Analytical solution of minority-carrier transport in silicon solar cell emitters

A general analytical solution for minority-carrier transport in a nonhomogeneously doped silicon region with a power-law doping profile N(x)=A(x+B)^C is derived. It is based on empirical relations between bandgap narrowing, minority-carrier mobility, and minority-carrier lifetime on the one hand and doping density on the other hand. This solution permits calculation of the minority-carrier concentration and dark saturation current density of various device configurations. It is used to evaluate solar cell emitter design. It is found that the use of graded emitters is favored over the use of step junction in the case of a low surface recombination velocity, yielding a reduction of the emitter saturation current density by a factor of two.