68
3 Light–Matter Interactions for Photonic Applications
the influence of the environment (modified screening) and the low-dimensionality
of atomically-thin monolayers (strong quantum confinement) (see e.g. [109] for a
detailed discussion of 2D excitons, also see Rytova–Keldysh potential for 2D systems
[110–112]).
In fact, in the above many-body Hamiltonian (3.3), the bosonic lattice vibrations’ Hamiltonian H ph is similar to the one for the bosonic light field, with phonon
oscillation frequency and phonon creation/annihilation operators instead of light
frequency and photon creation/annihilation operators. For the sake of clarity, the
different indices corresponding to the different modes, polarisation, quantum states
for the particles involved, i.e. phonons, photons and excitons, respectively, have
been skipped in this overview representation. For theoretical details and elaborate
descriptions of the individual Hamiltonians and their role in the dynamics of semiconductors, the interested reader is referred to general semiconductor quantum theory
described in textbooks (e.g. [113]) and recent monolayer TMDC related theoretical
considerations (e.g. [114]).
3.2 Matter Excitations
Optical transitions and the resulting measurable “optical band gap” are very characteristic for absorption and emission properties of semiconductor quantum structures [115, 116]. In the low density regime, they represent excitonic modes hosting
correlated Coulomb-bound charge carriers in a dilute gas, whereas at intermediate densities a bath of correlated free charge carriers adds up to the Coulombbound excitations of the system (see [117]), where multi-particle scattering processes
and excitation-induced dephasing raise. At high densities, the non-equilibrium system is governed by an incoherent electron–hole plasma (see [118]), where it also
experiences density-dependent band-gap renormalisation (for a quantum-theoretical
description, see [113]). All these fundamental regimes can play an important role
in semiconductor device physics. One typical example, where a transition from a
low-density to a high-density charge-carrier regime is sought, is that of laser diode
operation under the Bernard–Duraffourg condition, i.e. in a non-equilibrium regime
of optical transparency at the effective gap wavelength for optical amplification by
stimulated emission
4 (see [119], and, for the history of laser conditions in semiconductors, [120]). Commonly, “population inversion” is a term used to express
4 This is a quantum physical effect that refers to the induced emission—the opposite process to
(induced) absorption—which relaxes an electronic charge carrier from its excited state to its ground
state in a simplified two-level picture under emission of a photon with ω = E 2 − E 1 with certain
probability, provided that a resonant photon is present in the system. This stimulated emission process results in the release of a clone of the existing (irradiated) photon, which has equal energy, phase,
polarisation and propagation direction. Thus, the resulting light field is coherent, characterised by
a random photon number distribution, and its photons exhibit phase relation over relatively long
distances.
3 Light–Matter Interactions for Photonic Applications
the influence of the environment (modified screening) and the low-dimensionality
of atomically-thin monolayers (strong quantum confinement) (see e.g. [109] for a
detailed discussion of 2D excitons, also see Rytova–Keldysh potential for 2D systems
[110–112]).
In fact, in the above many-body Hamiltonian (3.3), the bosonic lattice vibrations’ Hamiltonian H ph is similar to the one for the bosonic light field, with phonon
oscillation frequency and phonon creation/annihilation operators instead of light
frequency and photon creation/annihilation operators. For the sake of clarity, the
different indices corresponding to the different modes, polarisation, quantum states
for the particles involved, i.e. phonons, photons and excitons, respectively, have
been skipped in this overview representation. For theoretical details and elaborate
descriptions of the individual Hamiltonians and their role in the dynamics of semiconductors, the interested reader is referred to general semiconductor quantum theory
described in textbooks (e.g. [113]) and recent monolayer TMDC related theoretical
considerations (e.g. [114]).
3.2 Matter Excitations
Optical transitions and the resulting measurable “optical band gap” are very characteristic for absorption and emission properties of semiconductor quantum structures [115, 116]. In the low density regime, they represent excitonic modes hosting
correlated Coulomb-bound charge carriers in a dilute gas, whereas at intermediate densities a bath of correlated free charge carriers adds up to the Coulombbound excitations of the system (see [117]), where multi-particle scattering processes
and excitation-induced dephasing raise. At high densities, the non-equilibrium system is governed by an incoherent electron–hole plasma (see [118]), where it also
experiences density-dependent band-gap renormalisation (for a quantum-theoretical
description, see [113]). All these fundamental regimes can play an important role
in semiconductor device physics. One typical example, where a transition from a
low-density to a high-density charge-carrier regime is sought, is that of laser diode
operation under the Bernard–Duraffourg condition, i.e. in a non-equilibrium regime
of optical transparency at the effective gap wavelength for optical amplification by
stimulated emission
4 (see [119], and, for the history of laser conditions in semiconductors, [120]). Commonly, “population inversion” is a term used to express
4 This is a quantum physical effect that refers to the induced emission—the opposite process to
(induced) absorption—which relaxes an electronic charge carrier from its excited state to its ground
state in a simplified two-level picture under emission of a photon with ω = E 2 − E 1 with certain
probability, provided that a resonant photon is present in the system. This stimulated emission process results in the release of a clone of the existing (irradiated) photon, which has equal energy, phase,
polarisation and propagation direction. Thus, the resulting light field is coherent, characterised by
a random photon number distribution, and its photons exhibit phase relation over relatively long
distances.