Implementation of Fermi–Dirac statistics and advanced models in PC1D for precise simulations of silicon solar cells

Abstract

In this work we present a modified version of the commonly used semiconductor simulation program PC1D, named cmd-PC1D 6.0, which applies Fermi–Dirac (F–D) statistics, thus improving on the existing Boltzmann approximation that is employed in the original program. Several up-to-date models for crystalline Si have been implemented in the new program, including injection dependent band gap narrowing, carrier mobility and Auger recombination. The results obtained using cmd-PC1D 6.0 are verified against well-accepted and modern simulations tools for a range of both phosphorus- and boron-doped emitters with varying surface concentration. We find a good correspondence between the simulation results obtained with the different programs, with a deviation of less than 2fA/cm2 for the calculated emitter saturation current density using F–D statistics and less than 0.8 % relative deviation in all the main solar cell parameters under 1 sun illumination. By using the correct carrier statistics and the appropriate set of models it is now possible to avoid the commonly used effective models and adapted values, thus taking a large step in bringing PC1D further towards a more general, consistent and physically meaningful simulation tool for Si solar cells. The new program can be run from a command line or within a recently developed, powerful graphical user interface. Both cmd-PC1D 6.0 and the graphical user interface are freely available for download.