Electrolyte electroreflectance (EER) is used to study the band structure of semiconductors [1] and the semiconductor-electrolyte (SC/EL) interface [2]. In the first case, the relevant information is mainly obtained from the position and lineshape of the EER signal, which are determined by parameters of the electronic transitions, such as energy, dimension, lifetime of carriers, and band curvature. Under low electric fields, producing a smaller change in electronic energy than the intrinsic uncertainty determined by lifetime broadening, the EER signals present well defined structures with third derivative lineshape [3]:

DR/R= Re{C e^iq (E - Eg + iG)^{n/2 - 4}} (1)

where C, q and G are the intensity, phase and width of the signal, Eg and n are energy and dimension of the transition, and E is the photon energy.
For the study of the SC/EL junction, however, the relevant information is obtained from the evolution of intensity and lineshape of the signal with experimental parameters such us applied dc voltage (V_DC) and modulation frequency (w). For example, the signal from the semiconductor space charge layer (SCL) disappears under zero electric field conditions, an effect used to determine the flat-band potential. Also, under fixed electric field conditions in SCL, the intensity of the signal is proportional to the modulation amplitude, hence the presence of surface-states which absorb part of the applied ac voltage (V_AC) is reflected by a diminution of EER intensity. This phenomenon can be used to map differences in surface states density over the electrode surface with the help of an electroreflectance mapping technique [4]. More information concerning the SC/EL structure is available from frequency dependent EER measurements [5-7]. Electroreflected intensity comes from the semiconductor SCL and from surface and near surface layers which reflectivity is also modulated by V_AC, giving rise to corresponding (DR/R)_SCL and (DR/R)_S signals. The distribution of V_AC is represented in the equivalent circuit of Fig.1.

Fig.1. Equivalent circuit.

Modulations at C_SCL and C_S are given by:

V_SCL = DV_SCL(w) exp{i(wt-g_SCL(w))}

V_S = DV_S(w) exp{i(wt-g_S(w))} (2)

The EER spectrum will be composed of SCL and surface signals:

DR/R(w) = Re {L_SCL V_SCL(w) exp(-ig_SCL(w)) + L_S DV_S(w) exp(-ig_S(w))} (3)

where L_i are basic lineshape functions for which eq.(1) can be used as low field approximation, and DV_i(w) and g_i(w) are modulation amplitudes and phases. In fact, EER at variable frequency probes the electrical impedance of the SC/EL junction through DV_i(w) and g_i(w), which give rise to frequency dependent intensities and lineshapes [5]. The surface circuit accounts for the Helmholtz layer, surface states, and/or adsorbed layers which can modify the electrical impedance of the junction. Plots of DV_i and g_i with logw are shown in Figs.2A and B for two sets of values of C_i and R_i of the circuit in Fig.1. Only when the surface RC is low enough (Fig.2B) a significant change in intensity and lineshape of the EER signal is expected [5].

Fig.2. Dependence with modulation frequency (w) of the amplitudes DVi and phases gi drop on SCL and S capacitors from Fig.1. Parameters are: A) CS=10-5F, RS=1ohm; B) CS=10-3 F, RS=15ohm. Other components are CSCL=10-7F, RSCL=5ohm, Rsol=1ohm.

Fig.3 shows EER spectra corresponding to RuS₂/H₂O interface at two modulation frequencies, 15Hz (Fig.3A) and 300Hz (Fig.3B) and five different V_DC. The spectra show contribution from the RuS2 SCL, which is responsible for the structures in the 2.0-3.1eV energy range, and from the surface of the electrode, responsible for a broad peak at E<2.0eV [6]. The frequency dependence of the signals is reflected by a diminution of the intensity of (DR/R)_SCL and increment of (DR/R)_S at 15Hz, a clear effect of the electrical impedance of the electrode. The surface component is shown in Fig.3C, after mathematical elimination of (DR/R)_SCL contribution from the low frequency spectra. This signal is due to an interfacial layer, RuO_x, able to absorb part of the modulation amplitude, which at the same time is responsible for the good stability of RuS₂ against photocorrosion.

Fig. 3. EER spectra from n-RuS2 in contact with 0.5M H2SO4 solution. The columns correspond to A) 15Hz. B)300Hz. C) spectra resulting after elimating SCL signals from A [6]. Vac=300mV.

A similar signal is observable in the EER spectra of degenerate RuS₂ and RuO₂ [6]. The disappearance of (DR/R)_S at V_DC=0V vs MSE (Fig.3C) reflects the conditions for zero electric field at the surface; positive from it the hole transfer to electrolyte is kinetically favoured and oxygen photoevolution is possible.
For the study of the n-GaAs/H₂O₂ interface, frequency variable EER measurements have shown new important aspects, not evident from other techniques. This system shows sustained electrochemical oscillations when polarising at negative potentials, just before H₂ evolution (-0.8<V_DC<-1.2V vs. MSE)[8]. The oscillatory state is characterised by a negative faradaic impedance which gives rise to anomalous diminution of reduction current upon increasing cathodic polarization in the same range of potentials. Such phenomenon can be studied with frequency dependent EER [5,7].

Fig.4. A) Steady EER spectrum of n-GaAs in contact with 0.2M H2O2 + 1M H2SO4 at Vdc=-0.85V/MSE, DVac=200mV, w=300Hz. B) Three EER spectra of the same electrode as in Fig.5 in contact with1M H2O2 + 1M H2SO4, corresponding to three moments during an oscillation period . Vdc=-1.03V/MSE, DVac=200mV, w=15Hz. Acquisition time 30s. Calculated curves (eqs.1 and 3) for spectrum in A and 1 in B are given in dotted line.

The steady state EER spectrum of n-GaAs (N_D=2x10¹⁷cm^-3) is in Fig.4A, showing two signals corresponding to E₀ and E₀+D₀ transitions. In the oscillatory state, the spectrum at 15Hz evolves with oscillations in baseline, intensity and lineshape of both SCL signals, as shown in Fig.4B, due to oscillation of the electrical impedance of the n-GaAs/H₂O₂ junction. The negative faradaic impedance situation is reflected by changes in |g_SCL| greater than 90º, as in curve 1 of Fig.4B [5].
It is noticeable that these changes are more important for E₀+D₀ signal than for E₀, which reflects an inhomogeneous modulation of SCL, as depicted in Fig.5.

Fig.5. Band schemes for inhomogeneous modulation of the SCL electric field of a GaAs electrode, showing the negative (A), zero (B) and positive (C) cycles of the modulation period. Probing depths estimated for photons at E0 and E0+D0 energies and SCL width (W) at 1V surface potential are compared with segments.

The origin of this behaviour is attributed to a oscillatory intercalation of hydrogenic species in the near-surface GaAs lattice [5], where E₀+D₀ signal is more sensitive, giving rise to depth inhomogeneity in the electrical impedance. On the oscillatory spectra taken at higher modulation frequency, the baseline oscillation is no longer observable (Fig.6), because it comes from low interfacial states most probably related with an oscillating As⁰ layer. Intensity and lineshape oscillations are however still observable.
In conclusion, it is shown the possibility to study the SC/EL interface from the analysis of frequency dependent EER measurements.

Fig. 6. Oscillating EER spectra of the same electrode as in Fig.4, in contact with 1M H2O2 + 1M H2SO4, in the E0+D0 structure energy range, at four moments (1-4) of the oscillation period. Vdc=-0.795V/MSE, DVac=200mV, w=200Hz.

REFERENCES

[1]	M.Cardona, in Modulation Spectroscopy. Solid State Physics. Suppl.11, Academic Press, New York (1969).
[2]	A. Hamnett, in Comprehensive Chemical Kinetics, edited by G.Compton (Elsevier, Amsterdam, 1987), Vol. 27.
[3]	D.E.Aspnes. Surf.Sci. 37 (1973) 418.
[4]	A.M.Chaparro, P.Salvador and A.Mir. J.Electroanal.Chem. 418 (1996) 175-183.
[5]	A.M.Chaparro. J.Electroanal.Chem. 462 (1999) 251-258.
[6]	A.M.Chaparro, N.Alonso-Vante, P.Salvador and H.Tributsch. J.Electrochem.Soc. 144 (1997) 2991.
[7]	M.Koper, A.M.Chaparro, H.Tributsch and D.Vanmaekelbergh. Langmuir 14 (1998) 3926.
[8]	M.Koper and D.Vanmaekelbergh. J.Phys.Chem. 99 (1995) 3687.

Acknowledgement: Part of this work was carried out at Hahn-Meitner Institut (Berlin).

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Last updated March 26, 1999

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