Semiconductor physics and light-matter interaction
PHYS-433
Recorded version of Lecture 12
PHYS-433 Lecture 12
08.12.2021, 12:50
In this Lecture, we provide the theoretical framework behind the interband optical absorption process taking place in direct bandgap semiconductors. First, we make use of Fermi's Golden Rule to derive the transition rate between valence and conduction band states. In doing so, we show that energy and momentum conservation should be ensured. However, given the small value of the wave vector carried by the photons, we consider that for the transition energies of interest optical transitions are essentially vertical in k-space. We then derive the link between the imaginary part of the linear optical susceptibility and the absorption coefficient. The third important step deals with the derivation of a general expression for the absorption coefficient that is also valid out of equilibrium and that depends on the occupancy of the interconnected bands, i.e., we rely on Fermi-Dirac distributions involving quasi-Fermi levels. This allows us to introduce the notion of optical gain and the related Bernard-Duraffourg condition that is specific to semiconductors.
PHYS-433 Lecture 12
08.12.2021, 12:50
In this Lecture, we provide the theoretical framework behind the interband optical absorption process taking place in direct bandgap semiconductors. First, we make use of Fermi's Golden Rule to derive the transition rate between valence and conduction band states. In doing so, we show that energy and momentum conservation should be ensured. However, given the small value of the wave vector carried by the photons, we consider that for the transition energies of interest optical transitions are essentially vertical in k-space. We then derive the link between the imaginary part of the linear optical susceptibility and the absorption coefficient. The third important step deals with the derivation of a general expression for the absorption coefficient that is also valid out of equilibrium and that depends on the occupancy of the interconnected bands, i.e., we rely on Fermi-Dirac distributions involving quasi-Fermi levels. This allows us to introduce the notion of optical gain and the related Bernard-Duraffourg condition that is specific to semiconductors.
PHYS-433 Lecture 12
08.12.2021, 12:50
In this Lecture, we provide the theoretical framework behind the interband optical absorption process taking place in direct bandgap semiconductors. First, we make use of Fermi's Golden Rule to derive the transition rate between valence and conduction band states. In doing so, we show that energy and momentum conservation should be ensured. However, given the small value of the wave vector carried by the photons, we consider that for the transition energies of interest optical transitions are essentially vertical in k-space. We then derive the link between the imaginary part of the linear optical susceptibility and the absorption coefficient. The third important step deals with the derivation of a general expression for the absorption coefficient that is also valid out of equilibrium and that depends on the occupancy of the interconnected bands, i.e., we rely on Fermi-Dirac distributions involving quasi-Fermi levels. This allows us to introduce the notion of optical gain and the related Bernard-Duraffourg condition that is specific to semiconductors.
PHYS-433 Lecture 12
08.12.2021, 12:50
In this Lecture, we provide the theoretical framework behind the interband optical absorption process taking place in direct bandgap semiconductors. First, we make use of Fermi's Golden Rule to derive the transition rate between valence and conduction band states. In doing so, we show that energy and momentum conservation should be ensured. However, given the small value of the wave vector carried by the photons, we consider that for the transition energies of interest optical transitions are essentially vertical in k-space. We then derive the link between the imaginary part of the linear optical susceptibility and the absorption coefficient. The third important step deals with the derivation of a general expression for the absorption coefficient that is also valid out of equilibrium and that depends on the occupancy of the interconnected bands, i.e., we rely on Fermi-Dirac distributions involving quasi-Fermi levels. This allows us to introduce the notion of optical gain and the related Bernard-Duraffourg condition that is specific to semiconductors.
PHYS-433 Lecture 12
08.12.2021, 12:50
In this Lecture, we provide the theoretical framework behind the interband optical absorption process taking place in direct bandgap semiconductors. First, we make use of Fermi's Golden Rule to derive the transition rate between valence and conduction band states. In doing so, we show that energy and momentum conservation should be ensured. However, given the small value of the wave vector carried by the photons, we consider that for the transition energies of interest optical transitions are essentially vertical in k-space. We then derive the link between the imaginary part of the linear optical susceptibility and the absorption coefficient. The third important step deals with the derivation of a general expression for the absorption coefficient that is also valid out of equilibrium and that depends on the occupancy of the interconnected bands, i.e., we rely on Fermi-Dirac distributions involving quasi-Fermi levels. This allows us to introduce the notion of optical gain and the related Bernard-Duraffourg condition that is specific to semiconductors.
PHYS-433 Lecture 12
08.12.2021, 12:50
In this Lecture, we provide the theoretical framework behind the interband optical absorption process taking place in direct bandgap semiconductors. First, we make use of Fermi's Golden Rule to derive the transition rate between valence and conduction band states. In doing so, we show that energy and momentum conservation should be ensured. However, given the small value of the wave vector carried by the photons, we consider that for the transition energies of interest optical transitions are essentially vertical in k-space. We then derive the link between the imaginary part of the linear optical susceptibility and the absorption coefficient. The third important step deals with the derivation of a general expression for the absorption coefficient that is also valid out of equilibrium and that depends on the occupancy of the interconnected bands, i.e., we rely on Fermi-Dirac distributions involving quasi-Fermi levels. This allows us to introduce the notion of optical gain and the related Bernard-Duraffourg condition that is specific to semiconductors.