NNSE 508 EM
Lecture #9
1
Lecture
contents
•
Bloch theorem
•
k-vector
•
Brillouin zone
•
Tight-binding model
•
Almost free-electron model
•
Bands
•
Effective mass
•
Holes

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NNSE 508 EM
Lecture #9
2
Translational symmetry: Bloch theorem
)
(
)
(
R
r
V
r
V
3
3
2
2
1
1
a
m
a
m
a
m
R
)
(
)
(
2
2
r
E
r
r
V
m
p
If
V(r)
is a periodic function:
One-electron Schrödinger equation (each state can accommodate up to 2 electrons):
)
(
)
(
r
u
e
r
k
ikr
k
The solution is :
)
(
)
(
R
r
u
r
u
k
k
where
u
k
(r)
is a periodic function:
From:
•
Linearity of the Schrödinger
equation
•
Fourier
theorem
2
2
)
(
)
(
R
r
r
k
k
Quasi-wavevector
k
is analogous to a
wavevector for free electrons (V=const)
u
k
might be not a single valence electron
function but is close to linear combination of
valence electron wavefunctions
Important :