Semiconductor device optimization in the presence of thermal effects

Abstract

Optimal design problems for semiconductor devices with relevant thermal effects can be formulated by help of the energy transport model. In this paper we perform a sensitivity analysis to derive the first‐order necessary condition for the optimization. Exploiting the special structure of the KKT system we use a special variant of the classical Gummel iteration to provide a very fast optimization algorithm. Numerical results for a ballistic diode underline the feasibility of our approach.

The Quasi-Neutral Limit in Optimal Semiconductor Design

“…Note, that the first variation ofb λ for v ∈ Σ is in fact the weak formulation of nonlinear Poisson equation (P λ ) (cf. (11)).…”

“…Lemma 3.6. The mapping e λ as defined in (11) is Frchet differentiable. The actions of the derivative at a point (V, u) ∈ Σ × Y in a direction h ∈ H 1 (Ω) are given by…”

“…Meanwhile, there is a good understanding of the mathematical questions concerning the underlying optimization methods for different semiconductor models, like the drift-diffusion or the energy transport model (for the specific models see also [36,33] and the references therein). Further, fast and reliable numerical algorithms were designed on basis of the special structure of the device models, which use adjoint information to provide the necessary derivative information [3,22,6,31,11,4]. But not only the classical model hierarchy was used, also macroscopic quantum models, e.g., the quantum drift-diffusion model [44,5] and the quantum Euler-Poisson model [37] were investigated.…”

Modeling the Dependence of Power Diode on Temperature and Radiation

“…This is particularly important in reliability studies and when trying to predict the survival of these systems in space. Finally, much work had been done by the authors and others which include experimental and/or theoretical data on temperature and radiation effects in semiconductors [3][4][5][6][7][8]. So, the present paper is a trial to shed further light on such very interest and important field.…”

The Semi-Classical Limit of an Optimal Design Problem for the Stationary Quantum Drift-Diffusion Model

“…So far, the mathematical semiconductor design has focussed on classical macroscopic semiconductor model hierarchy, i.e., the stationary drift-diffusion equations [5,12,14], as well as on the energy transport model [8,9]. These macroscopic models, in combination with modern optimization algorithms, proved to be a reliable tool for the optimal design of semiconductor doping profiles.…”