Abstract

Chapter 5
Conclusion
In this work, modern numerical methods were applied to the Wigner-Poisson equa-
tions to gain an understanding of the quantum mechanical effects which will develop
in nanoscale semiconductor devices. Simulating the electron distribution accurately
required solving for a large number of unknowns, on the order of 10 6 . Iterative meth-
ods and the use of parallel computing are the only way to obtain efficient solution of
such large scale nonlinear problems. Notable accomplishments from this work are
• Implementing an implicit time-integration method that is faster than the pre-
vious semi-implicit time-integration scheme used in [40]. Developing a precon-
ditioner to allow GMRES efficiently solve the required linear systems.
• Parallelizing the RTD simulator in order to handle a fine grid discretization of
(x, k) space.
• Connecting the parallel RTD simulator and LOCA to perform a bifurcation
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