Space-charge capacitance measurement

Determination of e and nT(t) can be performed by measuring the reverse current through the diode, or the change in space-charge capacitance. For t > 0 the total current at the plane x = W can be calculated (Sah et al, 1970) as the sum of the conduction current caused by the emission of electrons from traps... 

Fig. 8.11. Equivalent circuit for a photoelectrochemical cell under potentiostatic conditions. The externally measured photocurrent is less than the generated current at high frequencies because the space charge capacitance shunts the cell resistance.

In ideal semiconductor/electrolyte junctions, the presence of an energetic barrier in the semiconductor phase, originated from the equilibrium of the Fermi level in the solid and liquid phases, can be approached by the semiconductor depletion layer capacitance or space charge capacitance, Cgc- Measurement of capacitance versus... 

The upper limit to the electron injection rate constants that can be measured by IMPS is determined by Xceii and potentiostat performance. If the space charge capacitance is high, it may be impossible to determine kinj. This is the case, for example, for formic acid oxidation on Ti02, where the IMPS response is dominated by the combination of the space charge and Helmholtz capacitances [84]. It would be interesting to explore the possibilities of using intensity modulated photopotential to overcome this limitation. 

It is important to stress that the density of states shown in Fig. 50 is not a fit to theory it is merely a diflFerent representation of the DLTS spectra shown in Fig. 46 that removes the nonlineaiities inherent in the response of the space-charge capacitance due to thermal emission from states at different energy depths. These nonlinearities are negligible for crystals with JVj, N-j but large for a-Si H because of the large number of deep states. The derived density of states follows directly from Poisson s equation based on our assumptions and auxiliary measurements. The energy scale is the superposition of two thermal emission energy scales one from the thermal emission of... 

The determination of the space-charge capacitance from free-carrier IR absorption is free from interference with the interface-state capacitance, which plagues the use of common capacitance measurements. The method in this respect is equivalent to what can be obtained from microwave reflectivity measurements (Drude absorption is nothing but ac Joule dissipation at an IR frequency). 

Another characteristic electrochemical property of a semiconductor/electrolyte contact is the double-layer capacitance, which is an approximation of the space-charge capacitance (Chapter 4). The space-charge capacitance can be determined by impedance measurements. If no current flows in the depletion region, the impedance is given by the reciprocal value of the space-charge capacitance. For other conditions the capacitance can be calculated from the complex impedance measurements. How to measure the impedance and to evaluate the data was described in Chapter 4 as well as the influence of diffusion processes in Chapter 5. 

The donor density (N in a semiconductor film can be determined by measuring the space charge capacitance, Csc> as a function of the applied potential, 0a- Since the derivation of this relationship was already given in Sect. 2.5.2, we only repeat the final result, which is the MottSchottky equation ... 

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. 

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. 

Three concentrations of each redox couple that ranged over two orders of magnitude were examined as well as a solution containing only electrolyte. The details of these comprehensive experiments will be published elsewhere (22.) however, several pertinent features are described here. The kinetic currents were measured at constant potential. In order to eliminate mass transfer limitations to the current, a jet electrode configuration was utilized (42). The capacitance of the space charge layer (Csc) was measured at the same potentials simultaneously with the kinetic currents. 

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

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