Electron-phonon Energy Exchange Research Articles

Multi-temperature modeling of femtosecond laser pulse on metallic nanoparticles accounting for the temperature dependences of the parameters

This review considers the fundamental dynamical processes of metal nanoparticles during and after the impact of a femtosecond laser pulse on a nanoparticle, including the absorption of photons. Understanding the sequence of events after photon absorption and their timescales is important for many applications of nanoparticles. Various processes are discussed, starting with optical absorption by electrons, proceeding through the relaxation of the electrons due to electron–electron scattering and electron–phonon coupling, and ending with the dissipation of the nanoparticle energy into the environment. The goal is to consider the timescales, values, and temperature dependences of the electron heat capacity and the electron–phonon coupling parameter that describe these processes and how these dependences affect the electron energy relaxation. Two- and four-temperature models for describing electron–phonon relaxation are discussed. Significant emphasis is paid to the proposed analytical approach to modeling processes during the action of a femtosecond laser pulse on a metal nanoparticle. These consider the temperature dependences of the electron heat capacity and the electron–phonon coupling factor of the metal. The entire process is divided into four stages: (1) the heating of the electron system by a pulse, (2) electron thermalization, (3) electron–phonon energy exchange and the equalization of the temperature of the electrons with the lattice, and (4) cooling of the nanoparticle. There is an appropriate analytical description of each stage. The four-temperature model can estimate the parameters of the laser and nanoparticles needed for applications of femtosecond laser pulses and nanoparticles.

Nonthermal acceleration of atoms as a mechanism of fast lattice heating in ion tracks

Atomic heating in a solid takes place after an impact of a swift heavy ion within a time of electronic cooling there, i.e., ∼100 fs. This implies an extremely fast electron–ion energy exchange (“electron–phonon coupling”) necessary for the production of detected ion tracks. In contrast, laser irradiation experiments and calculations show too slow electron–phonon energy exchange to cause structural changes detected in swift heavy ion tracks in solids. We demonstrate that this contradiction can be resolved by taking into account that electron–phonon coupling is not the sole mechanism of energy exchange between electrons and ions in condensed matter. Excitation of the electronic system alters the potential energy surface of atoms, causing them to accelerate and increase their kinetic energy at ultrashort times.

Analytical modeling of thermal processes during femtosecond laser pulse action on metallic nanoparticle

The analytical approach has been proposed for the modeling of the thermal processes during the action of femtosecond laser pulse on metallic (gold) nanoparticle with allowance for the temperature dependences of the electron heat capacity and the electron-phonon coupling factor of gold based on thermal excitation of electron density. This leads to novel dependence of the electron-phonon equal temperature and the coupling factor on the maximal electron temperature. Whole process of femtosecond nanoparticle action has been divided into three stages which include firstly the heating of electron system by pulse, secondly the electron-phonon energy exchange and the establishment of the equal temperature of electrons with lattice, and thirdly the nanoparticle cooling with the corresponding analytical description of each stage. The satisfactory agreement with the computer results for femtosecond pulses validates of used analytical approach. This model can be used for the estimation of laser and nanoparticle parameters in the fields of the applications of femtosecond laser pulses.

Designer photonic dynamics by using non-uniform electron temperature distribution for on-demand all-optical switching times

While free electrons in metals respond to ultrafast excitation with refractive index changes on femtosecond time scales, typical relaxation mechanisms occur over several picoseconds, governed by electron-phonon energy exchange rates. Here, we propose tailoring these intrinsic rates by engineering a non-uniform electron temperature distribution through nanostructuring, thus, introducing an additional electron temperature relaxation channel. We experimentally demonstrate a sub-300 fs switching time due to the wavelength dependence of the induced hot electron distribution in the nanostructure. The speed of switching is determined by the rate of redistribution of the inhomogeneous electron temperature and not just the rate of heat exchange between electrons and phonons. This effect depends on both the spatial overlap between control and signal fields in the metamaterial and hot-electron diffusion effects. Thus, switching rates can be controlled in nanostructured systems by designing geometrical parameters and selecting wavelengths, which determine the control and signal mode distributions.

Electron-phonon cooling power in Anderson insulators

First microscopic theory for electron-phonon energy exchange in Anderson insulators is developed. The major contribution to the cooling power as a function of electron temperature is shown to be directly related to the correlation function of the local density of electron states at small energy difference argument. In Anderson insulators not far from localization transition, this correlation function is strongly enhanced by wave-function's multi-fractality and, additionally, by the presence of Mott's resonant pairs of localized states. The theory we develop explains huge enhancement of the cooling power observed in insulating Indium Oxide films as compared to predictions of the theory previously developed for disordered metals. Our results open the way to predict the conditions appropriate for the observation of Many Body Localization transition those presence in electronic insulators was advocated in the seminal paper by Basko, Aleiner and Altshuler (2006) but have not been convincingly demonstrated yet.

Effect of boron and nitrogen doping on carrier relaxation dynamics of graphene quantum dots

In the present work, we perform ab initio nonadiabatic molecular dynamics to investigate the charge carrier relaxation dynamics in pristine, boron doped and nitrogen doped graphene quantum dots, respectively. Heteroatom doping changes the local bonding environment of carbon atoms, and induces the charge trapping states into the band gaps of boron doped graphene quantum dot (BGQD) and nitrogen doped graphene quantum dot (NGQD), respectively. Elastic electron-phonon energy exchange destroys the electronic coherence of charge trapping states resulting in a slower electron trapping in BGQDs and a slower hole trapping in NGQDs, respectively, which indicate the high electron mobility of BGQD and high hole mobility of NGQD. In addition, our calculation results suggest the slow and asymmetric electron and hole relaxations of BGQDs are beneficial for both oxidation and reduction reactions for water splitting, while the slower electron relaxation than hole relaxation promises NGQDs the oxidation activity for catalyzing the water splitting. Our work can be used to guide the chemical modification of electronic structures of graphene based QD materials.

Electron–phonon heat exchange in quasi-two-dimensional nanolayers

We study the heat power P transferred between electrons and phonons in thin metallic films deposited on free-standing dielectric membranes. The temperature range is typically below 1 K, such that the wavelengths of the excited phonon modes in the system is large enough so that the picture of a quasi-two-dimensional phonon gas is applicable. Moreover, due to the quantization of the components of the electron wavevectors perpendicular to the metal film’s surface, the electrons spectrum forms also quasi two-dimensional sub-bands, as in a quantum well (QW). We describe in detail the contribution to the electron–phonon energy exchange of different electron scattering channels, as well as of different types of phonon modes. We find that heat flux oscillates strongly with thickness of the film d while having a much smoother variation with temperature (T e for the electrons temperature and T ph for the phonons temperature), so that one obtains a ridge-like landscape in the two coordinates, (d, T e ) or (d, T ph ), with crests and valleys aligned roughly parallel to the temperature axis. For the valley regions we find P ∝ T e 3.5 – T ph 3.5 . From valley to crest, P increases by more than one order of magnitude and on the crests P cannot be represented by a simple power law. The strong dependence of P on d is indicative of the formation of the QW state and can be useful in controlling the heat transfer between electrons and crystal lattice in nano-electronic devices. Nevertheless, due to the small value of the Fermi wavelength in metals, the surface imperfections of the metallic films can reduce the magnitude of the oscillations of P vs. d, so this effect might be easier to observe experimentally in doped semiconductors.

Inelastic electron injection in a water chain

Irradiation of biological matter triggers a cascade of secondary particles that interact with their surroundings, resulting in damage. Low-energy electrons are one of the main secondary species and electron-phonon interaction plays a fundamental role in their dynamics. We have developed a method to capture the electron-phonon inelastic energy exchange in real time and have used it to inject electrons into a simple system that models a biological environment, a water chain. We simulated both an incoming electron pulse and a steady stream of electrons and found that electrons with energies just outside bands of excited molecular states can enter the chain through phonon emission or absorption. Furthermore, this phonon-assisted dynamical behaviour shows great sensitivity to the vibrational temperature, highlighting a crucial controlling factor for the injection and propagation of electrons in water.

Carrier heating and electron-phonon energy exchange effects on nonlinear transport phenomena in semiconductor films

Theory of nonlinear size effects is developed in semiconductor films in the presence of an external dc electric field. The electron and phonon temperatures are calculated self-consistently with the electron-phonon energy interaction taken into account and its influence on the electron current density is considered. The temperature distributions are calculated using appropriate boundary conditions at the surfaces of the semiconductor film. It is shown that the electron and phonon temperatures depend on the electron-phonon coupling factor and the film thickness. Because the electrical conductivity is a function of the electron and phonon temperature distributions, the electron current density in the semiconductor film becomes nonlinear as a function of the heating electric field. We discuss the nonlinear effects for different special cases.

The effect of electron–phonon energy exchange on thermal pulse propagation in semiconductors

In this work, the nonequilibrium electron and phonon temperature distributions in semiconductors, initially heated on the surface with a short laser pulse, are calculated as a function of position and time. The transient temperatures of both quasiparticle systems are calculated self-consistently with the electron–phonon energy interaction taken into account. The electron and phonon temperature distributions are calculated using the Fourier integral and the coupled time-dependent one-dimensional heat diffusion equations for electron and phonon systems with special boundary conditions according to the experimental set-up.

Hierarchical Energy Relaxation in Mesoscopic Tunnel Junctions: Effect of a Nonequilibrium Environment on Low-Temperature Transport

We develop a theory of far from the equilibrium transport in arrays of tunnel junctions. We find that if the rate of the electron-electron interactions exceeds the rate of the electron-phonon energy exchange, the energy relaxation ensuring the charge transfer may occur sequentially. In particular, cotunneling transport in arrays of junctions is dominated by the relaxation via the intermediate bosonic environment, the electron-hole excitations, rather than by the electron-phonon mechanism. The current-voltage characteristics are highly sensitive to the spectrum of the environmental modes and to the applied bias, which sets the lower bound for the effective temperature. We demonstrate that the energy gap in the electron-hole spectrum which opens below some critical temperature T* due to long-range Coulomb interactions gives rise to the suppression of the tunneling current.

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.

Peculiarity of electron–phonon energy exchange in metal nanoparticles and thin films

The size dependence of electron-lattice energy exchange in nanoparticles has been studied. Both surface and bulk energy exchange parameters are examined and it is demonstrated that the bulk energy exchange has non-monotonic oscillations versus size of the particles. It has been found that the amplitude of such oscillations increases with decreasing a particle size until the critical size reaches L c. These bulk interaction related oscillations disappear for the particles less than L c, and only the surface energy exchange remains as the energy flow between electrons and phonons subsystems. It has been shown that there exists an interval of particles sizes with total energy exchange of few orders less than in massive bulk metals. This condition is crucial for existence of hot electrons in stationary conditions in metal nanoparticles, metal island films and thin films as have been observed experimentally.

Effect of electron–phonon energy exchange on thermal wave propagation in semiconductors considering carrier diffusion and recombination

AbstractThe electron, hole, and phonon temperatures are calculated in semiconductors by taking into account the finite carrier diffusion and nonradiative recombination time in the sample. We assume that the energy of the modulated excitation radiation is greater than the energy gap and absorbed at the surface of the semiconductor, therefore, a source of heat and carrier generation at the surface of the sample are time dependent and must be considered in the photothermal theory. Under this situation, the coupled one‐dimensional heat transport (for each quasiparticle system) and carrier diffusion equations in the strong hole–phonon energy interaction approximation and charge quasineutrality condition are solved. Since the nonequilibrium carrier concentration depends sensitively on the electron and phonon fluctuation temperature, the heat power density generated in the sample due to the recombination of the electron–hole pair will be greatly influenced by the inhomogeneous quasiparticle temperature distributions. This latter effect comes through the recombination rate of carriers and it will be considered in the photothermal signal. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical study of ultra-short laser ablation of metals and of laser plume dynamics

Numerical modeling is used to investigate the physical mechanisms of the interaction of ultra-short (subpicosecond) laser pulses with metallic targets. The laser-target interaction is modeled by using a one-dimensional hydrodynamic code that includes the absorption of laser radiation, the electronic heat conduction, the electron-phonon or electron-ion energy exchange, as well as a realistic equation of state. Laser fluences typical for micromachining are considered. The results of the ID modeling are then used as the initial conditions for a 2D plasma expansion model. The dynamics of laser plume expansion in femtosecond regime is investigated. Calculations show that the plasma plume is strongly forward directed. In addition, a two-peaked axial density profile is obtained for 400 nm laser wavelength. The calculation results agree with the experimental observations.

Electron and phonon thermal waves in semiconductors: the effect of carrier diffusion and recombination on the photoacoustic signal

The electron and phonon temperature distributions are calculated in bipolar semiconductors by taking into account generation and heating of carriers on the surface due to the incident modulated laser beam as well as the finite carrier diffusion and recombination in the solid. We solve the coupled one-dimensional heat and carrier diffusion equations in the linear approximation using appropriate boundary conditions according to the photoacoustic experimental conditions. In addition, special emphasis is laid on the dependence of the electron system heat flux on the electron and phonon temperature. We also consider the influence of both temperatures on the recombination of the electron–hole pairs. The dependence of the amplitude of the electron and phonon temperatures on the modulation frequency are analyzed for different values of characteristic parameters of the problem: electron–phonon energy exchange and carrier thermal generation rate.

Femtosecond Nonlinear Optical Spectroscopy of the Acoustic Vibration of Metal Nanoparticles Under High Pressure

A time-resolved femtosecond optical pump-probe setup has been combined with a high hydrostatic pressure apparatus to investigate the pressure dependence of the electron and lattice ultrafast response of silver nanoparticles embedded in a glass. The short time scale measurements shows that the time constant of the electron-phonon energy exchange is unchanged over the studied pressure range (up to 60 kbar). The frequency of the coherent acoustic vibration of the nanoparticles observed on a longer time scale is found to linearly increase with pressure in agreement with the metal elastic property changes. The acoustic mode damping is also found to be modified by pressure, suggesting alteration of the metal-glass interface properties.

Effect of electron-phonon energy exchange on thermal wave propagation in semiconductors

Nonequilibrium, periodic (in both space and time) temperature distributions in the electron and phonon subsystems of a geometrically bounded semiconductor (thermal waves) are calculated self-consistently with the electron-phonon interaction taken into account. Modulated laser radiation, which is converted into heat on the surface of the sample, serves as the external source of energetic nonequilibrium. The dependence of the amplitude and phase of the electron and phonon temperatures on the modulation frequency is analyzed for different sample thicknesses and a number of characteristic parameters of the problem. It is shown that by varying the modulation frequency over a wide range (up to frequencies of the electron-phonon energy exchange) it is possible to generate thermal waves in the electron and phonon subsystems separately.

Size Effects on Nonequilibrium Laser Heating of Metal Films

Picosecond and sub-picosecond lasers have become important tools in the fabrication and study of microstructures. When the laser pulse duration becomes comparable with or less than the characteristic time of energy exchange among microscopic energy carriers, the excited carriers are no longer in thermal equilibrium with the other carriers, creating a nonequilibrium heating situation. The presence of interfaces in metals provides additional scattering processes for electrons, which in turn affects the nonequilibrium heating process. This work studies size effects, due to both surface scattering and grain-boundary scattering, on the thermal conductivity and the energy exchange between electrons and the material lattice. A simple formula is established to predict the influence of film thickness, grain size, interface scattering parameters, and the electron and lattice temperatures on the effective thermal conductivity of metal thin films. Predictions of the analysis agree with the available experimental data. A three-energy-level model is developed to characterize the energy exchange between electrons and the lattice. This study shows that the size effect reduces the effective thermal conductivity and increases the electron-phonon energy exchange rate. The results are useful for improving processing quality, interpreting diagnostic results, and preventing thermal damage of thin films during short-pulse laser heating.

Surface electron-phonon energy exchange in small metallic particles

Abstract In small metallic particles of certain dimensions, the well known ‘bulk’ electron-phonon energy exchange may become ineffective and, as a result, the governing effect proves to be that of interaction between electrons and surface modes. The paper presents a microscopic theory of such electron-surface energy exchange based upon a quantum-kinetic treatment.