454
16 Polarized Semiconductors
(a)
(b)
Ba
2
O
2
Ti
4
O
2
Fig. 16.5 a Crystal structure of BaTiO 3 (see Fig. 3.27). b Schematic tetragonal deformation below the Curie temperature,
generating a dipole moment
(a)
50
40
30
20
10
0
SbSI
T C
200
300
TO (cm )
-1
0
100
(b)
CaTiO 3
KTaO 3
SrTiO 3
Ca Sr TiO 3
Ba Sr TiO 3
BaTiO 3
1000/(T C
Fig. 16.6 a Decrease of the transverse phonon mode of SbSI close to the Curie temperature of T C = 288 K. The dashed
curved line represents a |T − T C | 1/2 dependence. Adapted from [1495]. b Dielectric constant of various perovskites
versus 1/(T − T C ) in the paraelectric phase (T > T C ). Adapted from [1496]
Another class of ferroelectrics are A
V B
VI C
VII compounds, such as SbSI, SbSBr, SbSeI, BiSBr.
These materials have a width of the forbidden band in the ∼ 2 eV range. A further class of ferroelectric
semiconductors are A
V
2 B
VI
3 compounds, such as Sb 2 S 3 .
16.3.2 Soft Phonon Mode
The finite displacement of the sublattices in the ferroelectric means that the related lattice vibration
has no restoring force. The displacement is, however, finite due to higher-order terms (anharmonicity).
Thus, for T → T C ω TO → 0. Such a mode is called a soft phonon mode. The decrease of the phonon
frequency is shown in Fig. 16.6a for SbSI.
From the LST relation (9.26), it follows that the static dielectric function must increase strongly.
The increase is ∝ (T − T C )
−1 (Fig. 16.6b).
16 Polarized Semiconductors
(a)
(b)
Ba
2
O
2
Ti
4
O
2
Fig. 16.5 a Crystal structure of BaTiO 3 (see Fig. 3.27). b Schematic tetragonal deformation below the Curie temperature,
generating a dipole moment
(a)
50
40
30
20
10
0
SbSI
T C
200
300
TO (cm )
-1
0
100
(b)
CaTiO 3
KTaO 3
SrTiO 3
Ca Sr TiO 3
Ba Sr TiO 3
BaTiO 3
1000/(T C
Fig. 16.6 a Decrease of the transverse phonon mode of SbSI close to the Curie temperature of T C = 288 K. The dashed
curved line represents a |T − T C | 1/2 dependence. Adapted from [1495]. b Dielectric constant of various perovskites
versus 1/(T − T C ) in the paraelectric phase (T > T C ). Adapted from [1496]
Another class of ferroelectrics are A
V B
VI C
VII compounds, such as SbSI, SbSBr, SbSeI, BiSBr.
These materials have a width of the forbidden band in the ∼ 2 eV range. A further class of ferroelectric
semiconductors are A
V
2 B
VI
3 compounds, such as Sb 2 S 3 .
16.3.2 Soft Phonon Mode
The finite displacement of the sublattices in the ferroelectric means that the related lattice vibration
has no restoring force. The displacement is, however, finite due to higher-order terms (anharmonicity).
Thus, for T → T C ω TO → 0. Such a mode is called a soft phonon mode. The decrease of the phonon
frequency is shown in Fig. 16.6a for SbSI.
From the LST relation (9.26), it follows that the static dielectric function must increase strongly.
The increase is ∝ (T − T C )
−1 (Fig. 16.6b).