Excess minority carrier profiles

In the following, an approach is used that has been developed for the quantitative description of combined stationary excess microwave conductivity experiments and photocurrent spectroscopy [45]. The model uses analytical expressions for the 

In the diffusion region, the general statement for the continuity equation in the stationary case dp (x)/dt = 0 is 

b = lO cms solid line, Lp = 500pm dashed line, Lp = 100pm dotted line, Lp = 20pm. 

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In the expression for the excess carrier concentration at the boundary to the space charge layer, Ap(W), the recombination velocity at the back contact, S,b, is contained (see equations A8, A9 in [45].). The terms C, C, D, D and the prefactor A contain expressions that are independent of the variable x. They are given in Appendix 2.A. Figure 2.4 shows examples of excess minority carrier profiles for a back contact recombination velocity Srb of 10 cm s which is in the range of the thermal velocity [46] for a set of minority carrier diffusion lengths that range from poor bulk mate-... 

Figure 2.4 Light-induced excess minority carrier profiles for different diffusion lengths of n-Si ...

The efficiency of photoelectrochemical devices is based on effective charge transfer while suppressing surface recombination and corrosion. While the photocurrent is a direct measure of the irreversibly transferred electrons, it is not trivial to obtain a measure for the losses at surfaces due to recombination. As will be shown in Section 2.3.1, stationary microwave reflectivity is a method that measures the integral of the excess minority carrier profile. Such profiles are shown in Figures 2.3-2.6. The simultaneous recording of photocurrent and excess microwave reflectivity in an electrochemical cell allows the assessment of the relative contributions of kr and Sr for well-defined systems. These parameters are defined as follows ... 

The charge distribution for the semiconductor-electrolyte system is given by the excess minority carrier profile Ap(x) (2.40a) and the corresponding neutralizing majority carrier profile. The microwave signal due to the minority carriers, AR, is given by the excess carrier distribution throughout the sample ... 

Thus, the recorded signal corresponds to the integral of the excess minority carrier profile throughout the sample modulated by the relative carrier mobilities. This finding was the basis for the analysis of the charge transfer and surface recombination velocity profiles above (cf Figures 2.16 and 2.17). 

The excess minority carrier concentration can be viewed as an additional stationary concentration term that enters the chemical potential although this terminology is strictly only valid in equilibrium. Extending the consideration to a stationary illumination situation where an excess carrier concentration profile exists for a given minority carrier lifetime and for defined boundary conditions, the concept of quasi-Fermi levels can be introduced. Using the Boltzmann... 

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