Electron-phonon Energy Relaxation Research Articles

What Can we Learn from Nonequilibrium Response of a Strange Metal?

We critically address the recent experiment by L. Chen et al. [Science 382, 907 (2023)] on nonequilibrium transport and noise in a strange metal YbRh2Si2 patterned into the nanowire shape. In the long device, resistivity, differential resistance and current noise data seem to be consistent allowing us to extract electron–phonon coupling and the temperature dependence of electron–phonon scattering length. The obtained values can be reconciled with the experimental data for the short device only assuming the significant contact resistance. We discuss its possible origin as due to the current redistribution between YbRh2Si2 and its gold covering, and reveal that this redistribution contact resistance should be proportional to the YbRh2Si2 resistivity. We also discuss some subtleties of the noise measurements. Overall, neglecting electron–phonon energy relaxation even in the shortest devices is arguable so that the observed shot noise suppression can hardly be attributed to the failure of quasiparticle concept.

Momentum and energy relaxation in femtosecond-scale energy transport in metals

In the current report we investigate the processes of heat transport and energy relaxation in metals using Boltzmann transport equation for the electron distribution function perturbation, simultaneously accounting both energy and momentum relaxation. Mutual influence of electron-electron and electron-phonon energy relaxation on the electron distribution function is considered using linearized integro-differential collision integrals. These energy exchange effects provide main contribution to the difference between results obtained using Boltzmann equation solution and widely considered two-temperature model.

Photoinduced Anomalous Electron Transfer Dynamics at a Lateral MoS2-Graphene Covalent Junction.

Photoinduced charge separation significantly affects the optoelectronic performance of the lateral MoS2-graphene junctions. Generally, an adiabatic mechanism governs electron transfer (ET) at a chemically binding interface. Counterintuitively, we demonstrate, using nonadiabatic (NA) molecular dynamics, that an NA mechanism dominates the ET from MoS2 to graphene in the lateral MoS2-graphene covalent junction. The anomalous ET mechanism arising from the built-in electric field formed at the interface that decreases the donor-acceptor interaction by driving electrons and holes moving to opposite directions. Driven by both graphene and MoS2 vibrations, the photoexcited electrons on MoS2 rapidly transfer into graphene by the NA mechanism within 200 fs, which is faster than electron-phonon energy relaxation and ensures that "hot" electrons can be successfully extracted before they cool and lose energy to heat. The study establishes a mechanistic understanding of the complex charge-phonon dynamics in the lateral MoS2-graphene junctions that are key to optoelectronic and photovoltaic applications.

Phonon-induced long-lasting nonequilibrium in the electron system of a laser-excited solid

Electron-electron thermalization and electron-phonon relaxation processes in laser-excited solids are often assumed to occur on different timescales. This is true for the majority of the conduction band electrons in a metal. However, electron-phonon interactions can influence the thermalization process of the excited electrons. We study the interplay of the underlying scattering mechanisms for the case of a noble metal with help of a set of complete Boltzmann collision integrals. We trace the transient electron distribution in copper and its deviations from a Fermi-Dirac distribution due to the excitation with an ultrashort laser pulse. We investigate the different stages of electronic nonequilibrium after an excitation with an ultrashort laser-pulse of 800 nm wavelength and 10 fs pulse duration. Our calculations show a strong nonequilibrium during and directly after the end of the laser pulse. Subsequently, we find a fast thermalization of most electrons. Surprisingly, we observe a long-lasting nonequilibrium, which can be attributed to the electron-phonon scattering. This nonequilibrium establishes at energies around peaks in the density of states of the electrons and persists on the timescale of electron-phonon energy relaxation. It influences in turn the electron phonon coupling strength.

Weak Donor-Acceptor Interaction and Interface Polarization Define Photoexcitation Dynamics in the MoS2/TiO2 Composite: Time-Domain Ab Initio Simulation.

To realize the full potential of transition metal dichalcogenides interfaced with bulk semiconductors for solar energy applications, fast photoinduced charge separation, and slow electron-hole recombination are needed. Using a combination of time-domain density functional theory with nonadiabatic molecular dynamics, we demonstrate that the key features of the electron transfer (ET), energy relaxation and electron-hole recombination in a MoS2-TiO2 system are governed by the weak van der Waals interfacial interaction and interface polarization. Electric fields formed at the interface allow charge separation to happen already during the photoexcitation process. Those electrons that still reside inside MoS2, transfer into TiO2 slowly and by the nonadiabatic mechanism, due to weak donor-acceptor coupling. The ET time depends on excitation energy, because the TiO2 state density grows with energy, increasing the nonadiabatic transfer rate, and because MoS2 sulfur atoms start to contribute to the photoexcited state at higher energies, increasing the coupling. The ET is slower than electron-phonon energy relaxation because the donor-acceptor coupling is weak, rationalizing the experimentally observed injection of primarily hot electrons. The weak van der Waals MoS2-TiO2 interaction ensures a long-lived charge separated state and a short electron-hole coherence time. The injection is promoted primarily by phonons within the 200-800 cm-1 range. Higher frequency modes are particularly important for the electron-hole recombinations, because they are able to accept large amounts of electronic energy. The predicted time scales for the forward and backward ET, and energy relaxation can be measured by time-resolved spectroscopies. The reported simulations generate a detailed time-domain atomistic description of the complex interplay of the charge and energy transfer processes at the MoS2/TiO2 interface that are of fundamental importance to photovoltaic and photocatalytic applications. The results suggest that even though the photogenerated charge-separated state is long-lived, the slower charge separation, compared to the electron-phonon energy relaxation, can present problems in practical applications.

Slow Electron–Phonon Cooling in Superconducting Diamond Films

We have measured the electron–phonon energy-relaxation time, ${\boldsymbol{\tau }_{{{\rm eph}}}}$ , in superconducting boron-doped diamond films grown on silicon substrate by chemical vapor deposition. The observed electron–phonon cooling times vary from 160 ns at 2.70 K to 410 ns at 1.8 K following a ${\boldsymbol{T}^{ - 2}}$ -dependence. The data are consistent with the values of ${\boldsymbol{\tau }_{{{\rm eph}}}}$ previously reported for single-crystal boron-doped diamond films epitaxially grown on diamond substrate. Such a noticeable slow electron–phonon relaxation in boron-doped diamond, in combination with a high normal-state resistivity, confirms a potential of superconducting diamond for ultrasensitive superconducting bolometers.

The role of conduction electrons in the formation of thermal boundary resistance of the metal-dielectric interface and resistivity of metal films, at low temperatures (Review Article)

This review article is a discussion of the role played by conduction electrons in the formation of an effective acoustic transparency at the interface between narrow metal films and dielectric substrates with high thermal conductivity, within the framework of the acoustic mismatch between solids. We consider both steady and transient regimes of phonon radiation from metal films heated by electric current or short laser pulses, at low temperatures. We discuss in detail how the electron-phonon energy relaxation τe and the average exit time of the phonons from the films τes can be found using the experiment. A theoretical analysis of these problems is carried out using kinetic equations for the phonon and electron distribution functions. We examine the steady modes of relaxation and diffusion heat removal from the moving plane phase transition front in the film geometry. In most cases, we discuss the relationship between the theoretical results of the review authors and the existing experimental situation.

Unusual transient absorption dynamics of silver nanoparticles in solutions of carboxylated amine complexons

We present the results of research on fast relaxation dynamics in the electronic excitation of silver nanoparticles synthesized in the presence of carboxylated amine complexons (NTA, Na2EDTA, DTPA) without any reductant or polymeric stabilizer. Unusual transient absorption dynamics in these objects after femtosecond laser irradiation was found, manifesting as the appearance of an additional long-lived bleaching band. The effect may be assigned to the inhomogeneous and porous shell of silver nanoparticles synthesized by such a procedure, as the consequence of a partial fragmentation of this shell due to heating under femtosecond laser excitation of plasmonic nanoparticles and subsequent electron–phonon energy relaxation.

Electron–Phonon Energy Relaxation Time in Thin Strongly Disordered Titanium Nitride Films

We have measured the energy relaxation times from the electron bath to the phonon bath in strongly disordered TiN films grown by atomic layer deposition. The measured values of τ eph vary from 12 to 91 ns. Over a temperature range from 3.4 to 1.7 K, they follow T -3 temperature dependence, which are consistent with values of τ eph reported previously for sputtered TiN films. For the most disordered film, with an effective elastic mean free path of 0.35 nm, we find a faster relaxation and a stronger temperature dependence, which may be an additional indication of the influence of strong disorder on a superconductor.

Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres

AbstractIn this paper the size-dependence of energy relaxation, which is induced by the electron-phonon (e-ph) interactions and the electron-surface (e-s) interactions in noble metal nanoparticles, is investigated. Then based on the analysis and the derivation of the e-s coupling constant in metal nanospheres, the formula of the effective electron-phonon coupling constant Geff of hollow gold nanospheres (HGNs) is deduced. Moreover, the correctness of the formulae gets proved by contrast analyses of the calculated Geff values and experimental values obtained from literature.

Exciton Multiplication from First Principles

Third-generation photovolatics require demanding cost and power conversion efficiency standards, which may be achieved through efficient exciton multiplication. Therefore, generating more than one electron-hole pair from the absorption of a single photon has vast ramifications on solar power conversion technology. Unlike their bulk counterparts, irradiated semiconductor quantum dots exhibit efficient exciton multiplication, due to confinement-enhanced Coulomb interactions and slower nonradiative losses. The exact characterization of the complicated photoexcited processes within quantum-dot photovoltaics is a work in progress. In this Account, we focus on the photophysics of nanocrystals and investigate three constituent processes of exciton multiplication, including photoexcitation, phonon-induced dephasing, and impact ionization. We quantify the role of each process in exciton multiplication through ab initio computation and analysis of many-electron wave functions. The probability of observing a multiple exciton in a photoexcited state is proportional to the magnitude of electron correlation, where correlated electrons can be simultaneously promoted across the band gap. Energies of multiple excitons are determined directly from the excited state wave functions, defining the threshold for multiple exciton generation. This threshold is strongly perturbed in the presence of surface defects, dopants, and ionization. Within a few femtoseconds following photoexcitation, the quantum state loses coherence through interactions with the vibrating atomic lattice. The phase relationship between single excitons and multiple excitons dissipates first, followed by multiple exciton fission. Single excitons are coupled to multiple excitons through Coulomb and electron-phonon interactions, and as a consequence, single excitons convert to multiple excitons and vice versa. Here, exciton multiplication depends on the initial energy and coupling magnitude and competes with electron-phonon energy relaxation. Multiple excitons are generated through impact ionization within picoseconds. The basis of exciton multiplication in quantum dots is the collective result of photoexcitation, dephasing, and nonadiabatic evolution. Each process is characterized by a distinct time-scale, and the overall multiple exciton generation dynamics is complete by about 10 ps. Without relying on semiempirical parameters, we computed quantum mechanical probabilities of multiple excitons for small model systems. Because exciton correlations and coherences are microscopic, quantum properties, results for small model systems can be extrapolated to larger, realistic quantum dots.

Electron–phonon energy relaxation in bismuth excited by ultrashort laser pulse: temperature and fluence dependence

We present analysis of the experiments on excitation of bismuth by ultrafast laser pulses and compare with heating bismuth in equilibrium conditions. The analysis shows that the electron–phonon relaxation time is a strong function of the lattice temperature. We developed a kinetic theory, which predicts well the experimental results. We demonstrate that lattice heating and re-structuring with the temperature-dependent energy exchange rates occurs much faster than what follows from the two-temperature model with constant relaxation factor. The analytic formulae corrected by equilibrium and non-equilibrium data allowed the interpretation of various experiments without controversy. We demonstrate that all observed ultrafast transformation of bismuth are purely thermal in nature, thus excluding the conjectures about non-thermal melting.

Photo-induced Charge Separation across the Graphene–TiO2 Interface Is Faster than Energy Losses: A Time-Domain ab Initio Analysis

Graphene-TiO(2) composites exhibit excellent potential for photovoltaic applications, provided that efficient photoinduced charge separation can be achieved at the interface. Once charges are separated, TiO(2) acts as an electron carrier, while graphene is an excellent hole conductor. However, charge separation competes with energy losses that can result in rapid electron-hole annihilation inside metallic graphene. Bearing this in mind, we investigate the mechanisms and, crucially, time scales of electron transfer and energy relaxation processes. Using nonadiabatic molecular dynamics formulated within the framework of time-domain density functional theory, we establish that the photoinduced electron transfer occurs several times faster than the electron-phonon energy relaxation (i.e., charge separation is efficient in the presence of electron-phonon relaxation), thereby showing that graphene-TiO(2) interfaces can form the basis for photovoltaic and photocatalytic devices using visible light. We identify the mechanisms for charge separation and energy losses, both of which proceed by rapid, phonon-induced nonadiabatic transitions within the manifold of the electronic states. Electron injection is ultrafast, owing to strong electronic coupling between graphene and TiO(2). Injection is promoted by both out-of-plane graphene motions, which modulate the graphene-TiO(2) distance and interaction, and high-frequency bond stretching and bending vibrations, which generate large nonadiabatic coupling. Both electron injection and energy transfer, injection in particular, accelerate for photoexcited states that are delocalized between the two subsystems. The theoretical results show excellent agreement with the available experimental data [Adv. Funct. Mater. 2009, 19, 3638]. The state-of-the-art simulation generates a detailed time-domain atomistic description of the interfacial charge separation and relaxation processes that are fundamental to a wide variety of applications, including catalysis, electrolysis, and photovoltaics.

Phase sensitive electron-phonon coupling in a superconducting proximity structure

We study the role of the superconducting proximity effect on the electron-phonon energy exchange in diffusive normal metals (N) attached to superconductors (S). The proximity effect modifies the spectral response of the normal metal, in particular the local density of states. This leads to a weakening of the electron-phonon energy relaxation. We show that the effect is easily observable with modern thermometry methods, and predict that it can be tuned in structures connected to multiple superconductors by adjusting the phase difference between superconducting order parameters at the two NS interfaces.

Intervalley-Scattering-Induced Electron-Phonon Energy Relaxation in Many-Valley Semiconductors at Low Temperatures

We report on the effect of elastic intervalley scattering on the energy transport between electrons and phonons in many-valley semiconductors. We derive a general expression for the electron-phonon energy flow rate at the limit where elastic intervalley scattering dominates over diffusion. Electron heating experiments on doped n-type Si samples with electron concentrations (3.5-16.0) x 10(25) m(-3) are performed at sub-Kelvin temperatures. We find a good agreement between the theory and the experiment.

Femtosecond pump-probe reflectivity study of silicon carrier dynamics

We have studied the ultrafast optical response of native-oxide terminated Si(001) with pump-probe reflectivity using 800 nm, 28 fs pulses at an excitation density of $(5.5\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{18}{\mathrm{cm}}^{\ensuremath{-}3}.$ Time-dependent reflectivity changes comprise third-order-response coherent-transient variations arising from anisotropic state filling and linear-response variations arising from excited free carriers, state filling, and lattice heating. A time constant of $32\ifmmode\pm\else\textpm\fi{}5\mathrm{fs}$ associated with momentum relaxation is extracted from the coherent-transient variations. The state-filling and free-carrier responses are sensitive to carrier temperature, allowing an electron-phonon energy relaxation time of $260\ifmmode\pm\else\textpm\fi{}30\mathrm{fs}$ to be measured. The recovery of the reflectivity signal back towards its initial value is largely governed surface recombination: a surface recombination velocity of $(3\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{4}\mathrm{cm}\mathrm{}{\mathrm{s}}^{\ensuremath{-}1}$ is deduced for native-oxide terminated Si(001).

ELECTRON KINETIC THEORY APPROACH FOR PICOSECOND LASER PULSE HEATING

Nonequilibrium heating occurs in a metallic substrate as the heating time approaches the electron-phonon energy relaxation time. In this case, the Fourier heating model fails to predict the correct temperature rise in the surface vicinity of the substrate. Consequently, the heating process needs to be examined at the microscopic level. In thisstudy, laser picosecond pulse heating of gold is considered. The governing transport equation is derived introducing an electron kinetic theory approach. The resulting high-order differential equation describing the energy transport is decomposed into two differential equations similar to those in the two-equation model. The predictions of the electron kinetic theory approach are compared with the two-equation model results for different values of the thermophysical properties of the substrate. It is found that for particular values of mean-free path and the fraction of excess electron energy transfer to lattice site, both predictions are identical. Moreover, the material response to heating pulse is very sensitive as the values of the thermophysical properties of the substrate change.

ELECTRON KINETIC THEORY APPROACH FOR PICOSECOND LASER PULSE HEATING

Nonequilibrium heating occurs in a metallic substrate as the heating time approaches the electron-phonon energy relaxation time. In this case, the Fourier heating model fails to predict the correct temperature rise in the surface vicinity of the substrate. Consequently, the heating process needs to be examined at the microscopic level. In thisstudy, laser picosecond pulse heating of gold is considered. The governing transport equation is derived introducing an electron kinetic theory approach. The resulting high-order differential equation describing the energy transport is decomposed into two differential equations similar to those in the two-equation model. The predictions of the electron kinetic theory approach are compared with the two-equation model results for different values of the thermophysical properties of the substrate. It is found that for particular values of mean-free path and the fraction of excess electron energy transfer to lattice site, both predictions are identical. Moreover, the material response to heating pulse is very sensitive as the values of the thermophysical properties of the substrate change.

ELECTRON KINETIC THEORY APPROACH FOR PICOSECOND LASER PULSE HEATING

Nonequilibrium heating occurs in a metallic substrate as the heating time approaches the electron-phonon energy relaxation time. In this case, the Fourier heating model fails to predict the correct temperature rise in the surface vicinity of the substrate. Consequently, the heating process needs to be examined at the microscopic level. In thisstudy, laser picosecond pulse heating of gold is considered. The governing transport equation is derived introducing an electron kinetic theory approach. The resulting high-order differential equation describing the energy transport is decomposed into two differential equations similar to those in the two-equation model. The predictions of the electron kinetic theory approach are compared with the two-equation model results for different values of the thermophysical properties of the substrate. It is found that for particular values of mean-free path and the fraction of excess electron energy transfer to lattice site, both predictions are identical. Moreover, the material response to heating pulse is very sensitive as the values of the thermophysical properties of the substrate change.

Pulse thermodiffusive processes in semiconductors

A one-dimensional problem for the determination of transient electron and phonon temperatures in bounded semiconductors is solved analytically and an exact expression is obtained. The model includes the heating of one of the surfaces of the sample by a rectangular thermal pulse of an arbitrary duration, separate electron and phonon heat boundary conditions, and electron-phonon energy interaction. The characteristic times of the transient processes are introduced through the electron and phonon thermal diffusion time, τ e,p , and electron-phonon energy relaxation time, τ e . For nondegenerate semiconductors, the electron subsystem is described by the essentially nonequilibrium temperature whereas the phonon temperature is equal to the ambient equilibrium temperature. The heat diffusion process is characterised by parameter τ e in the case of a thin sample as compared with the electron cooling length, while time τ e becomes the characteristic relaxation parameter for long samples. The thermoelectric response is obtained and the analysis is made for the long and short heat pulses.