258
9 Optical Properties
Table 9.1 Spectral ranges with relevance to semiconductor optical properties
Range
Wavelengths
Energies
Deep ultraviolet
DUV
<250 nm
>5 eV
Ultraviolet
UV
250–400 nm
3–5 eV
Visible
VIS
400–800 nm
1.6–3 eV
Near infrared
NIR
800 nm–2 µm
0.6–1.6 eV
Mid-infrared
MIR
2–20 µm
60 meV–0.6 eV
Far infrared
FIR
20–80 µm
1.6–60 meV
THz region
THz
>80 µm
<1.6 meV
9.2 Complex Dielectric Function
The dielectric function (DF) fulfills the relation between the displacement field D, the polarization
P and the electric field E,
D = 0 E + P = 0 E ,
(9.2)
and is generally a tensor of rank 2 since D and E must not be collinear. For cubic materials, the DF
is isotropic and can be described with a (complex) scalar . Less symmetric crystals are optically
anisotropic and the DF must be used in tensor form. Also, external fields can induce optical anisotropy
in an otherwise isotropic material as discussed in Sect. 15.2.2 for magnetic fields or has been observed
for mechanical strain fields. The general form of the dielectric function tensor for various crystal
symmetries is compiled in Table 9.2.
In most cases in the following, will be used as scalar (isotropic case). The dielectric function is frequency dependent (ω) due to the various oscillators playing a role and decreases (non-monotonically)
from its static value (for ω = 0) to 1 for ω → ∞. Major influence on the DF stems from (optical)
Table 9.2 General form of the tensor form of the dielectric function for the seven crystallographic systems
Crystal system
Optical symmetry
Examples
Cubic
Isotropic
⎛
⎜
⎝
a 0 0
0 a 0
0 0 a
⎞
⎟
⎠
Si, GaAs, MgO, ZnSe, CuI
tetragonal
hexagonal
trigonal
uniaxial
⎛
⎜
⎝
a 0 0
0 a 0
0 0 c
⎞
⎟
⎠
CuGaSe 2 , GaN, ZnO,
Bi 2 Se 3
orthorhombic
biaxial
⎛
⎜
⎝
a 0 0
0 b 0
0 0 c
⎞
⎟
⎠
κ-Ga 2 O 3 , Sb 2 Se 3
monoclinic
biaxial
⎛
⎜
⎝
a 0 d
0 b 0
d 0 c
⎞
⎟
⎠
β-Ga 2 O 3 , anthracene
triclinic
biaxial
⎛
⎜
⎝
a d e
d b f
e f c
⎞
⎟
⎠
K 2 Cr 2 O 7 , tetracene
9 Optical Properties
Table 9.1 Spectral ranges with relevance to semiconductor optical properties
Range
Wavelengths
Energies
Deep ultraviolet
DUV
<250 nm
>5 eV
Ultraviolet
UV
250–400 nm
3–5 eV
Visible
VIS
400–800 nm
1.6–3 eV
Near infrared
NIR
800 nm–2 µm
0.6–1.6 eV
Mid-infrared
MIR
2–20 µm
60 meV–0.6 eV
Far infrared
FIR
20–80 µm
1.6–60 meV
THz region
THz
>80 µm
<1.6 meV
9.2 Complex Dielectric Function
The dielectric function (DF) fulfills the relation between the displacement field D, the polarization
P and the electric field E,
D = 0 E + P = 0 E ,
(9.2)
and is generally a tensor of rank 2 since D and E must not be collinear. For cubic materials, the DF
is isotropic and can be described with a (complex) scalar . Less symmetric crystals are optically
anisotropic and the DF must be used in tensor form. Also, external fields can induce optical anisotropy
in an otherwise isotropic material as discussed in Sect. 15.2.2 for magnetic fields or has been observed
for mechanical strain fields. The general form of the dielectric function tensor for various crystal
symmetries is compiled in Table 9.2.
In most cases in the following, will be used as scalar (isotropic case). The dielectric function is frequency dependent (ω) due to the various oscillators playing a role and decreases (non-monotonically)
from its static value (for ω = 0) to 1 for ω → ∞. Major influence on the DF stems from (optical)
Table 9.2 General form of the tensor form of the dielectric function for the seven crystallographic systems
Crystal system
Optical symmetry
Examples
Cubic
Isotropic
⎛
⎜
⎝
a 0 0
0 a 0
0 0 a
⎞
⎟
⎠
Si, GaAs, MgO, ZnSe, CuI
tetragonal
hexagonal
trigonal
uniaxial
⎛
⎜
⎝
a 0 0
0 a 0
0 0 c
⎞
⎟
⎠
CuGaSe 2 , GaN, ZnO,
Bi 2 Se 3
orthorhombic
biaxial
⎛
⎜
⎝
a 0 0
0 b 0
0 0 c
⎞
⎟
⎠
κ-Ga 2 O 3 , Sb 2 Se 3
monoclinic
biaxial
⎛
⎜
⎝
a 0 d
0 b 0
d 0 c
⎞
⎟
⎠
β-Ga 2 O 3 , anthracene
triclinic
biaxial
⎛
⎜
⎝
a d e
d b f
e f c
⎞
⎟
⎠
K 2 Cr 2 O 7 , tetracene