Semiconductor electrode capacitance

Under depletion conditions there is a relation between 1/C f. and the potential, where Csc is the semiconductor electrode capacitance. For n-type semiconductors the following relation is found ... 

Electric Breakdown in Anodic Oxide Films Physics and Applications of Semiconductor Electrodes Covered with Metal Clusters Analysis of the Capacitance of the Metal-Solution Interface. Role of the Metal and the Metal-Solvent Coupling Automated Methods of Corrosion Measurement... 

Based on the discussion above, it seems evident that a detailed understanding of kinetic processes occurring at semiconductor electrodes requires the determination of the interfacial energetics. Electrostatic models are available that allow calculation of the spatial distributions of potential and charged species from interfacial capacitance vs. applied potential data (23.24). Like metal electrodes, these models can only be applied at ideal polarizable semiconductor-solution interfaces (25)- In accordance with the behavior of the mercury-solution interface, a set of criteria for ideal interfaces is f. The electrode surface is clean or can be readily renewed within the timescale of... 

In an attempt to rationalize the measured capacitance values, and especially the low value for the basal plane (ca. 3pF/cm2), these authors first concluded that space charge within the electrode is the dominant contribution (rather than the compact double layer with ca. 15-20 pF/cm2, or the diffuse double layer with >100 pF/cm2). They then applied the theory of semiconductor electrodes to confirm this and obtained a good agreement by assuming for SAPG a charge carrier density of 6 x 1018/cm3 and a dielectric constant of 3 for GC, they obtained 13 pF/cm2 with the same dielectric constant and 1019 carriers per cubic centimeter. 

Thus, we have to conclude that, without knowing the physical nature of the frequency dependence of the differential capacitance of a semiconductor electrode, the donor (or acceptor) concentration in the electrode cannot be reliably determined on the basis of the Schottky theory, irrespective of the Mott-Schottky plot presentation format. Therefore, the reported in literature acceptor concentrations in diamond, determined by the Schottky theory disregarding the frequency effect under discussion, must be taken as an approximation only. However, we believe that the o 2 vs. E plot (the more so, when the exponent a approaches 1), or the Ccaic 2 vs. E plot, are more convenient for a qualitative comparison of electrodes made of the same semiconductor material. 

It is all but impossible to prepare any semiconductor electrode without some surface film being present. The III/V semiconductors, for example, will normally possess oxide films whose thickness will vary from less than 10 A to more than 40 A after exposure to air and similar observations have been reported for silicon [77], Although the capacitance of these films will normally be considerably larger than that of the depletion layer, the film may affect the a.c. response both by virtue of the analysis leading to eqn. (72) and, if Css becomes sufficiently large, that the impedance of the depletion layer falls to a value comparable with that of the film. If the film has a finite resistivity, which may be ionic in character, then the equivalent circuit takes the form... 

Another very important use of capacitance measurements in dealing with semiconductor electrodes is as a means of determining the flat-band potential" (3). This quantity is analogous... 

No complete characterizatl071 of an electrode process, combining capacitance, floating junction, and simple kinetic measurements as outlined above, has yet been made on a semiconductor electrode. A number of semi-quantitative studies have been made on germanium electrodes using the floating-junction technique (or variations on it) described above. 

J. F. DEWALD The flat-band potential is the potential of the semiconductor electrode (with respect to some reference electrode like calomel for example) when the charge inside the semiconductor is zero. At this point the "bands are flat" -right up to the surface. It is closely analogous to the potential of the electrocapillary maximum at a metal electrode, differing significantly only if there are a sizable number of surface states. There are a number of ways of determining Vpg as discussed above, capacitance and photovoltaic measurements being most prominent. 

As seen in equation (5.81), the capacitance of an interface is dominated by the part with the smaller capacitance. For this reason, the capacitance of semiconductor electrodes can be expressed as consisting only of the capacitance of the space-charge region. 

Mott-Schottky plots of l/C c versus E using capacitance data at different applied potentials for semiconductor electrodes in contact with aqueous media... 

This section presents results that show how the rates of photoelectrochemical processes can be derived from time resolved measurement of the photoinduced current or potential in the external circuit of a photoelectrochemical cell. The capacitance of the Helmholtz-double layer is of the order of lO Fcm , the depletion layer capacitance of an extrinsic semiconductor junction is typically 10 -10 Fcm , while the capacitance of an insulator is orders of magnitude lower. With a value of 100 Ohm for the resistance Rd + R of the cell, the time constant of photoelectrochemical cells is 10 s for metallic electrodes, 10 -10" s for semiconductor electrodes and much lower for insulator electrodes. The rates of photoelectrochemical processes also span a wide range. This makes photoelectrochemical kinetics a rich, albeit demanding, area for research. 

Determining Eft, is based on the Mott-Schottky (M-S) relationship involves measuring the capacitance of the space charge layer (Csc) of the semiconductor electrode as a function of the applied potential (E) and applying the relationship according to Eq. (6.1) [9]. 

For a semiconductor electrode a third term, the capacitance of the space-charge layer, must be added... 

Usually the capacitance of the Helmholtz layer and at higher electrolyte concentrations the capacitance of the Gouy-Chapman layer are much larger than the capacitance of the space-charge layer. Therefore, the reciprocal term can be neglected. The space-charge layer is the dominant element and represents the properties of the double layer for semiconductor electrodes... 

Light-induced changes in the electrostatics at the semiconductor-electrolyte interface are conveniently probed by capacitance-voltage measurements in the dark and under illumination of the semiconductor electrode. If charge trapping at the interface plays a decisive role (whatever be the mechanism), the voltage... 

The capacitance of the semiconductor-electrolyte interface can be measured by use of a semiconductor electrode, in which the front side of the semiconductor is in contact with the electrolyte and the rear side is electrically connected with a metallic leading wire via an ohmic contact. 

Fig. 3 Experimental setup for measurements of capacitance at the semiconductor—electrolyte interface. W.E. working electrode (semiconductor electrode), C.E. counter electrode, and R.E. reference electrode.

Because of the high concentration of free electrons in the metal counter electrode, the SCR inside the metal is extremely thin ( 1 A) and can therefore be ignored. The structure of the Helmholtz layer at the metal/electrol34 e interface is similar to that described for the semiconductor, and the capacitance is also in the order of 10-20 pF/cm. As already hinted in the previous paragraph, the potential drop across the Helmholtz layer depends on the kinetics of electron transfer across the interface. This is because any overpotential applied to a metal electrode must fall across the Helmholtz layer. This is quite different from the case of an external potential applied to a semiconductor electrode, which is discussed in the next section. 

Thus, a potential-dependent smooth background in IR spectra can be due to modulation of concentration/population of free carries and surface states. In contrast to common capacitance measurements, IR spectra of free carrier can provide information on the space charge capacitance of the semiconductor electrode under accumulation as well as under depletion conditions, without interference from the surface state capacitance. The DA-potential plots under depletion conditions allow measurements of the flat-band potential, while absorption of charge carriers in conducting polymer films can be used for estimating the film conductivity. It is also possible to follow the filling of surface states and relate these energy levels to the chemical composition of the interface. 

The complete ac equivalent circuit of an EIS is complex, as it involves components such as the bulk resistance and space-charge capacitance of the semiconductor, the capacitance of the gate insulator, the interface impedance at the insulator-electrolyte interface, the double-layer capacitance, the resistance of the bulk electrolyte solution and the impedance of the reference electrode [58-60]. However, considering usual values of insulator thickness ( 30-100 nm), the ionic strength of the electrolyte solution (>10 -10 M) and low frequencies (<1000 Hz), the equivalent circuit of an EIS structure can be simplified as a series connection of insulator capacitance and space-charge capacitance for the semiconductor, which is similar to the MIS capacitor [58-60]. Therefore, the capacitance of the EIS structure may be expressed in terms of the electrolyte solution/ insulator interface potential (cp) as ... 

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