5.2 Lattice Vibrations
113
-1
12
C As
GaAs
Exp.
Th.
Fig. 5.19 Experimental (Exp., T = 4.2 K, resolution 0.03 cm −1 ) and theoretical (Th., artificial Lorentzian broadening)
infrared spectra of LVM of 12 C As in GaAs. The positions and oscillator strengths of the theoretical transitions involving
different configurations with 69 Ga and 71 Ga isotopes are shown as vertical bars. Data from [382]
0
0 . 5
1
gap
mode
localized
mode
LO 1
TO 1
LO 2
TO 2
0
0 . 5
1
localized
mode
LO 1
TO 1
LO 2
TO 2
0
0 . 5
1
gap
mode
LO 1
TO 1
LO 2
TO 2
0
0 . 5
1
LO
TO
Composition
Composition
Composition
Composition
Frequency
(a)
(b)
(c)
(d)
Fig. 5.20 Schematic behavior of phonon modes in an alloy. a Two-mode behavior with gap mode and localized mode,
(b, c) mixed-mode behavior, b only localized mode allowed, c only gap mode allowed, d one-mode behavior with neither
localized mode nor gap mode allowed
M B < μ AC =
M A M C
M A + M C
< M A , M C
(5.48)
is a necessary and sufficient condition (unless the force constants between A–B and A–C are significantly different) for two-mode behavior [389]. A detailed discussion is given in [390]. Equation (5.48)
is a stronger condition than the previous one (5.47). If (5.48) is not fulfilled the compound exhibits
one-mode behavior. As an example, we show the mass relations for CdS 1−x Se x and Cd x Zn 1−x S in
Table 5.1 and the experimental phonon energies in Fig. 5.21. Also in Table 5.1 the masses for GaP 1−x As x
(GaAs 1−x Sb x ) exhibiting two- (one-) mode behavior are shown.
113
-1
12
C As
GaAs
Exp.
Th.
Fig. 5.19 Experimental (Exp., T = 4.2 K, resolution 0.03 cm −1 ) and theoretical (Th., artificial Lorentzian broadening)
infrared spectra of LVM of 12 C As in GaAs. The positions and oscillator strengths of the theoretical transitions involving
different configurations with 69 Ga and 71 Ga isotopes are shown as vertical bars. Data from [382]
0
0 . 5
1
gap
mode
localized
mode
LO 1
TO 1
LO 2
TO 2
0
0 . 5
1
localized
mode
LO 1
TO 1
LO 2
TO 2
0
0 . 5
1
gap
mode
LO 1
TO 1
LO 2
TO 2
0
0 . 5
1
LO
TO
Composition
Composition
Composition
Composition
Frequency
(a)
(b)
(c)
(d)
Fig. 5.20 Schematic behavior of phonon modes in an alloy. a Two-mode behavior with gap mode and localized mode,
(b, c) mixed-mode behavior, b only localized mode allowed, c only gap mode allowed, d one-mode behavior with neither
localized mode nor gap mode allowed
M B < μ AC =
M A M C
M A + M C
< M A , M C
(5.48)
is a necessary and sufficient condition (unless the force constants between A–B and A–C are significantly different) for two-mode behavior [389]. A detailed discussion is given in [390]. Equation (5.48)
is a stronger condition than the previous one (5.47). If (5.48) is not fulfilled the compound exhibits
one-mode behavior. As an example, we show the mass relations for CdS 1−x Se x and Cd x Zn 1−x S in
Table 5.1 and the experimental phonon energies in Fig. 5.21. Also in Table 5.1 the masses for GaP 1−x As x
(GaAs 1−x Sb x ) exhibiting two- (one-) mode behavior are shown.