Chapter 12: Solid state physics
67
12.5.3
The Halleffect
If a magnetic Feld is applied
⊥
to the direction of the current the charge carriers will be pushed aside by the
Lorentz force. This results in a magnetic Feld
⊥
to the ±ow direction of the current. If
±
J
=
J
±
e
x
and
±
B
=
B
±
e
z
than
E
y
/E
x
=
μB
. The Hall coefFcient is deFned by:
R
H
=
E
y
/J
x
B
, and
R
H
=

1
/ne
if
J
x
=
neμE
x
.
The Hall voltage is given by:
V
H
=
Bvb
=
IB/neh
where
b
is the width of the material and
h
de height.
12.5.4
Thermal heat conductivity
With
²
=
v
F
τ
the mean free path of the electrons follows from
κ
=
1
3
C
±
v
²
²
:
κ
electrons
=
π
2
nk
2
T
τ
/
3
m
.
²rom this follows for the
WiedemannFranz ratio
:
κ
/
σ
=
1
3
(
π
k/e
)
2
T
.
12.6
Energy bands
In the
tightbond
approximation it is assumed that
ψ
=e
ikna
φ
(
x

na
)
. ²rom this follows for the energy:
±
E
²
=
±
ψ

H

ψ
²
=
E
at

α

2
β
cos(
ka
)
. So this gives a cosine superimposed on the atomic energy, which
can often be approximated by a harmonic oscillator. If it is assumed that the electron is nearly free one can
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Ye
 Electron, Charge, Current, Force, Solid State Physics, Condensed matter physics, Electronic band structure, Egap

Click to edit the document details