Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis

People Research Publications Teaching

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Subject: The operation principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operation principle. Secondly, is to predict and optimize in advance qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Finally, the results of quantum mechanical simulations of semiconductor nano structures can be used by upscaling methods to deliver parameters needed in semi-classical models for semiconductor devices such as quantum well lasers. This book covers in detail all these three aspects using a variety of illustrating examples.

Purpose: Multiband Effective Mass Approximations have been increasingly attracting interest over the last decades, since it is an essential tool for effective models in semiconductor materials. This book is concerned with several mathematical models from the most relevant class of kp-Schrödinger Systems We will present both mathematical models and state-of-the-art numerical methods to solve adequately the arising systems of differential equations.
The designated audience is graduate and Ph.D. students of mathematical physics, theoretical physics and people working in quantum mechanical research or semiconductor / opto-electronic industry that are interested in new mathematical aspects.

The book is designed to be consisting of a collection of contributed chapters. Outstanding experts working successfully in this challenging research area will be invited to contribute each a chapter of roughly 30-40 pages to this volume.

Academic Level: The principal audience is graduate and Ph.D. students of (mathematical) physics: research Lecturer of mathematical physics: teaching, research people working in semiconductor, opto-electronic industry: professional reference

Introduction / Preface

  Title - an Introduction (pages )
     by Matthias Ehrhardt, Bergische Universität Wuppertal, Wuppertal, Germany
     and Thomas Koprucki, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany.

Abstract:

Part I: Physical Models

Part II: Numerical Methods

Part III: Applications

Part IV: Advanced Mathematical Topics

Confirmed contributions:

  Title (pages )
     by Dieter Bimberg Institut für Festkörperphysik, Technische Universität Berlin, Berlin, Germany
     and Andrei Schliwa, Division Scientific Computing, Department Numerical Analysis and Modelling, Konrad Zuse Institute, Berlin, Germany.

Abstract:

  Title (pages )
     by Stefan Odermatt, Synopsys, Zürich, Switzerland.
     and Sebastian Steiger, Purdue University, West Lafayette, USA.
     and Ratko Veprek, ETH Zürich, Switzerland.

Abstract:

  Title (pages )
     by Eoin O'Reilly, Tyndall National Institute, Ireland.
     and Sorcha Healy, Tyndall National Institute, Ireland.
     and Aleksey Andreev, The University of Surrey, Guildford, Surrey, United Kingdom.

Abstract: Sinusbasis-Method / plane-wave approach to calculate strain and also solve 8-band kp and related models for quantum well and quantum dot structures

  Title (pages )
     by Bernd Witzigmann, Computational Electronics and Photonics, University of Kassel, Kassel, Germany.
     and

Abstract:

  TBC / Transient Simulation (pages )
     by Andrea Zisowsky, Institute of Mathematics, Technische Universität Berlin, Berlin, Germany
     and Anton Arnold, Institute for Analysis und Scientific Computing, Vienna University of Technology, Austria.
     and Matthias Ehrhardt, Bergische Universität Wuppertal, Wuppertal, Germany
     and Thomas Koprucki, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany.

Abstract:

  TBC / Stationary States (pages )
     by Dirk Klindworth, Modelling and Simulation, Fraunhofer Institute for Laser Technology, Aachen, Germany
     and Matthias Ehrhardt, Bergische Universität Wuppertal, Wuppertal, Germany
     and Thomas Koprucki, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany.

Abstract:

  Efficient WKB-Schemes for stationary kp Schrödinger-Systems (pages )
     by Jens Geier and Anton Arnold, Institute for Analysis und Scientific Computing, Vienna University of Technology, Austria.

Abstract: