Decay Of Optical Phonons Research Articles

Temperature dependence of Raman scattering in filled double-walled carbon nanotubes

Four types of filled double-walled carbon nanotubes (DWNTs) (Se@DWNT; Te@DWNT; HgTe@DWNT; and PbI2@DWNT) have been studied by high-resolution transmission electron microscopy and micro-Raman spectroscopy in the temperature interval from 80 to 700 K employing 785 nm excitation wavelength. The temperature dependence of the dominant bands (D-band, G-band, and the (2D)-band) are analyzed in terms of the model developed by Klemens, Hart, Agraval, Lax, and Cowley and extended by Balkanski for anharmonic decay of optical phonons. The quasiharmonic frequencies and the anharmonicity constants were obtained from the temperature dependences of the analyzed Raman bands. The findings were compared to analogous study for empty DWNTs. The strength of the van der Waals interaction between the guest material and the carbon nanotube (CNT) estimated through the quasiharmonic frequencies was found to decrease in the following order: Se@DWNT; Te@DWNT; PbI2@DWNT, and HgTe@DWNT. In agreement with this, the anharmonicity due to the phonon–phonon interactions was found to decrease in the same order.

Thermal conductivity of silicon bulk and nanowires: Effects of isotopic composition, phonon confinement, and surface roughness

We present a rigorous analysis of the thermal conductivity of bulk silicon (Si) and Si nanowires (Si NWs) which takes into account the exact physical nature of the various acoustic and optical phonon mechanisms. Following the Callaway solution for the Boltzmann equation, where resistive and nonresistive phonon mechanisms are discriminated, we derived formalism for the lattice thermal conductivity that takes into account the phonon incidence angles. The phonon scattering processes are represented by frequency-dependent relaxation time. In addition to the commonly considered acoustic three-phonon processes, a detailed analysis of the role of the optical phonon decay into acoustic phonons is performed. This optical phonon decay mechanism is considered to act as acoustic phonon generation rate partially counteracting the acoustic phonon scattering rates. We have derived the analytical expression describing this physical mechanism which should be included in the general formalism as a correction to the resistive phonon-point-defects and phonon-boundary scattering expressions. The phonon-boundary scattering mechanism is taken as a function of the phonon frequency, incidence angles, and surface roughness. The importance of all the mechanisms we have involved in the model is demonstrated clearly with reference to reported data regarding the isotopic composition effect in bulk Si and Si NW samples. Namely, our model accounts for previously unexplained experimental results regarding (i) the isotope composition effect on the thermal conductivity of bulk silicon reported by Ruf et al. [Solid State Commun. 115, 243 (2000)], (ii) the size effect on κ(T) of individual Si NWs reported by Li et al. [Appl. Phys. Lett. 83, 2934 (2003)], and (iii) the dramatic decrease in the thermal conductivity for rough Si NWs reported by Hochbaum et al. [Nature (London) 451, 163 (2008)].

Stress and its effect on optical properties of AlN nanorods

The stress states in AlN nanorods deposited on Si and its effect on optical properties have been investigated by means of Raman scattering and photoluminescence methods. The observed frequency downshift and linewidth broadening from temperature-dependent Raman scattering can be well described by an empirical relationship taking into account the contributions of the thermal expansion and decay of optical phonons. The phonon-energy difference of the E2(high) mode between the stress-free bulk-AlN and AlN nanorods appears to increase with increasing temperature, demonstrating that differential thermal expansion between the Si-substrate and AlN nanorods is the key parameter reflecting the stress in the nanorods.

Plasmon-enhanced heat dissipation in GaN-based two-dimensional channels

Decay of nonequilibrium longitudinal optical (LO) phonons is investigated at room temperature in two-dimensional electron gas channels confined in nearly lattice-matched InAlN/AlN/GaN structures. A nonmonotonous dependence of the LO-phonon lifetime on the supplied electric power is reported for the first time and explained in terms of plasmon–LO-phonon resonance tuned by applied bias at a fixed sheet density (8×1012 cm−2). The shortest lifetime of 30±15 fs is found at the power of 20±10 nW/electron.

Directional dependence of AlN intrinsic complex dielectric function, optical phonon lifetimes, and decay channels measured by polarized infrared reflectivity

The directional dependence of AlN intrinsic complex dielectric function, the phonon lifetimes, and decay channels are investigated by means of polarized infrared reflectivity measurements on several facets of self-nucleated wurtzite AlN crystal of high crystalline quality. The measurement technique and the AlN single crystal used have been selected with the purpose to reduce, as much as possible, any instrumental-based effects as well as phonon scattering mechanisms due to defects. The experimental arrangements necessary to detect well-defined crystallographic orientations and phonons are detailed. The dielectric parameters and the phonon lifetimes are precisely determined as functions of the crystallographic direction from a careful Kramers–Kronig and damped Lorentz oscillator analysis. The ordinary (ε∞⊥) and extraordinary (ε∞∥) high frequency dielectric constants for high quality AlN crystal are found to be 3.93 and 4.05, respectively, and the ordinary (ε0⊥) and extraordinary (ε0∥) static dielectric constants are found to be 7.37 and 8.60, respectively. Our values obtained for the pure character phonon lifetimes are in good agreement with Raman measurements when these are obtained with the necessary care to eliminate linewidth broadening due to the finite slit width. The lifetime of a transversal phonon is found to increase with increasing the phonon energy, while that of a longitudinal phonon is found to decrease with increasing the phonon energy. Based on these observations, preferential decay channels for the AlN phonons are estimated. The results show that in the case of AlN, the widely assumed symmetric optical phonon decay into two phonons of lower energy cannot be justified for the zone center longitudinal phonons.

Micro-Raman scattering of selenium-filled double-walled carbon nanotubes: Temperature study

Selenium-filled double-walled carbon nanotubes (Se@DWNT) have been studied by high resolution transmission electron microscopy (HRTEM) and micro-Raman spectroscopy in the temperature interval from 80to600K employing 785nm excitation wavelength. The temperature dependences of the dominant bands (G-band and G′-band) are analyzed in terms of the model developed by Klemens [Phys. Rev. 148, 845 (1966)], Hart et al. [Phys. Rev. B 1, 638 (1970)], Cowley [J. Phys. (France) 26, 659 (1965)] and extended by Balkanski et al. [Phys. Rev. B 26, 1928 (1983)] for anharmonic decay of optical phonons. The findings were compared to analogous study for empty double-walled carbon nanotubes (DWNTs). The DWNT interatomic force constant modification as a result of the presence of the Se atoms inside the tubes is revealed through larger anharmonicity constants describing the temperature dependences of the G′-band and the inner tube tangential modes (G-band).

Polaron relaxation in a quantum dot due to anharmonic coupling within a mean-field approach

We study the electronic relaxation in a quantum dot within the polaron approach by focusing on the reversible anharmonic decay of longitudinal optical (LO) phonons forming the polaron into longitudinal-acoustic (LA) phonons. The coherent coupling between the LO and LA phonons is treated within a mean-field approach. We derive a temperature-dependent interlevel coupling parameter, related to the Gr\"uneisen parameter and the thermal-expansion coefficient, which characterizes an effective decay channel for the electronic (or excitonic) states. Within this theory, we obtain a characteristic anharmonic decay time of 1 ns, 2--3 orders of magnitude longer than previous predictions based on the Fermi's Golden Rule. We suggest that coherent relaxation due to carrier-carrier interaction is an efficient alternative to the (too slow) polaron decay.

Birth and decay of coherent optical phonons in femtosecond-laser-excited bismuth

The transient reflectivity of bismuth crystal excited by a 45 fs laser pulse in the near-infrared range has been recovered with an accuracy of ${10}^{\ensuremath{-}5}$, at initial sample temperatures ranging from 50 to 510 K, and at pump fluences from $2\text{ }\text{mJ}/{\text{cm}}^{2}$ to $21\text{ }\text{mJ}/{\text{cm}}^{2}$. The coherent phonon excitation and decay processes were imprinted into the time-dependent reflectivity and this allows us to uncover the temporal phonon history preceding the structural transformation of solid Bi. Analysis showed that the first coherent atomic displacement was produced by the polarization force and the electron pressure force during the laser pulse, and that manifests itself by a negative change in the reflectivity. The frequency of the subsequent reflectivity oscillations was chirped, redshifted from the initial value due to the lattice heating. The amplitude decreased gradually while electrons transferred their energy to the lattice. Heating and thermal expansion of the lattice transformed the initially coherent harmonic vibrations of atoms into strongly nonlinear chaotic motion that signifies the onset of disordering of the solid. This process was identified through measurement of the damping rate of the reflectivity oscillations and interpretation of this rate as the decay rate of an optical phonon into two acoustic phonons. The analysis of the reflectivity oscillations provides evidence that the overheated solid experiences only the onset of the solid-liquid phase transition but did not proceed into the liquid phase. General relations between the laser-exerted forces, the atomic motion, and the optical parameters were established. The proposed theory reproduces well the measured transient reflectivity across a wide range of crystal temperatures and laser excitation fluences.

Hot optical phonon decay in carbon nanotubes

We simulate hot optical phonon decay in small diameter (<0.7 nm) carbon nanotubes, solving the phonon Boltzmann transport equation using Monte Carlo methods incorporating the full phonon spectrum and phonon-phonon scattering. Results indicate decay times inversely proportional to the lattice temperature with negligible dependence on hot phonon polarization/wave vector or nanotube diameter and chirality. Nonequilibrium optical phonons with energies of ∼0.2 eV decay by emitting two ∼0.1 eV optical phonons, corresponding to out-of-plane polarization modes in graphitic materials. Modes polarized perpendicular to the nanotube axis may allow manipulation of hot phonon effects by the near environment of the nanotube.

Role of optical phonon in Ge thermal conductivity

We report on the contribution of optical phonon decay into acoustic phonon to the thermal conductivity [k(T)] of semiconductors. We have considered this mechanism as an acoustic phonon generation rate within the full modified Callaway theory to accurately describe experimental data of k(T) for Ge as a function of isotopic composition. The proposed model requires only one adjustable parameter for each mode. Our approach to describe k(T) in semiconductors is found to provide much better agreement with the experimental results than previously reported models, which did not account for the role of optical phonon.

Lifetime of optical phonons in fs-laser excited bismuth

This paper presents experimental and theoretical results on the temperature-dependent optical response of a single crystal of bismuth to excitation by femtosecond laser pulses. We demonstrate that the measured damping rate of the transient reflectivity oscillations relates to the lifetime of optical phonons. The lifetime is the inverse rate of the decay of optical phonons into two acoustic phonons. This lifetime also indicates the approach to the vibration instability (catastrophe) threshold that manifests the beginning of the disordering of a solid crystal and transition to a liquid state. We observe the red shift of phonon frequency, which increases with the rise of the initial lattice temperature. The red shift is different from the previously observed red shift proportional to the electron temperature, and thus to the excitation laser fluence. The coherent phonon excitation process imprinted into the initial change in the reflectivity and the following reflectivity oscillations allowed us to uncover the temporal phonon history preceding the structural transformation of solid Bi.

Contribution of the decay of optical phonons into acoustic phonons to the thermal conductivity of AlN

The thermal conductivity along two high-symmetry directions of several aluminum nitride (AlN) single crystals differing in their mass-fluctuation phonon-scattering parameter is described accurately in the full temperature range by taking into account the contribution of optical phonon decay into acoustic phonon. The accuracy of the proposed model shows the fundamental role of the optical phonon in the thermal conductivity of semiconductor materials.

Electron Transport and Terahertz Gain in Quantum-Dot Cascades

Electron transport through quantum-dot (QD) cascades was investigated using the formalism of nonequilibrium Green's functions within the self-consistent Born approximation. Polar coupling to optical phonons, deformation potential coupling to acoustic phonons, as well as anharmonic decay of longitudinal optical phonons were included in the simulation. A QD cascade laser structure comprising two QDs per period was designed and its characteristics were simulated. Significant values of population inversion enabling lasing in the terahertz frequency range were predicted, with operating current densities being more than an order of magnitude smaller than in existing terahertz quantum-well-based quantum-cascade lasers.

Effects of high carrier densities on phonon and carrier lifetimes in Si by time-resolved anti-Stokes Raman scattering

The relaxation times T1 of nonequilibrium populations of elementary excitations in Si are studied by time-resolved Raman scattering using a subpicosecond pump-probe method. Incoherent anti-Stokes Raman scattering is used to monitor the decay of the nonequilibrium populations of holes and the generation and decay of zone-center longitudinal optical (LO) phonons. At lower levels of laser excitation, hole and LO phonon T1 lifetimes are less than 0.2ps and greater than 1.6ps, respectively. At higher laser intensities, the lifetime of holes increases and the lifetime of LO phonons decrease toward a common value of T1∼0.4ps.

Temperature dependence of Raman scattering in GaMnN

A detailed investigation of temperature-dependent Raman scattering has been carried out on ion-implanted GaMnN with different Mn doses. The observed frequency downshift and linewidth broadening with increasing temperature can be well described by a model taking into account the contributions of the thermal expansion and decay of optical phonons into two and three phonons of lower energy. The authors have demonstrated clear dependence of the phonon frequency, linewidth, and decay process on the Mn concentration in GaMnN, which is found to be closely related to the crystal structure.

Monte Carlo simulation of hot phonon effects in resonant-phonon-assisted terahertz quantum-cascade lasers

We study the influence of nonequilibrium optical phonons on the electron transport in resonant-phonon-assisted terahertz (THz) quantum-cascade lasers (QCLs). The hot phonon effect is included in the Monte Carlo simulation by introducing a time constant accounting for the decay of polar optical phonons into other phonon modes. We find that nonequilibrium polar optical phonons may modify the electron-phonon interaction, affect the electron distribution in different subbands, and consequently change the device current. We conclude that the hot phonon effect should be taken into account in the study of the transport properties of resonant-phonon-assisted THz QCLs.

InP acoustic cavity phonon spectra probed by Raman scattering

We present a Raman scattering study of the phonon spectra of an InP acoustic phonon cavity. ${\mathrm{Ga}}_{0.47}{\mathrm{In}}_{0.53}\mathrm{As}∕{\mathrm{Al}}_{0.48}{\mathrm{In}}_{0.52}\mathrm{As}$ phonon mirrors, lattice matched with InP, are used for the acoustic phonon confinement. High-resolution backscattering Raman measurements evidence a doubling of the folded acoustic phonon spectra. Photoelastic model calculations, with a continuum model for the acoustic vibrations that include the appropriate boundary conditions at the structure-air interface, are presented to interpret the data. The Raman spectra are shown to be highly sensitive to the details of the structure, thus allowing a proper characterization of the device. We found that the InP cavity longitudinal optical phonon linewidth is increased by residual strain and disorder, but that the anharmonic contribution is substantial at room temperature. This implies that acoustic cavities could be used for optical phonon decay time engineering in InP optoelectronic devices.

The operation threshold of a double barrier phonon laser

We make an adaptation of laser modeling equations to describe the behavior of a phonon laser (saser). Our saser consists of an AlGaAs/GaAs double barrier heterostructure designed to generate an intense beam of transversal acoustic (TA) phonons. To study our system, we begin with a Hamiltonian that describes the decay of primary longitudinal optical phonons (LO1) into secondary (LO2) and TA (LO1→LO2+TA) and its inverse process (recombination). Using this Hamiltonian, a set of coupled equations of motion for the phonons is obtained. We also consider the interaction between the phonons and its reservoirs. These interactions are introduced in the equations of motion leading to a set of coupled Langevin equations. In order to obtain an expression to describe our saser, we apply, in the Langevin equations, an adiabatic elimination of some variables of the subsystem. Following the method above we obtain the value of the injection threshold for the operation of our phonon laser. At this threshold occurs a phase transition from a disordered to a coherent state. It is shown that a big “optical” pumping is not necessary to get a sasing region.

Effects of stimulated optical phonon decay on hot carriers in GaAs

We have considered energy transfer from highly nonequilibrium electron gas to crystal lattice via emission of high-frequency longitudinal optical (LO) phonons and their subsequent transformations. At high intensity of electron excitation, the daughter LA phonons resulting from LO-phonon decay accumulate in considerable numbers and cause the LO-phonon decay to be a stimulated process. The stimulated decay effectively decimates the LO phonons and thus prevents their reabsorption by the electrons. These effects being incorporated in description of the electron–phonon kinetics, we have obtained considerable intensification of energy transfer from the electron subsystem. We also qualitatively discuss the effects of stimulation for alternative channels of LO-phonon decay.

Temperature dependence of optical phonon lifetimes in ZnSe

Temperature-dependent Raman scattering experiments were performed on the 〈111〉 face of crystallin ZnSe to estimate the phonon lifetimes for the LO and TO phonons for temperatures between 20 and 300 K. The lifetimes at higher temperatures are mainly due to the anharmonic decay of optical phonons into low-energy phonons. The temperature-independent contributions from inherent crystal defects and from boundary scattering become comparable to the phonon scattering contribution at lower temperatures. The temperature dependence of the population of the acoustic mode (2TA) is found to follow Bose-Einstein statistics.