164
6 Band Structure
Fig. 6.38 Hole dispersion
dashed line in relation to
the electron dispersion in
the valence band (solid
line)
k
E
k e
k h
hole is positive at the top of the valence band, m
∗
h = −m
∗
e . Therefore, the drift velocities of an electron
and hole are opposite to each other. The resulting current, however, is the same.
6.10.2 Hole Dispersion Relation
The valence band at the -point is 3-fold degenerate. The band developed from the atomic (bonding)
p states; the coupling of the spin s = 1/2 electrons with the orbital angular momentum l = 1 leads to
a total angular momentum j = 1/2 and j = 3/2. The latter states are degenerate at in zincblende
bulk material and are called heavy holes (hh) for m j = ±3/2 and light holes (lh) for m j = ±1/2
due to their different dispersion (Fig. 6.39a). The two (m j = ±
/ 2) states of the j = 1/2 state are
split-off from these states by an energy 0 due to spin-orbit interaction and are called split-off (s-o)
holes. The spin-orbit interaction increases with increasing atomic order number Z of the anion since
the electrons are located preferentially there (Fig. 6.40). A detailed discussion of the spin-orbit splitting
in zincblende semiconductors is given in [520].
All three holes have different mass. In the vicinity of the -point the dispersion for heavy and light
holes can be described with (+:hh, −:lh)
Fig. 6.39 a Simplified
band structure with
conduction band and three
valence bands and (b)
three-dimensional
visualization (E versus
(k x , k y )) of the valence
bands of Ge (including
warping). Part b from [521]
(a)
(b)
6 Band Structure
Fig. 6.38 Hole dispersion
dashed line in relation to
the electron dispersion in
the valence band (solid
line)
k
E
k e
k h
hole is positive at the top of the valence band, m
∗
h = −m
∗
e . Therefore, the drift velocities of an electron
and hole are opposite to each other. The resulting current, however, is the same.
6.10.2 Hole Dispersion Relation
The valence band at the -point is 3-fold degenerate. The band developed from the atomic (bonding)
p states; the coupling of the spin s = 1/2 electrons with the orbital angular momentum l = 1 leads to
a total angular momentum j = 1/2 and j = 3/2. The latter states are degenerate at in zincblende
bulk material and are called heavy holes (hh) for m j = ±3/2 and light holes (lh) for m j = ±1/2
due to their different dispersion (Fig. 6.39a). The two (m j = ±
/ 2) states of the j = 1/2 state are
split-off from these states by an energy 0 due to spin-orbit interaction and are called split-off (s-o)
holes. The spin-orbit interaction increases with increasing atomic order number Z of the anion since
the electrons are located preferentially there (Fig. 6.40). A detailed discussion of the spin-orbit splitting
in zincblende semiconductors is given in [520].
All three holes have different mass. In the vicinity of the -point the dispersion for heavy and light
holes can be described with (+:hh, −:lh)
Fig. 6.39 a Simplified
band structure with
conduction band and three
valence bands and (b)
three-dimensional
visualization (E versus
(k x , k y )) of the valence
bands of Ge (including
warping). Part b from [521]
(a)
(b)