Electron-phonon Coupling Factor Research Articles

Evaluating size effects on the thermal conductivity and electron-phonon scattering rates of copper thin films for experimental validation of Matthiessen’s rule

As metallic nanostructures shrink towards the size of the electronic mean free path, thermal conductivity decreases due to increased electronic scattering rates. Matthiessen’s rule is commonly applied to assess changes in electron scattering rates, although this rule has not been validated experimentally at typical operating temperatures for most of the electronic systems (e.g., near room temperature). In this study, we experimentally evaluate the validity of Matthiessen’s rule in determining the thermal conductivity of thin metal films by measuring the in-plane thermal conductivity and electronic scattering rates of copper (Cu) films with varying thicknesses (27 nm — 5 µm), microstructures, and grain boundary segregation. Comparing total electron scattering rates measured with infrared ellipsometry to infrared ultrafast pump-probe measurements, we find that the electron-phonon coupling factor is independent of film thickness, whereas the total electronic scattering rate increases with decreasing film thickness. Our findings provide experimental validation of Matthiessen’s rule for electron transport in thin metal films at room temperature and also introduce an approach to discern critical heat transfer processes in thin metal interconnects, which holds significance for the advancement of future CMOS technology.

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.

Increased thermal conductivity and decreased electron–phonon coupling factor of the aluminum scandium intermetallic phase (Al3Sc) compared to solid solutions

Aluminum scandium alloys and their intermetallic phases have arisen as potential candidates for the next generation of electrical interconnects. In this work, we measure the in-plane thermal conductivity and electron–phonon coupling factor of aluminum scandium alloy thin films deposited at different temperatures, where the temperature is used to control the grain size and volume fraction of the Al3Sc intermetallic phase. As the Al3Sc intermetallic formation increases with higher deposition temperature, we measure increasing in-plane thermal conductivity and a decrease in the electron–phonon coupling factor, which corresponds to an increase in grain size. Our findings demonstrate the role that chemical ordering from the formation of the intermetallic phase has on thermal transport.

Modelling thermal energy transfer in a femtosecond pulsed laser ablation of metal using a coupled spring-mass oscillator

Femtosecond pulsed laser ablation (fs-PLA) is an interesting yet complicated field of study especially for undergraduate students entering the field. Hence, a bridging concept using classical and mechanical analog will be helpful. In this paper, we modelled the thermal energy transfer between electron and lattice system in a fs-PLA of metal described by two temperature model (TTM) using a coupled spring-mass oscillator. This was achieved by providing correspondence of TTM parameters to the coupled spring-mass oscillator, with temperature as position, electron thermal conductivity as coefficient of friction, electron-phonon coupling factor as spring term, electron/lattice heat capacity as the mass m 1/m 2 respectively, and laser source term as the driving force. The thermophysical properties considered are temperature dependent leading to position dependent parameters of coupled spring-mass oscillator. Results showed that the coupled spring-mass oscillator exhibit many behavior similar to the TTM. Additionally, maximum positions achieved by m 2 behave similarly with maximum lattice temperature after achieving certain threshold value. However, many features of TTM such as spatial dependence and crater formation are not observed in the coupled spring-mass oscillator. Despite its limitation, the coupled spring-mass oscillator model was able to represent many features of the thermal energy transfer of fs-PLA, and could be an easy and useful model in understanding fs-PLA.

Pump-probe reflectivity studies of ultrashort laser-induced acousto-mechanical strains in ZnO films

In the current work we report on the generation of acoustic strains in thin ZnO layers using optoacoustic transduction of ultrashort laser pulses into acoustic waves on an Au thin film transducer. After absorption of energy by the electron system of the metal, energy conversion, thermal expansion and mechanical deformation takes place. The generation and propagation of the induced acoustic strains are monitored in time via a degenerate pump-probe transient reflectivity optical setup at 800 nm, as opposed to most commonly used schemes that employ different wavelengths for the pump and probe beams, mostly in the vicinity of ZnO maximum absorption. The experimental results include energy relaxation times and phonon scattering frequencies and are supported by a thermal vibro-acoustic finite element model. The model is based on the combination of a revised two-temperature approach and elasticity theory, and considers anisotropic properties for the ZnO film and the computation of the elastic wave velocity for the first time. The outcomes are discussed in the context of electron–phonon coupling factors and other material properties. A good agreement between the experimental findings and the results from the numerical simulations has been established, regarding outcomes like the mean velocity of the strain waves, establishing a novel characterization method applicable to a variety of materials and structures.

Modeling laser interactions with aluminum and tantalum targets using a hybrid atomistic-continuum model

A hybrid atomistic-continuum method can model the microstructure evolution of metals subjected to laser irradiation. This method combines classical molecular dynamics (MD) simulations with the two-temperature model (TTM) to account for the laser energy absorption and heat diffusion behavior. Accurate prediction of the temperature evolution in the combined MD-TTM method requires reliable accuracy in electron heat capacity, electron thermal conductivity, and electron–phonon coupling factor across the temperatures generated. This study uses the electronic density of states (DOS) obtained from first-principle calculations. The calculated electron temperature-dependent parameters are used in MD-TTM simulations to study the laser metal interactions in FCC and BCC metals and the phenomenon of laser shock loading and melting. This study uses FCC Al and BCC Ta as model systems to demonstrate this capability. When subjected to short pulsed laser shocks, the dynamic failure behavior predicted using temperature-dependent parameters is compared with the experimentally reported single-crystal and nanocrystalline Al and Ta systems. The MD-TTM simulations also investigate laser ablation and melting behavior of Ta to compare with the ablation threshold reported experimentally. This manuscript demonstrates that integrating the temperature-dependent parameters into MD-TTM simulations leads to the accurate modeling of the laser–metal interaction and allows the prediction of the kinetics of the solid–liquid interface.

Femtosecond laser melting NbMoTaW refractory high entropy alloy: A micro-scale thermodynamic simulation

Refractory high entropy alloys (RHEA) exhibit excellent material properties, such as high strength, high hardness, high melting point and high temperature oxidation resistance. Ultrafast laser fabricating RHEAs is potential widely used in extreme environments at high temperature. In the present study, a multiscale simulation of the femtosecond laser pulse melting NbMoTaW RHEA film was performed to observe the transient interaction process between femtosecond laser and RHEA at the atomic scale. The temperature dependent electron thermophysical parameters (electron heat capacity, electron thermal conductivity and effective electron–phonon coupling factor) were calculated from density functional theory. The two temperature model coupling molecular dynamics was used to reveal the temperature change, the density variation and the pressure evolution during the interaction of a single pulse laser with the NbMoTaW RHEA. The simulated ablation and melting depths varied differently with laser fluence parameters. The ablation depth increases with the laser fluence, while the non-removed melting depth varies little with laser energy beyond the ablation threshold. The research reveals the mechanisms in melting process at atomic-level, and the results are helpful to the fabrication of RHEA.

Electronic effects on the radiation damage in high-entropy alloys

High-entropy alloys (HEAs) are exceptional candidates for radiation-resistant materials due to their complex local chemical environment and slow defect migration. Despite commonly overlooked, electronic effects on defects evolution in radiation environments also play a crucial role by dissipating excess energy through electron-phonon coupling and electronic heat conduction during cascade events. We present a systematic study on electronic properties in random-solid solutions (RSS) in four and five principal elements HEAs and their effect on defect formation, clustering, and recombination. Electronic properties, including electron-phonon coupling factor (Ge−ph), the electronic specific heat (Ce), and the electronic thermal conductivity (κe), are computed within first-principles calculations. Using the two-temperature molecular dynamics simulations, we show that the electron-phonon coupling factor and electronic specific heat play a critical role in Frenkel pairs formation. Specifically, the electron-phonon coupling factor quickly dissipates the kinetic energy during primary knock-on atom events via plasmon excitations and is subsequently dissipated via the free-electrons conduction. We show that these effects are more critical than the elastic distortion effects produced by the atomic mismatch. Of tremendous interest, we show that including lighter elements helps to increase Ge−ph suggesting the possibility to improve radiation resistance in HEA through optimal composition.

Transient ferromagnetic-like state in thermally induced magnetization switching: Analysis of the Langevin field and the exchange field

An attractive avenue for a memory device is offered by thermally induced magnetization switching (TIMS), which is expected to increase the storage density. As an essential step in TIMS, the transient ferromagnetic-like state (TFLS) has attracted much attention. Here, our research analyzes the TFLS from the perspective of magnetization rate based on extensive atomic spin simulations in a parameter space necessary for the formation of TIMS. The results demonstrate that the evolution of the magnetization rate for both Fe and Gd sublattices has two peaks at different timescales, and the two peaks are driven by the Langevin field and the exchange field, respectively. By modulating the pulse fluence, the initial temperature, the pulse duration, the electron–phonon coupling factor, and the damping constant, we find that the first peak of the magnetization rate depends not only on the electron thermal bath and temperature of the phonon but also on the energy transfer rate between the electronic system and the spin system. Moreover, we elucidate the role played by the Langevin field and the exchange field in TFLS formation when modulating the pulse fluence, initial temperature, and pulse duration. The simulation results show that the enhancement of the Langevin field prolongs the duration of TFLS. The enhancement of the exchange field at a long pulse duration before the electron system cools down leads to the shortening of the TFLS duration. However, the time required for Gd demagnetization after the electron system cools down to the Curie temperature changes only slightly when modulating these simulated parameters.

Bright short-wavelength infrared organic light-emitting devices

Organic LEDs that emit light in the short-wavelength infrared (SWIR) region, which spans the 1–2 μm region, are attractive for applications in biosensors, biomedical imaging and spectroscopy, and surveillance. However, fabrication of such devices with high radiance has not yet been achieved owing to an intrinsic limitation imposed by the energy-gap law, which leads to extremely low emission efficiencies. Here, we report that acceptor–donor–acceptor-type molecules with high coplanarity, rigid π-conjugated backbones, an extremely small reorganization energy and an electron–phonon coupling factor are capable of simultaneously providing a strongly suppressed non-radiative recombination rate and a high operation stability at high current density. We achieve electrically driven SWIR organic LEDs with an irradiance of up to 3.9 mW cm−2 (corresponding to 7% of direct sunlight infrared irradiance). These findings should open a wide avenue to a new class of organic SWIR light sources for a broad range of applications.

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.

Determination of electron and phonon temperatures in gold thin film irradiated with an ultrashort laser pulse

We measured transient reflectivity of single-crystalline and polycrystalline gold thin films in the wavelength region of 450–700 nm pumped by a 400 nm femtosecond pulse. The observed reflectivity changes were reproduced well by a reflectivity model that we developed based on the joint-density-of-states calculated from the band structure of gold and the Drude model. By a combination use of the reflectivity model and the two-temperature model, we evaluated the temporal evolution of the electron and phonon temperatures from the observed reflectivity changes. Based on the resultant electron and phonon temperatures, we derived the electron–phonon coupling factors, which were consistent with the literature values, in the wide range of the absorbed energy density.

The temperature-variable electron-phonon coupling and its role in the inelastic thermal spike in 3C-SiC

In Two Temperature Model calculations of the inelastic thermal spike produced by swift ions, the electron–phonon coupling factor is often treated as a constant. However, recent first principles calculations in 3C-SiC have shown that this factor is strongly dependent on the electron temperature. The evolution of the electron and phonon temperatures were calculated using both an electron-temperature-variable electron–phonon coupling as well as constant couplings. Temperatures were compared for different stopping powers and at different radii from the ion path. While the use of constant couplings appears to be justified for certain combinations of radius and stopping power, the high energy densities at the center of ion paths formed by swift heavy ions are capable of greatly enhancing the coupling, sometimes by several orders of magnitude. This work emphasizes the importance of the temperature parameterization of the electron–phonon coupling in Two Temperature Model calculations.

Electron–phonon coupling factor and electron heat capacity of 6H-SiC

ABSTRACT For high-energy single ion events, the relationship between electronic energy loss mechanism and atomic processes is generally described by the inelastic thermal spike model. However, the parameters required for the model are not accurately known and are often estimated from a free electron gas model. To ensure this model is more reliable and predictive, a more accurate calculation for the parameters should be taken. In this paper, the temperature dependence of the electronic heat capacity and electron–phonon coupling factor (e-ph) has been calculated, using density functional theory (DFT). The calculation results demonstrate that the effect of electron thermal excitation on the thermodynamic parameters is sensitive to the bandgap, and these parameters vary immensely with the electron temperature. Besides, to verify the accuracy of obtained parameters, both the swift heavy ions (SHI) irradiation in crystalline 6H-SiC and amorphous 6H-SiC are simulated, using the inelastic thermal spike model. And the results are more consistent with the experiment conclusion, for the obtained parameters by DFT. Hence, the calculated temperature-dependent parameters are more suitable for the inelastic thermal spike model.

Ab initio calculation of electron temperature dependent electron heat capacity and electron-phonon coupling factor of noble metals

Noble metal nanoparticles show fantastic catalytic property in various practical applications. It is a promising way to obtain nanoparticles from femtosecond laser ablation of noble metals. The calculation concentrates on electron heat capacity and electron–phonon coupling factor, which are two pivotal parameters describing the femtosecond laser-induced electron heating and the electron–phonon coupled energy transportation. The evolutions of these two parameters with increasing electron temperature are presented. It is found that the evolutions of the electron heat capacity and electron–phonon coupling factor are mainly affected by the electron density of states and the Fermi-Dirac distribution function.

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.

Vacancy-induced enhancement of electron–phonon coupling in cubic silicon carbide and its relationship to the two-temperature model

The electron–phonon coupling factor was calculated for both pristine and vacancy-rich 3C-SiC. Ab initio calculations were performed within the framework of the density functional perturbation theory. Wannier functions were used to interpolate eigenvalues into denser grids through the electron–phonon using Wannier code. The coupling factor was determined through calculations of the electron self-energy, electron–phonon relaxation time, and electronic specific heat. These parameters were extrapolated to high temperatures using a hybrid model which mixes band calculations for electrons below an energy cutoff with the free electron gas model for electrons above the energy cutoff. The electron relaxation times, specific heats, electron drift mobilities, and electron–phonon coupling factors were calculated as a function of electron temperature. Si and C vacancies were found to have a profound effect on electron–phonon coupling for all temperatures, while electronic specific heat capacity was found to be most affected at cryogenic temperatures. The electron drift mobility was calculated at different temperatures using the scattering time. Calculated mobilities were validated with Hall mobility measurements reported in the literature. The importance of structural defects on the electron–phonon coupling is discussed in the context of the two-temperature model, a model that has been widely used to understand aspects of the interaction of solids with pulsed laser irradiation and swift heavy ion irradiation.

Temperature dependent electron–phonon coupling of Au resolved via lattice dynamics measured with sub-picosecond infrared pulses

The detailed understanding of energy transfer between hot electrons and lattice vibrations at non-cryogenic temperatures relies primarily upon the interpretation of ultrafast pump–probe experiments, where thermo-optical models provide insight into the relationship between optical response and temperature of the respective sub-systems; in one of the more studied materials, gold, the Drude model provides this relationship. In this work, we investigate the role of intra- and interband contributions applied to transient optical responses in ultrafast pump–probe experiments using both experiments and first-principle calculations, with probe wavelengths spanning from UV wavelengths into the infrared. We find that during conditions of electron–phonon equilibrium, the Drude model is not applicable to visible wavelengths due to interband transitions. Instead, at probe wavelengths far from these interband transitions (e.g., infrared wavelengths), the optical response is linearly proportional to the temperature of the phonon sub-system and is no longer obfuscated by Fermi-smearing, thus greatly simplifying the extraction of the electron–phonon coupling factor. Our intraband-probe measurements on the electron–phonon coupling factor of Au are in excellent agreement with analytical models and ab initio calculations; we observe a constant electron–phonon coupling factor up to electron temperatures of at least ∼2000 K.

Band alignment and defects influence the electron–phonon heat transport mechanisms across metal interfaces

We report on the experimental determination of electron–electron conductance at Au/TiOx interfacial regions and electron–phonon coupling of thin TiOx layers for x = 0–2.62. Our study demonstrates that the electronic energy transport mechanisms at metal/metal oxide interfaces are enhanced through metallic defects that lead to electronic band alignment between the metal and metal oxide (in our case, Au and TiOx). Electronic heat transport processes are interrogated via a pump/probe technique, utilizing sub-picosecond laser pulses to monitor the ultrafast thermoreflectance responses of Au/TiOx systems, which were analyzed using a two-temperature model to extract electron–electron conductances at Au/TiOx interfaces and the electron–phonon coupling in TiOx layers. We find that TiOx stoichiometries near TiO2 have ultrahigh electron–phonon coupling factors similar to that of pure Ti and that electronic energy transmission from Au to TiOx layers is comparable to that of Au to Ti due to the presence of Ti0 defects. For x = 2.62 in TiOx, electron–phonon coupling is reduced by more than a factor of 5. Our experimental data are corroborated by real-time time-dependent density functional theory calculations, which show that excited electrons in Au do not participate in the TiOx phonon relaxation process, resulting in lower electron–electron energy transmission from Au and electron–phonon coupling due to the difference in the Fermi energy of Au relative to the conduction band minimum of TiOx when x >2.

Ablation study in gold irradiated by single femtosecond laser pulse with electron temperature dependent interatomic potential and electron–phonon coupling factor

The interactions of femtosecond lasers with gold targets are investigated with a numerical method combining molecular dynamics and two-temperature model and temperature dependent thermodynamic parameters. The influence of the electron temperature dependent (ETD) interatomic potential on ablation processes was analyzed. We also adopted an ETD electron–phonon coupling factor and further analyzed different ablation mechanisms under absorbed fluences ranging from Our simulation results showed good agreements on melting and ablation depth with both experiments and other simulations. Three ablation mechanisms were identified: nonthermal ablation caused by electronic pressure from the ETD interatomic potential, spallation by stresses from a rapid heating of the target and phase explosion due to explosive boiling. With a continuously updated ETD potential in accordance with electron temperature, one can explain the unique U shape profile of plume atomization degree as a function of laser fluence found in experiments.