15.2 Magnetic Fields
443
Fig. 15.15 Oscillatory
(theory, T = 6 K) behavior
of a 2DEG
(GaAs/(Al,Ga)As) in a
magnetic field: a Fermi
level, b magnetization, c
specific heat, d
thermoelectric power. A
Gaussian broadening of
0.5 meV was assumed.
Adapted from [1123, 1456]
(b)
(a)
(d)
(c)
2
0
0
1
6
8
4
Thermoelectric
(meV)
Magnetization
35
30
25
0.3
0.2
0.1
0
30
20
10
0
-10
-20
-30
15
10
5
0
1
B
=
e
h
1
n s
.
(15.39)
The carrier density of a 2DEG can therefore be determined from the oscillations of magnetoresistance,
and is proportional to the density of states at the Fermi level (Shubnikov-de Haas effect). A corresponding measurement with varying field and fixed electron density is shown in Fig. 15.16. The periodicity
with 1/B is obvious. Since only the component of the magnetic field perpendicular to the layer affects
the (x, y) motion of the carriers, no effect is observed for the magnetic field parallel to the layer.
In another experiment the carrier density was varied at constant field (Fig. 15.17). The electron
density in an inversion layer in p-type silicon is (linearly) varied with the gate voltage of a MOS
(metal-oxide-semiconductor) structure (inset in Fig. 15.17, for MOS diodes cf. Sect. 24.5). In this
experiment, the Fermi level was shifted through the Landau levels. The equidistant peaks show that
indeed each Landau level contributes the same number of states.