Phonon Sideband Structure Research Articles

The underdamped Brownian oscillator model with Ohmic dissipation: Applicability to low-temperature optical spectra

The multimode Brownian oscillator (MBO) model with Ohmic dissipation has frequently been used to interpret photon echo and spectral data on solvation dynamics of chromophores in liquids at room temperature. We report on the applicability of this model to high-resolution linear electronic absorption spectra of chromophores in solid hosts at low temperatures, where the zero-phonon line (ZPL) is resolved from phonon sideband structure. The results are also relevant to frequency and time domain nonlinear spectra. In the MBO model, active BOs (phonons) are linearly coupled to bath modes. This coupling endows the bath modes with absorption intensity which, with Ohmic dissipation (white light spectrum for the bath modes), results in the bath modes contributing to absorption in the region of the ZPL. Experimental results for a multitude of molecular systems indicate that the ZPL profile is determined by electronic dephasing, which is not accounted for in the MBO model. Thus, it is important to assess the contribution of the MBO bath modes to the ZPL profile. To this end, closed-form, finite temperature expressions for the underdamped MBO (UMBO) model are derived for the linear response function, linear absorption spectrum, and width and Franck–Condon factor of the ZPL. It is proven formally that the UMBO ZPL width is zero at T=0 K. Results of calculations for model systems whose parameter values (BO damping constant, frequency and Huang–Rhys factor) are typical of real systems are presented. It is concluded that Ohmic dissipation leads to unphysically large ZPL widths as well as asymmetric ZPL profiles that appear not to have been observed. Moreover, the ZPL width adds to those of the multi-BO (phonon) transitions. Thus, use of the UMBO model with Ohmic dissipation to interpret data on relaxation dynamics of nuclear modes may result in erroneous conclusions. It is shown that Franck–Condon factors of the ZPL obtained with the UMBO model can differ significantly from those calculated with the conventional formula.

Acoustic phonon problem in nanocrystal–dielectric matrix systems

It has been shown that the energy spectrum of acoustic phonons in semiconductor quantum dots (QDs) embedded in a dielectric matrix is continuous despite the three-dimensional spatial confinement. This immediately follows from the analysis of the vibrational spectrum of such composite material, treating the QDs and host matrix as a unified system. Then, the confinement only modifies the acoustic phonon wave functions in QDs as compared to the bulk. From this point of view the phonon sideband structure in optical spectra of the QDs has been analyzed.

Phonon sidebands of exciton bound to NN 1 traps in [formula omitted] alloys

Using selective excitation technology, the phonon sidebands of NN 1 pair emission are observed in GaAs 1−x P x :N (x=0.88) alloys. Due to fluorescence line narrowing, the fine structure of phonon sidebands of NN 1 pair emission, which is very similar to that of N x in GaAs 1−x P x :N and to that of NN 1 in GaP:N, including TA, LA, LO As and LO phonons, has been identified. The results experimentally confirm that the NN 1 center does exist in GaAs 1−x P x :N alloys.

Pseudolocal phonons in p-terphenyl: pentacene single crystals

The structural nature of the phonon sidebands in the fluorescence and excitation spectra of pentacene guests in p-terphenyl crystals at 4.2 K are investigated using site-selective spectroscopy. The distinct features in the phonon sideband structure were observed to depend significantly on the guest site configuration of pentacene occupying four inequivalent sites in the triclinic p-terphenyl lattice. The sharp peaks dominating the phonon sideband structure are assumed to arise from the pseudolocal phonons. The eigenvalues and eigenvectors of the pseudolocal phonons are calculated carrying out a modified normal mode analysis on the distinct pentacene site configurations including the contribution of all intermolecular atom-pair interactions.

Localisation of excitons at small Te clusters in diluted ZnSe1-xTex solid solutions

The low-temperature recombination luminescence of ZnSe1-xTex solid solutions is studied in the Te concentration range 1%<or=x<or=2%. The dependence of the spectra on Te content and on excitation photon energy allows the authors to discriminate three different emission components. They are ascribed to recombination of excitons localised at clusters very probably consisting of two and more than two Te atoms. Selective excitation reveals substantial inhomogeneous broadening of states due to fluctuations in the local environment of the clusters. The phonon side-band structure concomitantly observed gives strong support to their model in which the large-radius exciton is tightly bound through the hole. The excitation spectra of the LO phonon replica intensity and of its polarisation degree provide information on the energy distribution of the localised states and their dynamic properties. The strong modification of the localised state emission spectrum found at higher Te concentration can be qualitatively understood by the increasing cluster interaction.

The phonon sidebands of NN i pair emission in GaP:N

By using selective excitation technique, the phonon sidebands belonged to each NN i pair center were successfully resolved out from the seriously overlapping spectrum under above gap excitation. The TA and LA phonon sidebands of NN 3 center were clearly seen at low temperature. This work confirmed that NN 1, NN 3 and isolated N centers have almost the same phonon sideband structure.

The effect of the crystal field strength on the optical spectra of Cr3+ in gallium garnet laser crystals

We have investigated the basic spectroscopic properties of Cr3+-doped gallium garnets. Weak crystal fields (Dq/B=2.39–2.55) lead to broad4 T 2→4 A 2 fluorescence in the 700–950 nm range depending on the chemical composition of the crystals. At room temperature the4 T 2→4 A 2 transition is homogeneously broadened, whereas the 4 K spectra of the2 E→4 A 2 transition show inequivalent Cr3+ sites and inhomogeneous linewidths of 8 cm−1 in these laser crystals. From 300 to 4 K, the oscillator strength of the4 T 2→4 A 2 transition is reduced by a factor of about 0.6 due to the temperature dependent electron phonon coupling. The transition probability of the2 E→4 A 2 transition correlates with the energetic position of the4 T 2 level, which is admixed into the2 E level via spin-orbit coupling. The comparison of the2 E→4 A 2 phonon sideband structure in garnets of different chemical compositions allows the assignment of some peaks to GaO4-tetrahedron modes of the garnet structure.

Vibronic coupling and implications in the copper related 1.014 eV photoluminescence spectrum in silicon

The 1.014 eV photoluminescence spectrum observed in Cu diffused, quenched silicon crystals exhibits a characteristic strong phonon sideband structure. It is shown that the intensity decrease of the no-phonon transition from 4.2 to 40 K is not due to vibronic coupling but originates in the population of excited electronic states of the defect. The thermal luminescence data and published lifetime measurements can consistently be explained by the electronic level scheme which was recently proposed.

Exciton—Phonon Luminescence of Perfect and Doped Naphthalene Crystals

The structure of phonon side bands in luminescence spectra of local excitons is investigated both theoretically and experimentally. A gradual transition from a spectrum behaviour peculiar for deep impurity centers (with wide phonon side band) to that peculiar for low temperature intrinsic luminescence (the side band becomes split into several bands corresponding to long wave lattice phonons) is investigated depending on the local exciton level depth. Experimental investigations of deuteronaphthalene solutions are presented.

Structure of phonon sidebands of the ν1 vibration absorption band of the NCO− impurity ion in KI:KCl and KBr:KCl mixed single crystals

AbstractThe change of the structure due to local vibrations of the perturbed environment is studied at 10°K in the phonon sideband (PS) of the ν1 vibration absorption band of the impurity ion NCO− in mixed KI:KCl and KBr:KCl lattices. It is found that at increased concentration of Cl− ions beginning from 1 wt% the intensity of a high‐frequency structure is sharply decreased and the number and half‐width of the gap‐local‐vibration bands increase; one fraction of these shifts to the high‐frequency side, the other to the long‐wave one. These effects are explained by the different locations of Cl− near NCO− in KI and KBr matrix lattices and, consequently, changes different in sign of the perturbed force constants of the axial interaction of the ν1 stretching vibration with lattice phonons.

Shape and structure of phonon sidebands of the ν1 stretching‐vibration absorption band of the NCO− impurity ion in alkali halide crystals

AbstractExperimental data are compared of the shape and structure of the phonon sidebands (PS) of the ν1 intramolecular vibration (IMV) of the impurity ion NCO− in KCl, KBr, and KI matrices obtained at 10 °K with their theoretical calculations. It is shown that in f.c.c. host lattices the shape (distribution of absorption coefficient K(ωk)) of the acoustic branch of PS is in quantitative agreement with the expression magnified image × × 〈sin2 (κ, ι)〉 g (ωκ), where ωk is the frequency displacement from the centre of the IMV absorption band (frequency of lattice phonon), ωm the maximum frequency of the phonon spectrum of the matrix, g(ωk) the density of its phonon states, k the quasimomentum of matrix phonon, and l the vector of the nearest neighbour of the impurity. In the optical branch of PS the agreement is qualitative. Assuming a change of the force constants of the two nearest axial neighbours of the linear impurity conditions are obtained of the appearance of local vibrations (LV) separating into the gap of the phonon spectrum of the matrix crystal and above ωm· The treatment is given of a sharp structure observed at the short‐wave side of PS and in the region of PS corresponding to the frequency gap of the f.c.c. matrices (doublets). Corresponding limiting changes of the force constants in the impurity crystals are evaluated.

An energy denominator study of the phonon side band in isotopic mixed naphthalene crystals

The fluorescence phonon sidebands of C10H8 and 1,4,5,8-C10D4H4 guests in C10H8 are studied and compared at 2 K. The mild differences are attributed to the increased delocalization of the C10D4H41B2u electronic state. The relative importance of the diagonal (Franck-Condon) versus off-diagonal (Herzberg-Teller) electron-phonon coupling terms is discussed. We also demonstrate that the dispersion force coupling (and not the resonance force coupling) dominates the 1B2u (and 3B1u) C10H8 in C10D8 phonon sideband structure, and is responsible for its intensity distribution (and the difference therein between fluorescence and phosphorescence).

Theory of Paraelectric Resonance and Relaxation

The theory of paraelectric resonance (PER) and relaxation is reformulated to allow a consistent treatment of dynamic lattice processes, even in the case when coupling to the lattice is strong. A simple model Hamiltonian is used and certain response functions are calculated without using perturbation theory. It is shown that the main effect of the strong lattice coupling at low temperatures is to induce a renormalization of the tunneling parameter of the paraelectric dipoles. The structure of phonon sidebands in PER is discussed. The theory predicts a strong transfer of intensity from the PER lines to the sidebands above a certain characteristic temperature. A treatment is given of paraelectric relaxation using the same techniques. A calculation of the temperature dependence of dipole-lattice relaxation time agrees well with experiment with adjustment of two parameters.