Solid State Physics
II
Level 4
Semester 1
Course Content
L1. Introduction to solid state physics - The free electron theory : Free levels in one dimension.
L2. Free electron gas in three dimensions.
L3. Electrical conductivity – Motion in magnetic field- Wiedemann-Franz law.
L4. Nearly free electron model - origin of the energy band.
L5. Bloch functions - Kronig Penney model.
L6. Dielectrics I : Polarization in dielectrics
L7 .Dielectrics II: Types of polarization - dielectric constant
L8. Assessment
L9. Experimental determination of dielectric constant
L10. Ferroelectrics (1) : Ferroelectric crystals
L11. Ferroelectrics (2): Piezoelectricity
L12. Piezoelectricity Applications
L1 : Solid State Physics
Solid state physics is the study of rigid matter, or solids,
,through methods such as quantum mechanics,
crystallography, electromagnetism and metallurgy.
It is the largest branch of condensed matter physics.
Solid-state physics studies how the large-scale
properties of solid materials result from their atomic-
scale properties.
Thus, solid-state physics forms the theoretical basis of
materials science.
It also has direct applications, for example in the
technology of transistors and semiconductors.
Crystalline solids & Amorphous solids
Solid materials are formed from densely-packed atoms, which
interact intensely.
These interactions produce :
the mechanical (e.g. hardness and elasticity),
thermal,
electrical,
magnetic
and optical properties of solids.
Depending on the material involved and the conditions in
which it was formed
, the atoms may be arranged in a regular, geometric pattern
(crystalline solids, which include metals and ordinary water ice)
, or irregularly (an amorphous solid such as common window
glass).
Crystalline solids & Amorphous solids
The bulk of solid-state physics theory and research is
focused on crystals.
Primarily, this is because the periodicity of atoms in a
crystal facilitates mathematical modeling.
Also, crystalline materials often have electrical,
magnetic, optical, or mechanical properties that can
be exploited for engineering purposes.
Free Electron Theory
Properties of materials such as electrical conduction
and heat capacity are investigated by solid state physics.
An early model of electrical conduction was the Drude
model.
It applied kinetic theory to the electrons in a solid.
What are its main assumptions?
What are the physical experimental results that could be
explained by Drude’s model?
And what results it had overestimated?
Free Electron Theory
Arnold Sommerfeld combined the classical Drude model
with quantum mechanics in:
the free electron model (or Drude-
Sommerfeld model).
What are its main assumptions?
The free electron model gave improved predictions for
the heat capacity of metals, however, it was unable to
explain the existence of insulators.
Free Electron Fermi Gas
From many types of experiments
: it was found that a conduction electron in a metal can
move freely in a straight path over many atomic
distances, undeflected by collisions with other
conduction electrons or by collisions with the atom
cores.
In a very pure specimen at low temperatures the mean
free path may be as long as 108 interatomic spacings
(more than 1 cm).
Free Electron Fermi Gas
Why is a condensed matter so transparent to conduction
electrons ?
The answer is:
1. A conduction electron is not deflected by ion cores
arranged on a periodic lattice because matter waves
propagate freely in a periodic structure.
2. A conduction electron is scattered only by other
conduction electrons as a consequence of Pauli exclusion
principle.
By a free electron Fermi gas we mean a gas of free
electrons subject to Pauli principle.
Free Levels in One Dimension
Free Levels in One Dimension
The wavefunction and the energy
The wavefunction and the energy
In a linear solid, the quantum
numbers are n and ms only. Why?
The Fermi energy f :Definition
and equation.
The ground state
Fermi-Dirac distribution
Questions
1. What is Solid State Physics all about?
2. Solid materials are formed from densely-packed atoms,
which interact intensely, what are the direct results of these
interactions?
3:What are the main parameters which make a material
crystalline or non-crystalline ?
4: What is Drude model; write its main assumptions.
5: Why a conduction electron in a metal can move freely in
straight path over many interatomic spacings undeflected by
collisions as if the matter is transparent to it?
6: Find the wavefunction and the energy of a free electron of
mass m confined at a length L by infinite barriers. Then deduce
the Fermi energy f in an N electron system.
Internet and Text Book Research
Define shortly Fermi – Dirac
Statistics.
What are Fermions and Bosons?
Thank You Very Much
