The spatial variation of the quasi-Fermi potentials in p-n junctions

Approximate analytical solutions are obtained for symmetrical p-n junctions which provide the range of bias for constant quasi-Fermi potentials across the transition region under forward bias and small reverse bias. The solutions also show that the variations of the quasi-Fermi potentials are essentially complete in the transition region for large reverse bias. The actual spatial dependences are computed numerically for the step junction case, using the parabolic potential as first approximation and applied junction voltage as the parameter, and are graphed. Numerical calculations and curves are also made in this case for the total change of the quasi-Fermi potentials across the transition region as a function of bias voltage, with the barrier height as a parameter. These confirm the commonly adopted assumption that the quasi-Fermi potentials are essentially constant across the transition region for small bias.