9.10 Lattice Absorption
299
Fig. 9.50 Lattice absorption oscillator strength f from (9.86) for various elemental, III–V and II–VI semiconductors
as a function of their ionicity f i (cf. Table 2.1). Dashed line is linear dependence on ionicity for similar (reduced) mass,
dash-dotted lines are guides to the eye for similar ionicity and varying mass
=
ω
2
TO − ω
2
− iω
ω
2
TO − ω 2 − iω
.
(9.84)
The dispersion relation (without damping) can be rewritten as
= +
−
1 − (ω/ω TO ) 2 =
1 +
f
1 − (ω/ω TO ) 2
.
(9.85)
Thus the dimensionless oscillator strength (compare with (D.10)) is f = ( − 1. With the
LST relation (9.26) the oscillator strength is
f =
−
(∞)
=
ω
2
LO − ω
2
TO
ω
2
TO
≈ 2
ω LO − ω TO
ω TO
,
(9.86)
and thus proportional to the splitting LT = ω LO − ω TO between the longitudinal and transverse optical
phonon frequency. The approximation in (9.86) is valid for LT ω TO .
The oscillator strength increases with the ionicity, i.e. the electronegativity difference of the atoms
in the base (Fig. 9.50). Additionally, the oscillator strength depends on the reduced mass and the highfrequency polarizability; this can be seen, e.g., for the series of the Zn compounds that all have similar
ionicity. For the series of the nitrides, the mass effect is small since the reduced mass is dominated
by the light N mass. We refer to Fig. 5.23 for the change of phonon oscillator strength in an (Al,Ga)N
alloy.
9.10.2 Reststrahlenbande
The absorption of electromagnetic radiation by optical phonons is governed by the dielectric function
that has been derived in (9.84). For small damping, i.e. LT , the dielectric constant is negative
between ω TO and ω LO . From r = n
2
r − κ
2 it follows that κ
2 is much larger than n
2
r . Therefore,