Arclength continuation methods and applications to 2D drift‐diffusion semiconductor equations

Abstract

Shows how a strongly non‐linear semiconductor equation can be solved via homotopy deformation methods combined with the arclength continuation procedures. The fundamental goal of these methods is to overcome the instabilities or the failure of the classical Newton‐Raphson’s schemes which appear when the non‐linearity is strong or near limit or bifurcation points. The system, in its artificial transient form, is discretized by the non‐linear implicit scheme with local time steps. Uses the mixed finite element (MFE) approach. Presents numerical results, in two dimension, for a realistic device: an Abrupt Heterojunction Bipolar Transistor working as an amplifier.

Citation

El Boukili, A. (1996), "Arclength continuation methods and applications to 2D drift‐diffusion semiconductor equations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 15 No. 4, pp. 36-47. https://doi.org/10.1108/03321649610154203