Page 172 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Chapter 5 Statistics

The number of particles that occur in a semiconductor is extraordinarily
large. From chemistry we got to know the mol as a unit, which counts off
chunks of materials weighing in at a couple of grams, yet containing
23
1.6×10 particles (this is of course Avogadro’s number). If we wish to
calculate properties down at the individual particle level, as indeed the
molecular dynamics people do, then we can consider only a very small
amount of matter. One way out is to consider the statistical nature of the
particles, and this works well if we have very many of them, as is indeed
the case for most realistic physical systems.

Chapter Goal The goal of this chapter is to introduce the concepts of statistics and sta-
tistical mechanics necessary to understand the variety of pseudo particles
that we encounter in the study of the solid state.

Chapter Our road map is to first introduce the ensembles. These groups of parti-
Roadmap cles are convenient models from thermodynamics, and provide a basis for
a consistent theory. Next we consider ways to count particles and particle

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