Gartner model

Another interesting test which may give an idea of the use of the simplifications introduced in deriving the analytical formula for photoin-duced microwave conductivity can be obtained from a comparison between the simple Gartner model for the potential-dependent photocurrent18 and the theoretical photocurrent derived from the just-described approach. 

The Gartner model simulates charge collection by a potential-dependent space charge layer and considers diffusion into the space charge layer of charge carriers generated deep inside the semiconductor. The well-known Gartner formula for the photocurrent /ph is... 

Efficient photoelectrochemical decomposition of ZnSe electrodes has been observed in aqueous (indifferent) electrolytes of various pHs, despite the wide band gap of the semiconductor [119, 120]. On the other hand, ZnSe has been found to exhibit better dark electrochemical stability compared to the GdX compounds. Large dark potential ranges of stability (at least 3 V) were determined for I-doped ZnSe electrodes in aqueous media of pH 0, 6.3, and 14, by Gautron et al. [121], who presented also a detailed discussion of the flat band potential behavior on the basis of the Gartner model. Interestingly, a Nernstian pH dependence was found for... 

Figure 3. Experimental collection efficiency vs. wavelength with fit to data using Gartner model (measured values of t and N, and L = 1 pm were used to fit data)...

It should be mentioned here that Eq. (41) had already been derived by Gartner [86] for the photocurrent of a semiconductor-metal junction in reverse bias, assuming P = 0. In the derivation of Reichman [85], however, P was obtained in a manner consistent with the interface boundary conditions. Although the derivation of Reichman is much more general, most scientists only applied the Gartner-equation (see e.g. [87]). Later on, Wilson extended the Gartner model by including recombination via surface states [88]. 

Figure 20. Comparison of calculated current voltage profiles in the dark (curve d) and under illumination (curves a-c). Curve a is obtained from the basic Gartner model. Curve b considers surface recombination and curve c considers both surface recombination and recombination in the space-charge layer. These simulations are for an n-type semiconductor-electrolyte interface. (Reproduced with permission from Ref [230].)...

Gartner equation [25]. Later on Wilson extended the Gartner model by including recombination via surface states [26],... 

Thus, application of the Gartner model to data obtained from photocurrent versus potential measurement yields several important parameters of a semiconductor-electrolyte junctions (e.g. Eg, Vfb, Amin, r, and w). 

The Gartner model takes into consideration the e-h pair formation in the space charge region of the semiconductor (W) and in the field-free zone (L). The Gartner model can be written as ... 

Optical flat-band potential The potential of Iph = 0 (the optical flat-band potential) becomes dependent on the photon energy. The potential-dependence of the photocurrent is more complex than expected by the Gartner-model. A Poole-Frenkel effect may dominate the potential-dependence of the photocurrent according to ... 

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