Minority-carrier transport in nonuniformly doped silicon-an analytical approach

A general analytical solution for minority-carrier transport in a nonuniformly doped quasi-neutral silicon region is derived. It is shown that, in the cases of an exponential doping-density profile and a general power-law doping-density profile, a closed-form solution for the minority-carrier concentration can be obtained for doping densities up to 10²⁰ cm^-3. In the analysis, the experimentally observed dependencies of minority-carrier lifetime, minority-carrier mobility, and bandgap narrowing on doping density are taken into account. Contrary to earlier analytical solutions, the solution is free of integrals of minority-carrier transport parameters over the semiconductor region under study. Three important bipolar device configurations in which a nonuniform doping density plays a role are analyzed with the analytical solution. The first is the drift-field solar cell, for which a factor-of-20 reduction in the dark saturation current compared with a uniformly doped solar cell is calculated. Second, the effective back-surface recombination velocity of a high/low junction back-surface field (BSF) cell is shown to decrease with increasing BSF region thickness. Third, the influence of surface recombination velocity on the minority-carrier concentration profile in a heavily doped emitter is reduced when a strong power law doping profile in an n-p junction device is used