Theory of the small photocarrier grating under the application of an electric field.

Abstract

Presently, a highly reliable method for the determination of the minority-carrier diffusion length in noncrystalline materials is the photocarrier grating (PCG) technique. The theory and the application of this technique have been essentially limited to the low-electric-field regime, i.e., where the carriers drift lengths are negligible in comparison with the carriers diffusion lengths. Recently, closed-form solutions that connect the microscopic mobility-lifetime (\ensuremath{\mu}\ensuremath{\tau}) products with the experimentally derived parameter \ensuremath{\beta} have been given for the above regime, thus allowing for the determination of the conditions under which the interpretation of the experimental results in terms of the minority carrier \ensuremath{\mu}\ensuremath{\tau} is justified. In contrast, for the high-electric-field regime only numerical solutions are available at present. These solutions are not very useful for the unique determination of \ensuremath{\mu}\ensuremath{\tau} products, and they do not provide physical insight into the transport and kinetic processes taking place in the PCG. In this paper we present analytic solutions for the PCG conductance in the high-field regime by using a diffusion-drift ``perturbation'' approach. The results reveal the physical processes in the grating and yield a general explicit relation between the measured quantities and the microscopic transport and kinetic parameters. The important prediction of the present theory is that the PCG technique in the high-field regime can yield direct and unique values for the majority-carrier \ensuremath{\mu}\ensuremath{\tau} product. The advantage of the PCG, in comparison with the conventional photoconductivity measurement, which is used for the same purpose, is that it is independent of experimental parameters, which are hard to determine. In view of the application of the PCG method to materials where trapping plays a dominant role, our analysis considers the PCG when trapping takes place, yielding closed-form solutions that include the trapping parameters.