Phonon Distribution Research Articles

Kapitza thermal conductance at the interface between Lennard-Jones crystals using non-equilibrium molecular dynamics simulations

We characterize the thermal Kapitza conductance between Lennard-Jones solids using non-equilibrium molecular dynamics simulations. We consider a series of perfect interfaces between mass-mismatched solids. We show that both the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) fail to predict the interfacial conductance even for large acoustic mismatched solids. This poor agreement may be explained by the use of equilibrium distributions of phonons in the expression of the conductance. On the other hand, we show that an extension of AMM taking into account the out-of-equilibrium phonon distribution on both sides of the interface leads to a good agreement with the simulation results, even for interfaces between almost similar materials. This opens the way to understand interfacial heat transport across real semi-conductors and dielectrics.

Lattice controlled transport in quantum wires at low temperatures

Theory of acoustic scattering rate of the carriers in a quantum wire has been developed under the condition of low temperature when the approximations of the traditional theory are hardly valid. The scattering rates thus obtained are then used to estimate the zero-field mobility characteristics in a narrow channel GaAs–GaAlAs quantum wire. On comparison with other available results it is revealed that the finite energy of the acoustic phonons and the complete phonon distribution without any truncation lead to significantly different transport characteristics at low temperatures.

Non-equilibrium superconductivity in quantum-sensing superconducting resonators

Low temperature microwave superconducting resonators (SRs) are attractive candidates for producing quantum-sensitive, arrayable energy or power detectors for astrophysical and other precision measurement applications. Their readout uses a microwave probe signal with quanta of energy well below the threshold for pair-breaking in the superconductor. We have calculated the non-equilibrium quasiparticle and phonon distributions generated by the photons of the probe signal of a resonator operating well below its superconducting transition temperature Tc as the absorbed probe power was changed using the coupled kinetic equations described by Chang and Scalapino. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from their thermal equilibrium value for typical readout powers. From the driven quasiparticle distribution functions, the driven quasiparticle number densities and lifetimes were calculated. An effective temperature to describe the driven quasiparticles was defined. The non-equilibrium lifetimes were compared to the distribution-averaged thermal lifetimes at the effective temperature and good agreement was found typically within a few per cent. We used the non-equilibrium quasiparticle distribution to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter S21 of the SR as a function of absorbed power were found. The non-equilibrium S21 cannot be accurately modeled by a thermal distribution even at its own elevated temperature, having a higher quality factor in all cases studied, although for low absorbed powers the two effective temperatures are similar. From the non-equilibrium lifetimes and number densities we determined the achievable noise equivalent power (NEP) of the resonator used as a power detector as a function of absorbed microwave power. Simpler expressions to evaluate the effective quasiparticle temperature as a function of absorbed power have also been derived. We conclude that multiple photon absorption from the microwave probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator at temperatures well below Tc.

Negative differential resistance associated with hot phonons

We predict the existence of a hot-phonon negative differential resistance (NDR) in GaN. We show that this is a consequence of a wave-vector dependence of lifetime caused by the effect of coupled plasmon-phonons. Anti-screened long-wavelength modes have shorter lifetimes, screened shorter-wavelength modes have longer lifetimes, the boundary between them being determined by the temperature-dependent Landau damping. The higher density of screened modes means that the average lifetime is of order of the lifetime of the bare phonon. Its increase with electron temperature (field) is responsible for the NDR. We also find that the momentum relaxation rate (MRR) associated with the absorption of phonons can be negative in some circumstances, which can be seen to be a consequence of the non-uniform distribution of hot phonons in wave-vector space. We also point out that the ultra-short lifetimes sometimes deduced from experiment should more properly be regarded as electron energy- relaxation times.

Phonon engineering in nanostructures: Controlling interfacial thermal resistance in multilayer-graphene/dielectric heterojunctions

Using calculations from first principles and the Landauer approach for phonon transport, we study the Kapitza resistance in selected multilayer graphene/dielectric heterojunctions (hexagonal BN and wurtzite SiC) and demonstrate (i) the resistance variability (∼50−700×10−10 m2K/W) induced by vertical coupling, dimensionality, and atomistic structure of the system and (ii) the ability of understanding the intensity of the thermal transmittance in terms of the phonon distribution at the interface. Our results pave the way to the fundamental understanding of active phonon engineering by microscopic geometry design.

Phonon thermal conductivity of GaN nanotubes

We theoretically investigated the phonon thermal conductivity of gallium nitride (GaN) nanotubes with diameters ranging from a few nanometers to 120 nanometers using the Boltzmann transport equation and took into account the phonon dispersion relations of the nanotubes and the influence of boundary scattering on the non-equilibrium phonon distribution. The calculation results show that the phonon thermal conductivity of GaN nanotubes is much lower than that of the bulk counterpart and it depends on the thickness, inner and outer diameters, and surface roughness of the nanotubes. A small thickness or a large surface roughness leads to a small thermal conductivity. The reduction of the phonon thermal conductivity of the nanotubes is mainly due to the decrease of the phonon group velocity, change of the phonon relaxation rate, and enhancement of phonon boundary scattering. The understanding and results on the thermal conductivity obtained in this work are important for the optoelectronic devices based on GaN nanotubes and nanowires, and the developed calculation method on the phonon thermal conductivity is generally applicable and can be used for other nanotube systems.

Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times

A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time model employs a single-mode relaxation time, but the relaxation time is derived from detailed consideration of three-phonon interactions satisfying conservation rules, and is a function of wave vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior. A critical issue in the model development is the role of three-phonon normal (N) scattering processes. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulations by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted thermal conductivities of bulk silicon and silicon thin films with experimental measurements. The model is then used for simulating thermal transport in a silicon metal-oxide-semiconductor field effect transistor (MOSFET) and leads to results close to the full-scattering model, but uses much less computation time.

Derivation of second-order nonlinear optical conductivity by the projection-diagram method

A projection-diagram method is introduced for optical conductivity with lineshape functions, which takes into account the population criterion that the electron and phonon distribution functions are multiplicatively combined along with the energy conservation factors for proper interpretation of emission and absorption of phonons and photons in all the processes of electron transitions. It is further shown that the second order nonlinear optical conductivity of the system of electrons interacting with phonons, obtained using this method, is identical with that derived by using the state dependent projectors and the KC reduction identities [J. Phys. A: Math. Theor. 43, 165203 (2010)]. We expect that this method can reduce the amount of many-body calculation and can be of help in providing physical intuition into solid state quantum dynamics and representing perturbation expressions for such systems.

The lattice Boltzmann Peierls Callaway equation for mesoscopic thermal transport modeling

The lattice Boltzmann Peierls Callaway (LBPC) method is a recent development of the versatile lattice Boltzmann formalism aimed at a numerical experiment on mesoscale thermal transport in a multiphase phonon gas. Two aspects of mesoscopic thermal transport are discussed: the finite phonon mean free path and the interface thermal resistance. Based on the phonon momentum screening length measured in the LBPC computational apparatus, the validity of the Umklapp collision relaxation time in the Callaway collision operator is examined quantitatively. The discrete nature of the spatio-temporal domain in the LBPC method, along with the linear approximation of the exponential screening mechanism in the Callaway operator, reveals a large discrepancy between the effective phonon mean free path and the analytic phonon mean free path when the relaxation time is small. The link bounce back interface phonon collision rule is used to realize the interface thermal resistance between phonon gases with dissimilar dispersion relations. Consistent with the Callaway collision operator for the bulk phonon dynamics, the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution uniquely defined by the energy conservation principle. The interface thermal resistance is linearly proportional to the relaxation time of the proposed phonon interface collision rule.

Energy Down-Conversion and Thermalization in Metal Absorbers

Absorbers play an important role in all radiation detectors, providing effective energy absorption, fast relaxation and spatial expansion of the excitation volume. A review of the details of energy down-conversion in metal absorbers, both normal metals and superconductors, is given. We discuss the initial absorption of a quantum of energy and ejection of a single photoelectron, followed by fast energy down-conversion via the electron-electron and electron-phonon interactions. We describe the spatial and spectral evolution of the distributions of electronic excitations and phonons, together with the mean energy loss and fluctuations. We also review some recent results regarding thermalization in superconductors at low temperatures, a poorly understood area but one which is crucial for many low temperature devices.

AN ANALOG FLUID MODEL FOR SOME TACHYONIC EFFECTS IN FIELD THEORY

We consider the sound radiation from an acoustic point-like source moving along a supersonic ("space-like") trajectory in a fluid at rest. We call it an acoustic "tachyonic" source. We describe the radiation emitted by this supersonic source. After quantizing the acoustic perturbations, we present the distribution of phonons generated by this classical tachyonic source and the classical wave interference pattern.

Effects of electron-phonon coupling on Landau levels in graphene

We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency ${\ensuremath{\omega}}_{E}$ not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies ${E}_{n}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}_{E}$, where ${E}_{n}$ is the energy of the $n$th LL. If one of these new peaks lies sufficiently close to an LL, it causes the LL to split in two; if the system contains an energy gap, an LL may be split in three. The new peaks occur outside the interval $(\ensuremath{-}{\ensuremath{\omega}}_{E},{\ensuremath{\omega}}_{E})$, leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results.

Ising instability of a Holstein phonon mode in graphene

We study the thermal distribution of phonons in a graphene sheet. Due to the two electronic bands there are two out-of-plane phonon modes with respect to the two sublattices. One of these modes undergoes an Ising transition by spontaneously breaking the sublattice symmetry. We calculate the critical point, the renormalization of the phonon frequency and the average lattice distortion. This transition might be observable in Raman scattering and in transport properties.

Multiscale thermodynamics and mechanics of heat

Heat transfer is investigated on three levels of description: Fourier, Cattaneo, and Peierls. The microscopic nature of the heat that becomes important, in particular in nanoscale systems, is characterized by a vector field related to the heat flux on the Cattaneo level and by the phonon distribution function on the Peierls level. All dynamical theories discussed in the paper are fully nonlinear and all are proven to be compatible among themselves, with equilibrium thermodynamics, and with mechanics. An investigation of the first two compatibilities gives rise to potentials having the physical interpretation of nonequilibrium entropies. The compatibility with mechanics is manifested by the Hamiltonian structure of the time-reversible part of the time evolution.

Kapitza resistance in the lattice Boltzmann-Peierls-Callaway equation for multiphase phonon gases

The interface thermal resistance becomes more and more important as device miniaturization for better performance renders a large surface-to-volume ratio and invariably requires a device design with multiple materials inducing thermal interfaces across the material heterogeniety. Toward developing a comprehensive computational methodology for thermal transport prediction, incorporating the interface effects in a heterogeneous medium, a novel boundary collision rule is devised in the lattice Boltzmann computational scheme to realize a thermal interface between phonon gases with dissimilar dispersion relations. Consistent with the Callaway collision operator for Umklapp process, the interface phonon collision process is regarded as a linear relaxation mechanism toward the local pseudo-equilibrium phonon distribution, which is uniquely defined by the energy conservation principle. The Kapitza length and the interface thermal resistance are determined by the relaxation parameter and the local phonon properties. The implementation of the proposed mesoscopic boundary collision rule in the lattice Boltzmann computational framework provides a methodology of predicting the thermal properties of a heterogeneus medium incorporating both normal and Umklapp collision processes of phonon.

β-Zn4Sb3 Nanocantilevers and Their Thermoelectric Properties

Cantilever-like nanostructures of β-Zn4Sb3 were firstly obtained from ZnO nanocantilevers and stibine using vapor deposition. The as-fabricated β-Zn4Sb3 products are characterized by different instruments and morphologies and the size of the samples is strongly dependent on ZnO nanocantilevers because they act as a source and sacrificial template. A typical width and length of the as–synthesized β-Zn4Sb3 nanocantilevers are ∼100 nm and ∼2 μm, respectively. The bulk β-Zn4Sb3 composed of nanocantilevers was tested by independent measurements of thermoelectric properties, which was very good with a ZT value of 1.49 at 675 K—the best—which may originate from local properties of phonon and electron distribution.

Impact of Self-Heating Effect on the Electrical Characteristics of Nanoscale Devices

Hot phonon generation and its impact on the current conduction in a nanoscale Si-device are investigated using a Monte Carlo simulation technique. In the quasi-ballistic transport regime, electrons injected from the source lose their energies mainly by emitting optical phonons in the drain. Due to the slow group velocity of the optical phonons, the efficiency of the heat dissipation is so poor that a region with a nonequilibrium phonon distribution, i.e., a hot spot, is created. In this study, we have implemented the hot phonon effect in an ensemble Monte Carlo simulator for the electron transport, and carried out the steady state simulations. Although it is confirmed that the optical phonon temperature in the hot spot is larger than that of acoustic phonons by > 100 K, the electron current density is not significantly affected. The local heating would degrade the hot electron cooling efficiency and the parasitic resistance in the drain, but they have a minor impact on the quasi-ballistic electron transport from the source to the drain.

LO-Phonon Band Filling by Means of Charge Carriers Accelerated in Electric Fields

Non-thermal phonons attract increasing attention in the theory of electron and hole dynamics in crystals subjected to high electric fields. Of special interest is the population inversion of the bands of lattice vibrations, e.g., increasing number of longitudinal optical (LO) phonons relative to the lower-energy (transverse optical — TO, longitudinal acoustic — LA, or transverse acoustic — TA) modes. Inversion is the necessary condition for constructing the phonon-difference laser [1] — the device harnessing lattice vibrations for midor far-infrared light generation. The term of phonon laser is sometimes misused for designation of ultrasound generator based on stimulated emission and reflection of mechanical waves [2]. We are interested in such situations when a higher-energy phonon mode transforms to the lower-energy one, and the difference of phonon energies gives rise to photon emission. Seeking to reveal the conditions of creating the phonon-difference laser, we investigate the changes of phonon distributions among the LO and lower bands under influence of charge carriers accelerated in high electric fields. We use Monte Carlo (MC) method for modeling the carrier and lattice dynamics. Simulation includes charge carrier scattering on LO and LA phonons, piezoelectric and impurity ion potentials. Among the examined crystals (Si [3], GaN [4], InSb [5], and others [6]), the covalent-bond n-type Si crystals are particularly interesting because LO phonons are accumulated there predominantly due to the g-type electron umklapp (electron transfer between the equivalent valleys). The process is characteristic of many other indirect-gap semiconductors. In the direct-gap polar semiconductors, LO

Effects of dislocations on small signal high frequency hot electron mobility in n-GaN at low and high temperatures under high magnetic fields including hot phonon effect

The small signal high-frequency ac mobility of hot electrons in n-GaN in the extreme quantum limit at low- and high-temperatures has been calculated considering the non-equilibrium phonon distribution as well as the thermal phonon distributions. The energy loss rate has been calculated considering the dominance of the piezo electric coupling scattering and the polar optical phonon scattering while the momentum loss rate has been calculated considering the acoustic phonon scattering via deformation potential and the piezo electric coupling and the dislocation scattering.

Phonon‐assisted exciton spin relaxation in (In,Ga)As/GaAs quantum dots

AbstractIn this work, we study the temperature‐dependent spin relaxation of exciton‐bound carriers in (In,Ga)As/GaAs quantum dots. The exciton population mapped by a time‐resolved differential transmission signal reveals a decay on two different time scales, reflecting the fractions of optically active and inactive excitons. The underlying exciton states are split from each other by the exchange interaction. The phonon‐assisted spin‐orbit interaction induces spin flips of an exciton‐bound electron or hole which convert the exciton populations into each other. The temperature‐dependent relaxation rate follows a thermal phonon distribution. Deviations indicate that two‐phonon processes involving higher orbitals may contribute significantly to the total relaxation process. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)