Space charge region capacitance

An interesting special application has been proposed by Schlichthorl and Peter.31,41 It aims at deconvolution of electrochemical impedance data to separate space charge and surface capacitance contributions. The method relies on detection of the conductivity change in the semiconductor associated with the depletion of majority carriers in the space charge region via potential-modulated microwave reflectivity measurements. The electrode samples were n-Si(lll) in contact with fluoride solution. 

FIGURE 7.3 Simplified equivalent circuit of an original (unmodified) EIS structure (a) and EIS biosensor functionalized with charged macromolecules (b). Cj, Cx and CML are capacitances of the gate insulator, the space-charge region in the semiconductor, and the molecular layer, respectively / u is the resistance of... 

Occasionally, the impedance spectra of diamond electrodes are well described by the Randles equivalent circuit with a frequency-independent capacitance (in the 1 to 105 Hz range) [66], Shown in Fig. 11 is the potential dependence of the reciprocal of capacitance squared, a well-known Mott-Schottky plot. Physically, the plot reflects the potential dependence of the space charge region thickness in a semiconductor [6], The intercept on the potential axis is the flat-band potential E whereas the slope of the line gives the uncompensated acceptor concentration NA - Nd in what follows, we shall for brevity denote it as Na ... 

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... 

The measurements utilise one-sided pn junction (p+n or pn ) and Schottky diodes, which possess a voltage modulated space charge region near the p/n and metal/semiconductor interface, respectively [8], The common feature of capacitance transient techniques is that the electronic properties of deep levels are determined by monitoring the transient high-frequency differential capacitance response of the diode as the electron occupancy of metastably charged deep levels located within the space charge... 

In general, Csc is orders of magnitude smaller than the Helmholtz capacitance, reflecting the fact that the major apart of any change in electrode potential appears across the space charge region. 

As shown in the Figure, electro capillary curves are affected by - specific adsorption of ions (here, anions) at the electrode surface. Additionally, they are influenced by the - space charge region of the electrical double layer. Thus, electrocapillary curves as well as capacitance curves provide useful information on the electrical double-layer structure of electrode surfaces. 

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. 

The capacitance of the space-charge region C is determined through... 

Equation (12.34) provides a relationship between the capacitance of the space-charge region of the semiconductor, the electric field at the interface, and the charge density at the interface. 

The resistor R and capacitor C shown in Table 16.1 can take on different meanings for different electrochemical systems. The resistance may, for example, be associated with the charge-transfer resistance of an electrochemical reaction, with the resistance of an oxide or porous layer, or with the electronic resistance of a semiconductor. The capacitor C may be associated with the double layer for an electrode in electrolyte, with surface capacitance of a film, or with the space-charge region of a semiconductor. The resistor Re may be associated with the Ohmic resistance of the electrolyte or with the frequency-independent resistance of a solid. 

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