A simple method of calculating the minority-carrier current in heavily doped silicon

Abstract

It is shown that the calculation of the one-dimensional minority-carrier current density in heavily doped silicon can be described by two coupled differential equations of the first order. These equations are derived with a minimum of assumptions and approximations and without the explicit use of an electric field. The relevant input parameters to these equations are the product of the equilibrium hole density with the diffusion coefficient and the product of the equilibrium hole density with the reciprocal value of the lifetime. These equations can very easily be solved numerically and the solution gives the minority-carrier density and the current density as a function of space coordinate. It is shown that values of the band gap narrowing cannot be derived from current measurements alone.