Chapter 2
ELECTRONIC LEVELS
IN SEMICONDUCTORS
2.1 INTRODUCTION
Semiconductor electronic and optoelectronic devices depend upon how electrons inside ma-
terials behave and how they are influenced by external perturbations which may be electrical,
electromagnetic, mechanical, or magnetic, etc. The simplest approach to understanding such
properties would be to use classical physics. Based on classical physics the general problem
could be solved by using Newton’s equation
dp
dt=e(E+v×B)wherepis the electron momentum,vthe velocity, andEandBare the electrical and magnetic
fields, respectively. Additional forces, if present, can be added on the right-hand side of the equa-
tion. Although classical physics has been successful in describing many of nature’s phenomena,
it fails completely when it is used to describe electrons in solids. To understand the underlying
physical properties that form the basis of modern intelligent information devices, we need to use
quantum mechanics.
According to quantum mechanics particles such as electrons behave as waves while waves
such as electromagnetic waves behave as particles. The wave nature of particles is manifested for
electrons in solids. To the level needed in device physics, the electronic properties are described
by the Schrodinger equation. However, It turns out we can develop ̈ effectivedescriptions for the
behavior of electrons and then use simple classical physics. Of course to develop this effective
description we have to solve the Schrodinger equation. But once this description is developed we ̈
can use Newton’s equation to understand how electrons respond to external forces. This allows
us to use simple models to describe electronic devices.
In this chapter we will review a few important outcomes of quantum mechanics. In particular
we will discuss the following: