Multi-Band Effective Mass Approximations

Advanced Mathematical Models and Numerical Techniques

  • Matthias Ehrhardt
  • Thomas Koprucki

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 94)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Physical Models

    1. Front Matter
      Pages 1-1
    2. Luigi Barletti, Giovanni Frosali, Omar Morandi
      Pages 3-56
    3. Andrei Schliwa, Gerald Hönig, Dieter Bimberg
      Pages 57-85
    4. Stanko Tomić, Nenad Vukmirović
      Pages 87-126
  3. Numerical Methods

    1. Front Matter
      Pages 127-127
    2. Ratko G. Veprek, Sebastian Steiger
      Pages 129-154
    3. Eoin P. O’Reilly, Oliver Marquardt, Stefan Schulz, Aleksey D. Andreev
      Pages 155-189
  4. Applications

  5. Advanced Mathematical Topics

    1. Front Matter
      Pages 245-245
    2. Andrea Zisowsky, Anton Arnold, Matthias Ehrhardt, Thomas Koprucki
      Pages 247-272
    3. Dirk Klindworth, Matthias Ehrhardt, Thomas Koprucki
      Pages 273-318
  6. Back Matter
    Pages 319-326

About this book


This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational 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 operational principle. Secondly, they allow us to predict and optimize in advance the 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. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used with 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 illustrative examples.

Readers will gain detailed insights into the status of the multiband effective mass method for semiconductor nano structures. Both users of the kp method as well as advanced researchers who want to advance the kp method further will find helpful information on how to best work with this method and use it as a tool for characterizing the physical properties of semiconductor nano structures.

The book is primarily intended for graduate and Ph.D. students in applied mathematics, mathematical physics and theoretical physics, as well as all those working in quantum mechanical research or the semiconductor / opto-electronic industry who are interested in new mathematical aspects.


Multi-Band Effective Mass Approximations (MEMA) kp-Schrödinger equations models of semiconductors nano structures: quantum wells, quantum wires, quantum dots numerical simulation in quantum mechanics

Editors and affiliations

  • Matthias Ehrhardt
    • 1
  • Thomas Koprucki
    • 2
  1. 1.& Numerische MathematikBergische Universität Wuppertal Lehrstuhl für Angewandte MathematikWuppertalGermany
  2. 2.Forschungsgruppe “Partielle Differentialgleichungen"Weierstraß-Institut für Angewandte Analysis und StochastikBerlinGermany

Bibliographic information

Industry Sectors
Oil, Gas & Geosciences
Finance, Business & Banking
Energy, Utilities & Environment