Relative Errors of Free-Carrier Density at Different Temperatures Calculated from Approximations for the Fermi-Dirac Integral

Abstract
We present the relative errors of the free-carrier concentration in a semiconductor at all temperatures associated with three different approximations for the Fermi-Dirac integral of the order of 1/2. The results suggest that the errors peak at around 200 K and decrease outside this temperature range for all three doping concentrations considered (1018, 1019, and 1020cm-3).