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

Erratum: Fluorescence line narrowing, localized exciton states, and spectral diffusion in the mixed semiconductor CdS x Se 1-x

We report measurements of low-temperature luminescence spectra, lifetime, and excitation spectra for excitons in ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ (${x}_{c}lxl0.55$, where ${x}_{c}=0.435$ is the direct-to-indirect crossover value) over a wide range of excitation levels. The no-phonon line, \ensuremath{\sim}6 meV wide, decays nonexponentially at low excitation levels. The decay rate depends strongly on excitation intensity and on temperature (for $2lTl30$ K) while the position and width remain unchanged. We show that in the low-temperature, low-excitation limit, the nonexponential decay, and its dependence on $x$, can be quantitatively explained in terms of emission from a small number of localized indirect excitons scattered by alloy fluctuations. Above 8 K these excitons become mobile and their decay is exponential. Most of the excitons are mobile even at 2 K. They dominate the emission when the excitation is sufficiently strong to neutralize the ionized impurities, which quench the luminescence at low intensities. The localized excitons show strong LO-phonon sidebands, while the mobile ones do not. The theory of the decay rate yields a mean value of the scattering strength $J\ensuremath{\sim}0.2$ eV, in reasonable agreement with estimates from the Al-Ga electronegativity difference. The nitrogen-bound exciton with a wide range of binding energies, previously reported in ion-implanted samples, is found to be split, possibly by a disorder-induced axial field.

Dynamics of intrinsic and nitrogen-induced exciton emission in indirect-gap Ga 1 − x Al x As

Structural Phase Transitions in PrAlO 3

The electron spin resonance of ${\mathrm{Gd}}^{3+}$ impurities in single crystals of PrAl${\mathrm{O}}_{3}$ has been studied in the temperature range 4.2 to 295 K. The fine structure can be explained in terms of a spin Hamiltonian whose largest term is an almost axial second-rank tensor, which is closely related to the local distortion at the rare-earth site. The direction of the principal axis of this tensor shifts discontinuously from [111] to [$10\overline{1}$] at the 205-K trigonal-orthorhombic phase transition. Below the 151-K second-order phase transition, the angle between the principal axis and [$10\overline{1}$] varies continuously with temperature. Below 70 K the principal axis lies within 1\ifmmode^\circ\else\textdegree\fi{} of [001], and the symmetry is almost exactly tetragonal. From the direction of the principal axis we derive an order parameter describing local ("internal") displacements. We also measured the splitting and symmetry of the lowest electronic states of PrAl${\mathrm{O}}_{3}$ by optical absorption. Our results are more accurate than previous fluorescence measurements. From this splitting, an "electronic" order parameter can be derived. We find that for $Tg0.8{T}_{c}$ these two order parameters are equal to each other and to a third, the reduced macroscopic strain, which has been measured previously by Birgeneau et al. This agreement is predicted by Feder and Pytte's theory of cooperative Jahn-Teller phase transitions. The order parameters are found to follow the classical ${({T}_{c}\ensuremath{-}T)}^{\frac{1}{2}}$ behavior to within 0.2\ifmmode^\circ\else\textdegree\fi{} of ${T}_{c}$. At 118 K ($0.785{T}_{c}$), where a pronounced acoustic anomaly has been reported by Fleury et al., we find only a very weak anomaly in the temperature dependence of the internal-displacement order parameter, and no detectable effect on that of the other two parameters.

E. Cohen

Papers

Erratum: Fluorescence line narrowing, localized exciton states, and spectral diffusion in the mixed semiconductor CdS x Se 1-x

Dynamics of intrinsic and nitrogen-induced exciton emission in indirect-gap Ga 1 − x Al x As

Structural Phase Transitions in PrAlO 3

Microscopic order parameters in PrAl O 3

Electronic Raman Effect and Spectroscopic Studies of NdAlO3