- 35 -
University of California, Berkeley
EE230 - Solid State Electronics
Prof. J. Bokor
Free Electron Gas
(Read Kittel Ch. 6)
Assume non-interacting particles, mass m, spin 1/2, in a 3-D box
periodic boundary conditions:
etc. for y,z.
plane wave solutions.
energy (dispersion relation)
momentum
velocity
Mode counting
Each state (mode) occupies volume
in k-space.
Total # of states N, with wavevector
≤
k :
total # states N, with energy
is:
L
L
L
Volume V = L
3
ψ
r
( )
Ae
ik
r
⋅
=
N
2
4
π
3
------
k
3
2
π
L
------
⎝
⎠
⎛
⎞
3
--------------
⋅
V
3
π
2
--------
k
3
=
=
spin
E
≤

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