Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices

M. Nedjalkov, H. Kosina, S. Selberherr, Christian Ringhofer, D. K. Ferry

Research output: Contribution to journalArticlepeer-review

152 Scopus citations


Small semiconductor devices can be separated into regions where the electron transport has classical character, neighboring with regions where the transport requires a quantum description. The classical transport picture is associated with Boltzmann-like particles that evolve in the phase-space defined by the wave vector and real space coordinates. The evolution consists of consecutive processes of drift over Newton trajectories and scattering by phonons. In the quantum regions, a convenient description of the transport is given by the Wigner-function formalism. The latter retains most of the basic classical notions, particularly, the concepts for phase-space and distribution function, which provide the physical averages. In this work we show that the analogy between classical and Wigner transport pictures can be even closer. A particle model is associated with the Wigner-quantum transport. Particles are associated with a sign and thus become positive and negative. The sign is the only property of the particles related to the quantum information. All other aspects of their behavior resemble Boltzmann-like particles. The sign is taken into account in the evaluation of the physical averages. The sign has a physical meaning because positive and negative particles that meet in the phase space annihilate one another. The Wigner and Boltzmann transport pictures are explained in a unified way by the processes drift, scattering, generation, and recombination of positive and negative particles. The model ensures a seamless transition between the classical and quantum regions. A stochastic method is derived and applied to simulation of resonant-tunneling diodes. Our analysis shows that the method is useful if the physical quantities do not vary over several orders of magnitude inside a device.

Original languageEnglish (US)
Article number115319
Pages (from-to)115319-1-115319-16
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - Sep 2004

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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