The co-operative Jahn-Teller effect is a phase transition which is driven by the interaction between localized orbital electronic states and the crystal lattice. The possible origins, symmetries and properties of the electron-lattice interactions and how they lead to possible hamiltonians for the coupled system are discussed. The relation of these interactions with quadrupolar interactions and magnetostriction is included. The methods of solution of the hamiltonians lead to an understanding of the electronic states, the phonon spectrum and the mixed normal modes. The wide variety of experimental techniques used on this problem are reviewed in detail and the results are compared with theoretical expressions whenever possible. The application of external stress and magnetic field is of particular significance in the case of the rare earth compounds, because they can product effects which are larger than the low-temperature spontaneous effects.

http://iopscience.iop.org/article/10.1088/0034-4885/38/1/001/pdf

Co-operative Jahn-Teller effects

A thorough discussion of the various features of the photoluminescence spectra of undoped, p‐doped and n‐doped AlxGa1−xAs (0≤x≤1) alloys is given. This review covers spectral features in the energy region ranging from the energy band gap down to ≂0.8 eV, doping densities from isolated impurities to strongly interacting impurities (heavy‐doping effects) and lattice temperatures from 2 to 300 K. The relevance of photoluminescence as a simple but very powerful characterization technique is stressed also in comparison with other experimental methods. The most recent determinations of the Al concentration dependence of some physical properties of the alloy (energy gaps, carrier effective masses, dielectric constants, phonon energies, donor and acceptor binding energies, etc.) are given. The main physical mechanisms of the radiative recombination process in semiconductors are summarized with particular emphasis on the experimental data available for AlxGa1−xAs. The effects of the nature of the band gap (direct ...

Photoluminescence of AlxGa1−xAs alloys

The authors report time-resolved photoluminescence spectroscopy of highly porous silicon. Their results show that the luminescence is due to localized quantum-confined excitons in undulating crystalline silicon wires. The resonantly excited photoluminescence spectrum exhibits satellite structure due to momentum-conserving phonons of crystalline silicon. This provides a clear signature of the crystalline-silicon electronic band structure. The spin states of the localized exciton are split by the electron-hole exchange interaction. This splitting is manifested both in the strong dependence of the luminescence lifetime on temperature, and as an energy gap in the resonantly excited photoluminescence spectrum. The experimental splitting is in good agreement with the value calculated for a localized exciton in crystalline silicon.

https://iopscience.iop.org/article/10.1088/0953-8984/5/7/003/pdf

Identification of radiative transitions in highly porous silicon

The mechanism for low-temperature photoluminescence (PL) emissions in GaNAs epilayers and GaAs/GaNxAs1−x quantum well (QW) structures grown by molecular-beam epitaxy is studied in detail, employing PL, PL excitation, and time-resolved PL spectroscopies. It is shown that even though quantum confinement causes a strong blueshift of the GaNAs PL emission, its major characteristic properties are identical in both QW structures and epilayers. Based on the analysis of the PL line shape, its dependence on the excitation power and measurement temperature, as well as transient data, the PL emission is concluded to be caused by a recombination of excitons trapped by potential fluctuations in GaNAs.

Mechanism for low-temperature photoluminescence in GaNAs/GaAs structures grown by molecular-beam epitaxy

The electronic band structures of III nitride semiconductors calculated within the adiabatic approximation give essential information about the optical properties of materials. However, atoms of the lattice are not at rest; their displacement away from the equilibrium positions perturbs the periodic potential acting on the electrons in the crystal, leading to an electron-phonon interaction energy. Due to different ways that the lattice vibration perturbs the motions of electrons, there are various types of interaction, such as Frohlich interaction with longitudinal optical phonons, deformation-potential interactions with optical and acoustic phonons and piezoelectric interaction with acoustic phonons. These interactions, especially the Frohlich interaction, which is very strong due to the ionic nature of III nitrides, have a great influence on the optical properties of the III nitride semiconductors. As a result of electron-phonon interaction, several phenomena, such as phonon replicas in the emission spectra, homogeneous broadening of the excitonic line width and the relaxation of hot carriers to the fundamental band edge, which have been observed in GaN and its low dimensional heterostructures, are reviewed.

https://iopscience.iop.org/article/10.1088/0953-8984/13/32/312/pdf

Influence of electron-phonon interaction on the optical properties of III nitride semiconductors

We report luminescence studies of pulse photoexcited, indirect-gap ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ in the temperature range of 2-150 K. Two spectral features are observed: excitons scattered by random potential fluctuations, and the electron-hole plasma (EHP). For $0.44\ensuremath{\le}x\ensuremath{\le}0.53$ we find a plasma density between 0.5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The plasma binding energy, relative to the free exciton, is very small and may be negative. A strong no-phonon band is observed, which we attribute to scattering by potential fluctuations, as well as momentum-conserving phonon-assisted transitions. The lifetime of the EHP below 20 K is about five times shorter than that of the "intrinsic" exciton and is predominantly radiative. There is good, if not definitive, evidence that plasma-exciton phase separation occurs. Stimulated emission from the EHP is observed in nominally undoped, indirect-gap material, for $x\ensuremath{\le}0.46$. Further spectral features are present at moderate to high excitation, which may result from multiexciton complexes.

Electron-hole plasma in photoexcited indirect-gap Al x Ga 1 − x As

Magnetic field-induced structural reorientation in PrAlO3

The polarized Raman scattering between the electronic levels of the $^{4}T_{1g}$ ground term of ${\mathrm{Co}}^{2+}$ in ${\mathrm{CsMgCl}}_{3}$ has been observed at 2\ifmmode^\circ\else\textdegree\fi{}K. We calculated the fine structure of $^{4}T_{1g}$ for this system as well as for ${\mathrm{Co}}^{2+}$ in ${\mathrm{CdCl}}_{2}$ (observed by Lockwood and Christie). Second-order perturbation theory has been employed for a Hamiltonian containing the trigonal crystal field $\ensuremath{\Delta}$ and spin-orbit interaction $\ensuremath{\lambda}$. The data are fit satisfactorily with $\frac{\ensuremath{\Delta}}{|\ensuremath{\lambda}|}=+4.4 \mathrm{and} \ensuremath{-}2.5$, respectively. Using the crystal-field wave functions we calculated the spectral intensities of the electronic Raman lines as a function of $\frac{\ensuremath{\Delta}}{|\ensuremath{\lambda}|}$, within the framework of Axe's theory. The theory predicts a small asymmetry between $\mathrm{xz}$ and $\mathrm{zx}$ polarizations and a very weak scattering in $\mathrm{zz}$ polarization. These predictions result mainly from the fact that the intermediate configuration $3{d}^{6}4p$ lies more than 100 000 ${\mathrm{cm}}^{\ensuremath{-}1}$ above the $3{d}^{7}$ configuration, making the closure assumption an adequate approximation. Good agreement is obtained between observed and calculated spectral intensities for both crystals.

E. Cohen

Papers

Electron-hole plasma in photoexcited indirect-gap Al x Ga 1 − x As

Magnetic field-induced structural reorientation in PrAlO3

Electronic Raman scattering of Co 2+ in CdCl 2 and CsMgCl 3

Internal-Displacement Order Parameter below the 151-K Phase Transition in PrAlO 3