Two-dimensional numerical simulation of bipolar semiconductor devices taking into account heavy doping effects and Fermi statistics

A numerical method for the solution of steady-state equations describing the processes in heavy doped bipolar devices is proposed. The calculations were carried out for Fermi as well as Boltzmann statistics. The dependence of heavy doping effects on injection level was taken into account as well. It is shown that the current gain values obtained using different statistics may differ remarkably in the case of large donor and acceptor concentrations at the emitter-base junction (Nd = Na ≈ 10¹⁸cm^?3).