Surface states capacitance

Surface state capacitance. Surface states at a semiconductor-electrolyte interface allow for charge buildup via a capacitive effect. 

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

The capacitance Css and the resistance Rss connected parallel to Csc, which are introduced to describe the effect of surface states. 

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

A more complicated model situation is demanded if one thinks of the equivalent circuit for an electrode covered with an oxide film. One might think of A1 and the protective oxide film that grows upon it during anodic polarization. One has to allow for the resistance of the solution, as before. Then there is an equivalent circuit element to model the metal oxide/solution interface, a capacitance and interfacial resistance in parallel. The electrons that enter the oxide by passing across the interfacial region can be shown to go to certain surface states (Section 6.10.1.8) on the oxide surface, and they must be represented. Finally, on the way to the underlying metal, the electron... 

As discussed previously, the surface states responsible for the reduction peak could be intrinsic surface states or states associated with a surface-attached intermediate in the series of reactions leading to O-evolution. The latter possibility was deemed to be more likely since no change in voltage across the Helmholtz layer (no change in capacitance) was observed when these states are in the oxidized form. 

The magnitude of the errors in determining the flat-band potential by capacitance-voltage techniques can be sizable because (a) trace amounts of corrosion products may be adsorbed on the surface, (b) ideal polarizability may not be achieved with regard to electrolyte decomposition processes, (c) surface states arising from chemical interactions between the electrolyte and semiconductor can distort the C-V data, and (d) crystalline inhomogeneity, defects, or bulk substrate effects may be manifested at the solid electrode causing frequency dispersion effects. In the next section, it will be shown that the equivalent parallel conductance technique enables more discriminatory and precise analyses of the interphasial electrical properties. 

Figure 7. Equivalent circuit for interphase (Raei) resistance of semiconductor (Retec) electrolyte resistance, (Rfar) fara-daic resistance (Csc) space charge capacitance (CDl) double-layer capacitance and (z) parallel impedances associated with surface states, faradaic reactions, etc.

A related analysis follows from a more general consideration of the semiconductor-electrolyte interphase [149] (see Equation 5.14). Because of the usually much larger double-layer capacitance (Cdl > 20 pi 7cm2), the overall capacitance is typically of the same order of magnitude as the space charge capacitance (Csc < 1 pF/cm2). In ACs, the latter is expected to be much larger because of the contribution from surface states, and both contributions are expected to be important. 

Another approach involves impedance analysis (Section 7.5.13). One measures impedance as a function of frequency of the applied current and finds that (for the imaginary impedance, say) there is an unexpected maximum on the Z -log co plot. Analysis of the data allows one to numerically isolate the unexpected anomaly in the impedance plot, obtain the equivalent capacitance and resistance, and then interpret these in a model as representing a surface state. 

The capacitance of surface states is undoubtedly frequency-dependent. However, in order to ensure the linear C 2 vs. E dependence observed experimentally, one has to make very strict assumptions concerning the energy distribution function of the surface states, and this appears very unnatural. Therefore, a slow ionization, in the space charge region of a diamond crystal, of atoms with a relatively deep-lying... 

Oskam et al. [66] have used IMPS to investigate the role of surface states at the n-Si(lll)/NH4F interface. In this case, the redox reaction is simpler, and appears not to involve holes trapped at surface states. This is probably due to the presence of a surface oxide layer. Electron transfer is evidently exceptionally slow in this case, since these authors observed a modulated photocurrent even at potentials far from the flatband potential where recombination is expected to be negligible. Accumulation of holes modifies the potential drop across the Helmholtz (and presumably also surface oxide region), leading to a capacitive charging current. This effect has also been treated in more detail by Peter et al. [71]. 

If the insulating medium between the plates of a condenser is not air or vacuum but a solid insulator, decreasing its thickness can increase its capacitance C, by orders of magnitude, so it becomes possible to fill (saturate) completely the surface states that may be present. Based on this idea, the... 

Fig. 29. Plot of log10(B /a> - C8c) vs. log]0a> for n-Fe203(lm/oTi02) in lMNaOH at (a) -0.3V and (b) 0.0 V vs. SCE where S is the susceptance of the parallel ZU/CK circuit and Z( is assumed to be very large. (B /co - Clc) represents the capacitance equivalent of the surface-state impedance Zaa.

If C8S/Ch is relatively small, or caCssi ss 1, this will approximate to our original formula, since either the effect of the surface states on the potential distribution is insignificant or the kinetics are too slow to allow the occupancy of the surface state to be significantly altered during a potential cycle. If, however, coCaaRsa < 1, the equivalent circuit will again resemble that discussed above, but the factor [(CSS/CH) + 1] will premultiply the capacitive part. The effect will be to reduce the apparent admittance by this factor, which will, in turn, reduce the apparent capacitance by [1 + (Css/ CH)] and increase the apparent resistances by the same factor. 

If Nt rises above 1013cm 2, it may be anticipated that the complete emptying of such states will affect the potential drop in the Helmholtz layer. From above, the change in potential is rO = rNtfJNM, where Nm is the maximum possible number of surface states. Writing y = riVt/iVM, we may approximate y from the estimated double-layer capacitance of 10-20/iFcm-2 this gives y (0.08-0.16) x 10"13 Nt V. The rate constants k, and ka will also depend on yft specifically... 

This technique has been elaborated as an electrochemical tool by Tench and co-workers [164-166]. Its main purpose is to explore the deep-lying bulk and surface levels and the principle of the technique is that the main role of sub-bandgap irradiation in a semiconductor will be to cause optical excitation to or from a bulk or surface state this, in turn, will cause an alteration in the potential distribution from that existing in the dark this alteration will manifest itself in the behaviour of the interfacial capacitance. 

Fig. 3. Mott-Schottky plots of capacitance vs bias for two typical zinc oxide crystals. The dotted lines represent absolute theoretical predictions in the absence of surface states.

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