Nonequilibrium Electron Research Articles

Ultra-Short Pulses Laser Heating of Dielectrics: A Semi-Classical Analytical Model

Femtosecond laser pulses are currently regarded as an emerging and promising tool for processing wide bandgap dielectric materials across a variety of high-end applications, although the associated physical phenomena are not yet fully understood. To address these challenges, we propose an original, fully analytical model combined with Two Temperatures Model (TTM) formalism. The model is applied to describe the interaction of fs laser pulses with a typical dielectric target (e.g., Sapphire). It describes the heating of dielectrics, such as Sapphire, under irradiation by fs laser pulses in the range of (1012–1014) W/cm2. The proposed formalism was implemented to calculate the free electron density, while numerical simulations of temperature field evolution within the dielectrics were conducted using the TTM. Mathematical models have rarely been used to solve the TTM in the context of laser–dielectric interactions. Unlike the TTM applied to metals, which requires solving two heat equations, for dielectrics the free electron density must first be determined. We propose an analytical model to solve the TTM equations using this parameter. A new simulation model was developed, combining the equations for non-equilibrium electron density determination with the TTM equations. Our analyses revealed the non-linear nature of the physical phenomena involved and the inapplicability of the Beer–Lambert law for fs laser pulse interactions with dielectric targets at incident laser fluences ranging from 6 to 20 J/cm2.

Hot carrier transfer from plasmon decay in Ag20at H-Si(111) surface: Real-time TDDFT simulation in Wannier gauge.

Plasmon decay is believed to play an essential role in inducing hot carrier transfer at the interfaces between plasmonic nanoparticles and semiconductor surfaces. In this work, we employ real-time time- dependent density functional theory (RT-TDDFT) simulation in the Wannier gauge to gain quantum- mechanical insights into the nonlinear dynamics of the plasmon decay in the Ag20 nanoparticle at a semiconductor surface. The first-principles simulations show that the plasmon decay is more than two times faster when the Ag20 nanoparticle is adsorbed on a hydrogen-terminated Si(111) surface, taking place within 100 femtoseconds of the plasmon excitation. Hot carrier transfer across the interface is observed as the plasmon decay takes place, and nearly 30% of holes are generated deep in the valence band of the semiconductor surface. The use of Wannier gauge in RT-TDDFT simulation is particularly convenient for gaining quantum-mechanical insights into non-equilibrium electron dynamics in complex heterogeneous systems.

Phonon growth characteristics in one-dimensional cylindrical quantum wires at low lattice temperatures

The phonon growth characteristics in a cylindrical quantum wire structure has been theoretically analysed here under the condition of low lattice temperature. The present theory takes into account the effects of finite barrier height, energy band non-parabolicity of the material and the non-zero values of the transverse components of the phonon wave vector. At the low lattice temperatures again, the interaction of the non-equilibrium electrons with acoustic phonons becomes inelastic and consequently the phonon distribution cannot be approximated by the simple equipartition law. Hence the full form of the Bose-Einstein distribution for the phonon ensemble is taken into consideration. The numerical results that follow from the present theory for the wire samples of GaAs/Ga0.7Al0.3As and Ga0.47In0.53As/InP turn out to be quite different from what follows in the traditional simplified framework.

THE COMPOSITION OF IMPURITIES AND DEFECTS IN Cd1-XMgXTe:In, NECESSARY TO ENSURE STABLE DETECTOR PROPERTIES

A model study of the promising new material Cd0.92Mg0.08Te:In, intended for X-ray and gamma radiation detectors operating at room temperature, was carried out. The paper highlights the results of quantitative studies of the influence of the content of impurities and structural defects on the electrophysical and detector properties of Cd0.92Mg0.08Te:In. An analysis of the calculated values of resistivity ρ and concentrations of free charge carriers, life time of non-equilibrium electrons τn, and holes τp, charge collection efficiency η with different composition of impurities and defects in this material at temperature T = 298 K was carried out. The optimal ranges of energy and concentration of alloying deep donor, which ensure a stable high-resistive state and acceptable values of η, are established. Compensation of cadmium vacancies with indium admixture was studied. Assumption was made regarding possibility of increasing the operating time of the detector having semi-insulating properties and great charge collection efficiency. A direction for further research has been formulated in order to clarify the nature of a suitable doping deep donor that ensures stable properties of the detector.

Hot Electron Cooling in n-Doped Colloidal Nanoplatelets Following Near-Infrared Intersubband Excitation.

Intersubband transition was recently discovered in colloidal nanoplatelets, but the associated intersubband carrier relaxation dynamics remains poorly understood. In particular, it is crucial to selectively excite the intersubband transition and to follow the hot electron dynamics in the absence of valence-band holes. This is achieved herein by exciting the predoped electrons in CdSe/ZnS nanoplatelets using near-infrared femtosecond pulses and monitoring nonequilibrium electron dynamics using broad-band visible pulses. We find that the n = 2 electrons relax to the n = 1 subband and establish a Fermi-Dirac distribution within 200 fs, and finally reach an equilibrium with the lattice within a few ps. The cooling dynamics depend mainly on the excitation fluence but weakly on the doping density and the lattice temperature. These characteristics are well captured by our numerical simulation that explicitly accounts for the state occupation effect and optical phonon scattering.

Resolving plasmon-mediated high-order multiphoton excitation pathways in dolmen nanostructures using ultrafast nonlinear optical interferometry.

The multiphoton excitation pathways of plasmonic nanorod assemblies are described. By using dolmen structures formed from the directed assembly of three gold nanorods, plasmon-mediated three-photon excitation is resolved. These high-order multiphoton excitation channels were accessed by resonantly exciting a hybrid mode of the dolmen structure that was resonant with the 800-nm carrier wavelength of an ultrafast laser system. Rotation of the exciting field polarization to a non-resonant configuration did not generate third-order responses. Hence, the multiphoton excitation and resultant non-equilibrium electron distributions were generated by structure- and mode-selective excitation. Correlation between high-order and resonant plasmon excitation was achieved through sub-cycle time-resolved interferometric detection of incoherent nonlinear emission signals. The results illustrate the advantages of nonlinear optical interferometry and Fourier analysis for distinguishing plasmon-mediated processes from those that do not require plasmon excitation.

Reversible modulation of superconductivity in thin-film NbSe2 via plasmon coupling

In recent years, lightwave has stood out as an ultrafast, non-contact control knob for developing compact superconducting circuitry. However, the modulation efficiency is limited by the low photoresponse of superconductors. Plasmons, with the advantages of strong light-matter interaction, present a promising route to overcome the limitations. Here we achieve effective modulation of superconductivity in thin-film NbSe2 via near-field coupling to plasmons in gold nanoparticles. Upon resonant plasmon excitation, the superconductivity of NbSe2 is substantially suppressed. The modulation factor exceeds 40% at a photon flux of 9.36 × 1013 s−1mm−2, and the effect is significantly diminished for thicker NbSe2 samples. Our observations can be theoretically interpreted by invoking the non-equilibrium electron distribution in NbSe2 driven by the plasmon-associated evanescent field. Finally, a reversible plasmon-driven superconducting switch is realized in this system. These findings highlight plasmonic tailoring of quantum states as an innovative strategy for superconducting electronics.

Transmissions of an x-ray free electron laser pulse through Al: Influence of nonequilibrium electron kinetics.

A theoretical model for investigating the radiative transfer of an x-ray free electron laser (XFEL) pulse is developed based on a one-dimensional radiative transfer equation. The population dynamics of energy levels is obtained by rate equationapproximation coupling with the Fokker-Planck equation, in which the electron energy distribution function (EEDF) is self-consistently determined. As an illustrative example, XFEL pulse propagation through a solid-density aluminum (Al) is investigated. The characteristics of the temporal evolution of the x-ray pulse shape, level population, and EEDF are demonstrated. The EEDF usually has two parts in XFEL-Al interactions: the near equilibrium part in the lower energy regions and the nonequilibrium part in the higher energy region. The deep gap between the two parts is quickly filled in the solid-density Al plasma. The pulse shape is distorted and the duration shortens as the x-ray pulse propagates through the Al sample. The x-ray transmission spectra were compared with experimental and other theoretical results, and good agreement was found. There are slight discrepancies between the transmission obtained by solving the Fokker-Planck equationand Maxwellian assumptions because nonequilibrium electrons in the higher energy region account for only a small fraction of the total electrons.

Impacts of hot electron diffusion, electron–phonon coupling, and surface atoms on metal surface dynamics revealed by reflection ultrafast electron diffraction

Metals exhibit nonequilibrium electron and lattice subsystems at transient times following femtosecond laser excitation. In the past four decades, various optical spectroscopy and time-resolved diffraction methods have been used to study electron–phonon coupling and the effects of underlying dynamical processes. Here, we take advantage of the surface specificity of reflection ultrafast electron diffraction (UED) to examine the structural dynamics of photoexcited metal surfaces, which are apparently slower in recovery than predicted by thermal diffusion from the profile of absorbed energy. Fast diffusion of hot electrons is found to critically reduce surface excitation and affect the temporal dependence of the increased atomic motions on not only the ultrashort but also sub-nanosecond times. Whereas the two-temperature model with the accepted physical constants of platinum can reproduce the observed surface lattice dynamics, gold is found to exhibit appreciably larger-than-expected dynamic vibrational amplitudes of surface atoms while keeping the commonly used electron–phonon coupling constant. Such surface behavioral difference at transient times can be understood in the context of the different strengths of binding to surface atoms for the two metals. In addition, with the quantitative agreements between diffraction and theoretical results, we provide convincing evidence that surface structural dynamics can be reliably obtained by reflection UED even in the presence of laser-induced transient electric fields.

Nanoscale thermal imaging of hot electrons by cryogenic terahertz scanning noise microscopy.

Nanoscale thermal imaging and temperature detection are of fundamental importance in diverse scientific and technological realms. Most nanoscale thermometry techniques focus on probing the temperature of lattice or phonons and are insensitive to nonequilibrium electrons, commonly referred to as "hot electrons." While terahertz scanning noise microscopy (SNoiM) has been demonstrated to be powerful in the thermal imaging of hot electrons, prior studies have been limited to room temperature. In this work, we report the development of a cryogenic SNoiM (Cryo-SNoiM) tailored for quantitative hot electron temperature detection at low temperatures. The microscope features a special two-chamber design where the sensitive terahertz detector, housed in a vacuum chamber, is efficiently cooled to ∼5K using a pulse tube cryocooler. In a separate chamber, the atomic force microscope and the sample can be maintained at room temperature under ambient/vacuum conditions or cooled to ∼110K via liquid nitrogen. This unique dual-chamber cooling system design enhances the efficacy of SNoiM measurements at low temperatures. It not only facilitates the pre-selection of tips at room temperature before cooling but also enables the quantitative derivation of local electron temperature without reliance on any adjustable parameters. The performance of Cryo-SNoiM is demonstrated through imaging the distribution of hot electrons in a cold, self-heated narrow metal wire. This instrumental innovation holds great promise for applications in imaging low-temperature hot electron dynamics and nonequilibrium transport phenomena across various material systems.

Non-thermal emission in gap-mode plasmon photoluminescence

Photoluminescence from spatially inhomogeneous plasmonic nanostructures exhibits fascinating wavelength-dependent nonlinear behaviors due to the intraband recombination of hot electrons excited into the conduction band of the metal. The properties of the excited carrier distribution and the role of localized plasmonic modes are subjects of debate. In this work, we use plasmonic gap-mode resonators with precise nanometer-scale confinement to show that the nonlinear photoluminescence behavior can become dominated by non-thermal contributions produced by the excited carrier population that strongly deviates from the Fermi-Dirac distribution due to the confinement-induced large-momentum free carrier absorption beyond the dipole approximation. These findings open new pathways for controllable light conversion using nonequilibrium electron states at the nanoscale.

Numerical investigation of nonequilibrium electron effects on the collisional ionization rate in the collisional-radiative model.

The interplay of kinetic electron physics and atomic processes in ultrashort laser-plasma interactions provides a comprehensive understanding of the impact of the electron energy distribution on plasma properties. Notably, nonequilibrium electrons play a vital role in collisional ionization, influencing ionization degrees and spectra. This paper introduces a computational model that integrates the physics of kinetic electrons and atomic processes, utilizing a Boltzmann equationfor nonequilibrium electrons and a collisional-radiative model for atomic state populations. The model is used to investigate the influence of nonequilibrium electrons on collisional ionization rates and its effect on the population distribution, as observed in a widely known experiment [Young et al., Nature (London) 466, 56 (2010)0028-083610.1038/nature09177]. The study reveals a significant nonequilibrium electron presence during XFEL-matter interactions, profoundly affecting collisional ionization rates in the gas plasma, thereby necessitating careful consideration of the Collisional-Radiative model applied to such systems.

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics.

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Real-time observation of non-equilibrium phonon-electron energy and angular momentum flow in laser-heated nickel.

Identifying the microscopic nature of non-equilibrium energy transfer mechanisms among electronic, spin, and lattice degrees of freedom is central to understanding ultrafast phenomena such as manipulating magnetism on the femtosecond timescale. Here, we use time- and angle-resolved photoemission spectroscopy to go beyond the often-used ensemble-averaged view of non-equilibrium dynamics in terms of quasiparticle temperature evolutions. We show for ferromagnetic Ni that the non-equilibrium electron and spin dynamics display pronounced variations with electron momentum, whereas the magnetic exchange interaction remains isotropic. This highlights the influence of lattice-mediated scattering processes and opens a pathway toward unraveling the still elusive microscopic mechanism of spin-lattice angular momentum transfer.

Two-Step Relaxation of Non-Equilibrium Electrons in Graphene: The Key to Understanding Pump–Probe Experiments

In the majority of experiments targeting nonlinear optical phenomena, the application of high-intensity pulses drives electrons in graphene into a strongly non-equilibrium state. Under these conditions, conventional perturbation theory falls short in explaining graphene’s intricate optical response because of significant deviations in electron distribution over energy states from the equilibrium Fermi-Dirac one. In this work, we present a two-step relaxation model capable of predicting the transient dynamics of graphene’s carriers out of equilibrium, from the generation of spectrally narrow populations of non-thermalized electrons and holes to the establishment of a hot-electron gas and its subsequent cooling toward equilibrium with the crystal lattice. By comparing our model calculations to experimental results, we demonstrate its reliability and relevance to pump–probe experiments, providing insights into the pivotal role of hot electrons in comprehending ultrafast dynamics in graphene.

Influence of Energetic Particles and Electron Injection on Minority Carrier Transport Properties in Gallium Oxide

The influence of various energetic particles and electron injection on the transport of minority carriers and non-equilibrium carrier recombination in Ga2O3 is summarized in this review. In Ga2O3 semiconductors, if robust p-type material and bipolar structures become available, the diffusion lengths of minority carriers will be of critical significance. The diffusion length of minority carriers dictates the functionality of electronic devices such as diodes, transistors, and detectors. One of the problems in ultrawide-bandgap materials technology is the short carrier diffusion length caused by the scattering on extended defects. Electron injection in n- and p-type gallium oxide results in a significant increase in the diffusion length, even after its deterioration, due to exposure to alpha and proton irradiation. Furthermore, post electron injection, the diffusion length of an irradiated material exceeds that of Ga2O3 prior to irradiation and injection. The root cause of the electron injection-induced effect is attributed to the increase in the minority carrier lifetime in the material due to the trapping of non-equilibrium electrons on native point defects. It is therefore concluded that electron injection is capable of “healing” the adverse impact of radiation in Ga2O3 and can be used for the control of minority carrier transport and, therefore, device performance.

Ultrafast Laser-Induced Dynamics of Non-Equilibrium Electron Spill-Out in Nanoplasmonic Bilayers.

Contemporary quantum plasmonics capture subtle corrections to the properties of plasmonic nano-objects in equilibrium. Here, we demonstrate non-equilibrium spill-out redistribution of the electronic density at the ultrafast time scale. As revealed by time-resolved 2D spectroscopy of nanoplasmonic Fe/Au bilayers, an injection of the laser-excited non-thermal electrons induces transient electron spill-out thus changing the plasma frequency. The response of the local electronic density switches the electronic density behavior from spill-in to strong (an order of magnitude larger) spill-out at the femtosecond time scale. The superdiffusive transport of hot electrons and the lack of a direct laser heating indicate significantly non-thermal origin of the underlying physics. Our results demonstrate an ultrafast and non-thermal way to control surface plasmon dispersion through transient variations of the spatial electron distribution at the nanoscale. These findings expand quantum plasmonics into previously unexplored directions by introducing ultrashort time scales in the non-equilibrium electronic systems.

Electronic nonequilibrium effect in ultrafast-laser-irradiated solids

This paper describes the effects of electronic nonequilibrium in a simulation of ultrafast laser irradiation of materials. The simulation scheme based on tight-binding molecular dynamics, in which the electronic populations are traced with a combined Monte Carlo and Boltzmann equation, enables the modeling of nonequilibrium, nonthermal, and nonadiabatic (electron-phonon coupling) effects simultaneously. The electron-electron thermalization is described within the relaxation-time approximation, which automatically restores various known limits such as instantaneous thermalization (the thermalization time τe−e→0 ) and Born-Oppenheimer (BO) approximation ( τe−e→∞ ). The results of the simulation suggest that the non-equilibrium state of the electronic system slows down electron-phonon coupling with respect to the electronic equilibrium case in all studied materials: metals, semiconductors, and insulators. In semiconductors and insulators, it also alters the damage threshold of ultrafast nonthermal phase transitions induced by modification of the interatomic potential due to electronic excitation. It is demonstrated that the models that exclude electron-electron thermalization (using the assumption of τe−e→∞, such as BO or Ehrenfest approximations) may produce qualitatively different results, and a reliable model should include all three effects: electronic nonequilibrium, nonadiabatic electron-ion coupling, and nonthermal evolution of interatomic potential.

First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems.

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Optical Electron-Nuclear Resonance in Semiconductors

A considerable number of investigations have by now been made on optical pumping of spin-oriented electrons in semiconductors. The optical-pumping method makes it possible to produce easily a high polarization of the electron spins in the conduction band, and to detect it optically [1–3]. The use of this method for the investigation of semiconductors turned out to be very fruitful; the spin orientation of the minority [1–3] and majority [4] carriers was determined, the lifetimes of the non-equilibrium electrons were measured [2, 3, 5], the mechanisms of spin relaxation of “cold” [2, 5] and “hot” [2, 6] electrons were investigated, spin orientation of excitons was effected [7], and electron paramagnetic resonance with non-equilibrium electrons was registered [8].