Abstract

CHAPTER 1. OVERVIEW 6
and identfying biological and chemical warfare agents. In a battlefield environment,
the ability to remotely detect biological and chemical warfare agents would reduce the
risk of injuries and casualties. Also, computational efficiency and data transmission
will be greatly increased once sustainable terahertz frequencies are possible. The goal
of this research is to create a numerical tool for engineers and scientists to use in order
to understand the physical mechanisms behind the RTD’s operation and potentially
exploit these mechanisms to create terahertz frequency devices.
The problem of numerically simulating nanoscale semiconductor devices with the
Wigner formalism is an active field of research. The numerical method we use is a
finite-difference approximation as described in [8]. Other discretizations can be used.
In [32], [31], the author considers using a spectral discretization. Here, functions
are approximated by a truncated Fourier series, where the coefficients on the finite-
dimensional Fourier basis are computed. In [32], the author proposed a mixed finite
difference-spectral method (differences in x and t space, spectral in k space) for the
coupled Wigner-Poisson equations. This is for a bounded domain in one-dimensional
x space, with time-dependent Dirchlet boundary conditions. In the paper, the author
derives errors estimations and establishes consistency of the method, gets a priori nu-
merical bounds on the solution, and presents numerical results. The author, though,
do not account for scattering effects that will occur within the semiconductor. This
was an extension of [31], where the author only considered the linear Wigner equation
(i.e. no coupling with Poisson’s equation, only a fixed potential U is given). A reason