We perform a rigorous comparison between the Spherical Harmonic (SH) and Monte
Carlo (MC) methods of solving the Boltzmann Transport Equation (BTE), on a 0.05 μm
base BJT. We find the SH and the MC methods give very similar results for the energy
distribution function, using an analytical band-structure, at all points within the tested
devices. However, the SH method can be as much as seven thousand times faster than the
MC approach for solving an identical problem. We explain the agreement by asymptotic
analysis of the system of equations generated by the SH expansion of the BTE.
A method is developed to analyze the transient response of semiconductor devices in phase space. This is achieved by solving the space and time dependent electron Boltzmann transport equation self-consistently with the Poisson and transient hole-current-continuity equation. The result gives the details of the time evolution of the distribution function. The method is applied to analyze a bipolar junction transistor. The model predicts the limits in which the steady-state response approximation can be applied. The model exposes a transient overshoot in the high energy tail of the distribution function.
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