Deterministic kinetic solvers for charged particle transport in semiconductor devices

M. J. Cáceres, J. A. Carrillo, I. M. Gamba, A. Majorana, C. W. Shu

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12 Citations (Scopus)


© 2007, Birkhäuser Boston. Statistical models [F91], [L00], [MRS90], [To93] are used to describe electron transport in semiconductors at a mesoscopic level. The basic model is given by the Boltzmann transport equation (BTE) for semiconductors in the semiclassical approximation: (Formula Presented.) where f represents the electron probability density function (pdf) in phase space k at the physical location x and time t. ħ and e are physical constants; the Planck constant divided by 2π and the positive electric charge, respectively. The energy-band function ε is given by the Kane non-parabolic band model, which is a non-negative continuous function of the form (Formula Presented.) where m* is the effective mass and α is the non-parabolicity factor. In this way we observe that setting α = 0 in Equation (7.1.2) the model is reduced to the widely used parabolic approximation.
Original languageEnglish
Title of host publicationModeling and Simulation in Science, Engineering and Technology
Number of pages20
ISBN (Electronic)2164-3725
Publication statusPublished - 1 Jan 2007


  • Boltzmann transport equation (BTE)
  • Weighted essentially non-oscillatory (WENO) schemes
  • direct simulation Monte Carlo (DSMC)
  • metal oxide semiconductor field effect transistor (MOSFET)
  • metal semiconductor field effect transistor (MESFET)
  • semiconductor device simulation


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