Monte Carlo simulation of high-field transport equations
The author has studied the importance of the intracollisional field effect in the quantum transport equation derived by Khan, Davies and Wilkins (Phys. Rev. B36, 2578(1987)) via Monte Carlo simulations. This transport equation is identical to the integral form of the Boltzmann transport equation except that the scattering-in rates contain the auxiliary function of energy width {radical}{vert bar}{alpha}{vert bar} instead of the sharp delta function of the semiclassical theory where {alpha} = {pi}{h bar}{sup 2} e/m* E {center dot} q. Here, E is the electric field, q is the phonon wave vector of m* is the effective mass. The transport equation studied corresponds to a single parabolic band of infinite width and is valid in the field dominated limit, i.e. {radical}{vert bar}{alpha}{vert bar} {much gt} h/{tau}{sub sc}, where {tau}{sup {minus}1} is the electron scattering-out rate. In his simulation, he takes the single parabolic band to be the central valley of GaAs with transition to higher valleys shut off. Electrons are assumed to scatter with polar optic and acoustic phonons with the scattering parameters chosen to simulate GaAs. The loss of intervalley scattering mechanism for high electric fields is compensated for by increasing each of the four scattering rates relative to the real values in GaAs by a factor {gamma}. The transport equation studied contains the auxilliary function which is not positive definite. Therefore, it can not represent a probability of scattering in a Monte Carlo simulation. The question whether or not intracollisional field effect is important can be resolved by replacing the nonpositive definite auxilliary function by a test positive definite function of width {radical}{vert bar}{alpha}{vert bar} and comparing the results of the Monte Carlo simulation of this quantum transport equation with those of the Boltzmann transport equation. If the results are identical, the intracollisional field effect is not important.
- Research Organization:
- The Ohio State Univ., Columbus, OH (United States)
- OSTI ID:
- 5098552
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
CHARGED-PARTICLE TRANSPORT THEORY
EQUATIONS
BOLTZMANN EQUATION
CHARGED-PARTICLE TRANSPORT
COLLISIONS
COMPARATIVE EVALUATIONS
ELECTRIC FIELDS
ELECTRONS
GALLIUM ARSENIDES
MONTE CARLO METHOD
SCATTERING
SEMICLASSICAL APPROXIMATION
ARSENIC COMPOUNDS
ARSENIDES
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EVALUATION
FERMIONS
GALLIUM COMPOUNDS
LEPTONS
PARTIAL DIFFERENTIAL EQUATIONS
PNICTIDES
RADIATION TRANSPORT
TRANSPORT THEORY
654001* - Radiation & Shielding Physics- Radiation Physics
Shielding Calculations & Experiments