Transport Of Nonequilibrium Phonons Research Articles

Quantitative Analysis of Nonequilibrium Phonon Transport Near a Nanoscale Hotspot

Understanding thermal transport by phonons near nanoscale hotspots is critical for many engineering applications, especially for nanoscale thermal measurements and nanoelectronics. Previous studies usually adopted the gray phonon Boltzmann transport equation to consider ballistic phonon transport or the multitemperature model to consider selective phonon excitation. However, nonequilibrium phonon transport near a nanoscale hotspot cannot be fully captured by either method. In this work, we employ the more rigorous nongray phonon Boltzmann transport equation to investigate phonon transport near nanoscale hotspots. We first consider hotspots in a one-dimensional system with two phonon modes to extract the underlying physics. Thermal transport is found to be less efficient near these hotspots, leading to significantly smaller effective thermal conductivity. The mechanism behind this is that different phonon modes have different temperatures and are therefore not in equilibrium. Nonequilibrium is caused by both the selective electron-phonon interaction and ballistic phonon transport. For relatively large hotspots, nonequilibrium is primarily contributed to by the selective excitation effect. When the hotspot size further reduces, the contribution from ballistic phonon transport becomes increasingly more important. Furthermore, we quantitatively study the thermal transport of laser-heated hotspots in Raman experiments and Joule heating in fin field-effect transistors (FETs) using the nongray phonon Boltzmann transport equation. We find that the measured thermal conductivity of single-layer graphene can be significantly underestimated if the nonequilibrium effect is ignored. Additionally, the peak temperature rise in a silicon fin FET is much larger than that calculated by the heat-diffusion equation.

Nonequilibrium phonon transport across nanoscale interfaces

Despite the ubiquity of applications of heat transport across nanoscale interfaces, including integrated circuits, thermoelectrics, and nanotheranostics, an accurate description of phonon transport in these systems remains elusive. Here we present a theoretical and computational framework to describe phonon transport with position, momentum, and scattering event resolution. We apply this framework to a single-material nanoparticle for which this multidimensional resolution offers insight into the physical origin of phonon thermalization and the length-scale dependent anisotropy of driven phonon distributions. We extend the formalism to handle interfaces and investigate the specific case of semicoherent materials interfaces by computing the coupling between phonons and interfacial strain resulting from a periodic array of misfit dislocations. We calculate the thermal interface conductance within the technologically relevant Si-Ge heterostructures and obtain $G=173.2\phantom{\rule{4.pt}{0ex}}\text{MW}\phantom{\rule{0.16em}{0ex}}{\text{m}}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}{\text{K}}^{\ensuremath{-}1}$, in good agreement with previous experimental and theoretical work. Finally we comment on future applications of our framework including coherent and driven phonon effects in nanoscale materials, which are increasingly accessible via ultrafast, terahertz, and near-field spectroscopies.

Theoretical model of phonon propagation in micro- and nanostructural materials

Peculiarities of the kinetics of weakly nonequilibrium thermal phonons (λph = 10−50 nm) in nanodispersed ceramics are investigated. The features of the phonon spectrum in the wavelength range λph ∼ Rg (where Rg is the average size of a ceramic grain) are studied. The conditions yielding the formation of a gap in the phonon spectrum of nanodispersed materials are analyzed. It is shown that the presence of inclusions with characteristic sizes smaller than the grain size of the parent ceramic material (pores, inclusions of other phases) shifts the gap toward the high-frequency range of the phonon spectrum. Peculiarities of the transport of nonequilibrium phonons during the transition from nano- to microdispersed sizes of the ceramic structure are analyzed.

Kinetics of thermal phonons and the structure of nanodispersed iron-containing corundum-based cermets at liquid-helium temperatures

The kinetics of weakly nonequilibrium subterahertz thermal phonons is studied in nanodispersed iron-containing corundum-based cermets at liquid-helium temperatures. For the chosen method of fabricating cermets (which restricts grain growth), iron inclusions are shown to be described as point trapping centers of phonons. The transport of nonequilibrium phonons is analyzed in a ceramic matrix containing metallic trapping centers.

Dynamics of vibrations in a mixed amorphous-nanocrystalline Si system

We present results of pulsed Raman and phonon-induced luminescence experiments on a mixed amorphous-nanocrystalline silicon system $(a\ensuremath{-}\mathrm{nc}\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}).$ With these experiments, the decay and transport of nonequilibrium phonons in $a\ensuremath{-}\mathrm{nc}\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ was examined and compared with the behavior of phonons of the same frequencies in $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ and $c\ensuremath{-}\mathrm{Si}.$ From the Raman measurements, we find that in the spectral region of the TO vibrations in the crystallites $(505--520 {\mathrm{cm}}^{\ensuremath{-}1}),$ phonons have shorter decay times than the TO phonons in $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H},$ but longer than in $c\ensuremath{-}\mathrm{Si}.$ In addition, the lifetimes increase with decreasing frequency, from less than 10 ns at $515 {\mathrm{cm}}^{\ensuremath{-}1}$ to $\ensuremath{\sim}30 \mathrm{ns}$ at $505 {\mathrm{cm}}^{\ensuremath{-}1}.$ We further show that phonons with a frequency of $\ensuremath{\sim}150 {\mathrm{cm}}^{\ensuremath{-}1}$ in $a\ensuremath{-}\mathrm{nc}\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ have longer lifetimes than in $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H} (\ensuremath{\tau}<10 \mathrm{ns}).$ Finally, the diffusion of $29\ensuremath{-}{\mathrm{cm}}^{\ensuremath{-}1}$ phonons through the $a\ensuremath{-}\mathrm{nc}\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ and $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ material was examined in phonon-induced luminescence experiments. Transport through the $a\ensuremath{-}\mathrm{nc}\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ film appears to be much slower than through the $a\ensuremath{-}\mathrm{S}\mathrm{i}:\mathrm{H}$ layer. We explain these results as effects of phonon confinement, and relate them to the extremely long phonon lifetimes found in Raman experiments on $a\ensuremath{-}\mathrm{Si}(:\mathrm{H}).$

The transport of non-equilibrium phonons in highly disordered ferroelectric ceramics

The phonon transport processes in ferroelectric crystals and ceramics was studied experimentally. It was shown that in BaTiO 3 crystals the phonon scattering is controlled by domain walls. For ferroelectrics with diffusive phase transition the effective diffusion coefficient was found to be D eff∝ T −5 for temperatures 1.7–3.8 K. This dependence is in good correlation with the “plateau” region in thermal conductivity.

Nonequilibrium phonon transport in amorphous layers.

Transport of nonequilibrium phonons in amorphous layers is studied. Inelastic scattering rates are calculated within the framework of the soft-potential model. It is shown that these rates can be comparable to the ones of elastic resonant scattering and are many orders of magnitude larger than those of inelastic phonon-phonon processes in crystals. The strength of the inelastic scattering is demonstrated to influence strongly the phonon signal. In particular, down-conversion effects an increase of the occupation numbers of low-frequency phonons, while up-conversion may prevent an observation of localization of high-frequency ones. Stationary phonon transport from the heat generator through the amorphous layer is shown to exhibit a strongly non-Planckian phonon signal. For the case of a strong pulse excitation of an amorphous sample the parameters of phonon transport allow the possibility of a ``hot-spot'' regime. The ``hot-spot'' evolution is shown to differ from the one in crystalline structures by the presence of slow relaxation phenomena. Some details concerning mode-conversion processes are considered. Effective inelastic surface scattering of phonons in crystalline samples, observed in experiments, is shown to be compatible with the model of a disordered near-surface layer. The theoretical results are shown to be consistent with existing experimental data.

Flourescence-line-narrowing and Monte Carlo studies of spectral transport of nonequilibrium phonons in ruby

Fluorescence line narrowing (FLN) in the three-level scheme 4A2-E(2E)-2A(2E) is used to probe, with high resolution, the spectrum of nonequilibrium 29 cm-1 phonons in near resonance with the E(2E)-2A(2E) transition in ruby following injection with a heater. The shape of the 29 cm-1 phonon spectrum is found to change dramatically with time due to frequency-dependent imprisonment and spectral transport. The development of the phonon spectrum is reproduced by Monte Carlo simulations following the itinerary of a phonon. The simulations explicitly take into account inelastic scattering as a result of one-site resonant Roman scattering by optically excited exchange-coupled Cr3+ pairs until escape out of the optically pumped zone.

A model of quasi-resonant phonon propagation

The influence of the electron-lattice interaction on the transport of non-equilibrium phonons is studied. The interaction model consists of a system of electronic two-level centres coupled to acoustic phonons. In this case it can be shown that phonons with energies comparable with the electronic level splitting (quasi-resonant) propagate more easily in the crystal than others which are far from resonance. The time dependence of the spatial distributions and the lifetimes of phonons with different frequencies are calculated and discussed.