Improved Monte Carlo method for the study of electron transport in degenerate semiconductors

Journal of Applied Physics

Volumn 84, Issue 7, 1998, Pages 3706-3709

  Borowik, Piotr ^a,b   Thobel, Jean Luc ^a  

^a INSTITUT D ELECTRONIQUE   (France)

^b WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; ELECTRON TRANSPORT PROPERTIES; ERRORS; MONTE CARLO METHODS;

DEGENERATE SEMICONDUCTORS; LUGLI-FERRY METHOD; PAULI PRINCIPLE;

SEMICONDUCTING INDIUM GALLIUM ARSENIDE;

EID: 0032185294     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.368547     Document Type: Article

References (11)

1. Although this expression for semiclassical transport equation is almost universally accepted, its rigorous derivation starting from full quantum theory is not an easy task, and may lead to some controversy. Kohn and Luttinger in their classical paper [Phys. Rev. 108, 590 (1957)] argued that quantum statistics does not alter the form of evolution equation and should be accounted for only in the initial conditions. They conclude that the collision terms remain linear on f(k). On the contrary Van Vliet [ J. Math. Phys. 20, 2573 (1978)], starting from Liouville-von Neuman equation for an ensemble of fermions and bosons and using linear response theory, derived a quantum Boltzmann equation, which in classical limit reduces to the usual BTE with the factor f(k)(1-f(k′)) in the scattering terms. We won't discuss further this difficult topic, which is beyond the scope of our article.
2. Although this expression for semiclassical transport equation is almost universally accepted, its rigorous derivation starting from full quantum theory is not an easy task, and may lead to some controversy. Kohn and Luttinger in their classical paper [Phys. Rev. 108, 590 (1957)] argued that quantum statistics does not alter the form of evolution equation and should be accounted for only in the initial conditions. They conclude that the collision terms remain linear on f(k). On the contrary Van Vliet [ J. Math. Phys. 20, 2573 (1978)], starting from Liouville-von Neuman equation for an ensemble of fermions and bosons and using linear response theory, derived a quantum Boltzmann equation, which in classical limit reduces to the usual BTE with the factor f(k)(1-f(k′)) in the scattering terms. We won't discuss further this difficult topic, which is beyond the scope of our article.
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