294
9 Optical Properties
Fig. 9.41 Plasma
wavelength λ p for n-type
GaAs with various electron
concentrations due to
different doping levels.
Filled circles: experimental
values, dashed line: n −1/2
dependence; the deviation
is due to nonparabolicity of
the electron mass (cf.
Fig. 9.53b). Data
from [918]
Fig. 9.42 Burstein–Moss
effect at InSb
(E g = 0.18 eV) at room
temperature. Theoretical
dependence and data points
for intrinsic InSb and
5 × 10 18 cm −3 n-type. Data
from [919]
-3
10
18
10
19
gap
0.4
0.6
0.8
4
1.0
0.2
2
1.5
1
7
3
17
10
g
E
InSb
9.9.2 Burstein–Moss Shift
In the discussion so far it has been assumed that all target states in the conduction band are empty. In
the presence of free carriers the absorption is modified by the
• change of the distribution function
• many-body effects (band gap renormalization).
The latter is discussed in the next section. For a degenerate electron distribution all states close to
the conduction-band edge are populated. Thus a transition from the valence band cannot take place
into such states. This shift of the absorption edge to higher energies is called the Burstein–Moss shift
[919, 920]. Originally, the Burstein–Moss shift was evoked to explain the absorption shift in InSb with
varying carrier concentration (Fig. 9.42).
k-conserving optical transitions between parabolic hole and electron bands have the dependence
E = E g +
2 k
2
2 m e
+
2 k
2
2 m h
= E g +
2 k
2
2 m r
,
(9.80)
where m r is the reduced mass of electron and hole. About 4kT below the Fermi level all levels in the
conduction band are populated (Fig. 9.43). Thus the k value at which the absorption starts is given as
ˆ
k =
2 m e
2 (E F − E C − 4kT ) .
(9.81)