Electron-phonon Relaxation Rate Research Articles

Effect of screening on energy-dependent electron–phonon relaxation rate via intrinsic and extrinsic scattering channels in graphene on GaAs substrate

We obtain analytical results on the effect of screening on electron–phonon (e-p) relaxation rate in single-layer graphene (SLG) placed on any substrate using the Boltzmann transport formalism (BTF). The screening has been taken into account through the Thomas-Fermi (TF) and Random Phase Approximation (RPA) model. The four intrinsic and extrinsic phononic modes considered for electron-phonon scattering are the acoustic, optic, surface polar acoustic (piezoelectric), and surface polar optic (SO) phonons. All the four considered phononic modes coupling with free carriers provide significant pathways for e-p relaxation. We further investigate the significance of screening in the four phononic modes in electron energy-dependent e-p relaxation rate in SLG on GaAs substrate in particular. The obtained screened analytical solutions are novel and are not reported elsewhere.

Electron single flexural phonon relaxation, energy loss and thermopower in single and bilayer graphene in the Bloch–Gruneisen regime

The flexural phonons serve as one of the important modes of interaction in graphene that can inhibit carrier mobility. For the estimation of scattering due to flexural phonons a two-phonon scattering process had been in place, as due to symmetry constraints out-of-plane deformations modulate electron hopping only in the second order. But recently it has been shown that electrostatic gating can break the planar mirror symmetry and activate single flexural phonon scattering processes (Gunst et al 2017 Phys. Rev. Lett. 118 046601). Motivated by this we perform single flexural phonon mechanism based analytical and numerical calculations of the electron phonon relaxation rate, energy loss rate and thermopower in single and bilayer graphene and obtain the power exponents of these quantities in the Bloch Gruneisen regime using the non-equilibrium Boltzmann transport equation. We find that the scattering by flexural phonons substantially changes the temperature dependencies from that observed due to in-plane phonons but the carrier concentration dependencies remain the same as of the in-plane phonons for all the three investigated quantities.

Strong Influence of Ti Adhesion Layer on Electron-Phonon Relaxation in Thin Gold Films: Ab Initio Nonadiabatic Molecular Dynamics.

Electron-phonon relaxation in thin metal films is an important consideration for many ultrasmall devices and ultrafast applications. Recent time-resolved experiments demonstrate a significant, more than a factor of five, increase in the electron-phonon coupling and acceleration in the electron-phonon relaxation rate when a narrow Ti adhesion layer is introduced between an Au film and a nonmetal substrate. Using nonadiabatic molecular dynamics combined with real-time time-dependent density functional theory, we identify the reasons that give rise to this strong effect. First, the Ti layer greatly enhances the density of states (DOS) in the energy region starting at 1 eV below the Fermi level and extending several electronvolts above it. Second, Ti atoms are four times lighter than Au atoms and therefore generate larger nonadiabatic (NA) electron-phonon coupling. Because the transition rates depend on coupling and DOS, both the factors accelerate the dynamics. Showing good agreement with the experiments, the time-domain atomistic simulations provide a detailed mechanistic understanding of the electron-phonon relaxation dynamics in thin gold films and related nanomaterials.

Chirality effect on electron phonon relaxation, energy loss, and thermopower in single and bilayer graphene in BG regime

We investigate the energy dependent electron-phonon relaxation rate, energy loss rate, and phonon drag thermopower in single layer graphene (SLG) and bilayer graphene (BLG) under the Bloch-Gruneisen (BG) regime through coupling to acoustic phonons interacting via the Deformation potential in the Boltzmann transport equation approach. We find that the consideration of the chiral nature of electrons alters the temperature dependencies in two-dimensional structures of SLG and BLG from that shown by other conventional 2DEG system. Our investigations indicate that the BG analytical results are valid for temperatures far below the BG limit (∼TBG/4) which is in conformity with a recent experimental investigation for SLG [C. B. McKitterick et al., Phys. Rev. B 93, 075410 (2016)]. For temperatures above this renewed limit (∼TBG/4), there is observed a suppression in energy loss rate and thermo power in SLG, but enhancement is observed in relaxation rate and thermopower in BLG, while a suppression in the energy loss rate is observed in BLG. This strong nonmonotonic temperature dependence in SLG has also been experimentally observed within the BG limit [Q. Ma et al., Phys. Rev. Lett. 112, 247401 (2014)].

Temperature Dependence of Electron–Phonon Interactions in Gold Films Rationalized by Time-Domain Ab Initio Analysis

The nonequilibrium dynamics of excited electrons in metals is probed by ultrafast laser measurements. Using a real-time Kohn–Sham time-dependent density functional theory and nonadiabatic molecular dynamics, we report direct modeling of such experiments, rationalizing the observed temperature dependence. Focusing on thin gold films, we analyze the effect of temperature on film structure, electronic state densities, nonadiabatic electron–phonon coupling, elastic electron–phonon scattering times, and electron–phonon relaxation rates. The effective electron–phonon coupling constants calculated at different temperatures are in good agreement with the values deduced from experiments and an alternative theory. A temperature increase accelerates both inelastic and elastic electron–phonon scattering and allows a larger number of higher-frequency phonon modes to couple to the electronic subsystem. The inelastic electron–phonon coupling is largest between nearest states, indicating that carrier relaxation involves ...

Mechanisms of nonequilibrium electron-phonon coupling and thermal conductance at interfaces

We study the electron and phonon thermal coupling mechanisms at interfaces between gold films with and without Ti adhesion layers on various substrates via pump-probe time-domain thermoreflectance. The coupling between the electronic and the vibrational states is increased by more than a factor of five with the inclusion of an ∼3 nm Ti adhesion layer between the Au film and the non-metal substrate. Furthermore, we show an increase in the rate of relaxation of the electron system with increasing electron and lattice temperatures induced by the laser power and attribute this to enhanced electron-electron scattering, a transport channel that becomes more pronounced with increased electron temperatures. The inclusion of the Ti layer also results in a linear dependence of the electron-phonon relaxation rate with temperature, which we attribute to the coupling of electrons at and near the Ti/substrate interface. This enhanced electron-phonon coupling due to electron-interface scattering is shown to have negligible influence on the Kapitza conductances between the Au/Ti and the substrates at longer time scales when the electrons and phonons in the metal have equilibrated. These results suggest that only during highly nonequilibrium conditions between the electrons and phonons (Te ≫ Tp) does electron-phonon scattering at an interface contribute to thermal boundary conductance.

Electron-electron scattering in three-dimensional highly degenerate semiconductors

We have measured the low-field magnetoresistances of a series of Sn-doped indium oxide thick films in the temperature T range of . The electron dephasing rate as a function of T for each film was extracted by comparing the magnetoresistance data with the three-dimensional weak-localization theoretical predictions. We found that the extracted varies linearly with . Furthermore, at a given T, varies linearly with , where kF is the Fermi wave number, and l is the electron elastic mean free path. These features are well explained in terms of the small-energy-transfer electron-electron scattering time in three-dimensional disordered conductors. This electron dephasing mechanism dominates over the electron-phonon scattering process because the carrier concentrations in our films are ∼ 3 orders of magnitude lower than those in typical metals, which resulted in a greatly suppressed electron-phonon relaxation rate. Our result is the first quantitative demonstration of this unique three-dimensional electron-electron scattering time in experiments.

Electron dephasing in homogeneous and inhomogeneous indium tin oxide thin films

The electron dephasing processes in two-dimensional homogeneous and inhomogeneous indium tin oxide thin films have been investigated in a wide temperature range 0.3--90 K. We found that the small-energy-transfer electron-electron ($e$-$e$) scattering process dominated the dephasing from a few K to several tens K. At higher temperatures, a crossover to the large-energy-transfer $e$-$e$ scattering process was observed. Below about 1--2 K, the dephasing time $\tau_\varphi$ revealed a very weak temperature dependence, which intriguingly scaled approximately with the inverse of the electron diffusion constant $D$, i.e., $\tau_\varphi (T \approx 0.3 \, {\rm K}) \propto 1/D$. Theoretical implications of our results are discussed. The reason why the electron-phonon relaxation rate is negligibly weak in this low-carrier-concentration material is presented.

Nonequilibrium electrons in tunnel structures under high-voltage injection

We investigate electronic distributions in nonequilibrium tunnel junctions subject to a high voltage bias $V$ under competing electron-electron and electron-phonon relaxation processes. We derive conditions for reaching quasi-equilibrium and show that, though the distribution can still be thermal for low energies where the rate of the electron-electron relaxation exceeds significantly the electron-phonon relaxation rate, it develops a power-law tail at energies of order of $eV$. In a general case of comparable electron-electron and electron-phonon relaxation rates, this tail leads to emission of high-energy phonons which carry away most of the energy pumped in by the injected current.

Nonequilibrium fluctuations of a thin metal diffuse film exposed to microwave radiation

Nonlinear fluctuations of the electron energy distribution function in a microwave-irradiated thin diffuse metal film are calculated in the nonlinear approximation for various energy relaxation models. The spectral density of the resulting nonequilibrium fluctuations is calculated as a function of the microwave-radiation power for various ratios between the electron-phonon and electron-electron relaxation rates.

Saturation of spin-polarized current in nanometer scale aluminum grains

We describe measurements of spin-polarized tunnelling via discrete energy levels of single Aluminum grains. In high resistance samples ($\sim G\Omega$), the spin-polarized tunnelling current rapidly saturates as a function of the bias voltage. This indicates that spin-polarized current is carried only via the ground state and the few lowest in energy excited states of the grain. At the saturation voltage, the spin-relaxation rate $T_1^{-1}$ of the highest excited states is comparable to the electron tunnelling rate: $T_1^{-1}\approx 1.5\cdot 10^6 s^{-1}$ and $10^7s^{-1}$ in two samples. The ratio of $T_1^{-1}$ to the electron-phonon relaxation rate is in agreement with the Elliot-Yafet scaling, an evidence that spin-relaxation in Al grains is governed by the spin-orbit interaction.

Electron-phonon relaxation rates and optical gain in a quantum cascade laser in a magnetic field

We present a model for calculating the optical gain in a midinfrared GaAs∕AlGaAs quantum cascade laser in a magnetic field, based on solving the set of rate equations that describe the carrier density in each level, accounting for the optical- and acoustic-phonon scattering processes. The confinement caused by the magnetic field strongly modifies the lifetimes of electrons in the excited state and results in pronounced oscillations of the optical gain as a function of the field. Numerical results are presented for the structure designed to emit at λ∼11.4μm, with the magnetic field varying in the range of 10–60T. The effects of band nonparabolicity are also included.

Deformation Electron-Phonon Coupling in Disordered Semiconductors and Nanostructures

We study the electron-phonon relaxation (dephasing) rate in disordered semiconductors and low-dimensional structures. The relaxation is determined by the interference of electron scattering via the deformation potential and elastic electron scattering from impurities and defects. We have found that in contrast with the destructive interference in metals, which results in the Pippard ineffectiveness condition for the electron-phonon interaction, the interference in semiconducting structures substantially enhances the effective electron-phonon coupling. The obtained results provide an explanation to energy relaxation in silicon structures.

Spectral features of the nonlinear response of high-temperature superconductor films in methods of degenerate four-photon spectroscopy

The electronic nonlinear response χ(3)ee of high-temperature superconductor films in methods of degenerate four-photon spectroscopy is calculated. It is shown that the model considering interband electronic transitions in a 'real' band structure with the only fitting parameter (the electron—phonon relaxation rate) well describes all the experimental spectral features of the response, and the methods of degenerate four-photon spectroscopy themselves can reveal, due to the interference character of χ(3)ee, the presence of the energy gap in the spectrum of states.

Temporal measurement of hot-electron relaxation in a phonon-cooled metal island

We report temporal measurements of the dynamic electronic temperature and the electron-phonon thermal relaxation rate in a micron-scale metal island, with an electronic heat capacity of order 1 fJ/K $(C\ensuremath{\sim}{10}^{7}{k}_{B}).$ We employed a superconductor--insulator--normal-metal tunnel junction, embedded in a radio-frequency resonator, as a fast $(\ensuremath{\sim}20\mathrm{MHz})$ thermometer. A resistive heater coupled to the island allowed us to pulse the electronic temperature well above the phonon temperature. Using this device, we have determined the thermal relaxation rate of a hot-electron population in a thin normal-metal film with a measurement bandwidth that exceeds the low-temperature thermal bandwidth.

Electron–optical-phonon scattering rates in spherical CdSe quantum dots in an external magnetic field

We calculate electron-phonon relaxation rates in CdSe spherical quantum dots in the presence of the quantizing magnetic field. The calculated scattering rates include the contributions of the confined and surface optical modes as obtained from the dielectric continuum model. The electron states are calculated within the strong-perturbation approximation. The effects of the competing contributions of the magnetic and spatial confinement on the optical-phonon scattering rates are studied. The enhancement of the scattering rates in the strong magnetic fields regime and the possibility of tuning efficient scattering channels are also discussed.

Phonon drag in disordered films and structures

Employing the quantum transport equation, we investigate the effect of electronic disorder on the phonon-drag thermopower. We consider the electron–phonon interaction via the deformation potential, which is strongly renormalized due to elastic electron scattering. The scattering potential of impurities, boundaries and defects is modeled by quasistatic scatterers and vibrating scatterers, which move in the same way as host atoms. In thin films, micro and nanostructures of the phonons relax mainly in a substrate, and the phonon-drag thermopower substantially depends on the character of electron scatterers. Vibrating scatterers decrease thermopower, while quasistatic scatterers (e.g. rigid boundaries) increase it. These changes in thermopower correlate to the disorder-induced modification of the electron–phonon relaxation rate.

Electron–phonon scattering in disordered metallic films

The quantum interference between ‘pure’ electron–phonon and electron-boundary/impurity scattering drastically changes the electron–phonon relaxation rate. If impurities and boundaries vibrate in the same way as the host lattice, the electron–phonon relaxation rate is significantly decreased. In the presence of the scattering potential that does not vibrate with phonons (e.g. rigid boundaries, interelectron scattering) the relaxation rate is substantially enhanced. Current work reviews recent progress in the theoretical investigations, gives quantitative explanations of available low-temperature data, and presents original experimental results for ultrathin Hf at ultralow temperatures.

Electron–phonon coupling in degenerate silicon-on-insulator film probed using superconducting Schottky junctions

Energy flow rate in degenerate n-type silicon-on-insulator (SOI) film is studied at low temperatures. The electrons are heated above the lattice temperature by electric field and the electron temperature is measured via semiconductor–superconductor quasiparticle tunneling. The energy flow rate in the system is found to be proportional to T 5, indicating that electron–phonon relaxation rate and electron–phonon phase breaking rate are proportional to T 3. The electron–phonon system in the SOI film is in the “dirty limit” where the electron mean free path is smaller than the inverse of the thermal phonon wave vector.

Effect of electronic disorder on phonon-drag thermopower

Using the quantum-transport equation and Keldysh diagrammatic technique, we investigate the phonon-drag thermopower in a disordered conductor. We consider phonon drag of three-dimensional electrons, which interact with longitudinal phonons via the deformation potential. The scattering potential of impurities, boundaries, and defects is modeled by quasistatic scatterers and vibrating scatterers, which move in the same way as host atoms. In thin films and nanostructures the phonons relax mainly in a substrate, and the phonon-drag thermopower substantially depends on the character of electron scatterers. Vibrating scatterers decrease thermopower, while static scatterers, such as rigid boundaries and heavy impurities, increase it. These changes in thermopower correlate to the disorder-induced modification of the electron-phonon relaxation rate. In bulk conductors, phonon-electron scattering dominates in the phonon relaxation, and the phonon-drag thermopower just slightly varies with electron mean free path.