262
9 Optical Properties
Fig. 9.4 Reflectance of the GaAs/vacuum interface (close to the band gap, n r = 3.347) for radiation from vacuum/air
(left panel) and from the GaAs (right panel), respectively, as a function of incidence angle and polarization
R =
n r − 1
n r + 1
2
.
(9.15)
For GaAs, the reflectance for vertical incidence is 29.2%.
9.4 Absorption
In the absorption process, energy is transferred from the electromagnetic field to the semiconductor. In
the case of a linear absorption process, when the probability of light absorption is proportional to the
incoming intensity, the decrease of intensity in the absorbing medium is exponential (Lambert–Beer’s
law [835, 836]),
2
I (x) = I (0) exp(−α x) .
(9.16)
The quantity α is the absorption coefficient, its reverse the absorption depth.
The spectral dependence α(E), the absorption spectrum, contains the information of the possible absorption processes, their energy, momentum and angular momentum selection rules, and their
oscillator strength.
In Fig. 9.5 a schematic absorption spectrum of a semiconductor is depicted. The transition of electrons from the valence to the conduction band begins at the band gap energy. The band gaps of Si,
Ge, GaAs, InP, InAs, InSb are in the IR, those of AlAs, GaP, AlP, InN in the VIS, those of GaN and
ZnO in the UV, MgO and AlN are in the deep UV. The Coulomb correlation of electrons and holes
leads to the formation of excitons that leads to absorption below the band gap. The typical exction
binding energy is in the range of 1–100 meV (see Fig. 9.19). Optical transitions from valence-band
electrons into donors and from electrons on acceptors into the conduction band lead to band–impurity
absorption. In the region from 10–100 meV the interaction with lattice vibrations (phonons) leads to
absorption if the phonons are infrared active. Further in the FIR lie transitions from impurities to the
2 In [836], the absorption coefficient μ was defined via I (d)/I (0) = μ d , i.e. μ = exp −α.
9 Optical Properties
Fig. 9.4 Reflectance of the GaAs/vacuum interface (close to the band gap, n r = 3.347) for radiation from vacuum/air
(left panel) and from the GaAs (right panel), respectively, as a function of incidence angle and polarization
R =
n r − 1
n r + 1
2
.
(9.15)
For GaAs, the reflectance for vertical incidence is 29.2%.
9.4 Absorption
In the absorption process, energy is transferred from the electromagnetic field to the semiconductor. In
the case of a linear absorption process, when the probability of light absorption is proportional to the
incoming intensity, the decrease of intensity in the absorbing medium is exponential (Lambert–Beer’s
law [835, 836]),
2
I (x) = I (0) exp(−α x) .
(9.16)
The quantity α is the absorption coefficient, its reverse the absorption depth.
The spectral dependence α(E), the absorption spectrum, contains the information of the possible absorption processes, their energy, momentum and angular momentum selection rules, and their
oscillator strength.
In Fig. 9.5 a schematic absorption spectrum of a semiconductor is depicted. The transition of electrons from the valence to the conduction band begins at the band gap energy. The band gaps of Si,
Ge, GaAs, InP, InAs, InSb are in the IR, those of AlAs, GaP, AlP, InN in the VIS, those of GaN and
ZnO in the UV, MgO and AlN are in the deep UV. The Coulomb correlation of electrons and holes
leads to the formation of excitons that leads to absorption below the band gap. The typical exction
binding energy is in the range of 1–100 meV (see Fig. 9.19). Optical transitions from valence-band
electrons into donors and from electrons on acceptors into the conduction band lead to band–impurity
absorption. In the region from 10–100 meV the interaction with lattice vibrations (phonons) leads to
absorption if the phonons are infrared active. Further in the FIR lie transitions from impurities to the
2 In [836], the absorption coefficient μ was defined via I (d)/I (0) = μ d , i.e. μ = exp −α.