Tài liệu Chapter XXIV Crystalline Solids doc

GENERAL PHYSICS III
GENERAL PHYSICS III
Optics
&
Quantum Physics
Chapter XXIV
Chapter XXIV
Crystalline Solids
Crystalline Solids
§1. Wavefunctions and energy band of electrons
§2. Electronic conduction in metals
§3. Semiconductors
To have a quantum-mechanical treatment we model a crystalline solid as
matter in which the atoms have long-range order, that is a recurring
(periodical) pattern of atomic positions that extends over many atoms.
We will describe the wavefunctions and energy levels of electrons in
such periodical atomic structures.
 We want to answer the question: Why do some solids conduct currWe want to answer the question: Why do some solids conduct currentent
and others donand others don’’t?t?
§1. Wavefunctions and energy band of electrons:
1.1 Potential energy of electrons:
+e
r
n = 3
n = 2
n = 1
+e
r
+e
r
e

)r(U
2


2
2
1
2
rr
e
rr
e
)r(U





Atom H
Two atoms (molecule H
2
)
+e
r
n = 3
n = 2
n = 1
Atom Solid
Discrete atomic states  band of crystal states  Fill according to Pauli Principle
• A simple (1-D) model of the recurring structure is shown below.

• An electron interacts not with one, but with many nuclei  every
energy level splits into a band of energies
1.2 Wavefunctions
1.2 Wavefunctions
and
and
Energies:
Energies:
• Atomic ground state:
• Molecular states:
+e
r
n = 1

A
Bonding state Antibonding state
r
e
)r(U
2


0
a/r
e)r(



Now we fill these orbitals with the 2 available electrons (one from
each hydrogen atom). Both can go into ‘bonding’, thanks to spin

+e
r
+e

even
+e
r
+e

odd
What do these crystal states look like?
-- approximately linear combinations of atomic orbitals.
Again start with
simple atomic state:
+e
r
n = 1

A
Bring N atoms together together forming a 1-D crystal (a periodic lattice)
(N atomic states N crystal states):
Energy
band
• 1-D periodic lattice:
•• SimpleSimple model of a crystalmodel of a crystal withwith covalentcovalent bonding:bonding:

N
Highest energy orbital (N-1 nodes)

1

Lowest energy orbital (zero nodes)
“in between” states