Appendix F
Review of Solid State Concepts
As there are some aspects of the solid state that need to be understood when dealing
with semiconductors and their properties, we shall review briefly a few of the
relevant concepts needed for our discussion. It is not our intent here to provide
a rigorous treatment of the subject, but simply to attempt to give a more or less
qualitative overview of some important aspects of the solid state. We shall do this
by utilizing a model approach introduced by Feynman and known as the coupled
modes approach. The essence of the Feynman approach is to divide a system into
its components and study what happens to the system if the components are weakly
coupled to one another. Thus, it is a type of perturbation approach (similar to the
concept discussed in an introductory quantum mechanics course).
F.1 The Feynman Model and Energy Bands
We shall introduce the concept and the model by considering a simple homonuclear
diatomic species and the formation of molecular energy levels associated with the
molecular orbital description of molecules that you will have encountered in an
introductory general chemistry course.
The simplest homonuclear diatomic molecule is the hydrogen molecular ion, H
+
2 ,
which consists of two protons and one electron. It is simple enough for it to be solved
exactly, and is the molecular analogon of the H atom for atoms. We begin with the
time-dependent Schrödinger equation, which is
−
¯
h 2
2m
∇
2
+
V
(r, t) = i ¯
h
∂∂
∂t
,
(F.1.1)
© Springer Nature Switzerland AG 2021
F. R. W. McCourt, Statistical Thermodynamics for Pure and Applied Sciences,
https://doi.org/10.1007/978-3-030-52006-9
645
Review of Solid State Concepts
As there are some aspects of the solid state that need to be understood when dealing
with semiconductors and their properties, we shall review briefly a few of the
relevant concepts needed for our discussion. It is not our intent here to provide
a rigorous treatment of the subject, but simply to attempt to give a more or less
qualitative overview of some important aspects of the solid state. We shall do this
by utilizing a model approach introduced by Feynman and known as the coupled
modes approach. The essence of the Feynman approach is to divide a system into
its components and study what happens to the system if the components are weakly
coupled to one another. Thus, it is a type of perturbation approach (similar to the
concept discussed in an introductory quantum mechanics course).
F.1 The Feynman Model and Energy Bands
We shall introduce the concept and the model by considering a simple homonuclear
diatomic species and the formation of molecular energy levels associated with the
molecular orbital description of molecules that you will have encountered in an
introductory general chemistry course.
The simplest homonuclear diatomic molecule is the hydrogen molecular ion, H
+
2 ,
which consists of two protons and one electron. It is simple enough for it to be solved
exactly, and is the molecular analogon of the H atom for atoms. We begin with the
time-dependent Schrödinger equation, which is
−
¯
h 2
2m
∇
2
+
V
(r, t) = i ¯
h
∂∂
∂t
,
(F.1.1)
© Springer Nature Switzerland AG 2021
F. R. W. McCourt, Statistical Thermodynamics for Pure and Applied Sciences,
https://doi.org/10.1007/978-3-030-52006-9
645