Asymptotic Analysis of a Semiconductor Model Based on Fermi–Dirac Statistics

✍ Scribed by Ansgar Jüngel

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 928 KB
• Volume: 19
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19960325)19:5<401::aid-mma795>3.0.co;2-l

✦ Synopsis

Communicated by H. Neunzert

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 proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard driftdiffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.