6.10 Holes
165
Fig. 6.40 Spin-orbit
splitting 0 for elemental
(diamonds) and various
III–V and II–VI (circles)
semiconductors. The data
are plotted as empty (filled)
circles as a function of the
cation (anion) order
number. Obviously, 0
correlates with the anion Z .
The dashed line is
proportional to Z 2
Fig. 6.41 Dispersion at the
valence band edge of GaAs
for a, b heavy holes and
c,d light holes. a,c
Constant energy surfaces
and b,d isolines in the
(k x , k y )-plane (b and d
have different energy
scales)
(a)
(b) -4
-2
0
2
4
-4
-2
0
2
(c)
(d) -4
-2
0
2
4
-4
-2
0
2
E(k) = A k
2
±
B 2 k 4 + C 2
k 2
x k 2
y + k 2
y k 2
z + k 2
x k 2
z
.
(6.48)
For heavy and light holes there is a dependence of the dispersion, i.e. the mass, in the (001) plane. This
effect, sketched in Fig. 6.39b, is called warping. The warping at the GaAs valence-band edge is shown
in Fig. 6.41. Equation (6.48) can also be expressed in terms of angular coordinates [522].
The s-o holes have the dispersion
E(k) = − 0 + A k
2
.
(6.49)