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Title
A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation
AuthorRupp, Karl ; Jungemann, C. ; Hong, S.-M. ; Bina, M. ; Grasser, Tibor In der Gemeinsamen Normdatei der DNB nachschlagen ; Jüngel, Ansgar In der Gemeinsamen Normdatei der DNB nachschlagen
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Journal of Computational Electronics, 2016, Vol. 15, Issue 3, page 939-958
PublishedSpringer US, 2016
Edition
Published version
LanguageEnglish
Document typeJournal Article
Keywords (EN)Spherical harmonics / Boltzmann transport equation / Semiconductor device simulation / Silicon / Germanium / Hot carrier degradation / Box integration
ISSN1572-8137
URNurn:nbn:at:at-ubtuw:3-1764 Persistent Identifier (URN)
DOI10.1007/s10825-016-0828-z 
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 The work is publicly available
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A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation [1.37 mb]
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Abstract (English)

The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License