Page 194 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Chapter 6 Transport

Theory

The study of semi-classical time-dependent processes usually separates
the constitutive from the balance equations. The idea is the following:
constitutive equations describe the way in which a particular material can
influence a particular transport process, usually by adding resistance. For
example, the atoms of the silicon crystal represent scattering centers for
electrons moving through. Chapter 2 to Chapter 4 discussed these consti-
tutive relations in quite some detail without looking at either transport, or
the interaction between transporting particles. The balance equations
usually implement some postulate of mechanics—these are often called
integrals of the motion. The balance equations demand the conservation
of an extensive property, such as energy, or momentum, and so on. When
we are dealing with an ensemble of particles, with a distribution among
some states, and we do not want to track each particle individually, then
we require a transport theory which is adjusted to this view. Since elec-
trons have many features, and electron transport is so very important in
device engineering, we focus much of our attention on describing the
transport of electrons through silicon. In describing transport we intro-

Semiconductors for Micro and Nanosystem Technology 191