Effective minority carrier lifetime in double-sided macroporous silicon

Abstract

In this paper, we showed that the effective lifetime of minority charge carriers in double-sided macroporous silicon is determined from a system of two transcendental equations. This system of equations is transformed into a system of equations for determining the effective lifetime of minority charge carriers for monocrystalline silicon in the absence of macropores. The system of equations was found by solving the diffusion equation for minority carriers, recorded for two macroporous layers and a monocrystalline substrate between them. The solution of the nonstationary diffusion equation written for two layers of macroporous silicon and a monocrystalline substrate between them is complemented with boundary conditions on the surfaces of the sample of macroporous silicon and on the boundary between each macroporous layer and the monocrystalline substrate. The effective lifetime of minority carriers in the double-sided macroporous silicon depends on such values as: the bulk lifetime of minority carriers, the diffusion coefficient of minority carriers, and the thickness of the monocrystalline substrate between macroporous layers. In addition, the effective lifetime depends on the values inherent to each macroporous layer: the depth of the macropores, average diameter of macropores, average distance between the centers of macropores, volume fraction of macropores, and rate of surface recombination. Effective recombination of excess charge carriers in the double-sided macroporous silicon is defined by the recombination of excess charge carriers on the surface of macropores and is limited by the diffusion of charge carriers from the monocrystalline substrate to recombination surfaces in each macroporous layer. We calculated the effective lifetime of minority carriers in the double-sided macroporous silicon depending on the depth of macropores. We used a numerical method to verify the accuracy of calculations performed using the system of analytical equations, which defines the effective lifetime of minority charge carriers in the double-sided macroporous silicon. The numerical method showed the coincidence of calculations aimed at the effective lifetime of minority carriers. We observed a discrepancy in calculations when the sum of the depths of macropores in two macroporous layers is close to the thickness of the macroporous silicon sample.