Phonon Dispersion Effects Research Articles

Temperature-dependent optical properties of ε-Ga2O3 thin films

We determined the complex dielectric functions of ε-Ga2O3 using optical transmittance and reflectance spectroscopies at temperatures from 10 K to room temperature. The measured dielectric-function spectra reveal distinct structures at bandgap energy. We fitted a model dielectric function based on the electronic energy-band structure to these experimental data. We analyzed the temperature dependence of the bandgap with a model based on phonon dispersion effects. One could explain it in terms of phonon-related parameters such as the optical phonon temperature. We compare phonon-related properties of ε-Ga2O3 with those of a large variety of element and binary semiconductors.

RETRACTED: A correlation study between size and etching time in Ge mesoporous toward the incorporation of phonon dispersion effect in PCM

In this work, a new correlation study based on the phonon confinement model (PCM) and some advanced characterization tools was performed to extract the size of germanium (Ge) nanocrystals (NCs) fabricated by bipolar electrochemical etching. The PCM was established by incorporating simultaneously the size distribution and phonon dispersion effects. A correlation study of Raman spectroscopy with Atomic force microscopy (AFM), and High-resolution scanning transmission electron microscope (HRSTEM) was confirmed the presence of a spherical core with an average size of 8 nm and very small crystallites of 3 nm. This study confirms that the phonon dispersion has an excellent contribution to the broadness and the shifting of the Raman lines of Ge NCs. In addition, an observation of the breaking down and deviation of the PCM model due to the presence of crystallites in the range of [1–5 nm] is confirmed. • Strong contribution of phonon dispersion effect to quantum confinement effect in Ge nanocrystals. • AFM and Raman spectroscopy as powerful probing tools for tuning the synthesis parameters of Ge porous layers. • Limitations of phonon confinement model (PCM) is confirmed in the size range of [2–5 nm].

Temperature dependence of dielectric functions in Yb2O3 and Lu2O3 epitaxial thin films on sapphire (0001)

The fundamental band-gaps of Yb2O3 and Lu2O3 films on sapphire (0001) substrates grown by pulsed laser deposition have been measured by optical transmission and reflectance spectroscopies as a function of temperature. The temperature dependence of the band-gap was analyzed by a model based on phonon dispersion effects and could be explained in terms of phonon-related parameters such as the optical phonon temperature. The phonon dispersion in Yb2O3 was found to fall into material trend based on the data for a large variety of element and binary semiconductors.

Polarons in highly doped atomically thin graphitic materials

Polaron spectral functions are computed for highly doped graphene-on-substrate and other atomically thin graphitic systems using the diagrammatic Monte Carlo technique. The specific aim is to investigate the effects of interaction on spectral functions when the symmetry between sub-lattices of a honeycomb lattice has been broken by the substrate or ionicity, inducing a band gap. Introduction of electron-phonon coupling leads to several polaronic features, such as band-flattening and changes in particle lifetimes. At the K point, differences between energies on each sub-lattice increase with electron-phonon coupling, indicating an augmented transport gap, while the spectral gap decreases slightly. Effects of phonon dispersion and long-range interactions are investigated, and found to lead to only quantitative changes in spectra.

An Ab-initio assessment of thermo-elastic properties of CaCO3 polymorphs: Calcite case

Calculation of total pressures, bulk modulus and thermal expansion, heat capacity and entropy of calcite were obtained through evaluation, at the Ab-initio level, of the unit cell volume dependence of the total static energy, and of the frequencies of the vibrational normal modes, at the Γ point, within the framework of the quasi-harmonic approximation. Thermo-elastic properties at zero pressure were corrected for the effects of phonon dispersion by calculating the vibrational frequencies at the Brillouin zone border, by using a supercell approach. Also, a modified Kieffer’s model was also tested to correct for dispersion effects concerning the acoustic modes only. Moreover, a correction to take into account intrinsic anharmonic contributions was performed by correcting all of the calculated frequencies by means of factors derived from literature experimental data.The algorithm allowed for the determination of (i) the equation of state, (ii) the thermal expansion as a function of pressure and temperature, and (iii) the evaluation of some thermodynamic properties (entropy and specific heat), together with their temperature dependences. The obtained results were compared with experimental data.The present work confirms previously experimentally determined parameters of the equation of state and thermodynamic properties of calcite. At room-temperature conditions, the calculated bulk modulus was 75.6 GPa which is to be compared with the corresponding experimental value of 76.9 GPa. The estimated thermal expansion at room temperature is 1.70⋅10−5K−1, which is in excellent agreement with the experimental datum (1.77⋅10−5K−1). The calculated entropy (S) and the constant pressure specific heat (CP) were respectively 91.4 and 81.8 J mol−1 K−1, which are also in close agreement with the experimental data [91.7 and 83.5 J mol−1 K−1, for S and CP respectively].

Effects of Phonon Dispersion and Anharmonicity on Thermo-physical Properties of Solids

Both phonon dispersion and anharmonicity contribute to the thermo-physical properties of solids in such a way that serious mistakes can be made, if these effects are not taken into account in the realization of semi-empirical equations of state (EOS) from limited experimental data sets. These effects are illustrated in comparisons of EOS data for different types of solids.

Comparison of Different Phonon Transport Models for Predicting Heat Conduction in Silicon-on-Insulator Transistors

The problem of self-heating in microelectronic devices has begun to emerge as a bottleneck to device performance. Published models for phonon transport in microelectronics have used a gray Boltzmann transport equation (BTE) and do not account adequately for phonon dispersion or polarization. In this study, the problem of a hot spot in a submicron silicon-on-insulator transistor is addressed. A model based on the BTE incorporating full phonon dispersion effects is used. A structured finite volume approach is used to solve the BTE. The results from the full phonon dispersion model are compared to those obtained using a Fourier diffusion model. Comparisons are also made to previously published BTE models employing gray and semi-gray approximations. Significant differences are found in the maximum hot spot temperature predicted by the different models. Fourier diffusion underpredicts the hot spot temperature by as much as 350% with respect to predictions from the full phonon dispersion model. For the full phonon dispersion model, the longitudinal acoustic modes are found to carry a majority of the energy flux. The importance of accounting for phonon dispersion and polarization effects is clearly demonstrated.

Phonon dispersion effects and the thermal conductivity reduction in GaAs/AlAs superlattices

The experimentally observed order-of-magnitude reduction in the thermal conductivity along the growth axis of (GaAs)n/(AlAs)n (or n×n) superlattices is investigated theoretically for (2×2), (3×3) and (6×6) structures using an accurate model of the lattice dynamics. The modification of the phonon dispersion relation due to the superlattice geometry leads to flattening of the phonon branches and hence to lower phonon velocities. This effect is shown to account for a factor-of-three reduction in the thermal conductivity with respect to bulk GaAs along the growth direction; the remainder is attributable to a reduction in the phonon lifetime. The dispersion-related reduction is relatively insensitive to temperature (100<T<300 K) and n. The phonon lifetime reduction is largest for the 2×2 structures and consistent with greater interface scattering. The thermal conductivity reduction is shown to be appreciably more sensitive to GaAs/AlAs force constant differences than to those associated with molecular masses.

Phonon dispersion effects on the motion of small polarons in molecular solids

The molecula crystal model (Holstein model) is studied versus temperature and dimensionality by taking into account the effect of the intermolecular forces. The phonon dispersion relations strongly influence the polaron band narrowing factor.

Forbidden Frölich-interaction-induced 2-LO Raman scattering in Pb 2Sr 2RCu 3O 8 (R=rare earth element)

The one- and two-phonon Raman scattering spectrum of single crystal Pb 2Sr 2RCu 3O 8, where R is a rare earth element, is examined under resonance conditions. Strong features appear in the one-phonon spectrum at the positions of longitudinal optical (LO) infrared modes as the laser energy approaches that of the charge transfer (CT) gap. These modes, which we interpret as Fröhlich-interaction-induced, are accompanied by a second order spectrum composed of overtones and combinations of the LO and ordinary Raman-allowed phonons. The forbidden LO scattering weakens with increasing metallicity of the samples due to the vanishing of the CT gap and the screening of the Frölich interaction. We examine the dependence on incident energy of both the lineshape and center position of the highest frequency two-phonon feature, which can be unambiguously attributed to a pure overtone of an infrared LO vibration. Due to the two-phonon nature of the scattering process the crystal momentum, Q, is no longer restricted to small wavevectors and one can expect to observe effects of phonon dispersion. We find, indeed, changes in the lineshape as the gap is approached, accompanied by a decrease in the center frequency to a value comparable to twice that of the Q∼0 one-phonon LO mode.

Observation of the effects of phonon dispersion on the Fröhlich-interaction-induced second-order Raman scattering in Pb2Sr2PrCu3O8.

The one- and two-phonon Raman-scattering spectrum of single-crystal ${\mathrm{Pb}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{PrCu}}_{3}$${\mathrm{O}}_{8}$ is examined under resonance conditions. Strong features appear in the one-phonon spectrum at the positions of longitudinal optical (LO) infrared modes as the laser energy approaches that of the charge transfer gap. These Fr\"ohlich-interaction-induced modes are accompanied by a second-order spectrum composed of overtones and combinations of the LO and ordinary Raman-allowed phonons. We examine the dependence on incident photon energy of both the line shape and center position of the highest-frequency two-phonon feature, which can be unambiguously attributed to a pure overtone of an infrared LO vibration. Due to the two-phonon nature of the scattering process the crystal momentum q is no longer restricted to small wave vectors and one can expect to observe effects of phonon dispersion. We find, indeed, changes in the line shape as the gap is approached, accompanied by a decrease in the center frequency to a value close to twice that of the q\ensuremath{\approxeq}0 one-LO-phonon (1-LO) mode. A detailed comparison to the free electron theory for two-LO-phonon (2-LO) scattering by Zeyher [Phys. Rev. B 9, 4439 (1974)] is carried out. Relationships between the effective lattice mass characterizing the dispersion of this LO branch and the electron and hole effective band masses are established, and an estimate of the effective electron and hole band masses is made based on the magnitude of the phonon dispersion in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6}$ as measured by neutron-scattering experiments.

Longitudinal phonons and high-temperature heat conduction in germanium

Using the relaxation time approach, the authors present a new analysis of phonon conductivity which shows that at high temperature (T> theta D, the Debye temperature), the longitudinal phonons are the dominant heat carriers in germanium. The present result, which is a consequence of the effect of phonon dispersion on the Callaway integral for lattice thermal conductivity, is contrary to the general belief that transverse phonons carry heat at T> theta D. A qualitative justification has also been given for the three-phonon scattering parameters obtained.

On the distortion wave vector in the blue bronzes

We present X-ray measurements of the distortion wave numbers and their temperature evolution in the blue bronzes K 0.3 MoO 3 and ″ K 0.28 MoO″ 3, the stoichiometry K/Mo of which has been established using structural refinements as well as an electron probe microanalysis. The results show an independence of the wave number upon the alcaline concentration. We find that both samples have the same wave vector Q≈(0, 0.75, 1 2 ) at low temperature, whereas in the quasi-one-dimensional band filling consideration and a Peierls scenario, the wave vector, for a K 0.28 MoO 3 stoichiometry, is expected to be Q = (0, 0.75, 1 2 ) . The results are discussed in terms of either an additional non-stoichiometry or possible warped Fermi surface and bare phonon dispersion effects.

Phonon dispersion effects on non-radiative transitions in solids

Abstract In this paper a new approximation is advanced for the calculation of non-radiative transition rates in a solid for which the electron-phonon coupling is linear. This scheme is exact in both low and high temperature situations and reduces to the Huang -Rhys expression in the single frequency limit. On the basis of numerical calculations, it is concluded that this new approximate scheme is adequate for a quantitative description of the energy gap law and of the temperature dependence of non-radiative decay rates in solids.

Generalised Viscosity and Dislocation Damping Constant in Diatomic Crystalline Solids

AbstractUsing Brailsford's model for the anharmonic dislocation drag, generalized viscosities and the damping constant have been calculated for a diatomic solid, represented by a modified Debye‐Einstein type phonon spectrum. The generalized viscosity and its temperature dependence have been examined in detail. It is shown that the effect of phonon dispersion is to increase the region in which the thermoelastic effect makes an appreciable contribution to the viscosity. Consequently, the dislocation drag constant for the Debye‐Einstein model is found to be enhanced by a factor \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{2}q_D l_A $\end{document} compared with the Debye model (qD is the Debye wave number, lA the mean free path of the acoustic phonons). It is also shown that in general the damping constant is very sensitive to temperature, shape of phonon spectrum and phonon lifetimes and it is difficult to predict its temperature dependence. The Debye‐Einstein model gives B α Tm, where m < 1 for intermediate temperatures and tends to one for high temperatures.

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

The attenuation of longitudinal 1-GHz phonons was measured as a function of temperature in liquid4He at svp and at 23 bar as well as in hcp4He at 36 bar. The lifetime of the phonons which were generated by stimulated Brillouin scattering was determined optically by a probing light pulse. The results in liquid4He are discussed in terms of relaxation processes in the phonon and roton gas and are in good agreement with existing work. The attenuation in hcp4He, which approximately shows aT 4 temperature dependence, is attributed to three-phonon processes with longitudinal thermal phonons. A quantitative comparison with Landau-Rumer theory gives satisfactory agreement with the data. No effect of phonon dispersion on sound attenuation is found down to 0.8 K.

Shapes of Two-Phonon Recombination Peaks in Silicon

The radiative recombination spectrum of excitons in $n$-type Si exhibits structure which has been analyzed in terms of one- and two-phonon processes. A model for radiative recombination of excitons is presented which predicts one-phonon peak shapes which are in good agreement with experiment and two-phonon peak shapes which are in fair agreement with experiment. Calculations are described with particular attention devoted to phonon decoupling approximations. The observed width of the ${\ensuremath{\Delta}}_{1}(25)$ two-phonon peak is accounted for very well by phonon dispersion effects. Neither the ${\ensuremath{\Sigma}}_{1}(60)$ nor the ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}(64)$ two-phonon peak alone can span the observed width of the assigned peak. We conclude that this peak is composite. The calculations provide the following best estimates of the magnitudes (meV) of intervalley electron-phonon matrix elements ${\ensuremath{\Delta}}_{1}(25)\ensuremath{-}261$, ${\ensuremath{\Sigma}}_{1}(48)\ensuremath{-}80$, ${\ensuremath{\Sigma}}_{1}(60)\ensuremath{-}178$, and the intravalley (valence band) matrix element ${\ensuremath{\Gamma}}_{{25}^{\ensuremath{'}}}(64)\ensuremath{-}403$ where the phonons are designated by their symmetry and energy (meV). Also included are certain intermediate results which show the effects of the approximations and permit modifications of the model to be tested without extensive calculation.

Effect of Phonon Dispersion on Heat-Pulse Shape

Effect of Phonon Dispersion on Heat-Pulse Shape