Modeling Multi-Band Effects of Hot-Electron Transport in Simulation of Small Silicon Devices by a Deterministic Solution of the Boltzmann Transport Equation Using Spherical Harmonic Expansion
Modeling Multi-Band Effects of Hot-Electron Transport in Simulation of Small Silicon Devices by a Deterministic Solution of the Boltzmann Transport Equation Using Spherical Harmonic Expansion
Files
Publication or External Link
Date
1998
Authors
Singh, Surinder Pal
Advisor
Mayergoyz, Isaak D.
Goldsman, Neil
Goldsman, Neil
Citation
DRUM DOI
Abstract
Solution of Boltzmann equation by a spherical-harmonic expansion
approach is a computationally-efficient alternative to Monte Carlo. In
this dissertation we extend this technique to compute the distribution
function in multiple bands of silicon, using a multi-band band-structure
which is accurate for high energies. A new variable transformation is
applied on the spherical harmonic equations. This transformation (a)
improves the numerical properties of the quations by enhancing the
diagonal dominance of the resulting equations; (b) accounts for
exponential dependence of the distribution function on energy as well as
electric potential; and (c) opens the possibility of using superior
Poisson solvers (d) while retaining the linearity of the original
equations intact. The resulting Boltzmann
equations are discretized using the current-conserving control-volume
approach. The discretized equation are
solved using line successive-over-relaxation (SOR) method. Numerical
noise in the distribution was analyzed to be originating from the
absence of coupling. Noise is removed by using acoustic phonons in
inelastic approximation. A novel self-adjoint easy-to-discretize
formulation for the inelastic acoustic phonons is developed. A test
case of thermal equilibrium for multi-band is derived and used to
validate the code. Hole-continuity and Poisson equation were solved
along with the multi-band Boltzmann equations. The equations are solved
in a Gummel-type decoupled loop.
A \nnn\ device is simulated to test the simulator. The simulator is
then applied to study a one-dimensional short-base bipolar junction
transistor. While these simulations are self-consistent, a
two-dimensional sub-micron MOSFET is simulated in a non-self-consistent
manner.