A freeware 1D emitter model for silicon solar cells

Heavily doped surfaces-often called emitters, diffusions, or back-surface fields-are complicated regions of a solar cell. In these regions, the dopant concentration varies over many orders of magnitude in a short distance, causing large variations in the minority carrier concentration, Auger recombination, Shockley-Read-Hall recombination, carrier mobility and even the band gap. Moreover, when the diffusion is heavily doped, the semiconductor becomes degenerate and the carrier concentrations must be calculated with Fermi-Dirac statistics rather than the simpler Boltzmann statistics. Until now, computer simulation packages that account for all of these aspects are either expensive or not freely accessible, and they do not cater specifically to the PV industry. We therefore present a new freeware computer program that models a 1D emitter in silicon. Given a user-defined dopant profile, a surface recombination velocity, and an incident spectrum, the program calculates recombination as a function of depth within the emitter and as a function of the applied voltage. This permits the computation of the emitter saturation current density, the transparency factor, the collection current density, and the collection efficiency. The program can be applied to both phosphorus and boron diffusions and will assist in their optimisation for practical solar cells. In this paper, we present the equations, the assumptions, and the procedure that are employed by the freeware program.