Carrier Relaxation and Lattice Heating Dynamics in Silicon Revealed by Femtosecond Electron Diffraction

Relativistic ultrafast electron diffraction at high repetition rates

The ability to resolve the dynamics of matter on its native temporal and spatial scales constitutes a key challenge and convergent theme across chemistry, biology, and materials science. The last couple of decades have witnessed ultrafast electron diffraction (UED) emerge as one of the forefront techniques with the sensitivity to resolve atomic motions. Increasingly sophisticated UED instruments are being developed that are aimed at increasing the beam brightness in order to observe structural signatures, but so far they have been limited to low average current beams. Here, we present the technical design and capabilities of the HiRES (High Repetition-rate Electron Scattering) instrument, which blends relativistic electrons and high repetition rates to achieve orders of magnitude improvement in average beam current compared to the existing state-of-the-art instruments. The setup utilizes a novel electron source to deliver femtosecond duration electron pulses at up to MHz repetition rates for UED experiments. Instrument response function of sub-500 fs is demonstrated with < 100 fs time resolution targeted in future. We provide example cases of diffraction measurements on solid-state and gas-phase samples, including both micro- and nanodiffraction (featuring 100 nm beam size) modes, which showcase the potential of the instrument for novel UED experiments.

Electron-Phonon Interaction and Longitudinal-Transverse Phonon Splitting in Doped Semiconductors

We study the effect of doping on the electron-phonon interaction and on the phonon frequencies in doped semiconductors, taking into account the screening in the presence of free carriers at finite temperature. We study the impact of screening on the Fröhlich-like vertex and on the long-range components of the dynamical matrix, going beyond the state-of-the-art description for undoped crystals, thanks to the development of a computational method based on maximally localized Wannier functions. We apply our approach to cubic silicon carbide, where in the presence of doping the Fröhlich coupling and the longitudinal-transverse phonon splitting are strongly reduced, thereby influencing observable properties such as the electronic lifetime.

Exchange-Striction Driven Ultrafast Nonthermal Lattice Dynamics in NiO

We use femtosecond electron diffraction to study ultrafast lattice dynamics in the highly correlated antiferromagnetic (AFM) semiconductor NiO. Using the scattering vector (Q) dependence of Bragg diffraction, we introduce Q-resolved effective temperatures describing the transient lattice. We identify a nonthermal lattice state with preferential displacement of O compared to Ni ions, which occurs within ∼0.3  ps and persists for 25 ps. We associate this with transient changes to the AFM exchange striction-induced lattice distortion, supported by the observation of a transient Q asymmetry of Friedel pairs. Our observation highlights the role of spin-lattice coupling in routes towards ultrafast control of spin order.

A Compact Ultrafast Electron Diffractometer with Relativistic Femtosecond Electron Pulses

We have developed a compact relativistic femtosecond electron diffractometer with a radio-frequency photocathode electron gun and an electron lens system. The electron gun generated 2.5-MeV-energy electron pulses with a duration of 55 ± 5 fs containing 6.3 × 104 electrons per pulse. Using these pulses, we successfully detected high-contrast electron diffraction images of single crystalline, polycrystalline, and amorphous materials. An excellent spatial resolution of diffraction images was obtained as 0.027 ± 0.001 Å−1. In the time-resolved electron diffraction measurement, a laser-excited ultrafast electronically driven phase transition in single-crystalline silicon was observed with a temporal resolution of 100 fs. The results demonstrate the advantages of the compact relativistic femtosecond electron diffractometer, including access to high-order Bragg reflections, single shot imaging with the relativistic femtosecond electron pulse, and the feasibility of time-resolved electron diffraction to study ultrafast structural dynamics.

Ultrafast electron diffraction from a Bi(111) surface: Impulsive lattice excitation and Debye-Waller analysis at large momentum transfer

The lattice response of a Bi(111) surface upon impulsive femtosecond laser excitation is studied with time-resolved reflection high-energy electron diffraction. We employ a Debye-Waller analysis at large momentum transfer of 9.3 Å^-1 ≤ Δ k ≤ 21.8 Å^-1 in order to study the lattice excitation dynamics of the Bi surface under conditions of weak optical excitation up to 2 mJ/cm² incident pump fluence. The observed time constants τ _int of decay of diffraction spot intensity depend on the momentum transfer Δk and range from 5 to 12 ps. This large variation of τ _int is caused by the nonlinearity of the exponential function in the Debye-Waller factor and has to be taken into account for an intensity drop ΔI > 0.2. An analysis of more than 20 diffraction spots with a large variation in Δk gave a consistent value for the time constant τ_T of vibrational excitation of the surface lattice of 12 ± 1 ps independent on the excitation density. We found no evidence for a deviation from an isotropic Debye-Waller effect and conclude that the primary laser excitation leads to thermal lattice excitation, i.e., heating of the Bi surface.

Sources of error in Debye-Waller-effect measurements relevant to studies of photoinduced structural dynamics

We identify and quantify several practical effects likely to be present in both static and ultrafast electron-scattering experiments that may interfere with the Debye-Waller (DW) effect. Using 120-nm thick, small-grained, polycrystalline aluminum foils as a test system, we illustrate the impact of specimen tilting, in-plane translation, and changes in z height on Debye-Scherrer-ring intensities. We find that tilting by less than one degree can result in statistically-significant changes in diffracted-beam intensities for large specimen regions containing > 10⁵ nanocrystalline grains. We demonstrate that, in addition to effective changes in the field of view with tilting, slight texturing of the film can result in deviations from expected DW-effect behavior. Further, we find that in-plane translations of as little as 20 nm also produce statistically-significant intensity changes, while normalization to total image counts eliminates such effects arising from changes in z height. The results indicate that the use of polycrystalline films in ultrafast electron-scattering experiments can greatly reduce the negative impacts of these effects as compared to single-crystal specimens, though it does not entirely eliminate them. Thus, it is important to account for such effects when studying thin-foil specimens having relatively short reciprocal-lattice rods.

Hot phonon and carrier relaxation in Si(100) determined by transient extreme ultraviolet spectroscopy

The thermalization of hot carriers and phonons gives direct insight into the scattering processes that mediate electrical and thermal transport. Obtaining the scattering rates for both hot carriers and phonons currently requires multiple measurements with incommensurate timescales. Here, transient extreme-ultraviolet (XUV) spectroscopy on the silicon 2p core level at 100 eV is used to measure hot carrier and phonon thermalization in Si(100) from tens of femtoseconds to 200 ps, following photoexcitation of the indirect transition to the Δ valley at 800 nm. The ground state XUV spectrum is first theoretically predicted using a combination of a single plasmon pole model and the Bethe-Salpeter equation with density functional theory. The excited state spectrum is predicted by incorporating the electronic effects of photo-induced state-filling, broadening, and band-gap renormalization into the ground state XUV spectrum. A time-dependent lattice deformation and expansion is also required to describe the excited state spectrum. The kinetics of these structural components match the kinetics of phonons excited from the electron-phonon and phonon-phonon scattering processes following photoexcitation. Separating the contributions of electronic and structural effects on the transient XUV spectra allows the carrier population, the population of phonons involved in inter- and intra-valley electron-phonon scattering, and the population of phonons involved in phonon-phonon scattering to be quantified as a function of delay time.

Through a Window, Brightly: A Review of Selected Nanofabricated Thin-Film Platforms for Spectroscopy, Imaging, and Detection

We present a review of the use of selected nanofabricated thin films to deliver a host of capabilities and insights spanning bioanalytical and biophysical chemistry, materials science, and fundamental molecular-level research. We discuss approaches where thin films have been vital, enabling experimental studies using a variety of optical spectroscopies across the visible and infrared spectral range, electron microscopies, and related techniques such as electron energy loss spectroscopy, X-ray photoelectron spectroscopy, and single molecule sensing. We anchor this broad discussion by highlighting two particularly exciting exemplars: a thin-walled nanofluidic sample cell concept that has advanced the discovery horizons of ultrafast spectroscopy and of electron microscopy investigations of in-liquid samples; and a unique class of thin-film-based nanofluidic devices, designed around a nanopore, with expansive prospects for single molecule sensing. Free-standing, low-stress silicon nitride membranes are a canonical structural element for these applications, and we elucidate the fabrication and resulting features-including mechanical stability, optical properties, X-ray and electron scattering properties, and chemical nature-of this material in this format. We also outline design and performance principles and include a discussion of underlying material preparations and properties suitable for understanding the use of alternative thin-film materials such as graphene.

Capturing Structural Dynamics in Crystalline Silicon Using Chirped Electrons from a Laser Wakefield Accelerator

Recent progress in laser wakefield acceleration has led to the emergence of a new generation of electron and X-ray sources that may have enormous benefits for ultrafast science. These novel sources promise to become indispensable tools for the investigation of structural dynamics on the femtosecond time scale, with spatial resolution on the atomic scale. Here, we demonstrate the use of laser-wakefield-accelerated electron bunches for time-resolved electron diffraction measurements of the structural dynamics of single-crystal silicon nano-membranes pumped by an ultrafast laser pulse. In our proof-of-concept study, we resolve the silicon lattice dynamics on a picosecond time scale by deflecting the momentum-time correlated electrons in the diffraction peaks with a static magnetic field to obtain the time-dependent diffraction efficiency. Further improvements may lead to femtosecond temporal resolution, with negligible pump-probe jitter being possible with future laser-wakefield-accelerator ultrafast-electron-diffraction schemes.

Quasimomentum-Space Image for Ultrafast Melting of Silicon

By exciting electron-hole pairs that survive for picoseconds strong femtosecond lasers may transiently influence the bonding properties of semiconductors, causing structure changes, in particular, ultrafast melting. In order to determine the energy flow during this process in silicon we performed ab initio molecular dynamics simulations and an analysis in quasimomentum space. We found that energy flows very differently as a function of increasing excitation density, namely, mainly through long wavelength, L-point, or X-point lattice vibrations, respectively.

Signatures of nonthermal melting

Intense ultrashort laser pulses can melt crystals in less than a picosecond but, in spite of over thirty years of active research, for many materials it is not known to what extent thermal and nonthermal microscopic processes cause this ultrafast phenomenon. Here, we perform ab-initio molecular-dynamics simulations of silicon on a laser-excited potential-energy surface, exclusively revealing nonthermal signatures of laser-induced melting. From our simulated atomic trajectories, we compute the decay of five structure factors and the time-dependent structure function. We demonstrate how these quantities provide criteria to distinguish predominantly nonthermal from thermal melting.

Ultrafast time-resolved electron diffraction revealing the nonthermal dynamics of near-UV photoexcitation-induced amorphization in Ge2Sb2Te5

Because of their robust switching capability, chalcogenide glass materials have been used for a wide range of applications, including optical storages devices. These phase transitions are achieved by laser irradiation via thermal processes. Recent studies have suggested the potential of nonthermal phase transitions in the chalcogenide glass material Ge2Sb2Te5 triggered by ultrashort optical pulses; however, a detailed understanding of the amorphization and damage mechanisms governed by nonthermal processes is still lacking. Here we performed ultrafast time-resolved electron diffraction and single-shot optical pump-probe measurements followed by femtosecond near-ultraviolet pulse irradiation to study the structural dynamics of polycrystalline Ge2Sb2Te5. The experimental results present a nonthermal crystal-to-amorphous phase transition of Ge2Sb2Te5 initiated by the displacements of Ge atoms. Above the fluence threshold, we found that the permanent amorphization caused by multi-displacement effects is accompanied by a partial hexagonal crystallization.

Relaxation of highly excited carriers in wide-gap semiconductors

The electron energy relaxation in semiconductors and insulators after high-level external excitation is analysed by a semi-classical approach based on a kinetic equation of the Boltzmann type. We show that the non-equilibrium distributions of electrons and holes have a customary Fermi-like shape with some effective temperature but also possess a high-energy non-Fermian 'tail'. The latter may extend deep into the conduction and valence bands while the Fermi-like component is localized within a small energy range just above the edge of the band gap. The effective temperature, effective chemical potential, and the shape of the high-energy component are governed by the process of electron-phonon interactions as well as by the rates of carrier generation and inter-band radiative recombination.

Rippled area formed by surface plasmon polaritons upon femtosecond laser double-pulse irradiation of silicon

The formation of near-wavelength laser-induced periodic surface structures (LIPSS) on silicon upon irradiation with sequences of Ti:sapphire femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied theoretically. For this purpose, the nonlinear generation of conduction band electrons in silicon and their relaxation is numerically calculated using a two-temperature model approach including intrapulse changes of optical properties, transport, diffusion and recombination effects. Following the idea that surface plasmon polaritons (SPP) can be excited when the material turns from semiconducting to metallic state, the "SPP active area" is calculated as function of fluence and double-pulse delay up to several picoseconds and compared to the experimentally observed rippled surface areas. Evidence is presented that multi-photon absorption explains the large increase of the rippled area for temporally overlapping pulses. For longer double-pulse delays, relevant relaxation processes are identified. The results demonstrate that femtosecond LIPSS on silicon are caused by the excitation of SPP and can be controlled by temporal pulse shaping.

Ultrafast Kikuchi diffraction: nanoscale stress-strain dynamics of wave-guiding structures

Complex structural dynamics at the nanoscale requires sufficiently small probes to be visualized. In conventional imaging using electron microscopy, the dimension of the probe is large enough to cause averaging over the structures present. However, by converging ultrafast electron bunches, it is possible to select a single nanoscale structure and study the dynamics, either in the image or using electron diffraction. Moreover, the span of incident wave vectors in a convergent beam enables sensitivity levels and information contents beyond those of parallel-beam illumination with a single wave vector Bragg diffraction. Here, we report the observation of propagating strain waves using ultrafast Kikuchi diffraction from nanoscale volumes within a wedge-shaped silicon single crystal. It is found that the heterogeneity of the strain in the lateral direction is only 100 nm. The transient elastic wave gives rise to a coherent oscillation with a period of 30 ps and with an envelope that has a width of 140 ps. The origin of this elastic deformation is theoretically examined using finite element analysis; it is identified as propagating shear waves. The wedge-shaped structure, unlike parallel-plate structure, is the key behind the traveling nature of the waves as its angle permits "transverse" propagation; the parallel-plate structure only exhibits the "longitudinal" motion. The studies reported suggest extension to a range of applications for nanostructures of different shapes and for exploring their ultrafast eigen-modes of stress-strain profiles.

Full characterization of RF compressed femtosecond electron pulses using ponderomotive scattering

High bunch charge, femtosecond, electron pulses were generated using a 95 kV electron gun with an S-band RF rebunching cavity. Laser ponderomotive scattering in a counter-propagating beam geometry is shown to provide high sensitivity with the prerequisite spatial and temporal resolution to fully characterize, in situ, both the temporal profile of the electron pulses and RF time timing jitter. With the current beam parameters, we determined a temporal Instrument Response Function (IRF) of 430 fs FWHM. The overall performance of our system is illustrated through the high-quality diffraction data obtained for the measurement of the electron-phonon relaxation dynamics for Si (001).

Chemical x-ray photodiffraction: principles, examples, and perspectives

X-ray photodiffraction (in the chemical literature also referred to as photocrystallography), which is based on the combination of X-ray diffraction methods with samples excited by UV or visible light to solve fundamental photochemical or photophysical issues, has developed in the last couple of decades into a very promising technique for direct observation of photoinduced chemical species in the solid state. The capability of providing direct information on very small perturbations in atomic positions and thus on the minute changes in molecular geometry during (or as a consequence of) photoexcitation appears to be the most important asset of this emerging analytical technique. When combined with other physicochemical methods, X-ray photodiffraction can be a powerful tool for analysis of steady-state photoinduced structures as well as slow or very fast time-dependent phenomena. Despite being a very useful approach, however, due to a number of practical requirements that it places with regard to the system to be studied, at the present stage of developments the technique is not widely and indiscriminately applicable to any photoinduced process. In some particular chemical systems the inherent pitfalls could be practically overcome by practical or theoretical means. In this short chapter, the basic principles of X-ray photodiffraction are briefly summarized, and the prospects of its application to "physical" and "chemical" problems is illustrated with selected examples from recent literature. Some possible future developments and alternative approaches with this and related methods are also presented.

`Making the molecular movie': first frames

Recent advances in high-intensity electron and X-ray pulsed sources now make it possible to directly observe atomic motions as they occur in barrier-crossing processes. These rare events require the structural dynamics to be triggered by femtosecond excitation pulses that prepare the system above the barrier or access new potential energy surfaces that drive the structural changes. In general, the sampling process modifies the system such that the structural probes should ideally have sufficient intensity to fully resolve structures near the single-shot limit for a given time point. New developments in both source intensity and temporal characterization of the pulsed sampling mode have made it possible to make so-called `molecular movies',i.e.measure relative atomic motions faster than collisions can blur information on correlations. Strongly driven phase transitions from thermally propagated melting to optically modified potential energy surfaces leading to ballistic phase transitions and bond stiffening are given as examples of the new insights that can be gained from an atomic level perspective of structural dynamics. The most important impact will likely be made in the fields of chemistry and biology where the central unifying concept of the transition state will come under direct observation and enable a reduction of high-dimensional complex reaction surfaces to the key reactive modes, as long mastered by Mother Nature.

Electronically driven structure changes of Si captured by femtosecond electron diffraction

The excitation of a high density of carriers in semiconductors can induce an order-to-disorder phase transition due to changes in the potential-energy landscape of the lattice. We report the first direct resolution of the structural details of this phenomenon in freestanding films of polycrystalline and (001)-oriented crystalline Si, using 200-fs electron pulses. At excitation levels greater than approximately 6% of the valence electron density, the crystalline structure of the lattice is lost in <500 fs, a time scale indicative of an electronically driven phase transition. We find that the relaxation process along the modified potential is not inertial but rather involves multiple scattering towards the disordered state.

X-ray diffuse scattering measurements of nucleation dynamics at femtosecond resolution

Femtosecond time-resolved small and wide angle x-ray diffuse scattering techniques are applied to investigate the ultrafast nucleation processes that occur during the ablation process in semiconducting materials. Following intense optical excitation, a transient liquid state of high compressibility characterized by large-amplitude density fluctuations is observed and the buildup of these fluctuations is measured in real time. Small-angle scattering measurements reveal snapshots of the spontaneous nucleation of nanoscale voids within a metastable liquid and support theoretical predictions of the ablation process.

Grating enhanced ponderomotive scattering for visualization and full characterization of femtosecond electron pulses

Real time views of atomic motion can be achieved using electron pulses as structural probes. The requisite time resolution requires knowledge of both the electron pulse duration and the exact timing of the excitation pulse and the electron probe to within 10 - 100 fs accuracy. By using an intensity grating to enhance the pondermotive force, we are now able to fully characterize electron pulses and to confirm many body simulations with laser pulse energies on the microjoule level. This development solves one of the last barriers to the highest possible time resolution for electron probes.