Electron-phonon Nonequilibrium Research Articles

Nonequilibrium electronic properties and stability consequences in metallic crystalline binary alloys under ultrafast laser excitation

This study undertakes an exhaustive exploration of properties under electron-phonon nonequilibrium for a series of ten industrially pertinent crystalline alloys, namely AlCu, AlNi, AlTi, AuCu, CuNi, CuTi, NbZr, NiTi, NiZr, and ZrCu. This comprehensive investigation encompasses electronic heat capacity, electron-phonon coupling factor, excited electron density, electronic pressure, dielectric function, refractive index, extinction coefficient, reflectivity, and optical penetration depth. Employing ab initio simulations, we meticulously analyze the nonequilibrium optoelectronic attributes inherent to these alloys change under electronic excitation across the temperature range going from 0 to 50,000 K. Additionally, to contextualize the findings, we employ classical Molecular Dynamics coupled with a Two Temperature Model simulation, notably to deliver a deep comprehension of the intricate mechanisms of the CuTi alloy ablation induced by femtosecond laser irradiation.

Effective electronic properties and coupling for two-temperature model-molecular dynamics simulation of ultrafast laser ablation of nickel

ABSTRACT The accuracy of hybrid two temperature model-molecular dynamics (TTM-MD) simulations in predicting the ultrafast laser ablation phenomena in metals is influenced by the functional definition of subsystem properties and electronic-lattice coupling. In this work, laser ablation of nickel is simulated using hybrid TTM-MD with empirical and density function theory (DFT) derived electronic and coupling parameter sets. The investigation revealed that the empirically derived temperature-dependent parameterisation of electronic specific heat, thermal conductivity, and coupling factor enhanced the fidelity of electron–phonon nonequilibrium dynamics when used in conjunction with simple optical absorption models, aligning closely with prior experimental observations for nickel specimens. The TTM-MD setup is then coupled utilising two widely used coupling techniques – the temperature difference scaled and Langevin thermostat. It is found that the former exhibits increased tensile stress due to artificial enhancement of the collision cascade owing to deterministic nature of the coupling force. While the probabilistic nature of the Langevin thermostat offers more accurate predictions of the ablation threshold/yield. Under these conditions, the TTM-MD scheme is tested for a range of absorbed laser fluence, with ablation threshold, and the onset of phase explosion is determined as 115 and 270 mJ/cm2, respectively for a 1 picosecond (ps-) laser pulse.

The effect of enhanced heat transfer across metal-nonmetal interfaces subject to femtosecond laser irradiation.

The heat transfer across metal-nonmetal interfaces inevitably affects the femtosecond laser processing of thin metal films coated on nonmetal substrates. In the present work, a two-temperature model with a metal-nonmetal interface is employed to numerically investigate the heat transfer across a metal-nonmetal interface. A parallel-series thermal circuit is considered under the drastic electron-phonon nonequilibrium induced by femtosecond laser irradiation. The interfacial thermal resistance affects temporal evolutions of surface electron temperature and phonon temperature, as well as the optical response simulated by the Drude-Lorentz model. By inserting an interlayer and reducing the interfacial thermal resistance, the enhanced heat transfer across Au-Al2O3 and Au-Si interfaces is confirmed. More heat transfers from a metal to a nonmetal due to lower total interfacial thermal resistance, which reshapes the temperature distributions of metal-electrons, metal-phonons, and nonmetal-phonons. Consequently, the higher damage threshold of thin Au films and the lower sensitivity of damage threshold versus film thickness are determined. It implies that the heat transfer across metal-nonmetal interfaces is found to affect the transient thermal reflectivity detection and the repeatable femtosecond laser processing of thin metal films.

Drude-Lorentz Model for Optical Properties of Photoexcited Transition Metals under Electron-Phonon Nonequilibrium

Evaluating the optical properties of matter under the action of ultrafast light is crucial in modeling laser–surface interaction and interpreting laser processing experiments. We report optimized coefficients for the Drude-Lorentz model describing the permittivity of several transition metals (Cr, W, Ti, Fe, Au, and Ni) under electron-phonon nonequilibrium, with electrons heated up to 30,000 K and the lattice staying cold at 300 K. A Basin-hopping algorithm is used to fit the Drude-Lorentz model to the nonequilibrium permittivity calculated using ab initio methods. The fitting coefficients are provided and can be easily inserted into any calculation requiring the optical response of the metals during ultrafast irradiation. Moreover, our results shed light on the electronic structure modifications and the relative contributions of intraband and interband optical transitions at high electron temperatures corresponding to the laser excitation fluence used for surface nanostructuring.

Thermal barrier effect from internal pore channels on thickened aluminum nanofilm

High thermal conductivity nanofilms play a key role in the heat dissipation of microdevices, and the preparation process greatly influences the thermal conductivity of the nanofilms. In this study, four Al nanofilms with different thicknesses were fabricated via the electron beam evaporation method, and their effective thermal conductivity (ETC) values were measured using a specially designed microsensor-based third harmonic 3ω method. Due to the internal pore channels and nanometer-level feature size, the ETC of nanofilms exhibited a downward trend when the thickness increases. Significantly, the pores produced by the preparation induce the electron-phonon nonequilibrium effect inside the film, resulting in an anomalous change of the film thermal conductivity versus the thickness.

Effects of the Filler Property, Electron–Phonon Coupling on Thermal Conductivity, and Strain Rate on the Mechanical Property of Polyethylene Nanocomposites

Electron–phonon interaction (EPI) plays an important role in the transport property of metals. Nevertheless, EPI in polymer nanocomposites containing metal fillers has not been fully investigated due to the complicated physical mechanisms. In this work, the copper–polyethylene (Cu–PE) nanocomposite is used as a model system, and nonequilibrium molecular dynamics (NEMD) simulation combined with the two-temperature model (TTM) is conducted to reveal the role of EPI in Cu–PE systems. The effects of filler length, filler property, and EPI strength on thermal conductivity are revealed. A dimensionless number (Θ) is defined to characterize the electron–phonon nonequilibrium (EPN) degree. The results show that the EPN degree has a significant impact on thermal conductivity. When the system is in a strong EPN state, the effects of EPI on thermal conductivity can be negligible. However, when the EPN degree gradually decreases, ignoring EPI can severely underestimate the thermal conductivity. Furthermore, the temperature profile of electrons and phonons is extracted and the equivalent thermal circuit is presented. The additional thermal resistances induced by the nonlocal and nonequilibrium effects are revealed. Phonon spectra analysis and heat current decomposition are performed to uncover the underlying mechanisms. In addition, the effects of atomic mass density and filler types on thermal conductivity are revealed. Stress–strain simulation is conducted to unravel the effects of strain rates on the mechanical property. The results are useful for designing polymer nanocomposites with controlled thermal conductivity.

Nondiffusive electron transport in metals: A two-temperature Boltzmann transport equation analysis of thermoreflectance experiments

We develop a theoretical framework based on the electron-phonon coupled Boltzmann transport equations (BTEs) for the interpretation of nondiffusive thermal conductivity measurements in metals made via frequency domain thermoreflectance (FDTR). The thermal conductivity of a bulk gold crystal was measured over a temperature range of 23--304 K as a function of FDTR's laser spot size. Our interpretation of these measurements by a two-temperature heat diffusion model finds that the thermal conductivity is suppressed when the laser spot size is comparable to electron mean free paths. Using a simplified spherical geometry that enables analytical solutions, we compare the two-temperature diffusion model with the coupled BTEs to identify a thermal conductivity suppression function. We also conclude that over the timescales of our experiment electron-phonon nonequilibrium is negligible, but that the length scale of heat deposition by hot electrons critically influences our interpretation.

Hot Electron Thermoreflectance Coefficient of Gold during Electron–Phonon Nonequilibrium

The temperature-dependent reflectivity of metals is quantified by the thermoreflectance coefficient, which is a material-dependent parameter that depends on the metallic band structure, electron scattering dynamics, and photon wavelength. After short-pulse laser heating, the electronic subsystem in a metal can be driven to temperatures much higher than that of the lattice, which gives rise to unique nonequilibrium electron and phonon scattering dynamics, leading to a “hot electron” thermoreflectance that is different from the traditionally measured equilibrium coefficient. In this work, we analytically quantify and experimentally measure this hot electron thermoreflectance coefficient through ultrafast pump–probe measurements of thin gold films on silica glass and sapphire substrates. We demonstrate the ability to not only quantify the thermoreflectance during electron–phonon nonequilibrium but also validate this coefficient’s predicted dependence on the absolute temperature of the electronic subsystem. T...

Mapping momentum-dependent electron-phonon coupling and nonequilibrium phonon dynamics with ultrafast electron diffuse scattering

Despite their fundamental role in determining material properties, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling (EPC and PPC, respectively) across the entire Brillouin zone (BZ) has proved difficult to obtain. Here we demonstrate that ultrafast electron diffuse scattering (UEDS) directly provides such information. By exploiting symmetry-based selection rules and time-resolution, scattering from different phonon branches can be distinguished even without energy resolution. Using graphite as a model system, we show that UEDS patterns map the relative EPC and PPC strength through their profound sensitivity to photoinduced changes in phonon populations. We measure strong EPC to the $K$-point transverse optical phonon of $A_1'$ symmetry ($K-A_1'$) and along the entire longitudinal optical branch between $\Gamma-K$, not only to the $\Gamma-E_{2g}$ phonon as previously emphasized. We also determine that the subsequent phonon relaxation pathway involves three stages; decay via several identifiable channels to transverse acoustic (TA) and longitudinal acoustic (LA) phonons (1-2 ps), intraband thermalization of the non-equilibrium TA/LA phonon populations (30-40 ps) and interband relaxation of the LA/TA modes (115 ps). Combining UEDS with ultrafast angle-resolved photoelectron spectroscopy will yield a complete picture of the dynamics within and between electron and phonon subsystems, helping to unravel complex phases in which the intertwined nature of these systems have a strong influence on emergent properties.

Effect of interlayer on interfacial thermal transport and hot electron cooling in metal-dielectric systems: An electron-phonon coupling perspective

It was reported that an interlayer with intermediate phonon spectra between two dielectric materials could reduce the phononic interfacial thermal resistance. In this work, we show that an appropriate choice of interlayer materials with relatively strong electron-phonon coupling could significantly enhance interfacial thermal transport across metal-dielectric interfaces. Our Boltzmann transport simulations demonstrate that such enhancement is achieved by the elimination of electron-phonon nonequilibrium near the original metal-dielectric interface. Moreover, we reveal that interlayer can substantially accelerate hot electron cooling in thin films with weak electron-phonon coupling, for example, Cu, Ag, and Au, supported on a dielectric substrate. At the same time, lattice heating in the thin film is largely reduced.

Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: A first-principles study

The electronic behavior of various solid metals (Al, Ni, Cu, Au, Ti, and W) under ultrashort laser irradiation is investigated by means of density functional theory. Successive stages of extreme nonequilibrium on picosecond time scale impact the excited material properties in terms of optical coupling and transport characteristics. As these are generally modelled based on the free-electron classical theory, the free-electron number is a key parameter. However, this parameter remains unclearly defined and dependencies on the electronic temperature are not considered. Here, from first-principles calculations, density of states are obtained with respect to electronic temperatures varying from 10^-2 to 10^5 K within a cold lattice. Based on the concept of localized or delocalized electronic states, temperature dependent free-electron numbers are evaluated for a series of metals covering a large range of electronic configurations. With the increase of the electronic temperature we observe strong adjustments of the electronic structures of transition metals. These are related to variations of electronic occupation in localized d bands, via change in electronic screening and electron-ion effective potential. The electronic temperature dependence of nonequilibrium density of states has consequences on electronic chemical potentials, free-electron numbers, electronic heat capacities, and electronic pressures. Thus electronic thermodynamic properties are computed and discussed, serving as a base to derive energetic and transport properties allowing the description of excitation and relaxation phenomena caused by rapid laser action.

Ultrafast thermoelectric properties of gold under conditions of strong electron-phonon nonequilibrium

The electronic scattering rates in metals after ultrashort pulsed laser heating can be drastically different than those predicted from free electron theory. The large electron temperature achieved after ultrashort pulsed absorption and subsequent thermalization can lead to excitation of subconduction band thermal excitations of electron orbitals far below the Fermi energy. In the case of noble metals, which all have a characteristic flat d-band several electron volts well below the Fermi energy, the onset of d-band excitations has been shown to increase electron-phonon scattering rates by an order of magnitude. In this paper, we investigate the effects of these large electronic thermal excitations on the ultrafast thermoelectric transport properties of gold, a characteristic noble metal. Under conditions of strong electron-phonon nonequilibrium (relatively high electron temperatures and relatively low lattice temperatures, Te⪢TL), we find that the Wiedemann–Franz law breaks down and the Seebeck coefficient is massively enhanced. Although we perform representative calculations for Au, these results are expected to be similar for the other noble metals (Ag and Cu) due to the characteristic large d-band separation from the Fermi energy.

Contribution of d-band electrons to ballistic transport and scattering during electron-phonon nonequilibrium in nanoscale Au films using an ab initio density of states

Electron-interface scattering during electron-phonon nonequilibrium in thin films creates another pathway for electron system energy loss as characteristic lengths of thin films continue to decrease. As power densities in nanodevices increase, excitations of electrons from sub-conduction-band energy levels will become more probable. These sub-conduction-band electronic excitations significantly affect the material’s thermophysical properties. In this work, the role of d-band electronic excitations is considered in electron energy transfer processes in thin Au films. The electronic structure and density of states for gold are calculated using a plane wave pseudopotential density function approach. In thin films with thicknesses less than the electron mean free path, ballistic electron transport leads to electron-interface scattering. The ballistic component of electron transport is studied by a ballistic-diffusive approximation of the Boltzmann transport equation with input from ab initio calculations. The effects of d-band excitations on electron-interface energy transfer are analyzed during electron-phonon nonequilibrium after short pulsed laser heating in thin films.

Modeling Electron-Phonon Nonequilibrium in Gold Films Using Boltzmann Transport Model

Ultrashort-pulsed laser irradiation on metals creates a thermal nonequilibrium between electrons and the phonons. Previous computational studies used the two-temperature model and its variants to model this nonequilibrium. However, when the laser pulse duration is smaller than the relaxation time of the energy carriers or when the carriers’ mean free path is larger than the material dimension, these macroscopic models fail to capture the physics accurately. In this paper, the nonequilibrium between energy carriers is modeled via a numerical solution of the Boltzmann transport model (BTM) for electrons and phonons, which is applicable over a wide range of lengths and time scales. The BTM is solved using the discontinuous Galerkin finite element method for spatial discretization and the three-step Runge–Kutta temporal discretization. Temperature dependent electron-phonon coupling factor and electron heat capacity are used due to the strong electron-phonon nonequilibrium considered in this study. The results from the proposed model are compared with existing experimental studies on laser heating of macroscale materials. The model is then used to study laser heating of gold films, by varying parameters such as the film thickness, laser fluence, and pulse duration. It is found that the temporal evolution of electron and phonon temperatures in nanometer size gold films is very different from the macroscale films. For a given laser fluence and pulse duration, the peak electron temperature increases with a decrease in the thickness of the gold film. Both film thickness and laser fluence significantly affect the melting time. For a fluence of 1000 J/m2, and a pulse duration of 75 fs, gold films of thickness smaller than 100 nm melt before reaching electron-phonon equilibrium. However, for the film thickness of 2000 nm, even with the highest laser fluence examined, the electrons and phonons reach equilibrium and the gold film does not melt.

Effects of electron-boundary scattering on changes in thermoreflectance in thin metal films undergoing intraband excitations

As characteristic sizes and lengths scales continue to decrease in nanostructures, carrier scattering processes at the geometric boundaries and interfaces in nanosystems become more prevalent. These scattering events can lead to additional resistances. This paper investigates electron-boundary scattering processes by examining changes in thermoreflectance signals in thin films after short pulsed laser heating. To take electron-boundary scattering into account, an additional scattering term is introduced into the Drude model for the complex dielectric function. Using an intraband thickness-dependent reflectance model, transient thermoreflectance data of Au films subject to intraband excitations are analyzed with the electron-boundary scattering Drude model introduced in this work. The electron-boundary scattering rate is determined from Au thermoreflectance data, showing that after short pulsed laser heating, electron-boundary scattering rates can be almost three orders of magnitude greater than the electron-electron and electron-phonon scattering rates. The scattering rates determined from the thermoreflectance data agree well with the theoretical predictions for electron-boundary scattering calculated from an electron-boundary scattering model for disordered conductors in the event of an electron-phonon nonequilibrium.

Contribution of Ballistic Electron Transport to Energy Transfer During Electron-Phonon Nonequilibrium in Thin Metal Films

AbstractWith the ever decreasing characteristic lengths of nanomaterials, nonequilibrium electron-phonon scattering can be affected by additional scattering processes at the interface of two materials. Electron-interface scattering would lead to another path of energy flow for the high-energy electrons other than electron-phonon coupling in a single material. Traditionally, electron-phonon coupling in transport is analyzed with a diffusion (Fourier) based model, such as the two temperature model (TTM). However, in thin films with thicknesses less than the electron mean free path, ballistic electron transport could lead to electron-interface scattering, which is not taken into account in the TTM. The ballistic component of electron transport, leading to electron-interface scattering during ultrashort pulsed laser heating, is studied here by a ballistic-diffusive approximation of the Boltzmann transport equation. The results for electron-phonon equilibration times are compared with calculations with TTM based approximations and experimental data on Au thin films.

Effects of electron scattering at metal-nonmetal interfaces on electron-phonon equilibration in gold films

Electron scattering at interfaces between metals and dielectrics is a major concern in thermal boundary conductance studies. This aspect of energy transfer has been extensively studied and modeled on long time scales when the electrons and phonons are in equilibrium in the metal film. However, there are conflicting results concerning electron-interface scattering and energy transfer in the event of an electron-phonon nonequilibrium, specifically, how this mode of energy transfer affects the electron cooling during electron-phonon nonequilibration. Transient thermoreflectance (TTR) experiments utilizing ultrashort pulsed laser systems can resolve this electron-phonon nonequilibrium, and the thermophysical property relating rate of equilibration to electron-phonon scattering events G can be quantified. In this work, G in Au films of varying thicknesses are measured with the TTR technique. At large fluences (which result in high electron temperatures), the measured G is much larger than predicted from traditional models. This increase in G increases as the film thickness decreases and shows a substrate dependency, with larger values of G measured on more conductive substrates. The data suggest that in a highly nonequilibrium system, there could be some thermal energy lost to the underlying substrate, which can affect G.

Measurement and evaluation of the interfacial thermal resistance between a metal and a dielectric

We used a sandwiched film structure of dielectric, metal, and dielectric to measure and also to estimate theoretically the metal-dielectric interfacial thermal resistance. In this structure, a metal layer with a thickness of about 10 nm, including chromium, titanium, aluminum, nickel, and platinum, is sandwiched between two SiO2 layers with a thickness of 100 nm prepared by plasma enhanced chemical vapor deposition. The estimates, 10−10–10−9 m2 K W−1, calculated with a continuum two-fluid model are significantly smaller than the measured values, ∼10−8 m2 K W−1. The continuum two-fluid model, according to the phenomena of electron-phonon nonequilibrium near the interface in a metal, cannot explain completely the cause of this metal-dielectric interfacial thermal resistance. From photographs of the transmission electron microscopy cross section, we argue that defects at an interface likely play an important role in the magnitude of the interfacial thermal resistance.

Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium

The dependence of the strength of the electron-phonon coupling and the electron heat capacity on the electron temperature is investigated for eight representative metals, Al, Cu, Ag, Au, Ni, Pt, W, and Ti, for the conditions of strong electron-phonon nonequilibrium. These conditions are characteristic of metal targets subjected to energetic ion bombardment or short-pulse laser irradiation. Computational analysis based on first-principles electronic structure calculations of the electron density of states predicts large deviations (up to an order of magnitude) from the commonly used approximations of linear temperature dependence of the electron heat capacity and a constant electron-phonon coupling. These thermophysical properties are found to be very sensitive to details of the electronic structure of the material. The strength of the electron-phonon coupling can either increase (Al, Au, Ag, Cu, and W), decrease (Ni and Pt), or exhibit nonmonotonic changes (Ti) with increasing electron temperature. The electron heat capacity can exhibit either positive (Au, Ag, Cu, and W) or negative (Ni and Pt) deviations from the linear temperature dependence. The large variations of the thermophysical properties, revealed in this work for the range of electron temperatures typically realized in femtosecond laser material processing applications, have important implications for quantitative computational analysis of ultrafast processes associated with laser interaction with metals.

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.