Semiconductor equations.

*(English)*Zbl 0765.35001
Wien: Springer-Verlag. x, 248 p. (1990).

A continuously growing set of PDEs is currently used in the modeling of charge transport in semiconductor devices. Depending on the physical level of description the resulting PDEs are of mathematically quite different types.

The book under review uses the underlying physics as the organizing principle of the covered material: The semiconductor models are ordered in a hierarchy ranging from basic kinetic transport equations, both classical and quantum mechanical, to hydrodynamic models and to drift diffusion models, the latter being the most widely used models today. Each of these three classes is investigated in one chapter of the book, a final chapter investigates specific semiconductor devices.

The book does not attempt a rigorous mathematical analysis of these models, and a reader who looks for proofs will have to consult the numerous references. Instead, the book concentrates on the derivation of the models and the relations between them and emphasizes the physical assumptions and principles involved. Since only a fair amount of knowledge of the latter can enable a mathematician to ask meaningful questions and to choose the appropriate mathematical tools for their treatment, the book should be of great value to anybody who wants to work in this rapidly growing field of applied mathematics.

The book under review uses the underlying physics as the organizing principle of the covered material: The semiconductor models are ordered in a hierarchy ranging from basic kinetic transport equations, both classical and quantum mechanical, to hydrodynamic models and to drift diffusion models, the latter being the most widely used models today. Each of these three classes is investigated in one chapter of the book, a final chapter investigates specific semiconductor devices.

The book does not attempt a rigorous mathematical analysis of these models, and a reader who looks for proofs will have to consult the numerous references. Instead, the book concentrates on the derivation of the models and the relations between them and emphasizes the physical assumptions and principles involved. Since only a fair amount of knowledge of the latter can enable a mathematician to ask meaningful questions and to choose the appropriate mathematical tools for their treatment, the book should be of great value to anybody who wants to work in this rapidly growing field of applied mathematics.

Reviewer: G.Rein (München)

##### MSC:

35-02 | Research exposition (monographs, survey articles) pertaining to partial differential equations |

82-02 | Research exposition (monographs, survey articles) pertaining to statistical mechanics |

35Q99 | Partial differential equations of mathematical physics and other areas of application |

82D99 | Applications of statistical mechanics to specific types of physical systems |

76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |