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Self-consistent Solution Method of Multi-Subband BTE in Quantum Well Device Modeling  

Lee, Eun-Ju (Dept. of Information Communication Engineering, Hallym University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SD / v.39, no.2, 2002 , pp. 27-38 More about this Journal
Abstract
A new self-consistent mathematical model for semiconductor quantum well device was developed. The model was based on the direct solution of the Boltzmann transport equation, coupled to the Schrodinger and Poisson equations. The solution yielded the distribution function for a two-dimensional electron gas(2DEG) in quantum well devices. To solve the Boltzmann equation, it was transformed into a tractable form using a Legendre polynomial expansion. The Legendre expansion facilitated analytical evaluation of the collision integral, and allowed for a reduction of the dimensionality of the problem. The transformed Boltzmann equation was then discretized and solved using sparce matrix algebra. The overall system was solved by iteration between Poisson, Schrodinger and Boltzmann equations until convergence was attained.
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