General relation between carrier spatial distributions and the generation function in photoconductors

A Fourier transform analysis is used to derive a general formula for the determination of the dependence of the electron and hole spatial distribution functions on the carrier-generation function, under a small-signal nonuniform illumination of a photoconductor. The suggested procedure also yields general basic theorems regarding the relation between any carrier-generation function and the resulting electron and hole concentration distributions in the steady state. We do not know of any previous attempt to formulate such general theorems. In particular, we prove that in the most general case, provided the Einstein relation holds, the only carrier-generation function that can yield functionally similar distributions for the two types of carriers is spatially sinusoidal. The present results explain well the uniqueness of the sinusoidal generation function and provide the rigorous basis for the recently suggested photocarrier grating method, which is used for the experimental determination of the ambipolar diffusion length in photoconductors.