Impedance studies at semiconductor electrodes: classical and more exotic techniques

00134686/90$3.00+ 0.00 0 1990.Pergamon Press pk.

HecrrochimicaAcra, Vol. 35, No. IO,pp. 1545-1552,1990 Printed in Great Britain.

IMPEDANCE ELECTRODES:

STUDIES AT SEMICONDUCTOR CLASSICAL AND MORE EXOTIC TECHNIQUES J.-N. CHAZALVIEL

Laboratoire de Physique de la Mat&e Condenste, Ecole Polytechnique, 91128 Palaiseau-Cedex, France (Received for publication 11 April 1990)

Abstract-Unique characteristics of semiconductor electrodes are their large photosensitivity and the fact that an applied potential can penetrate quite sizeably into the electrode material (depletion layer _ 1 pm). These peculiar features have favored the development of many specific impedance or transient techniques. The classical electric impedance is mostly dominated by the capacitance of the depletion layer in the semiconductor, allowing for the determination of the flatband potential. More complex behaviors are often associated with the occurrence of surface states in the forbidden gap. Opto-electric impedance techniques include photocurrent and photopotential response to a modulated illumination. They provide additional information on the interface kinetics. Electra-optic impedance techniques include absorption and luminescence response to a potential modulation. Infrared absorption response provides detailed information on the nature of the charge being displaced upon potential modulation (free carriers or surface states). The concentration of free carriers near the interface may also be probed by the surface conductivity, measured at optical, microwave or d.c. frequencies. These “parallel” probes can be used in response to a light modulation or a potential modulation. Since they give a direct measure of the charge

(and not the current) they may be especially interesting at the lower frequencies. Key words: semiconductor

electrochemistry, time-resolved, opto-electric, electro-optic.

INTRODUCTION Much recent work has been devoted to semiconductor electrodes, especially in view of their potential interest for realizing the photoelectrochemical conversion of solar energy[l]. To a first approximation, the behavior of a semiconductor-electrolyte junction is dominated by the large photosensitivity of the semiconductor, and the thick (w 1 pm) depletion layer, which constitutes the space-charge region on the semiconductor side of the junction. The photocarriers created upon bandgap illumination are separated by the built-in space-charge electric field, and those reaching the interface may give rise to a photoelectrochemical reaction. However, the various problems that frequently arise (semiconductor corrosion, poor electrochemical transfer kinetics, carrier recombination, detrimental role of surface states) have stimulated fundamental studies on these systems. This has contributed to the development of a rich variety of experimental techniques, especially of several semiconductor-specific impedance and transient techniques[2]. We will first recall the basic principles of semiconductor-electrolyte junctions, together with the results that may be obtained from the classical electric impedance technique, then we will describe those techniques involving illumination; finally we will present the techniques using electrical transport parallel to the interface. We will mention the transient techniques besides the impedance techniques strict0 sensu, since the borderline between these two kinds of techniques is often difficult to draw. However, in spite of their close relationship,

one should keep in mind that the transient techniques often step out from the framework of linear response theory.

ELECTRIC

IMPEDANCE

Figure 1 recalls the energetical scheme of a semiconductor electrode (here n-type) polarized at a potential V in an ideally simple case, that is indifferent electrolyte and no charge reservoir at the surface. Under such ideal conditions, the electrostatic potential is affected only by the space-charge in the semiconductor and the ionic space charge in the Gouy-Chapman region and outer Helmholtz plane. The doping of the semiconductor is usually orders of magnitude smaller than the ion concentration in the electrolyte, so that the space-charge region in the semiconductor is much thicker than the ionic charge layer (typically 1 pm us 1 nm). From this it results that the change in electrostatic potential upon crossing the interface takes place essentially in the spacecharge region on the semiconductor side. In other words, in the framework of this simple model, the Helmholtz potential drop is negligible. The distribution of potential Q(x) in the semiconductor can be calculated from the Poisson equation A@ = -p/cc,, and the constitutive equation of the semiconductor, that gives the density of electric charge p(x) as a function of potential, eg for an n-type semiconductor, p(x) = eNn [l - exp(e(O - @,,)/kT)], where Nn is donor concentration. A most important case is that of a depletion of majority carriers (electron depletion

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negligible but stays constant independently of the applied potential and semiconductor doping. Such a situation may result, for example, from the occurrence of a ionic charge controlled by an acid-base equilibrium at the interface[4].) When a given redox system is added to the solution, the equivalent scheme of the interface must involve a Faradaic resistance (plus possibly a War@ AElectrostaticpotential burg element) in parallel with C,. The energetical scheme of the interface at the equilibrium potential + V redoxexhibits a band curvature e( V,, - V,,). This X is similar to a metal-semiconductor diode with “Schottky-barrier height” e( Vredox- V,). This highlights the importance of Vfbr as the band bending at rest potential appears as the most important parameter for the junction. For example, it represents the E Electmnenergy maximum photopotential that may be obtained under very strong illumination of the interface[S]. t Electric impedance measurements at semiconductE, 1 -S1-;vFtEF ing electrodes are usually performed by using the same kind of apparatus as for metallic electrodes: E, __________________________ ____ __ bridge techniques have been used in the past, but the lock-in technique is now more generally preferred, as it is more convenient[6]; for measurements above a Distance E few kHz, simultaneous measurement of current and l ” SEMICONDUCTOR ELECTROLYTE ’ potential is necessary[l. This is done by using a frequency response analyzer. Transient measureFig. 1. Electrostatic and energetical scheme of a semiconductor-electrolyte interface ( p is electric charge density; Cg ments using excitation by a potential step have also electrostatic potential; V the electrode potential relative to been used (see eg Ref.[8]). Also, for measurements in reference). the radio-frequency range, a pulse-reflection technique (“time-domain spectroscopy”) has been used for n-type, ie @ - 9, < 0) near the semiconductor in conjunction with a two-electrode cell, the countersurface. In such a case, one has p(x) x eNn and G(x) electrode being a metallic electrode with a large nearly follows a parabolic profile. Since the specific surface area[9]. This of course assumes that Helmholtz potential drop is negligible, the total varithe impedance of the semiconductor-electrolyte interation of electrostatic potential across the depletion face is much larger than that of the other series layer just follows the applied electrode potential elements in the cell (counter-electrode interface, elecQs - a0 = V,, - V, where Vfb, for obvious reasons, trolyte resistivity), a reasonable assumption indeed is the so-called “flatband potential”. Given the for the depletion range. parabolic variation of Q(x), the depletion layer thickReal systems, however, turn out to deviate from ness is W x [~LE~(V - Vfb)/eND]L/2. When the elec- the ideal model presented above. In practice, it has trode potential is modulated by an amount 6V, the been found that V, and V, may be dependent upon associated variation 6 W a [cc,,/2eND (V - Vr,)]“* 6V various factors. This occurs whenever the Helmholtz results in a change of stored charge SQ = eNo 6 W, potential drop can no more be neglected, for example hence the impedance of the interface is predicted to be if ions may become specifically adsorbed at the surface[lO] (this mechanism also accounts for pH equivalent to that of a capacitance C, = 8Q/8V cz [eN, &2( V - Vfb)]1/2. This, in principle, enables effects on oxide semiconductors[4]), if an insulating one to determine the flatband potential from an interlayer is present[ll], or if electric dipoles are impedance measurement by plotting l/C: as a funcattached to the electrode as a result of a different surface preparation[l2]. Finally, a most important tion of V. The obtained plot (“Mott-Schottky plot”) may be fitted with a straight line of exact equation case is that where “surface states” (electronic quantum states localized at the interface) are located in the l/CL = (2/eNo ~6~) ( V - VT,, - kT/e) whose zerosemiconductor bandgap. The associated surface ordinate intercept yields V,,[3]. Determining Vfb is very important for the undercharge may then be varied by electron transfer into or from these surface states. This may result in a standing of the interface. This allows one to locate dependence of V,, upon redox system (“Fermi-level the semiconductor band edges on the redoxpinning”)[l3, 141, electrode potential[15], and illumipotential scale: for the conduction band V, = VFb and for the valence band nation[l&18]. Also, variation of the surface-state (kTleM(NcIND) filling at the measuring frequency may result in the V, = VP,, + (kT/e)ln(N,/N,). (Here N,., is acceptor concentration, N, and N, conduction-band and apparition of a large capacitive component in the valence-band equivalent density of states, respecelectric response of the interface[l9]. The finite time tively.) If the neglect of the Helmholtz potential is a response of this mechanism results in the decrease of this effect at high frequency. This “surface-state eood anoroximation for both n and D cases. then one expects -Vv - V, = E,le, where E8 is-the bandgap of capacitance” is often taken into account by including the semiconductor. (Of course. this result will also a capacitance C,, together with a series resistance R,,, in the equivalent circuit of the interface. The hold true if the Hefmholtz potential becomes nonp, Charge density

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Fig. 2. Typical electric impedance results; (a) the Nyquist plot evidences the need for an equivalent circuit more complex than the ideal model; (b) equivalent circuit used; (c) resulting magnitude of the “surface-state capacitance” C, as a function of potential (after Refs [20, 241). example of such a circuit is shown in Fig. 2[20]. This is a rather expressive picture. However, such representations are not unique[20-231 and involve several imperfections. For example, the physical meanings of C,, and R, are not obvious, and also the circuit of Fig. 2 apparently overlooks possible transfers between surface states and electrolyte. Interpretation of the impedance data can alternately be derived directly from a kinetic model, without using the intermediate of an equivalent circuit. Various such models have been worked out[ll, 15,21,22,24]. Fitting the data enables one to determine the values of the kinetic constants (rate constants for electrochemical transfer, surface-state capture cross-sections, . . . ) involved in the model. A well-recognized difficulty is the problem of the unicity of the model (distinct models may provide equally good fits). For example, “capacitance peaks” at a potential V, are often interpreted as evidence for a surface state located at an energy e( V, - V,) from the conduction-band edge[25]. This step is directly inspired from the physics of MOS structures. However, if transfer between surface states and electrolyte is taken into account, such an analysis is no longer justified. Furthermore, in the presence of light, one finds that such peaks may occur even for a flat energy-distribution of surface states, and the position of the peak is only determined by the competition among the electron transfer processes between the various charge reservoirs[26]. As a result, impedance data do not appear to provide a fully reliable basis for determining the energies of the surface states. Optical spectroscopy techniques are more recommended for such determinations. An example is that of “photocapacitance spectroscopy”; when subjected to a sub-bandgap light illumination, electrons may be transferred from the surface states to the conduction band or from the valence band into surface states; such a change in surface charge results in a change in band bending, which may be detected as a change in the spacecharge layer capacitance. The recording of this change as a function of photon energy has been used

as a spectroscopic tool for the study of the surface states[27-301.

OPTO-ELECTRIC AND ELECTRO-OPTIC IMPEDANCES Opfo-electric impedances We will call “opt0-electric impedances” those techniques where the response of an electrical quantity to a modulated optical excitation is studied. Photocurrent response. Of special interest has been the study, under potentiostatic conditions, of the photocurrent response to a modulated bandgap illumination. It has been observed for a long time that when a photoelectrode is studied under chopped-light illumination, the current usually does not exhibit the same square-wave behavior as the light intensity. Instead when the light beam is turned on there is often a large initial photocurrent, which next decays to a smaller steady-state value. When the light beam is turned off, a negative undershoot is often observed, before the current relaxes to its dark value[ 181.These phenomena have been generally ascribed to surface state effects: the large initial photocurrent arises in part from charging of the surface states with minority carriers. This charging may affect the band bending and increases surface recombination, hence the smaller steady-state photocurrent. The negative undershoot upon turning off the beam can be understood as a recombination current which survives till the surface states are discharged. Such data bear all the information on the photocurrent-frequency response[3 1,321. However, these phenomena can be studied more accurately by using a variable-frequency light modulation and a lock-in detection[21,33,34]. The light modulation may be mechanical (chopper wheel) or use an electrooptic modulator for an extended frequency range. A very cheap method may consist in using for the light source a light-emitting diode, whose current is modulated. Lock-in detection of the photocurrent provides

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CHAZALVIEL

direct determination of the photocurrent response function. Higher-frequency studies are hindered by the limited frequency response of the potentiostat. A twoelectrode arrangement is then used, and pulse excitation is generally preferred[35-371. The pulsed light source. may be either a spark-gap lamp or a pulsed laser. The data are taken on a storage oscilloscope or on a boxcar acquisition system. By using a special two-electrode cell inserted in a stripline circuit, time resolutions better than loops have been achieved[37]. This allows one to reach fast phenomena, such as carrier recombination. For example the delayed photocurrent component due to the carriers created in the neutral region can be separated from the instantaneous component due to the carriers created in the depletion region[37]. Figure 3 shows electric impedance and photocurrent response data obtained for the same interface (n-Si-acetonitrile electrolyte + benzoquinone/ monoanion redox system). Here again an interpretation in terms of surface states has been given[21]. An important point, however, is that there is no obvious relation between the results of the two techniques (using the two techniques is similar to testing an electrical network at two different pairs of vertices). This makes the test of the theoretical model more stringent. Other recent data have shown the ability of the technique to disentangle the various steps associated with multielectron transfer processes[34].

Among the problems with the photocurrent response function, the question about linear response is of course of major concern. Whereas, for the electric impedance, linearity is guaranteed provided the potential modulation is much smaller than the “natural unit” kT/e = 25 mV, in the case of the optoelectric response there is no such “natural unit” of light intensity or photocurrent. Depending upon the models, non-linear effects may occur at very different light levels (in the GIrtner mode1[38], there are no nonlinear effects at all; on the other hand, in more refined models, eg the Reichman mode1[39], non-linear effects may arise as soon as the photocurrent reaches the order of magnitude of some characteristic recombination current, which can be as small as, eg 10e9 A/cm?). The pulsed laser experiments will most often fall in the non-linear range. In any case, studies as a function of light intensity are advisable. Another practical problem may arise if the series resistance Z, of the electrolyte is not negligible compared to interface impedance Z. In such a case, the interface will not be operated under true potentiostatic conditions (ie, the interface potential will vary upon turning the light on and off) and the measured photocurrent will be artificially reduced by a factor Z/(Z + Z,). We have also shown that the study of the photocurrent response may be performed for subgap as well as for bandgap photon energies. The optical processes then consist in transitions between the n-S1/ ACETONITRILE

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Fig. 3. Electric impedance and opto-electric impedance (photocurrent response) results, obtained for the same system, represented in a Bode plot. The curves are labeled with the value of the electrode potential (reference is Pt wire). Full curves are experimental, dashed curves are theoretical. Also shown are the (equivalent) Nyquist plot and time response to a step excitation for the opto-electric impedance corresponding to V = 0.05 V (after Ref. [21]).

Impedance studies at semiconductor electrodes

surface states and the semiconductor bands. The subgap photocurrent response has been suggested as a means for disentangling the two possible optical processes[40]. Photopotential response. The measurement of the photopotential induced upon a chopped light excitation has been shown to provide an alternate way for the measurement of the space-charge capacitance: the total amount of light sent while the beam is on will create a controlled amount of minority carriers; under depletion conditions, these will be driven to the surface, as a known charge SQ, hence a photopotential 6 V = SQ/C, is expected. This technique is seemingly less sensitive to surface imperfections than the standard electric impedance and good, rectilinear Mott-Schottky plots are more readily obtained here[41]. The arrangement requires applying the polarization to the electrode through a large resistance (N 10’ a). This may be a problem if a Faradaic process is present. On the other hand it is well-suited for the study of semiconductor/dielectric/electrolyte structures[42]. A related technique (“LMIER” method) has also been developed, where the polarization is applied to the electrode through a selfconductance L. Varying the light-chopping frequency allows one to search for the resonance, hence a measurement of C, through the condition LC, w2 = 1[43]. The high-frequency domain of photopotential response has been studied mostly by using pulsed-laser illumination and recording of the photopotential transient[44-47]. Time resolutions better than 100 ps may be achieved. Upon absorption of the light pulse, the photopotential rises sharply, then returns toward its dark value. The rising part bears information on photocarrier separation, and the decay gives information on recombination, trapping, and electrochemical transfer kinetics. The method may be applied starting from any initial potential, by using a potentiostat which is switched off just before sending the light pulse. A noticeable point, however, is that for these pulsed experiments the photopotentials are generally much larger than 25 mV, hence linear response conditions are not fulfilled. Electra-optic impedances

We will call “electro-optic impedances” those techniques studying the response of an optical property to a modulation of electrode potential. The optical absorption of the interface is usually reached through the measurement of reflectivity. Depending upon the spectral range investigated, the light beam may be sent either through the electrolyte or through the semiconductor. The change of reflectivity associated with a potential modulation is measured by using a lock-in detection (electroreflectance). For photon energies higher than the bandgap, the major optical processes are interband transitions in the semiconductor[48]. However, for subgap photon energies, surface-state absorption and free-carrier absorption become dominant[49]. Free-carrier absorption is detected upon electrode-potential modulation because of the modulation of the space charge. On the other hand, surface-state absorption is detected because of the modulation of the filling of the surface states. Since the spectral absorbances of free

1549

carriers and of surface states can be easily distinguished, this technique provides a means for reaching not only the total amount of charge being modulated but also its nature (“color”)[49]. Furthermore it is not sensitive to the transferred charge but only to the stored charge. This can be done in principle for a small potential modulation, and as a function of frequency (“colored” impedance technique). In practice, however, the sensitivity may be a problem if the modulation is taken much smaller than kT/e. Figure 4 shows data which have been taken at the n-Si-acetonitrile + 0.1 M TBAP interface, using a multiple internal reflection arrangement. The spectral absorptions of the free carriers (well-known) and of the surface states (previously unknown) are clearly distinguished. Notice that the technique provides at the same time a tool for spectroscopic information on the surface states[SO]. Luminescence at the semiconductor-electrolyte interface may occur from different mechanisms: it may arise from luminescence of a redox species which has been left in an excited electronic state upon electrochemical transfer[Sl, 521, but also from minority carrier recombination inside the semiconductor[53-551. Creation of off-equilibrium distributions of minority carriers in the semiconductor may be obtained either by avalanche breakdown upon strong reverse polarization of the junction, or more simply by injection of minority carriers under forward polarization (ie negative potential for n-type). This last mechanism is especially effective for redox species able to inject a hole once they have accepted an electron (eg S20i- + e--SO:+ SOi--2SO:+ h+). Timeresolved electroluminescence has been used in several of these cases[52,56]. The potential is stepped into the region where luminescence occurs, then stepped back to the rest position. Meanwhile the luminescence signal is sent to the oscilloscope. The observed transients are obviously affected by diffusion of the redox species. However, in the case of semiconductor luminescence, observations on a shorter time scale also bring information on the lifetimes of the minority carriers and of the intermediate redox species. Such experiments of course fall well outside the framework of linear response. Among the transient techniques, the use of pure optical transients should also be mentioned: study of the transient reflectance[57] or luminescence[5860] induced upon illumination by a laser pulse. Such experiments are of help in the study of recombination processes. They can in principle benefit from the good time resolution (_ 0.1 ps) of pure optical experiments, and can also be combined with the transient opto-electric techniques. Yet, up to now these techniques have seldom been used in situ[60]. TRANSPORT PARALLEL INTERFACE

TO THE

An interesting aspect of semiconductor electrodes is that the changes undergone by the interface may result in changes of the carrier densities near the surface, which are non-negligible relative to the bulk densities. Such changes may be probed by measuring the parallel conductivity of the sample, in response to

J.-N.

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Fig. 4. Electra-optic impedance results: ir absorption response to a potential modulation. The inset shows the schematic arrangement and a typical absorption response/photon energy recording. The contributions from free carriers and surface states are shown as the two dashed lines. Notice that only the surface-state contribution has an imaginary component (0 = 90”). (The superimposed vibrational peaks are not discussed here.) The figure shows the magnitude of the free-carrier and surface-state components (5 and [ respectively), as a function of electrode potential, together with the standard electric admittance curve, at the same frequency (1 kHz). This gives clearcut evidence that the peak in the admittance is associated with surface states. Potential modulation 6V = 75 mV (slightly outside the linear regime!) (after Ref. [49]).

either a potential modulation or a light excitation. This measurement may be taken at optical frequencies, microwave frequencies, or even at d.c. frequency (“field effect”). The response of the infrared conductivity to a modulation of potential has already been described above, among the electro-optic techniques (freecarrier absorption). A more sophisticated technique is that of the transient grating. Here the excitation is a pulsed optical beam which is not spatially uniform on the surface. Namely, the beam is obtained by splitting a parallel beam into two beams, and recombining them in order to generate an interference-fringe pattern in the plane of the interface. The photocarriers are generated according to this fringe pattern, and the spatially modulated free.-carrier absorption acts as an effective grating, which is probed as a function of time by measuring the intensity diffracted from a probe beam. This technique benefits from the inherently good (< 1 ps) time resolution of the pure optical techniques. The transient grating fades out by recombination, and also by lateral diffusion of the carriers. This gives a decay rate l/z,, = I/r + 4n2D/A2, where

_4 is the interfringe distance. Performing the experiment with various values for n allows direct in situ determination of the lifetime z and diffusion constant D of the photocarriers. The decay rate may further be affected by the presence of the electrolyte and provide information on the electrochemical transfer. For example, the appearance of a second, delayed component in the decay has been taken as evidence for minority-carrier injection following the initial electron-transfer step[61]. The density of carriers near the interface may be probed with a good sensitivity by measuring the microwave conductivity of the sample(621. This has been used for studying the density of photoinduced minority carriers near the surface as a function of potential. Also this technique can be made timeresolved[63]. If the microwave frequency is chosen, eg at 10 GHz, a maximum time resolution of _ 1 ns may be expected. This is sufficient to follow photocarrier recombination in many semiconductors. Finally, the density of carriers near the interface may be probed quite simply by measuring the d.c. (or low-frequency) resistance of the sample. Measuring

Impedance studies at semiconductor electrodes

the resistance of the sample requires some care in the presence of Faradaic processes, because part of the current injected into the sample may flow through the electrolyte[64]. Also, for optimum sensitivity, the semiconductor sample should be thin and low-doped, so that the surface conductance be a sizeable fraction of the total conductance. Figure 5 shows an arrangement that has been used for the study of the density of free electrons at a silicon-polymer-electrolyte interface[6.5]. This is just a field-effect transistor geometry. Conductance between the two n+ contacts occurs only through the n-inversion channel when the electrode is polarized to a sufficiently negative potential. It is then simply proportional to the free-electron surface concentration n, through the relation em = n,ep, where p is electron mobility in the inversion layer. The surface conductance has been studied in response to small variations of electrode potential. The response increases slowly with decreasing frequency 6n, N ln(l/o). Notice that in this strong inversion regime the potential drop across the Helmholtz layer can no more be neglected. The observed response has been ascribed to a slowing-down of the dynamics in the double layer of the polymer electrolyte upon decreasing the temperature toward the glassy transition point[65]. These data are essentially equivalent to a measurement of the interface capacitance as a function of frequency. However, a measurement by using the usual electric impedance

method would be difficult at such low frequencies, because of the troublesome contributions from the Faradaic processes due to residual impurities in the polymer electrolyte. The field-effect method is only sensitive to the stored charge, and it measures directly the charge en, (not the interface currentjoen,, as the usual impedance technique does), hence a decisive advantage at these very low frequencies.

CONCLUSION A large number of original impedance and transient techniques have been developed for the study of the semiconductor-electrolyte interface. Using these techniques has largely contributed to improving our understanding of the kinetic aspects of these interfaces. A more systematic use of several of these techniques on the same systems would provide more stringent tests and would probably allow confirmation or improvement of the existing models. On the other hand, it is noteworthy that the attention of the researchers has mostly focussed on the problems of the semiconductor side of the interface. Now, in those cases where the semiconductor side of the interface is well understood, one may hope that these techniques will be able to bring valuable information on lessunderstood aspects of the electrolyte side (doublelayer dynamics, complex-reaction kinetics, . , .).

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lo-2

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