Diffusion length and grain-boundary recombination velocity measurements with the scanning electron microscope in a finite polysilicon grain

Abstract

The three-dimensional boundary-value problem that defines the minority-carrier transport is solved analytically to obtain the EBIC response of a finite-sized polycrystalline grain. The collecting junction is perpendicular to two grain boundary surfaces which are in close proximity. The analysis requires incorporating an additional boundary condition for a second surface into the standard analysis for a junction perpendicular to a surface. The analytic solution uses an infinite number of images for the spherical generation volume and has been completely worked out for the case where the two surfaces have finite (not just zero or inifinite) surface recombination velocities. The resultant analytic expression for the EBIC current is a function of the grain size, the diffusion length in the bulk grain, the distance of the center of the generation volume from the grain boundary, the depth of the gneration volume, and the grain-boundary recombination velocities. Limitations of the solution are discussed and some experimental data, interpreted using the above theoretical analysis, are presented.