A self-consistent iterative scheme for one-dimensional steady state transistor calculations

TLDR

The approach is limited by using Boltzmann rather than Fermi statistics. The paper presents a self‑consistent iterative scheme to compute dc potentials and currents in a one‑dimensional transistor model. The scheme applies boundary conditions only at contacts and uses doping profiles, recombination parameters, mobility dependence, applied voltages, and a trial potential as inputs. The iterative scheme converges well at low and moderate injection levels.

Abstract

A self-consistent iterative scheme for the numerical calculation of dc potentials and currents in a one-dimensional transistor model is presented. Boundary conditions are applied only at points representing contacts. Input data are: doping profile, parameters governing excess carrier recombination, parameters describing the dependence of mobility on doping and on electric field, applied emitter and collector voltages, and a trial solution for the electrostatic potential. The major limitation of the present approach results from use of Boltzmann rather than Fermi statistics. Convergence of the iteration scheme is good for low and moderate injection levels.