Abstract
After introduction of the complex dielectric function, reflection, diffraction are briefly discussed. The focus lies on absorption mechanisms; several transition types (direct and indirect band-band transitions, impurity-related transitions, lattice absorption) are discussed including the effects of excitons, polaritons and high carrier density. Also the various effects of the presence of free carriers are given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The more exact numerical value in (9.1) is 1239.84.
- 2.
In [726], the absorption coefficient \(\mu \) was defined via \(I(d)/I(0)=\mu ^d\), i.e. \(\mu =\exp -\alpha \).
- 3.
Here we assume that the valence-band states are filled and the conduction-band states are empty. If the conduction-band states are filled and the valence-band states are empty, the rate is that of stimulated emission .
- 4.
The real and imaginary parts of the dielectric function are generally related to each other via the Kramers–Kronig relations.
- 5.
A flat optical phonon dispersion is assumed.
- 6.
Cf. (7.20); an electron bound to a donor can be considered as an exciton with an infinite hole mass.
- 7.
Such parameter can be directly determined from spectroscopic broadening (as in [756]) or a time-resolved measurement of the decay of the coherent polarization (four-wave mixing) as in [757]. In the latter, the decay constant of the dephasing \(T_2\) is related to the decay constant \(\tau \) of the FWM-signal by \(T_2=2 \tau \) for homogeneous broadening. The Fourier transform of \(\exp -t/(2 \tau )\) is a Lorentzian of the type \(\propto ((E-E_0)^2+\varGamma ^2/4)^{-1}\) with \(\varGamma =1/\tau \) being the FWHM.
- 8.
The dependence of the optical-phonon energies on k is typically too small to make spatial dispersion effects important. According to (5.19) \(\hat{D}=-\left( a_0 \omega _{\mathrm {TO}}/4c\right) ^2 \approx 4 \times 10^{-11}\) for typical material parameters (lattice constant \(a_0=0.5\) nm, TO phonon frequency \(\omega _{\mathrm {TO}}=15\) THz).
- 9.
The A line is due to excitons with \(J=1\), resulting of coupling of the electron spin 1/2 with the hole angular momentum of 3/2. The B-line is a dipole forbidden line due to ‘dark’ excitons with \(J=2\).
- 10.
Also the recombination (Sect. 10.3.2) is efficient and allows green GaP:N and yellow GaAsP:N light emitting diodes.
- 11.
Even at low temperature, \(n \approx N_{\mathrm {D}}\) since \(N_{\mathrm {D}} \gg N_{\mathrm {c}}\) (cf. [515] and Sect. 7.5.7).
- 12.
The much higher free-electron density in metals shifts the plasma frequency to the UV, explaining the reflectivity of metals in the visible and their UV transparency.
- 13.
CdO is an indirect semiconductor, the optical band gap is the energy of the direct transition at the \(\varGamma \)-point. The indirect transitions involve holes from other points in the Brillouin zone (cmp. Fig. 6.10).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Grundmann, M. (2016). Optical Properties. In: The Physics of Semiconductors. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-23880-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-23880-7_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23879-1
Online ISBN: 978-3-319-23880-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)