Classical Device Modeling

Abstract

In this chapter an overview of classical device modeling will be given. The first section is dedicated to the derivation of the Drift–Diffusion Transport model guided by physical reasoning. How to incorporate Fourier’s law to add a dependence on temperature gradients into the description, is presented. Quantum mechanical effects relevant for small devices are approximately covered by quantum correction models. After a discussion of the Boltzmann Transport equation and the systematic derivation of the Drift–Diffusion Transport model, the Hydrodynamic Transport model, the Energy Transport model, and the Six-Moments Transport model via a moments based method out of the Boltzmann Transport Equation, which is the essential topic of classical transport modeling, are highlighted. The parameters required for the different transport models are addressed by an own section in conjunction with a comparison between the Six-Moments Transport model and the more rigorous Spherical Harmonics Expansion model, benchmarking the accuracy of the moments based approach. Some applications of classical transport models are presented, namely, analyses of solar cells, biologically sensitive field-effect transistors, and thermovoltaic elements. Each example is addressed with an introduction to the application and a description of its peculiarities.