ASYMPTOTIC ANALYSIS OF A SEMICONDUCTOR MODEL-BASED ON FERMI-DIRAC STATISTICS

The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is prove d rigorously and error estimates are shown. We compute numerically sta tic voltage-current characteristics of a forward biased pn-junction di ode and compare the curves with the corresponding characteristics obta ined from the standard drift-diffusion model based on Boltzmann statis tics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injectio n conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.