Introduction to Nanomaterials and Devices

Chapter 3

Density of States in Semiconductor Materials

3.1 Introduction

Semiconductor heterojunctions and nanomaterials consist of large numbers of identical particles such as electrons, atoms, holes, and harmonic oscillators. In such cases, it is impossible to try to trace the motion of each individual particle. An alternative way of looking at these large numbers of particles is to settle for knowing averages of relevant dynamical quantities over the entire range of possible system configurations. This leads to the construction of the macroscopic properties of the system and to understanding of how energy, velocity, and momentum are distributed among the particles that form the system. The branch of physics that addresses the distribution function of a system is called statistical mechanics, which links the microscopic properties of the system with its macroscopic domains. For physical systems such as semiconductor nanomaterials, there are constraints associated with any distribution function. For example, the number of particles is finite, or the total energy of the system is constant. These constraints usually alter the probabilities associated with possible system configurations.

The techniques of statistical mechanics have been applied to a variety of physical problems such as gases, liquids, polymers, metals, semiconductors, transport theory, DNA, adsorption, spectroscopy, and optical and electrical properties of solids among many other fields of study. Statistical thermodynamics ...