NUMERICAL APPROXIMATION OF A DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORSWITH NONLINEAR DIFFUSION

This paper is concerned with the numerical approximation of tile trans ient, one-dimensional drift-diffusion model consisting of a Poisson eq uation for the electric potential and two nonlinear continuity equatio ns for the carrier densities. The nonlinear diffusion terms are such t hat the parabolic equations are of degenerate type. We show that the e quations admit transient solutions for which the carrier densities van ish locally. These solutions are called vacuum solutions. After recall ing an existence and uniqueness result and proving the regularity of t he solutions, we discretize the equations using the mixed exponential fitting method and present examples of vacuum solutions. We show numer ically that vacuum solutions also occur if a physically reasonable PN junction diode is considered. Due to the vacuum effect the growth of t he static voltage-current characteristic for a forward biased diode ch anges at the so-called threshold voltage. In the high injection regime of the forward biased diode the growth of the characteristic turns ou t to be polynomial.