Electron-phonon Relaxation Research Articles

Electron-phonon relaxation and excited electron distribution in gallium nitride

We develop a theory of energy relaxation in semiconductors and insulators highly excited by the long-acting external irradiation. We derive the equation for the non-equilibrium distribution function of excited electrons. The solution for this function breaks up into the sum of two contributions. The low-energy contribution is concentrated in a narrow range near the bottom of the conduction band. It has the typical form of a Fermi distribution with an effective temperature and chemical potential. The effective temperature and chemical potential in this low-energy term are determined by the intensity of carriers' generation, the speed of electron-phonon relaxation, rates of inter-band recombination, and electron capture on the defects. In addition, there is a substantial high-energy correction. This high-energy “tail” largely covers the conduction band. The shape of the high-energy “tail” strongly depends on the rate of electron-phonon relaxation but does not depend on the rates of recombination and trapping. We apply the theory to the calculation of a non-equilibrium distribution of electrons in an irradiated GaN. Probabilities of optical excitations from the valence to conduction band and electron-phonon coupling probabilities in GaN were calculated by the density functional perturbation theory. Our calculation of both parts of distribution function in gallium nitride shows that when the speed of the electron-phonon scattering is comparable with the rate of recombination and trapping then the contribution of the non-Fermi “tail” is comparable with that of the low-energy Fermi-like component. So the high-energy contribution can essentially affect the charge transport in the irradiated and highly doped semiconductors.

Role of spin fluctuations in the conductivity ofCrO2

We present a time-resolved terahertz spectroscopic study of the half-metallic ferromagnet ${\mathrm{CrO}}_{2}$. The ultrafast conductivity dynamics excited by an optical pump displays very short (several picoseconds) and a very long (several hundred picoseconds) characteristic time scales. We attribute the former to the electron-phonon relaxation and the latter to the spin-lattice relaxation. We use this distinction to quantify the relative contribution of the scattering by spin fluctuations to the resistivity of ${\mathrm{CrO}}_{2}$: We find that they contribute less than one half of all scattering events below room temperature. This contribution rises to $\ensuremath{\sim}70%$ as the temperature approaches ${T}_{C}=390$ K. The small effect of spin fluctuations on the resistivity is unexpected in light of the proposed double-exchange nature of the electronic and magnetic properties of ${\mathrm{CrO}}_{2}$.

Phenomenological model for prediction of complex ablation geometries in metal films using ultrashort laser pulses

Ablation of thin metal films with laser pulses having a pulse duration shorter than the electron-phonon relaxation time, so called ultrashort laser pulses, enables melt-free patterning of arbitrary geometries. Ablation with ultrashort laser pulses is an emerging process and is currently used in the field of microelectronics for the repair of photolithography masks and in the photovoltaic industry for patterning of indium tin oxide (ITO). Another current field of investigation is the patterning of thin film strain sensors. In order to achieve the desired ablation quality, a multipulse irradiation is often required. Currently, there is no “simple” model to predict line and more complex ablation geometries created by multipulse irradiation. Within this paper, an incubation threshold is introduced to enhance an existing incubation model, which is restricted to the prediction of point ablations. The resulting phenomenological model is experimentally verified on thin NiCr films using 10 ps laser pulses. The usability of the derived model is significantly higher than other existing models due to concentrating on the relevant criterion for patterning of electronic circuits: the removal threshold as well as an easy to handle procedure to determine the model parameters, which can be determined on a machining setup in industrial conditions.

Transient thermal and nonthermal electron and phonon relaxation after short-pulsed laser heating of metals

Several dynamic thermal and nonthermal scattering processes affect ultrafast heat transfer in metals after short-pulsed laser heating. Even with decades of measurements of electron-phonon relaxation, the role of thermal vs. nonthermal electron and phonon scattering on overall electron energy transfer to the phonons remains unclear. In this work, we derive an analytical expression for the electron-phonon coupling factor in a metal that includes contributions from equilibrium and nonequilibrium distributions of electrons. While the contribution from the nonthermal electrons to electron-phonon coupling is non-negligible, the increase in the electron relaxation rates with increasing laser fluence measured by thermoreflectance techniques cannot be accounted for by only considering electron-phonon relaxations. We conclude that electron-electron scattering along with electron-phonon scattering have to be considered simultaneously to correctly predict the transient nature of electron relaxation during and after short-pulsed heating of metals at elevated electron temperatures. Furthermore, for high electron temperature perturbations achieved at high absorbed laser fluences, we show good agreement between our model, which accounts for d-band excitations, and previous experimental data. Our model can be extended to other free electron metals with the knowledge of the density of states of electrons in the metals and considering electronic excitations from non-Fermi surface states.

Optimal electron, phonon, and magnetic characteristics for low energy thermally induced magnetization switching

Using large-scale computer simulations, we thoroughly study the minimum energy required to thermally induced magnetization switching (TIMS) after the application of a femtosecond heat pulse in transition metal-rare earth ferrimagnetic alloys. We find that for an energy efficient TIMS, a low ferrimagnetic net magnetization with a strong temperature dependence is the relevant factor for the magnetic system. For the lattice and electron systems, the key physics for efficient TIMS is a large electron-phonon relaxation time. Importantly, we show that as the cooling time of the heated electrons is increased, the minimum power required to produce TIMS can be reduced by an order of magnitude. Our results show the way to low power TIMS by appropriate engineering of magnetic heterostructures.

Wannier interpolation of the electron-phonon matrix elements in polar semiconductors: Polar-optical coupling in GaAs

We generalize the Wannier interpolation of the electron-phonon matrix elements to the case of polar-optical coupling in polar semiconductors. We verify our methodological developments against experiments, by calculating the widths of the electronic bands due to electron-phonon scattering in GaAs, the prototype polar semiconductor. The calculated widths are then used to estimate the broadenings of excitons at critical points in GaAs and the electron-phonon relaxation times of hot electrons. Our findings are in good agreement with available experimental data. Finally, we demonstrate that while the Fr\"ohlich interaction is the dominant scattering process for electrons/holes close to the valley minima, in agreement with low-field transport results, at higher energies, the intervalley scattering dominates the relaxation dynamics of hot electrons or holes. The capability of interpolating the polar-optical coupling opens new perspectives in the calculation of optical absorption and transport properties in semiconductors and thermoelectrics.

Ab Initio Nonequilibrium Thermodynamic and Transport Properties of Ultrafast Laser Irradiated 316L Stainless Steel

We present calculations of transient behavior of thermodynamic and transport coefficients on the time scale of electron–phonon relaxation upon ultrashort laser excitation of ferrous alloys. Their role defining energy deposition and primary microscopic material response to the laser irradiation is outlined. Nonequilibrium thermodynamic properties of 316L stainless steel are determined from first-principles calculations. Taking into account the complexity of multimetallic materials, the density functional theory is first applied to describe the electronic density of states of an alloy stainless steel matrix as a function of electronic heating. An increase of the localization degree of the charge density was found to be responsible for the modification of the electronic structure upon electronic heating, with consequences on chemical potential, electronic capacity, and pressure. It is shown that the electronic temperature dependence of stainless steel thermodynamic properties are consistent with the behavior...

Ab initio study of hot electrons in GaAs

Hot carrier dynamics critically impacts the performance of electronic, optoelectronic, photovoltaic, and plasmonic devices. Hot carriers lose energy over nanometer lengths and picosecond timescales and thus are challenging to study experimentally, whereas calculations of hot carrier dynamics are cumbersome and dominated by empirical approaches. In this work, we present ab initio calculations of hot electrons in gallium arsenide (GaAs) using density functional theory and many-body perturbation theory. Our computed electron-phonon relaxation times at the onset of the Γ, L, and X valleys are in excellent agreement with ultrafast optical experiments and show that the ultrafast (tens of femtoseconds) hot electron decay times observed experimentally arise from electron-phonon scattering. This result is an important advance to resolve a controversy on hot electron cooling in GaAs. We further find that, contrary to common notions, all optical and acoustic modes contribute substantially to electron-phonon scattering, with a dominant contribution from transverse acoustic modes. This work provides definitive microscopic insight into hot electrons in GaAs and enables accurate ab initio computation of hot carriers in advanced materials.

Hot carrier relaxation of Dirac fermions in bilayer epitaxial graphene

Energy relaxation of hot Dirac fermions in bilayer epitaxial graphene is experimentally investigated by magnetotransport measurements on Shubnikov–de Haas oscillations and weak localization. The hot-electron energy loss rate is found to follow the predicted Bloch–Grüneisen power-law behaviour of T4 at carrier temperatures from 1.4 K up to ∼100 K, due to electron-acoustic phonon interactions with a deformation potential coupling constant of 22 eV. A carrier density dependence in the scaling of the T4 power law is observed in bilayer graphene, in contrast to the dependence in monolayer graphene, leading to a crossover in the energy loss rate as a function of carrier density between these two systems. The electron–phonon relaxation time in bilayer graphene is also shown to be strongly carrier density dependent, while it remains constant for a wide range of carrier densities in monolayer graphene. Our results and comparisons between the bilayer and monolayer exhibit a more comprehensive picture of hot carrier dynamics in graphene systems.

Mechanisms of nonequilibrium electron-phonon coupling and thermal conductance at interfaces

We study the electron and phonon thermal coupling mechanisms at interfaces between gold films with and without Ti adhesion layers on various substrates via pump-probe time-domain thermoreflectance. The coupling between the electronic and the vibrational states is increased by more than a factor of five with the inclusion of an ∼3 nm Ti adhesion layer between the Au film and the non-metal substrate. Furthermore, we show an increase in the rate of relaxation of the electron system with increasing electron and lattice temperatures induced by the laser power and attribute this to enhanced electron-electron scattering, a transport channel that becomes more pronounced with increased electron temperatures. The inclusion of the Ti layer also results in a linear dependence of the electron-phonon relaxation rate with temperature, which we attribute to the coupling of electrons at and near the Ti/substrate interface. This enhanced electron-phonon coupling due to electron-interface scattering is shown to have negligible influence on the Kapitza conductances between the Au/Ti and the substrates at longer time scales when the electrons and phonons in the metal have equilibrated. These results suggest that only during highly nonequilibrium conditions between the electrons and phonons (Te ≫ Tp) does electron-phonon scattering at an interface contribute to thermal boundary conductance.

Auger-mediated electron relaxation is robust to deep hole traps: time-domain ab initio study of CdSe quantum dots.

By slowing down electron-phonon relaxation in nanoscale materials, one can increase efficiencies of solar energy conversion via hot electron extraction, multiple exciton generation, and elimination of exciton trapping. The elusive phonon bottleneck is hard to achieve, in particular, due to Auger-type energy exchange between electrons and holes. The Auger channel can be suppressed by hole trapping. Using time-domain ab initio simulation, we show that deep hole traps cannot fully eliminate the Auger channel. The simulations show that the hole-mediated electron relaxation is slowed down only by about 30%, which is in agreement with the recent experiments. The Auger energy exchange and hole relaxation to the trap state occur on similar time scales. Hole trapping is slow, because holes themselves experience a weak bottleneck effect. The study establishes the fundamental mechanisms of the electron and hole relaxation processes with and without hole traps. It shows that more sophisticated hole trapping strategies, for example, involving shell layers, are required in order to achieve the phonon bottleneck and to reduce electronic energy losses.

Experimental evidence of excited electron number density and temperature effects on electron-phonon coupling in gold films

The electronic transport properties of metals with weak electron-phonon coupling can be influenced by non-thermal electrons. Relaxation processes involving non-thermal electrons competing with the thermalized electron system have led to inconsistencies in the understanding of how electrons scatter and relax with the less energetic lattice. Recent theoretical and computational works have shown that the rate of energy relaxation with the metallic lattice will change depending on the thermalization state of the electrons. Even though 20 years of experimental works have focused on understanding and isolating these electronic relaxation mechanisms with short pulsed irradiation, discrepancies between these existing works have not clearly answered the fundamental question of the competing effects between non-thermal and thermal electrons losing energy to the lattice. In this work, we demonstrate the ability to measure the electron relaxation for varying degrees of both electron-electron and electron-phonon thermalization. This series of measurements of electronic relaxation over a predicted effective electron temperature range up to ∼3500 K and minimum lattice temperatures of 77 K validate recent computational and theoretical works that theorize how a nonequilibrium distribution of electrons transfers energy to the lattice. Utilizing this wide temperature range during pump-probe measurements of electron-phonon relaxation, we explain discrepancies in the past two decades of literature of electronic relaxation rates. We experimentally demonstrate that the electron-phonon coupling factor in gold increases with increasing lattice temperature and laser fluences. Specifically, we show that at low laser fluences corresponding to small electron perturbations, energy relaxation between electrons and phonons is mainly governed by non-thermal electrons, while at higher laser fluences, non-thermal electron scattering with the lattice is less influential on the energy relaxation mechanisms.

Coexistence of ferromagnetism and superconductivity in iron based pnictides: a time resolved magnetooptical study.

Ferromagnetism and superconductivity are antagonistic phenomena. Their coexistence implies either a modulated ferromagnetic order parameter on a lengthscale shorter than the superconducting coherence length or a weak exchange coupling between the itinerant superconducting electrons and the localized ordered spins. In some iron based pnictide superconductors the coexistence of ferromagnetism and superconductivity has been clearly demonstrated. The nature of the coexistence, however, remains elusive since no clear understanding of the spin structure in the superconducting state has been reached and the reports on the coupling strength are controversial. We show, by a direct optical pump-probe experiment, that the coupling is weak, since the transfer of the excess energy from the itinerant electrons to ordered localized spins is much slower than the electron-phonon relaxation, implying the coexistence without the short-lengthscale ferromagnetic order parameter modulation. Remarkably, the polarization analysis of the coherently excited spin wave response points towards a simple ferromagnetic ordering of spins with two distinct types of ferromagnetic domains.

Study on the absorbing properties of critically coupled resonator with graphene

A critically coupled resonator (CCR) is a thin-film structure that can absorb nearly all of the incident electromagnetic radiation, leading to null scattering. In order to effectively achieve and control the critical coupling (CC) phenomena, we replace the polymer absorbing layer by a graphene-based multi-film structure. FDFD (finite difference frequency domain) method is used to solve the Maxwell equation, and the graphene's surface conductivity is calculated by using the Kubo formula. Our results demonstrate that the CC phenomenon is realized at the near-infrared frequency and the frequency of absorption peak can be engineered by the Fermi energy of the graphene sheets. With increasing Fermi energy the absorption peak moves to the longer wavelength side. The effective permittivity of a multi-film structure has a strong dependence on the thickness of the dielectric and the layer number of the grapheme sheets in the multi-film structure. It is found that the central frequency of the absorption peak shifts towards longer wavelength side with increasing layer number of the graphene sheets M and the thickness of dielectric d1. Moreover, we also demonstrate that the absorption efficiency is affected by the electron-phonon relaxation time and the incident angle. It is clear that the central frequency of the absorption peak has a slight shift and the absorption is changed with the relaxing time and incident angle. The results offer the theoretical basis to the design of graphene-based critical coupling devices and optical detectors.

Two-phase isochoric Stefan problem for ultrafast processes

We establish a modification of the one-dimensional two-phase Stefan problem which is promising for the investigation of ultrafast processes in solids lasting less than the time of electron–phonon relaxation. Under such conditions the heat equations should be solved separately for ions and electrons at constant volume. We discuss the system of equations and boundary conditions for this special case and derive the computational scheme for the numerical solution. To demonstrate our new approach we calculate the electronic and ionic temperatures in an aluminum target subjected to a femtosecond laser pulse.

Linear temperature behavior of thermopower and strong electron-electron scattering in thick F-doped SnO2 films

Both the semi-classical and quantum transport properties of F-doped SnO2 thick films (∼1 μm) were investigated experimentally. We found that the resistivity caused by the thermal phonons obeys Bloch-Grüneisen law from ∼90 to 300 K, while only the diffusive thermopower, which varies linearly with temperature from 300 down to 10 K, can be observed. The phonon-drag thermopower is completely suppressed due to the long electron-phonon relaxation time in the compound. These observations, together with the fact that the carrier concentration has negligible temperature dependence, indicate that the conduction electrons in F-doped SnO2 films possess free-electron-like characteristics. At low temperatures, the electron-electron scattering dominates over the electron-phonon scattering and governs the inelastic scattering process. The theoretical predications of scattering rates of large- and small-energy-transfer electron-electron scattering processes, which are negligibly weak in three-dimensional disordered conventional conductors, are quantitatively tested in this lower carrier concentration and free-electron-like highly degenerate semiconductor.

Instantaneous Generation of Charge-Separated State on TiO2 Surface Sensitized with Plasmonic Nanoparticles

Photoexcitation of the plasmon band in metallic nanoparticles adsorbed on a TiO2 surface initiates many important photovoltaic and photocatalytic processes. The traditional view on the photoinduced charge separation involves excitation of a surface plasmon, its subsequent dephasing into electron-hole pairs, followed by electron transfer (ET) from the metal nanoparticle into TiO2. We use nonadiabatic molecular dynamics combined with time-domain density functional theory to demonstrate that an electron appears inside TiO2 immediately upon photoexcitation with a high probability (~50%), bypassing the intermediate step of electron-hole thermalization inside the nanoparticle. By providing a detailed, atomistic description of the charge separation, energy relaxation, and electron-hole recombination processes, the simulation rationalizes why the experimentally observed ultrafast photoinduced ET in an Au-TiO2 system is possible in spite of the fast energy relaxation. The simulation shows that the photogenerated plasmon is highly delocalized onto TiO2, and thus, it is shared by the electron donor and acceptor materials. In the 50% of the cases remaining after the instantaneous photogeneration of the charge-separated state, the electron injects into TiO2 on a sub-100 fs time scale by the nonadiabatic mechanism due to high density of acceptor states. The electron-phonon relaxation parallels the injection and is slower, resulting in a transient heating of the TiO2 surface by 40 K. Driven by entropy, the electron moves further into TiO2 bulk. If the electron remains trapped at the TiO2 surface, it recombines with the hole on a picosecond time scale. The obtained ET and recombination times are in excellent agreement with the experiment. The delocalized plasmon state observed in our study establishes a novel concept for plasmonic photosensitization of wide band gap semiconductors, leading to efficient conversion of photons to charge carriers and to hybrid materials with a wide variety of applications in photocatalysis and photovoltaics.

Theory of electronic relaxation in a metal excited by an ultrashort optical pump

The theory of the electron relaxation in metals excited by an ultrashort optical pump is developed on the basis of the solution of the linearized kinetic equation. The kinetic equation includes both the electron-electron and the electron-phonon collision integrals. The widely used two temperature model follows from the theory as the limiting case, when the thermalization due to the electronelectron collisions is fast with respect to the electron-phonon relaxation. It is demonstrated that the energy relaxation has two consecutive processes. The first and most important step describes the emission of phonons by the photo-excited electrons. It leads to the relaxation of 90% of the energy before the electrons become thermalized among themselves. The second step describes electronphonon thermalization and may be described by the two temperature model. The second stage is difficult to observe experimentally because it involves the transfer of only a small amount of energy from electrons. Thus the theory explains why the divergence of the relaxation time at low temperatures was never observed experimentally.

Relaxation phenomena in electronic and lattice subsystems on iron surface during its ablation by ultrashort laser pulses

Single-shot ablative spallation and fragmentation thresholds, as well as corresponding ablative crater depths, were measured on the surface of iron using optical interferometry, for different ultrashort laser pulse widths in the range τlas = 0.3–3.6 ps. The nonmonotonic dependence of these thresholds on τlas with the minimum near 1.2 ps (the characteristic electron-phonon relaxation time τep) represents transport and emission relaxation phenomena for nonthermalized and thermalized carriers, generated by sub- and picosecond laser pulses, respectively. Compared to rather slow spallative ablation, much faster—picosecond—fragmentation ablation of the iron surface through hydrodynamic expansion of its supercritical fluid ceased for τlas > τep as a result of evaporative cooling.

Ultrafast dynamics of high-contrast nano-grating formation on gold film induced by temporally shaped femtosecond laser

We theoretically investigated the ultrafast dynamics of high-contrast nano-grating formation on gold film surface with respect to non-equilibrium thermal excitation processes. It is proposed that the high-contrast nano-grating can be desirably achieved by optimizing the non-equilibrium thermal dynamics processes. The grating contrast can be largely promoted by 64% with adjusting thermal dynamics via tailoring temporally shaped femtosecond laser. The results are attributed to the competitive energy transfer routes between electrons thermal diffusion and electron–phonon relaxation processes during grating formation, which can be well manipulated by temporally shaped femtosecond laser. The study provides for strategy for production of high-quality periodic surface structures with sharp grating profiles.