Nonequilibrium Phonon Population Research Articles

Ultrafast electron diffuse scattering as a tool for studying phonon transport: Phonon hydrodynamics and second sound oscillations.

Hydrodynamic phonon transport phenomena, like second sound, have been observed in liquid helium more than 50 years ago. More recently second sound has been observed in graphite at over 200 K using transient thermal grating (TG) techniques. In this work, we explore signatures of phonon hydrodynamic transport and second sound oscillations in ultrafast electron diffuse scattering patterns, which can provide time, momentum, and branch resolved information on the state-of-excitation of the phonon system beyond that available through TG experiments. We use the density functional theory and solve the Boltzmann transport equation to determine time-resolved non-equilibrium phonon populations and model phonon transport in graphite. This model also provides the information necessary to calculate the time evolution of one-phonon structure factors and diffuse scattering patterns during thermal transport covering ballistic, diffusive, and hydrodynamic regimes where the effect of a second sound oscillation on the phonon distribution is observed. Direct measurements of how the phonon distribution varies in time and space in various thermal transport regimes should yield new insights into the fundamental physics of the underlying processes.

Hidden phonon highways promote photoinduced interlayer energy transfer in twisted transition metal dichalcogenide heterostructures.

Vertically stacked van der Waals (vdW) heterostructures exhibit unique electronic, optical, and thermal properties that can be manipulated by twist-angle engineering. However, the weak phononic coupling at a bilayer interface imposes a fundamental thermal bottleneck for future two-dimensional devices. Using ultrafast electron diffraction, we directly investigated photoinduced nonequilibrium phonon dynamics in MoS2/WS2 at 4° twist angle and WSe2/MoSe2 heterobilayers with twist angles of 7°, 16°, and 25°. We identified an interlayer heat transfer channel with a characteristic timescale of ~20 picoseconds, about one order of magnitude faster than molecular dynamics simulations assuming initial intralayer thermalization. Atomistic calculations involving phonon-phonon scattering suggest that this process originates from the nonthermal phonon population following the initial interlayer charge transfer and scattering. Our findings present an avenue for thermal management in vdW heterostructures by tailoring nonequilibrium phonon populations.

Vibrational Dichroism of Chiral Valley Phonons.

Valley degrees of freedom in transition metal dichalcogenides thoroughly influence electron-phonon coupling and its nonequilibrium dynamics. We conducted a first-principles study of the quantum kinetics of chiral phonons following valley-selective carrier excitation with circularly polarized light. Our numerical investigations treat the ultrafast dynamics of electrons and phonons on equal footing within a parameter-free ab initio framework. We report the emergence of valley-polarized phonon populations in monolayer MoS2 that can be selectively excited at either the K or K' valleys depending on the light helicity. The resulting vibrational state is characterized by a distinctive chirality, which lifts time-reversal symmetry of the lattice on transient time scales. We show that chiral valley phonons can further lead to fingerprints of vibrational dichroism detectable by ultrafast diffuse scattering and persist beyond 10 ps. The valley polarization of nonequilibrium phonon populations could be exploited as an information carrier, thereby extending the paradigm of valleytronics to the domain of vibrational excitations.

Multitemperature Modeling of Thermal Transport across a Au–GaN Interface from Ab Initio Calculations

With device dimensions shrinking toward nanoscale sizes, an accurate understanding and modeling of the thermal energy transfer mechanisms at metal–nonmetal interfaces becomes highly desirable. To model the thermal transport across the Au–GaN interface, we developed a general multitemperature model (MTM) that accounts for both electron and phonon transport and allows for a nonequilibrium phonon population described as a sum of thermal distributions of the phonon branches. The model is populated with material parameters computed from ab initio calculations and used to describe the temperature profile across a Au–GaN junction 400 nm in length subjected to constant temperature differential, continuous-wave laser heating of Au, and constant heat flux on GaN. The calculated steady-state and time-dependent temperature profiles reveal strongly nonequilibrium electron–phonon and phonon–phonon interfacial regions created through energy carrier coupling. Our results indicate that a multitemperature-based model is required for the accurate resolving of the thermal energy flow across metal–nonmetal interfaces. Our MTM will advance the theoretical tool to investigate nonequilibrium thermal transport across metal–nonmetal interfaces.

Atomic-Level, Energy-Conversion Heat Transfer

Abstract Heat is stored in quanta of kinetic and potential energies in matter. The temperature represents the equilibrium and excited occupation (boson) of these energy conditions. Temporal and spatial temperature variations and heat transfer are associated with the kinetics of these equilibrium excitations. During energy-conversion (between electron and phonon systems), the occupancies deviate from equilibria, while holding atomic-scale, inelastic spectral energy transfer kinetics. Heat transfer physics reaches nonequilibrium energy excitations and kinetics among the principal carriers, phonon, electron (and holes and ions), fluid particle, and photon. This allows atomic-level tailoring of energetic materials and energy-conversion processes and their efficiencies. For example, modern thermal-electric harvesters have transformed broad-spectrum, high-entropy heat into a narrow spectrum of low-entropy emissions to efficiently generate thermal electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes a high-entropy heat. In particular, the suggested phonovoltaic cell generates phonoelectricity by employing the nonequilibrium, low-entropy, and elevated temperature optical-phonon produced population—for example, by relaxing electrons, excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical-phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). Examples of these quanta and spectral heat transfer are reviewed, contemplating a prospect for education and research in this field.

Phonon linewidths in InAs/AlSb superlattices derived from first-principles—application towards quantum well hot carrier solar cells

Hot electrons generated by the absorption of high-energy photons typically thermalize by dissipating energy through phonon mediated relaxation pathways. Existence of non-equilibrium optical phonon populations (hot phonons) can suppress thermalization of electrons by facilitating a stable hot carrier population. In this work, we derive optical phonon scattering rates in InAs/AlSb superlattices using first-principles calculations and compare them with bulk InAs. Computations are performed for the two shortest period superlattices with equal widths of InAs and AlSb. While in pure InAs, the highest optical phonon scattering rates reach 5 cm−1; in the superlattice, the peak scattering rates of optical phonons with frequencies above the energy gap, are much smaller, reaching ∼1 cm−1. These lower scattering rates in the superlattice have important implications for design of high efficiency hot carrier solar cells and explain some of the robust hot carriers observed recently in InAs/AlAsSb quantum wells.

From thermoelectricity to phonoelectricity

Here, we review the history and progress of solid-state heat harvesting. Efficiency models, material metrics, and current research are discussed for thermoelectrics, thermionics, laser-coolers, and modern technologies. Then, we discuss nonequilibrium optical phonon harvest in the phonovoltaic cell. We make an effort to distinguish between the harvest of equilibrium heat, or thermal-electricity, and the targetted harvest of a particular nonequilibrium phonon mode, or phonoelectricity. We survey the state of phonovoltaic research, focusing on phonovoltaic materials, the electron-phonon coupling, and entropy production in a phonovoltaic cell. Throughout this review, discussions are connected to the electron and phonon structures, interactions, and transport. The modern thermal-electric harvesters are shown to reshape broad-spectrum, high-entropy heat into a narrow-spectrum of low-entropy emissions in order to efficiently generate thermal-electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes high-entropy heat. In particular, the phonovoltaic cell generates phonoelectricity by utilizing the nonequilibrium, low-entropy, and high temperature optical phonon population produced by, e.g., the relaxation of electrons excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). The phonovoltaic device has an electric diode, e.g., a p-n junction, such that the internal electric field of the diode splits the electrons and holes in order to produce an electric current, and thus, power. The low entropy and high-temperature of the nonequilibrium optical phonon population enable efficient, in-situ heat harvesting. Bilayer graphene, for example, can theoretically convert the nonequilibrium population of optical phonons generated in a field-effect transistor into electricity with an efficiency exceeding 70% of the Carnot limit. The thermal-electric devices, in contrast, are either inefficient or restricted to ex-situ power generation. Furthermore, as the phonoelectric Carnot limit is defined by the local nonequilibrium between electron and optical phonon populations, rather than the spatial nonequilibrium across the device, the Carnot limit can be very large without inducing melting.Here, we review the history and progress of solid-state heat harvesting. Efficiency models, material metrics, and current research are discussed for thermoelectrics, thermionics, laser-coolers, and modern technologies. Then, we discuss nonequilibrium optical phonon harvest in the phonovoltaic cell. We make an effort to distinguish between the harvest of equilibrium heat, or thermal-electricity, and the targetted harvest of a particular nonequilibrium phonon mode, or phonoelectricity. We survey the state of phonovoltaic research, focusing on phonovoltaic materials, the electron-phonon coupling, and entropy production in a phonovoltaic cell. Throughout this review, discussions are connected to the electron and phonon structures, interactions, and transport. The modern thermal-electric harvesters are shown to reshape broad-spectrum, high-entropy heat into a narrow-spectrum of low-entropy emissions in order to efficiently generate thermal-electricity. Phonoelectricity, in contrast, intervenes before a low-ent...

Current noise enhancement: channel mixing and possible nonequilibrium phonon backaction in atomic-scale Au junctions

We report measurements of the bias dependence of the Fano factor in ensembles of atomic-scale Au junctions at 77 K. Previous measurements of shot noise at room temperature and low biases have found good agreement of the Fano factor with the expectations of the Landauer–Büttiker formalism, while enhanced Fano factors have been observed at biases of hundreds of mV (Chen et al 2014 Sci. Rep. 4 4221). We find even stronger enhancement of shot noise at 77 K with an ‘excess’ Fano factor up to ten times the low bias value. We discuss the observed ensemble Fano factor bias dependence in terms of candidate models. The results are most consistent with either a bias-dependent channel mixing picture or a model incorporating noise enhancement due to current-driven, nonequilibrium phonon populations, though a complete theoretical treatment of the latter in the ensemble average limit is needed.

Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearized Boltzmann transport equation, also including the effect of nonequilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to $n$-doped silicon. In particular, we discuss a number of thermoelectric properties such as the thermal and electrical conductivities of electrons, the Lorenz number and the Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavors of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

A coherent phonon pulse model for transient phonon thermal transport

In this work, we present a novel heat source model, the coherent phonon pulse (CPP), composed of spatiotemporal Gaussian wave packets to mimic the coherent excitation of a non-equilibrium phonon population by ultrashort laser techniques, for the study of transient phonon thermal transport. Through molecular dynamic simulations of phonon transport in bicrystalline silicon-nanowires containing Σ3 and Σ19 grain-boundaries (GBs), we demonstrate that the new model facilitates not only a quantitative measurement of phonon-interface scattering, but also a mechanistic understanding of the highly non-equilibrium process of phonon transport with the coherent wave nature being preserved.

Transport through molecular junctions with a nonequilibrium phonon population

The calculation of the nonlinear conductance of a single-molecule junction is revisited. The self energy on the junction resulting from the electron-phonon interaction has at low temperatures logarithmic singularities (in the real part) and discontinuities (in the imaginary one) at the frequencies corresponding to the opening of the inelastic channels. These singularities generate discontinuities and logarithmic divergences (as a function of the bias voltage) in the low-temperature differential conductance around the inelastic thresholds. The self energy also depends on the population of the vibrational modes. The case of a vibrating free junction (not coupled to a thermal bath), where the phonon population is determined by the bias voltage is examined. We compare the resulting zero-temperature differential conductance with the one obtained for equilibrated phonons, and find that the difference is larger the larger is the bare transmission of the junction and the product of the electron dwell time on the junction with the phonon frequency.

Direct Measurement of the Lifetime of Optical Phonons in Single-Walled Carbon Nanotubes

Time-resolved anti-Stokes Raman spectroscopy has been applied to probe the dynamics of optical phonons created in single-walled carbon nanotubes by femtosecond laser excitation. From measurement of the decay of the anti-Stokes Raman signal in semiconducting nanotubes of (6,5) chiral index, a room-temperature lifetime for G-mode phonons of 1.1+/-0.2 ps has been determined. This lifetime, which reflects the anharmonic coupling of the G-mode phonons to lower-frequency phonons, is important in assessing the role of nonequilibrium phonon populations in high-field transport phenomena.

Electrothermal analysis of AlGaN/GaN high electron mobility transistors

Efficiency of AlGaN/GaN HEMTs used in high power, high frequency applications is thought to be limited by parasitic thermal effects. In this study, we investigate coupled electrical and thermal transport in AlGaN/GaN HEMTs using an ensemble Monte Carlo model. Calculation of the non-equilibrium phonon population reveals a hot spot in the channel that is localized at low drain-source bias, but expands towards the drain at higher bias, significantly degrading channel mobility.

Direct Observation of Mode Selective Electron−Phonon Coupling in Suspended Carbon Nanotubes

Raman spectra of individual pristine suspended single-walled carbon nanotubes are observed under high electrical bias. The LO and TO modes of the G band behave differently with respect to voltage bias, indicating preferential electron-phonon coupling and nonequilibrium phonon populations, which cause negative differential conductance in suspended devices. By correlating the electron resistivity to the optically measured phonon population, the data are fit using a Landauer model to determine the key scattering parameters.

Controlling Nonequilibrium Phonon Populations in Single-Walled Carbon Nanotubes

We studied spatially isolated single-walled carbon nanotubes (SWNTs) immobilized in a quasi-planar optical lambda/2-microresonator using confocal microscopy and spectroscopy. The modified photonic mode density within the resonator is used to selectively enhance or inhibit different Raman transitions of SWNTs. Experimental spectra are presented that exhibit single Raman bands only. Calculations of the relative change in the Raman scattering cross sections underline the potential of our microresonator for the optical control of nonequilibrium phonon populations in SWNT.

Heat dissipation and non-equilibrium phonon distributions in molecular devices

Using a density functional approach we compute vibrations of molecules adsorbed on metal and semiconducting substrates and the electronphonon coupling of these modes. A non-equilibrium Green’s function approach is used to compute the partially coherent transmission in molecular junctions due to electron-vibration scattering [1], [2]. The electronic power dissipated into molecular vibrations allows to set a rate equation for the phonon population in the vibrational degrees of freedom of the molecule. The rate equation includes the phonon emission rate and phonon decay due to absorption, electron-hole pair production and dissipation into the contacting leads, which are assumed to behave as reservoirs. The rate of phonon decay is computed using a microscopic approach which includes a first-principle calculation of the coupling of the molecular modes with the vibrations of the contacts. In turn, the calculated phonon lifetime is used to correct the phonon propagator. As the power dissipated in the molecular junction depends nontrivially on the phonon populations, the equilibrium distribution under bias condition is a complex issue. A self consitent loop allows to compute the steady state non-equilibrium phonon population of the molecular junction under bias condition. We find that the resulting average population is far from the equilibrium thermal distribution, frequently assumed in such calculations, which allows to obtain a mean temperature of the junction. As expected the deviations increase with applied bias. As molecular electronics is moving to semiconducting substrates, it is relevant to explore and understand thermal issues. Metallic substrates have in fact a very efficient channel of phonon damping into electron-hole pairs, while vibrational coupling to the substrate may not be very efficient due to ionic mass mismatch and a weaker bond. On the other hand the the electron-hole generation is prevented on semiconducting substrates, where instead vibrational coupling is stronger.We compare thermal behavior of organic molecules adsorbed on Si with molecules adsorbed on metallic substrates (Au or Cu) and determine the molecular temperature as a function of applied bias and for different temperatures of the termostats.

Hot-electron energy-loss rate via PO-phonon scattering in CdZnSe/ZnSe quantum wire

The hot-electron energy-loss rate conditioned by confined and interface polar-optical phonons for a Cd 0.35Zn 0.65Se quantum wire embedded in ZnSe medium is investigated theoretically. It is shown that the inclusion of the polar-optical phonon confinement effects is crucial for accurate calculation of the energy-loss rate in quantum wire. Taking into account the nonequilibrium phonon populations, the hot-electron energy-loss rate is derived by a model, which includes the lowest subband occupation and the phonon confinement effects. The contribution of intersubband transitions to electron energy-loss rate as well as the relaxation time of the electron temperature with and without hot-phonon bottleneck effect is estimated.

The energy-loss rate via polar-optical phonon scattering in quantum wires

The hot-electron energy-loss rate (ELR) conditioned by confined and interface polar-optical (PO) phonons for a quasi-one-dimensional cylindrical quantum wire embedded in a dielectric medium is investigated analytically. It is shown that the inclusion of the PO-phonon confinement effects is crucial for accurate calculation of the ELR in quantum wire. Taking into account the nonequilibrium phonon populations, the hot-electron ELR is derived by a model, which includes the lowest subband occupation and the phonon confinement effects. The contribution of intersubband transitions to electron ELR for the GaAs quantum wire embedded in Al x Ga 1− x As is estimated. The extrema on the ELR dependences on electron density are obtained.

Pure dephasing and phonon dynamics in GaAs- and GaN-based quantum dot structures: Interplay between material parameters and geometry

The pure dephasing of excitons in quantum dot structures due to their interaction with acoustic phonons as well as the spatiotemporal dynamics of the created nonequilibrium phonon population is studied theoretically. The theory is applied to GaAs- as well as GaN-based heterostructures. A detailed analysis of the interplay between different material parameters, different quantum dot geometries, and different electric fields is presented. The optical polarization induced by an ultrashort laser pulse exhibits a characteristic nonexponential behavior: it decays on a pico- or subpicosecond time scale to a value that strongly depends on temperature, structure, and material parameters and is then retained until, on a typically much longer time scale, it finally decays because of electron-hole recombination or transitions to other states. We find that, in general, the remnant optical polarization is much higher in the GaAs-based structures than in the GaN-based structure mainly because of the strongly enhanced piezoelectric coupling in GaN quantum dots. The optical excitation also leads to the buildup of a phonon population consisting of a polaron part that remains localized in the region of the quantum dot and a traveling part that leaves the dot region at the speed of sound. This traveling part exhibits characteristic anisotropies reflecting both the anisotropy of the quantum dot structure and of the coupling matrix elements.

The effect of hot phonons on the drift velocity in GaN/AlGaN two dimensional electron gas

We present the effect of hot-phonon production on the high-field drift velocity in the steady state in GaN/AlGaN heterostructures . The results are compared with a model taking into account the effect of hot phonon production on the high-field transport of electrons. Experimental results show that the drift velocity saturates at around v d ≈3.8×10 5 cm / s at an electric field of F≈8.9×10 2 V / cm at 3.8 K . The theoretical calculations show that the enhancement of the momentum relaxation rate due to the production of non-drifting hot phonons reduces the drift velocity at high field. The reduction in the drift velocity increases with increasing population of non-drifting non-equilibrium phonons (LO phonons).