Introduction to solid state physics
L3 Licence Physique et Applications
Anuradha JagannathanLaboratoire de physique des solides
Bât.510Université Paris-Sud
Orsay
references
C.Kittel Physique de l'état solide
H.Alloul Physique des électrons dans les solides
N.W. Ashcroft and N.D.Mermin Physique des solides
Types of solids
The solid state macroscopic characteristics: rigidity, resistance to deformation
microscopic viewpoint: each atom has a well-defined mean position
Two types of solid matter Crystalline: the distribution of atoms is periodic in space
Amorphous: atoms are randomly situated
Example of a 2D lattice the « 123 » high-Tc parent compound
(left) one unit cell of the YBa2Cu3O7 compound (right) one plane of Cu and O atoms
Current,voltage and resistance
Ohm's law : V = IR ↔ j = σEwhere
V=voltage (potential difference) = EL (E:electric field, L : length)
I = jS (j:current density, S : crosssection)
R = ρL/S (ρ = 1/σ : electrical resistivity)
R depends on the shape of the solid whereas ρ is an intrinsic property
The birth of a conduction electron
In the solid state, atoms may lose their outermost (or valence) electrons
Example: sodium (1 valence electron) ionizes to Na+ and the valence electron becomes delocalized.
the free electron gas
In this first chapter We assume that the ions create a fixed periodic positive charge We assume that the electron-electron Coulomb interactions can be
neglected
If we assume, in addition, that the positive charge is uniformly distributed, we
have a gas of free electrons
A solid (left)modelled by a gasof conduction electrons (right)
Classical theory of an electron gas in zero field
The kinetic theory of gases for particles of mass m in a volume V at a temperature T gives
CCaccording to this formula, at ambiant temperature thetypical speed of an electronIs approximately 105 m/s
Charged particles in a field
Problem :
A free electron in an electric field is subject to a constant force, and accelerates without limit, that is, its velocity (and the electrical current) → ∞ !
Solution :
The Drude model was introduced to explain the fact that the mean velocity remains finite, in a conductor, and that
j = σ E where σ is the electrical conductivity, which depends on the material, the
temperature, and eventually other factors (pressure, doping,defects,...)
We will next derive the Drude formula, which expresses σ as a function of the quantities n, e and τ
Microscopic model of electrical transport
For a fluid of identical charged particles subjected to an electric field, one can For a fluid of identical charged particles subjected to an electric field, one can show thatshow that
C C j = nqv j = nqvwhere
n :carrier concentration
v : velocity
q : charge per carrier
In a conductor,
q = -e (charge of the electron)
we can calculate n (next slide)
then, we need to calculate v(E)