Journal of Computational Electronics

, Volume 6, Issue 4, pp 401–408 | Cite as

An effective quantum potential for particle–particle interactions in three-dimensional semiconductor device simulations

  • Clemens Heitzinger
  • Christian Ringhofer


The classical Coulomb potential and force can be calculated efficiently using fast multi-pole methods. Effective quantum potentials, however, describe the physics of electron transport in semiconductors more precisely. Such an effective quantum potential was derived previously for the interaction of an electron with a barrier for use in particle-based Monte Carlo semiconductor device simulators. The method is based on a perturbation theory around thermodynamic equilibrium and leads to an effective potential scheme in which the size of the electron depends upon its energy and which is parameter-free. Here we extend the method to electron-electron interactions and show how the effective quantum potential can be evaluated efficiently in the context of many-body problems. Finally several examples illustrate how the momentum of the electrons changes the classical potential.


Comput Electron Classical Potential Quantum Mechanical Effect Ensemble Monte Carlo Simulation Semiconductor Device Simulation 
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Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsArizona State UniversityTempeUSA

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