Abstract

CHAPTER 1. OVERVIEW 17
1.5 The Wigner-Poisson Equations
The first equation in modelling the resonant tunneling diode is the Wigner equation,
which is
where W (f) isgivenby
∂f(x, k, t)
∂t
= W (f) (1.5)
W (f) =K(f)+P (f)+S(f) (1.6)
Here, f(x, k, t) is the Wigner distribution function, and it describes the distribution
of electrons within the RTD as a function of x, the spatial variable, k, the wave
number variable, and t, time. The RTD exists from x =0tox = L, whereL is the
length of the RTD. Table 1.1 summarizes all the physical constants that appear in
the equations.
The first term, K(f), is given by
K(f) = −hk
2πm∗ ∂f
∂x
(1.7)
where m ∗ is the electron’s effective mass. This term corresponds to the effects due to
kinetic energy on f.