface potential (eqn. 3) this places narrow constraints on the possible values of the two surface potentials. If the surface potential of one component becomes too large it will not contribute appreciably to the relaxation process so that only one semicircle is observed. If, on the other hand, the two surface potentials differ by more than 250 mV from each other, one area will tend to dominate the frequency response, and again only one semicircle is observed. The experimental ac photocurrent data obtained at 1.3 V vs. SCE can be compared with the results of calculations based on the model of two surface potentials. The calculation evidently reproduces satisfactorily the experimental frequency dependence of the ac photocurrent; the experimental complex plane plot is flattened slightly, but this effect is not unexpected since a distribution of potential will give rise to a depression of the plot as shown in Fig. 3 for a single maximum in the surface potential distribution. Equation (5) predicts that the zero frequency intercept of the complex plane ac photocurrent response should move away from the origin as the potential is made more positive and the density of free electrons at the surface falls. This shift of the intercept should be accompanied by an increase in T$ as the rate of majority carrier capture by surface states becomes smaller. These predictions are based on the assumption that a simple linear relationship exists between the bandbending and electrode potential. As we have shown elsewhere [6], this relationship will depart from linearity if the density of surface states is sufficiently high that changes in their occupation influence the potential drop in the Helmholtz layer. Under these circumstances “Fermi level pinning” occurs and plots of log 7, vs. electrode potential are expected to show a broad plateau when the Fermi level moves through the surface state 161. An indication that the behaviour of nGaAs is more complicated is given by Fig. 12a. It is clear that the zero frequency intercept does not move smoothly away from the origin as the potential is made more positive. Instead the intercept increases initially but then decreases over a potential range of ca 300 mV before increasing again towards unity as the saturation photocurrent regime is approached. Figure 13a shows that the magnitude of the ac photocurrent observed in 0.1 mol dm” KOH containing sulphide also passes through a maximum and a minimum before tending towards the saturation limit. A similar hump in the photocurrent response can be seen in the photocurrent voltage curves obtained with chopped illumination (Fig. 9), but it is important to point out here that the data shown in Fig. 13a are taken from frequency response analyses performed at a constant value of the electrode potential whereas the curves in Fig. 9 were obtained with a linear potential sweep. The maximum and minimum in Fig. 13a are therefore not due to dynamic effects related to slow surface transformations, but reflect instead the steadystate properties of the surface.
(a) 20
1 5 E/V YS SCE
I 0
(bf Frg. 13. (a) Plots of the magnitude of the phot~urrent at different frequenctes as a functton of potentral. Solution 0.1 mol drne3 KOH+O.l moi dm”‘” NazS+O.l mol dm’ S. Frequencies (I) 1 Hz. (2) 10 Hz, (3) 100 Hz. (4) 1 kHz, (5) 10 kHz. Note the appearance of a current mInImurn at around  1.3 V vs. SCE where two time constants are observed m the ac response (see Ftg. 12). (b) Dependence of the relaxatgon frequency (taken from the imaginary rna~lrnurn of the complex plane response) on electrode potentials. The limiting slope of (59 mV) ’ is shown by the dashed hnes. The shape of the expertmental curve provides a striking demonstration of the shifts m band edge posrtion that occur when the electrode potential IS changed.
23
(b) 20
Fig. 14. (a) Plots of the magmtude of the ph~t~urr~nt at different frequencies as a function of potential. Solution 0.1 mol dmp3 KOH. In thus case a broad minimum IS observed only at low frequencies. (b) Dependence of the relaxation frequency (taken from the imagmary maximum in the complex plane response) on electrode potential. The limtting slope of (59 mV) ’ ts shown by the dashed lmes. Note that the relaxation frequency remams almost constant over a potenttal range of 400 mV. suggesting that “Fermi level pinmng” occurs in this region as the result of changes in surface composition.
Figure 13b shows that the variation with potentiaf of the magnitude of the photocurrent is paralleled by the way in which the frequency corresponding to the maximum in the imaginary component changes with potential. This frequency corresponds to 7; ‘, and if the relationship between surface and electrode potentials is linear, 7;’ is expected to decrease monotonically as the density of free electrons at the surface falls with increasing potential. The experimental values of r\‘, on the other hand, pass successively through a minimum and a maximum before falling again as the saturation photocurrent regime is approached. Similar, but not identical, behaviour was observed in the absence of sulphide ions in the solution (Fig. 14). In this case the minimum in the photocurrent magnitude is seen only at low frequencies, and the ?,I potential plot corresponding to Fig. 13b shows a broad plateau rather than a well developed maximum and minimum. Interpretation of these results is more difficult, however, since the ac photocurrent response deviates considerably from the simple limiting forms observed when a solution redox species is present. The potential dependence of 7,’ shown in Fig. f3b is direct evidence that the variation of surface potential with electrode potential is not monotonic. A reversal of the potential dependence of r, cannot be explained in terms of Fermi level pinning which would simply lead to a plateau; the changes in surface potential must be related instead to variations of surface composition as a function of electrode potential. Similar results have been obtained by Lorenz et al. [12,13] using ac potential modulation where one or two ac photocurrent maxima are observed for nGaAs in KOH prior to the onset of the steadystate photocurrent. At this point it is possible to consider all the evidence for changes in surface composition of GaAs as a function of potential. The hysteresis in the MottSchottky plots (Fig. 5) and photocurrent voltage curves (Fig. 9) as well as the appearance of two time constants in the ac photo~urrent response demonstrate that the potential drop in the Helmholtz layer depends on electrode pretreatment. The fact that r,’ actually increases with potential in the range  1.5 V to  1.3 V vs. SCE (Fig. 13b) shows that the changing potential drop in the HehnhoItz layer more than compensates for the overall variation of the potential difference between the electrode and the solution. As a consequence, the bandbending decreases with potential over a range of 200 mV before increasing again. The potentialpH diagram for GaAs (Fig. 6a) identifies the potential range concerned in this anomalous behaviour as the region in which As is in equilibrium with GaO:, suggesting that As adatoms may be stable on the surface of GaAs or that the Ga/As ratio in the surface will tend to fall below unity. The dissolution of As adatoms becomes thermodynamically possible only at more positive potentials. Of course, the diagram refers to the equilibrium properties of the bulk phases whereas the photocurrents correspond to nonequilibrium processes involving minority carriers. The thermodynamic feasibility of reactions involving holes at the surface of nGaAs can be discussed using the quasiFermi level (QFL) concept, and in principle, valence band holes are capable of oxidising GaAs to Ga(III) and As(III) provided that the hole QFL lies below the corresponding redox level given by eqn.
25
(9). At the same time, however, the reactions of electrons at the surface of nGaAs must be taken into account. and the steady state is therefore established by the competition between majority and minority carrier reactions. The formation of an As rich surface layer can then be considered to occur by hole capture followed by electron capture. At more negative potentials the density of eIectrons at the surface is sufficiently high that any As(W) species in solution (formed for example by previous illumination at more positive potentials} will be reduced, forming an As rich overlayer on the electrode. On the other hand, prepolarisation under inversion conditions or under illumination will provide sufficient holes to restore the original surface composition by reoxidising As adatoms. In such a case the shifts in bandedge position are the result of a change in surface dipole potential rather than due to the accumulation of electronic charge in surface states. The ac photocurrent results show that recombination centres are present at both types of surface, and there appears to be no clear correlation between surface composition and surface state density. The close parallel between the plots of T;’ and / &,_ 1 against potential (Fig. 13) indicates that the density of surface states is essentially constant in the region where the surface composition is evidently changing considerably. On the other hand, the shift of the dc photocurrent onset potential to more positive potentials with increasing light intensity shows that the density of surface states is dependent on the light intensity, a conclusion that is in accord with the results of Allongue et al. [17,27]. At present it is not possible to identify the nature of the surface states, but it is clear that they must be produced as the result of minority carrier reactions at the surface. Allongue and Cachet [27] have reported that a thin surface layer of As,O, is formed by the photocorrosion of nGaAs in 1 mot dm” KOH, so that the surface states could be associated with such a layer. However, in view of the very high solubility of As,O, in alkaline solution, it seems unlikely that such a film could exist except at high current densities. Further insitu studies, for example by ellipsometry, are needed to identify the surface phases under illumination.
(V) CONCLUSIONS
The results discussed here show that the frequency response analysis of intensity modulated photocurrents gives directly information about surface recombination. In the case of nGaAs in alkaline solutions, it is clear that the surface is heterogeneous on a sufficiently coarse scale to produce at least two different relaxation time constants at low values of bandbending. In the absence of solution redox species, it appears that photodissolution gives rise to a range of surface intermediates which are characterised by a broad frequency spectrum. In the presence of solution redox species such as S’, however, the frequency response approximates closely to theoretical predictions based on a simple model of surface recombination. Further work is in progress to characterise the behaviour of nGaAs in Se’,,%solutions using the intensity modulation method.
26 ACKNDWLEDGEMENTS
Financial support for this work was provided by the Science and Engineering Research Council. The authors would like to thank Robert Peat for useful discussions of this work. REFERENCES 1 L.M. Peter m F. Silva (Ed.). Trends m Interfactal Electrochemistry. NATO Advanced Study Instttute. Retdel, Dordrecht, m press. 2 J. Retchman, Appl. Phys. Lett., 36 (1980) 574. 3 J. Retchman and M.A. Russak in A.J. Noztk (Ed.). Photoeffects at SemiconductorElectrolyte Interfaces, ACS Symposium Series 146. American Chemtcal Soctety. Washmgton, 1981, p. 351 4 R.H. Wtlson, J. Appl. Phys.. 48 (1977) 4292. 5 F. El Guibaly and K. Colbow, J. Appl. Phys., 53 (1982) 1737. 6 L.M. Peter. J. Li and R. Peat, J. Electroanal. Chem., 165 (1984) 29. 7 J. Li, R. Peat and L.M. Peter, J. Electroanal. Chem., 165 (1984) 41. 8 J. LI and L.M. Peter, J. Electroanai. Chem., 193 (1985) 27. 9 W.J. Albery and P.N. Bartlett, J. Electrochem. Sot., 129 (1982) 2254. 10 E. Kamteniecki. J. Appl. Phys., 54 (1983) 6481. 11 B. Wolf and W. Lorenz, Electrochim. Acta, 28 (1983) 699. 12 W. Lorenz and M. Handschuh, J. Electroanal. Chem.. 178 (1984) 197. 13 W. Lorenz. M. Handschuh, C. Aegerter and H. Hermberger. J. Electroanal. Chem.. 184 (1985) 61. 14 K.S. Cole and R.H. Cole, J. Chem. Phys., 9 (1984) 341. 15 E.H. Nicolhan and J.R. Brews, MOS (Metal Oxide Semiconductor) Physics and Technology, WtleyInterscience. New York. 1982. 16 E.H. Ntcollian and A. Goetzberger. Bell Syst. Tech. J., 46 (1967) 1055. 17 P. Allongue, H. Cachet and G. Horowitz. J. Electrochem. Sot , 131 (1984) 2861: see also P. Allongue and H. Cachet, Sohd State Commun., 55 (1985) 49. 18 K. Schrijder and R. Memmmg. Ber. Bunsenges. Phys. Chem., 89 (1985) 385. 19 0. Savodogo and A. Deschanvres, Bull. Sot. Chim. Fr.. 1112 (1983) I281. 20 J. Lt and L.M. Peter, unpublished results. 21 R. Peat and L.M. Peter, unpublished results. 22 SM. Park and M.E. Barber, J. Electroanal. Chem., 99 (1979) 67. 23 M. Pourbaix, Atlas of Electrochemtcal Equilibrta in Aqueous Solution, Pergamon Press, New York, 1966. 24 N.N. Siroto in R.K. Willardson and A.C. Academic Press, New York, 1968, p. 91. 25 D. Vanmaekelbergh, (1983) 2813.
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Vol. 4, 1. 79