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1) Starting from the collision integral and the matrix element for
acoustic phonons, derive the expressions given in class
for the acoustic phonon
collision term in the Boltzmann equation in terms of the LP expansion.
2) In class we formulated the Boltzmann equation in terms of a first order Legendre polynomial expansion, and then gave the solution for the parabolic band case. By solving the formulated BTE, verify that the solution given in class is correct. 3) Using numerical-sparse matrix methods, solve the LP formulated BTE for nonparabolic bands for the same homogeneous electric fields as in the Monte Carlo simulation. I will provide the deformation potentials and dispersion relation. (Hand in separately; due Nov. 19.) |