[Paper Review] Peculiarities of the Light Absorption and Emission by Free Electrons in Multivalley Semiconductors

P. M. Tomchuk|ArXiv.org|Nov 18, 2008

Semiconductor Quantum Structures and Devices3 citations

TL;DR

This paper derives general expressions for light absorption and spontaneous emission by free electrons in multivalley semiconductors, accounting for anisotropic electron dispersion and scattering mechanisms (impurity and acoustic). It reveals that both absorption and emission exhibit polarization dependence under unidirectional pressure or high irradiation, with emission intensity showing exponential suppression at high photon energies in the quantum regime, while remaining frequency-independent in the classical regime.

ABSTRACT

General expressions are obtained for the coefficient of light absorption by free carriers as well as the intensity of the spontaneous light emission by hot electrons in multivalley semiconductors. These expressions depend on the electron concentration and electron temperature in the individual valleys. An anisotropy of the dispersion law and electron scattering mechanisms is taken into account. Impurity-related and acoustic scattering mechanisms are analyzed. Polarization dependence of the spontaneous emission by hot electrons is found out. At unidirectional pressure applied or high irradiation intensities, the polarization dependence also appears in the coefficient of light absorption by free electrons.

Motivation & Objective

• To derive general expressions for light absorption and emission by free carriers in multivalley semiconductors.
• To account for the anisotropy of the electron dispersion law and scattering mechanisms in these materials.
• To analyze the influence of impurity and acoustic scattering on absorption and emission processes.
• To investigate the emergence of polarization dependence in both absorption and emission under non-equilibrium conditions.
• To establish the dependence of emission intensity on electron temperature, concentration, and valley-specific parameters.

Proposed method

• Formulates the electron Hamiltonian in the principal axes of the mass tensor, including electromagnetic field coupling via the vector potential.
• Solves the Schrödinger equation for the electron wave function in the presence of an electromagnetic wave using perturbation theory.
• Derives the collision integral for electron-ion scattering under an external electromagnetic field using the kinetic equation approach.
• Applies the method to both classical and quantum regimes, using the relaxation tensor components (τ⊥, τ∥) to describe scattering anisotropy.
• Evaluates the absorption coefficient and emission intensity through formal substitutions from the wave-field-induced emission framework.
• Uses the Debye screening model for the ion potential and assumes a monochromatic electromagnetic wave with frequency ω.

Experimental results

Research questions

• RQ1 How does the anisotropy of the electron dispersion law affect the absorption and emission of light by free carriers in multivalley semiconductors?
• RQ2 What is the role of impurity and acoustic scattering mechanisms in determining the polarization dependence of light emission by hot electrons?
• RQ3 Under what conditions does the absorption coefficient of free electrons in multivalley semiconductors exhibit polarization dependence?
• RQ4 How does the emission intensity vary with photon frequency in classical versus quantum regimes?
• RQ5 What is the dependence of emission and absorption on electron concentration and temperature in individual valleys?

Key findings

• The absorption coefficient and emission intensity depend explicitly on the electron concentration $ n_i $ and temperature $ heta_i $ in each valley, reflecting the multivalley nature of the system.
• In the classical frequency range ($ ar{h}ω \ll \theta_i $), the emission intensity is independent of the emitted photon frequency, as shown in Eq. (73).
• In the quantum frequency range ($ ar{h}ω \gg \theta_i $), the emission intensity drops exponentially with increasing photon energy, as given by Eq. (74).
• A polarization dependence emerges in both emission and absorption when unidirectional pressure is applied or when irradiation intensity is high, due to valley-specific anisotropy.
• The emission intensity is proportional to the inverse of the effective mass components ($ m_\bot, m_\| $) and the relaxation times $ \tau_\bot, \tau_\| $, weighted by the angle $ \varphi_i $ between the polarization and the symmetry axis.
• The derived expressions for emission and absorption are consistent across classical and quantum regimes, differing only in numerical coefficients due to different energy dependencies of the relaxation tensor.