✦ LIBER ✦

Non-unique solutions in drift diffusion modelling of phototransistors

✍ Scribed by S. J. Woods; S. P. Wilson; Alison B. Walker

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 243 KB
Volume: 13
Category: Article
ISSN: 0894-3370
DOI: 10.1002/(sici)1099-1204(200001/02)13:1<37::aid-jnm380>3.0.co;2-n

No coin nor oath required. For personal study only.

✦ Synopsis

We report non-unique solutions for the potential in a Drift Di!usion (DD) model of a two terminal phototransistor. These solutions are present under bias without illumination, and persist until high illumination levels. It is well known that the DD equations can yield non-unique solutions for pn structures which contain three or more junctions and two terminals with applied biases greater than k ¹ log 2 where k ¹ is the thermal energy at a temperature ¹, but DD models of phototransistors under illumination have been less well studied. The implicit belief is that one needs to arti"cially impose a potential in the base of the phototransistor in order to obtain a unique solution. We show here that this is only necessary because of a weakness in the numerical methods used to solve the equations, and describe two methods which circumvent this for which we show that this problem does not occur. These methods are used to investigate the operation of GaAs and In Ga As homojunction phototransistors, including the in#uence of the position of the illumination region and base doping.

📜 SIMILAR VOLUMES

Stationary solutions to the drift–diffus

Stationary solutions to the drift–diffusion model in the whole spaces

✍ Ryo Kobayashi; Masaki Kurokiba; Shuichi Kawashima 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 127 KB

## Abstract We study the stationary problem in the whole space ℝ^__n__^ for the drift–diffusion model arising in semiconductor device simulation and plasma physics. We prove the existence and uniqueness of stationary solutions in the weighted __L__^__p__^ spaces. The proof is based on a fixed point

TLM modelling of diffusion, drift and re

TLM modelling of diffusion, drift and recombination of charge carriers in semiconductors

✍ M. Y. Al-Zeben; A. H. M. Saleh; M. A. Al-Omar 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 442 KB

The paper provides an extension to the one-dimensional TLM diffusion model. The extended diffusion node presented here models the exact transport equation with diffusion drift and recombination of charge carriers in semiconductors. A general algorithm for providing a numerical solution to the transp

Lp Uniqueness of Non-symmetric Diffusion

Lp Uniqueness of Non-symmetric Diffusion Operators with Singular Drift Coefficients: I. The Finite-Dimensional Case

✍ Andreas Eberle 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 150 KB

Two uniqueness results for C 0 semigroups on weighted L p spaces over R n generated by operators of type 2+; } { with singular drift ; are proven. A key ingredient in the proofs is the verification of some kind of ``weak Kato inequality'' which seems to break down exactly for those drift singulariti

Existence of Weak Solutions of the Drift

Existence of Weak Solutions of the Drift Diffusion Model Coupled with Maxwell's Equations

✍ F. Jochmann 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 240 KB

E,H obeys Maxwell's equations 1.4 , 1.5 , and 1.6 . The unknown Ž . w . functions , , E, H depend on t, x g 0, ϱ , where t, x denote the time 1 2 and space variable resp. ⍀ ; ‫ޒ‬ 3 is a bounded Lipschitz-domain with Ѩ ⍀ s ⌫ j ⌫ , where ⌫ , ⌫ are disjoint subsets of Ѩ ⍀. ⌫ represents the D N D N D pe

Existence and Uniqueness of Scattering S

Existence and Uniqueness of Scattering Solutions in Non-smooth Domains

✍ A.G. Ramm; A. Ruiz 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 149 KB

A short and self-contained proof of the existence of the scattering solution in exterior domains is presented for some class of second order elliptic equations. The method does not use the integral equation; it is based on Fredholm theory and the limiting absorption principle for solutions in the wh

Galerkin Approximation of Weak Solutions

Galerkin Approximation of Weak Solutions of the Drift Diffusion Model for Semiconductors Coupled with Maxwell's Equations

✍ F. Jochmann 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 590 KB

We prove global existence of weak solutions of the drift diffusion model for semiconductors coupled with Maxwell's equations for the electromagnetic field by using a Galerkin method. The recombinations term for the density of electrons and holes may depend on the densities, the gradient of the densi