We study the electron density response in gold after excitation with XUV and visible light. We have introduced the concept of occupational nonequilibrium and developed multiband rate equations that track the occupation in each active electron band. The rate equations also track the energy content of the sp- and d-electrons and can be coupled to the phonons. Our results show that visible light excitation leads to an overpopulation of the sp-band, driven primarily by photo-excitation, while XUV irradiation results in an underpopulation of the sp-band, dominated by subsequent impact ionization. However, assuming that the excess energy from the Auger recombination process is transferred to multiple d-electrons, we showcase that XUV-exited gold can lead to an overpopulation of the sp-band. In addition, using a detailed balance of Auger and impact ionization coefficients, we show that a single-rate relaxation time approach is sufficient to describe the imbalance between the impact ionization rate and the Auger recombination rate.
Electron-phonon coupling plays a central role in describing the energy relaxation dynamics of solids excited by ultrafast laser pulses. It depends on electronic and phononic properties in different ways for different metals. In many calculations of the electron-phonon coupling parameter, the phonons are assigned a secondary role. In this work, we study the influence of the maximum phonon energy on the electron-phonon coupling parameter within the framework of the Debye model. We find a large increase of the coupling parameter with the Debye energy for all considered metals.
We report a comprehensive numerical study on laser-induced melting of copper applying the two-temperature description combined with molecular dynamics simulations (TTM-MD). It reveals the internal energy relaxation and melting dynamics of thin copper films irradiated with an ultrafast laser pulse. The TTM-MD simulations were performed utilizing different expressions for the electronic properties of copper including the temperaturedependent heat capacity and the electron-phonon coupling strength. We study the resulting melting times and structural evolution of the lattice that were found to vary in the picosecond range. The importance of the correct choice of the electron-phonon coupling parameter is underlined by its large influence on the heating and melting times of the lattice.
We report on an experimental and theoretical investigation on the laser ablation of silicon with THz bursts of fs pulses. Craters were generated by varying the burst features, i.e., the number of pulses and the intra-burst repetition rate, and compared to those obtained in Normal Pulse Mode (NPM). A general reduction of the thermal load was observed using bursts, though with a lower ablation rate. In fact, shallower craters were obtained when increasing the number of pulses and reducing the intra-burst repetition rates at fixed processing time and burst energy. However, for bursts at 2 THz, some combinations of process parameters allowed a higher specific ablation rate compared to NPM. Simulations based on the numerical solution of the density-dependent two temperature model showed that bursts with more pulses or with lower intra-burst repetition rates lead to a lower final temperature, thus supporting the experimental findings. This is ascribed to changes of the reflectivity dependent on the number of pulses. Accordingly, different amounts of energy are transferred from the laser pulse to the sample, which also leads to changes in specific ablation rates. The origin of such a behavior was found to be the non-linear absorption processes, especially the two-photon absorption.
A density-dependent two-temperature model is applied to describe laser excitation and the following relaxation processes of silicon in an external electric field. Two approaches on how to describe the effects of the external electric field are presented. The first approach avoids the buildup of internal electric fields due to charge separation by assuming ambipolar diffusion and adds an additional carrier-pair current. In the second approach, electrons and holes are treated separately to account for charge separation and the resulting shielding of the external electric field inside the material. The two approaches are compared to experimental results. Both the first approach and the experimental results show similar tendencies for optimization of laser ablation in the external electric field.
During the last decades laser micromachining became a valuable tool for many applications in automotive, medicine, tool construction, or mobile technology. Beside the quality, processing time and production costs are crucial questions. A promising approach to achieve high throughput combined with good processing quality represent laser ablation by an assisting magnetic-field. Therefore, we studied the influence of an applied magnetic field to the ablation behaviour of silicon by using short and ultrashort laser pulses. Based on the experimental results we report on a first theoretical model that addresses the energy distribution of the heated electrons in the irradiated area.
Ultrashort laser pulses generate free electrons in dielectrics and thus enable the absorption of laser energy. The electron density is a crucial parameter here, but also the energy distribution of the excited electrons plays a remarkable role. We calculate it in detail with help of full Boltzmann collision integrals. Here, we show a standard example of the evolution of the distribution function of electrons in valence- as well as in conduction band, and analyze the influence of different collision processes. The energy distribution can deviate from a Fermi distribution for several hundreds of femtoseconds, driven by an interplay of secondary ionization processes and the cooling by the lattice. We study in detail these relaxation processes and discuss their mutual influence.
When a silver sample is irradiated with an ultrashort laser pulse with a wavelength of 400 nm and 800 nm, at first only the electronic system is excited. They are driven out of equilibrium, i.e. they do not follow a Fermi-Dirac distribution directly after excitation. We calculate the transient distribution function with help of full Boltzmann collision integrals. We show the influence of laser parameters like wavelength and fluence on the initial electron nonequilibrium distribution, as well as on the thermalization process. We find an strong dependence of the excited electron distribution on characteristic features in the electronic density of states.
When band gap materials are irradiated with an ultrashort laser pulse, the free-carrier density increases tremendously. The resulting abrupt transformation from an insulator to a conducting material, where a large portion of the electrons is excited to the conduction band, induces huge changes in the optical parameters. The transient nature of these parameters is often modeled based on the Drude model, where there is much uncertainty concerning the Drude collision frequency. As this frequency has a great impact on the modeling results, this work discusses several approaches to its treatment. Additionally, we compare simulation results to experimental data discussing shortcomings of the Drude model in combination with a collision frequency based on Debye screening for dilute plasmas.
KEYWORDS: Molecules, Ionization, Scattering, Monte Carlo methods, Energy transfer, Liquids, Absorption, Pulsed laser operation, Femtosecond phenomena, Molecular energy transfer
We model numerically the interaction of an ultrashort VUV laser pulse (FWHM = 10 fs, photon energy of 100 eV) with liquid water. The incident laser photons interact with water by ionizing water molecules and creating free electrons. These excited electrons are elastically scattered by water molecules and are able to produce secondary electrons via ionization. To track each free electron and its collisions event by event, we use the Monte Carlo method similar to (N. Medvedev and B. Rethfeld, Transient dynamics of the electronic subsystem of semiconductors irradiated with an ultrashort vacuum ultraviolet laser pulse, New Journal of Physics, Vol. 12, p. 073037 (2010)). This approach allows us to describe the transient non-equilibrium behaviour of excited electrons on femtosecond time scales. We present transient electron energy distributions and a time resolved energy transfer, i.e.: the changing kinetic energy of excited electrons, the increase of the energy of holes, and excitation of water molecules via elastic collisions. We compare results obtained with different models for the energy levels in liquid water: either assuming dense water vapour or an amorphous semiconductor with a band gap.
To understand laser interaction with dielectrics on a wide time scale we apply different approaches: For a
subpicosecond time range we solve complete Boltzmann collision integrals or apply the multiple rate equation
(MRE), which focuses on the evolution of the conduction band electron density. The Boltzmann approach
includes the valence band dynamics and calculates the transient distribution function for electrons and phonons.
It also allows to extract important parameters, like the Auger recombination and impact ionization rate and the
electron-phonon coupling parameter, which can be used as input in other models. The multiple rate equation
includes density dependent optical parameters and is therefore independent of a critical density criterion to
follow dielectric breakdown. The flexibility of the MRE is used to examine, which set of laser parameters
causes breakdown, and to convert this knowledge into breakdown maps. It also allows to include a spatial
dimension which traces the density evolution in different material depths. This spatial information and the
parameters obtained by the Boltzmann approach can be used as input in the density dependent two temperature
model (nTTM). The nTTM models heat relaxation and carrier transport on a very wide time scale by using an
expanded two temperature model which also includes the transient free electron density. The combination of the
individual strengths of our models is capable to simulate a vast range of materials and laser pulses on a timescale
of up to several hundred picoseconds and to investigate the effect of transport on the damage threshold.
The energy of a laser beam irradiating a surface is primarily absorbed by electrons within the solid. In actual transparent materials, absorption is low. High-intensity lasers may, however, be absorbed by initially bounded electrons through nonlinear processes. The increase of free-electron density leads eventually to dielectric breakdown, and the material becomes highly absorbing. We present theoretical studies on the dynamics of electrons in dielectrics under irradiation with a visible high-intensity laser pulse. We consider microscopic processes determining absorption, redistribution of the energy among electrons, and transfer of energy to the crystal lattice. We review different aspects of electronic excitation, studied with time-resolved models as the Boltzmann kinetic approach and the time and spatial resolved multiple rate equation. Furthermore, we investigate criteria for damage thresholds. Two concepts are compared, namely a critical free-electron density and the melting threshold of the lattice. We show that in dielectrics both criteria are fulfilled simultaneously. Optical parameters depend on the density of free electrons in the conduction band of the solid, so the free-electron density directly leads to an increased energy absorption causing material modification. We present results on the spatial dependence of dielectric breakdown.
The energy of a laser beam, irradiating a surface, is primarily absorbed by electrons within the solid. In actual
transparent materials, absorption is low. High-intensity lasers may, however, be absorbed by initially bounded
electrons through nonlinear processes. The increase of free electron density leads eventually to dielectric breakdown
and the material becomes highly absorbing. We present theoretical studies on the dynamics of electrons
in dielectrics under irradiation with a visible high-intensity laser pulse. We consider microscopic processes determining
absorption, redistribution of the energy among electrons and transfer of energy to the crystal lattice.
We review different aspects of electronic excitation, studied with time-resolved models as the Boltzmann kinetic
approach and the time and spatial resolved multiple rate equation. Further we investigate criteria for damage
thresholds. Two concepts compare, namely a critical free electron density and the melting threshold of the
lattice. We show that in dielectrics both criteria are fulfilled simultaneously. Optical parameters depend on
the density of free electrons in the conduction band of the solid, so the free electron density directly leads to
an increased energy absorption causing material modification. We present results on the spatial dependence of
dielectric breakdown.
In solids under irradiation with femtosecond laser pulses, photoabsorption produces a strongly nonequilibrium highly
energetic electrons gas. We study theoretically the ionization of the electronic subsystem of either a semiconductor
(silicon) or a metal (aluminum) target, exposed to an ultra-short laser pulse (pulse duration ~10 fs) of VUV-XUV
photons. We developed a numerical simulation technique, based on the classical Monte-Carlo method, to obtain transient
distributions of electrons within conduction band. We extend the Monte-Carlo method in order to take into account
quantum effects such as the electronic band structure, Pauli's exclusion principle for electrons in the conduction band and
for holes within the valence band (for semiconductors), and free-free electron scattering (for metals).
In the presented work, the temporal distribution of the energy density of excited and ionized electrons were calculated.
The transient dynamics of electrons is discussed regarding the differences between semiconductors and metals. It is
demonstrated that for the case of semiconductors, since a part of the energy is spent to overcome ionization potentials,
the final kinetic energy of free electrons at the end of the laser pulse is much less than the total energy provided by the
laser pulse. In contrast, for metals all the energy is present as kinetic energy in the electronic subsystem, unless the
photon energy is greater that an ionization potential of a deep atomic shell. In the latter case, a part of the energy is
shortly kept by deep-shell holes, and is released back to the electrons by Auger-processes on femtosecond timescales.
We describe theoretically the interaction of an ultrashort VUV-XUV laser pulse (FWHM = 10fs, photon energy of 100eV)
with liquid water. Incident photons ionize water molecules and create free electrons. These excited electrons interact via
elastic collisions with other water molecules and produce secondary electrons due to impact ionization. To track each
free electron and its collisions event by event, we use the Monte Carlo method. This approach allows us to describe the
non-equilibrium behaviour of electrons in irradiated water on femtosecond timescales. As results we present the transient
electron particle- and energy-distributions. Furthermore, we exhibit a time resolved description of the total amount of
electrons and we also show the corresponding energy redistribution: change in the kinetic energy of excited electrons,
increase of the energy of holes, and energizing of water molecules via elastic collisions.
We investigate theoretically the interaction of a semiconductor with an ultrashort high-intensity VUV laser pulse
produced by new light source FLASH at DESY in Hamburg. Applying numerical simulations of excitations and
ionization of electronic subsystem within a solid silicon target, irradiated with femtosecond laser pulse (25 fs, photon
energy of 38 eV), the transient distribution of electrons within conduction band is obtained. The Monte Carlo method
(ATMC) was extended in order to take into account the electronic band structure and Pauli's principle for electrons
excited into the conduction band. Secondary excitation and ionization processes were included and simulated event by
event as well.
In the presented work the temporal distribution of the density of excited and ionized electrons, the energy of these
electrons and their energy distribution function were calculated. It is demonstrated that due to the fact that part of the
energy is spent to overcome ionization potentials, the final kinetic energy of free electrons is much less than the total
energy provided by the laser pulse. We introduce the concept of an 'effective energy gap' for collective electronic
excitation, which can be applied to estimate the free electron density after high-intensity VUV laser pulse. The effective
energy gap depends on properties of the material as well as on the laser pulse.
The motion of both Lennard-Jones solids and metals induced by ultrashort laser irradiation near the ablation threshold is
investigated by molecular dynamics simulation. The universality of the ablation threshold fluence with respect to the
cohesion energy of solids irradiated by femtosecond laser pulses is demonstrated for Lennard-Jones solid and metals
simulated by many-body EAM potentials.
Transparent solids may absorb energy from a laser beam of sufficient high intensity. Several models are under
consideration to describe the evolution of the free-electron density. Some of these models keep track of the energy
distribution of the electrons. In this work we compare different models and give rules to estimate which one
is applicable. We present the inclusion of a term in the multiple rate equation approach, recently introduced,
describing fast recombination processes to exciton states. Moreover, we present experimental results with temporally
asymmetric femtosecond laser pulses, impinging on a surface of fused silica. We found different thresholds for
surface material modification with respect to an asymetric pulse and its time reversed counterpart. This difference
is due to a different time-and-intensity dependence of the main ionization processes, which can be controlled with
help of femtosecond shaped laser pulses.
We study the mechanisms of ultrafast free-electron generation in laser-irradiated dielectrics. The transient free-electron density in laser-irradiated dielectrics is calculated with a widely applicable new model, the multiple rate equation. The system of simple rate equations keeps track of the nonstationary electron energy distribution. We clarify the role of different ionization processes in dependence on laser pulse duration and intensity.
When transparent solids are irradiated with laser intensities above a certain threshold, strong absorption of laser
energy occurs. The increasing absorptivity is caused by the formation of a free electron gas in the conduction band
of the dielectric. The transient free electron density is a fundamental parameter for numerous theoretical and
experimental investigations and applications. We study the mechanisms of free-electron generation in the frame of
different approaches. A full kinetic treatment reveals a non-stationary behavior, which is neglected when applying
the standard rate equation. A new model, the multiple rate equation, keeps track of the non-stationarity of the
electron energy distribution while maintaining the conceptual and analytic simplicity of standard rate equation.
We present the analytical asymptotic solution of the multiple rate equation which yields an expression for the
avalanche coefficient and provides information about the validity of the standard rate equation. The numerical
calculation shows the transient distribution of free electrons and the effect of the non-stationarity of its shape on
the impact ionization probability. We study the role of different ionization processes and its dependence on laser
pulse duration. The fraction of impact-ionized electrons is found to depend only on the product of pulse duration
and intensity, i.e. on the fluence. A remarkable effect of the shape of the laserpulse on the total free electron
density and the conditions for dielectric breakdown is found.
In order to investigate the ultrafast dynamics of free carriers generated in bulk dielectrics by intense femtosecond laser pulses we have designed a setup for ultrafast time-resolved imaging Mach-Zehnder interferometry. The application of the 2D-Fourier-transform technique allows us to accurately reconstruct the actual laser-induced phase shifts and transmission changes for the probe pulses, which provide the properties of free carriers. Interferometric measurements in high-purity fused silica clearly demonstrate that the dominant ionization mechanism for intensities below 10 TW/cm2 is multiphoton ionization.
Ultrashort laser pulse interaction with material involves a number of specialities as compared to longer irradiations. Applying femtosecond laser pulses, the fundamental physical processes such as excitation, melting and ablation are temporally separated, allowing a separate investigation of each of them. The irradiated material passes through highly non-equilibrium states of different kinds on different timescales after irradiation. Thus, the theoretical description of the investigated processes may differ strongly from the classical descriptions valid for equilibrium or steady-state conditions. On a femtosecond timescale we investigate the non-equilibrium of the laser-excited electron gas. With the help of a detailed microscopic approach we study the applicability of simplified macroscopic descriptions of laser absorption and free-electron excitation. We study different melting processes occurring on different timescales in the picosecond regime. The nature of the melting process depends on the laser and material parameters, respectively. Material removal, i.e. ablation, occurs on a pico- to nanosecond time scale, depending on excitation strength. We show theoretical and experimental investigations of the expansion dynamics of the excited material.
Ultrafast time resolved microscopy of femtosecond laser irradiated surfaces reveals a universal feature of the ablating surface on nanosecond time scale. All investigated materials show rings in the ablation zone, which were identified as an interference pattern (Newton fringes). Optically sharp surfaces occur during expansion of the heated material as a result of anomalous hydrodynamic expansion effects. Experimentally, the rings are observed within a certain fluence range which strongly depends on material parameters. The lower limit of this fluence range is the ablation threshold. We predict a fluence ratio between the upper and the lower fluence limit approximately equal to the ratio of critical temperature to boiling temperature at normal pressure. This estimate is experimentally confirmed on different materials (Si, graphite, Au, Al).
We present a theoretical model and results of the detailed numerical investigation of peculiarities accompanying the interaction of powerful sub-picosecond light pulses with a bulk dielectric sample.
We study the temporal evolution of the distribution functions of free electron gas in metals and insulators for the case of irradiation with a laser pulse of moderate intensity. A microscopical description on the basis of time- dependent Boltzmann equations is used. The results show the sequence of excitation and relaxation of the electron gas leading eventually to thermal equilibrium. Due to photon absorption the occupation number of electron gas differs significantly from Fermi distribution. For high enough intensities about damage threshold, the energy exchange between electrons and phonos can be described with the two- temperature model. For low excitations we find a delayed energy transfer from laser-excited electron gas to lattice as compared to the two-temperature model. We obtain fluence- dependent thermalization times of the electron gas. For dielectrics we find that the essential process of free- electron generation is strong-electric-field ionization; no avalanche develops in femtosecond time reign. We propose an extended system of two rate equation taking the effect of energy dependence of impact ionization into account. This averaging approach can reproduce the evolution of free electron density in SiO2 with reasonable accuracy.
Ultrafast time resolved microscopy of femtosecond laser irradiated surfaces reveals a universal feature of the ablating surface on nanosecond time scale. All investigated materials show rings in the ablation zone, which were identified as an interference pattern. Optically sharp surface occur during expansion of the heated material as a result of anomalous hydrodynamic expansion effects. Experimentally, the rings are observed within a certain fluence range which strongly depends on material parameters. The lower limit of this fluence range is the ablation threshold. We predict a fluence ratio between the upper and the lower fluence limit approximately equal to the ratio of critical temperature to boiling temperature at normal pressure. This estimate is experimentally confirmed on different materials.
Microscopic collision processes in solids occur on femtosecond time scales. A description of materials response to laser irradiation on this time scales should take these processes explicitly into account. Averaging descriptions are not applicable from the first. We calculate the distribution function of free electron gas in metals and insulators for the case of irradiation with a laser pulse of moderate intensity. A microscopical description on the basis of time-dependent Boltzmann equations is used. For the metal, photon absorption by free electrons, electron-electron collisions and electron-phonon collisions are considered each by a corresponding collision integral. In dielectrics, additional terms for two ionization processes (strong-electric-field ionization and impact ionization) are included. With this model, describing explicitly materials transient behavior, we are able to check the applicability of common averaging equations. For metals irradiated with sufficient high intensities about and above damage threshold the energy exchange between electrons and phonons can be described with the two temperature model, whereas for low excitation the non- equilibrium in the electron gas affects the electron-phonon coupling. For dielectrics we show that the commonly used rate equation for collisional ionization is not applicable for pulse durations below hundred femtoseconds. We propose an extended system of two rate equations taking the effect of energy dependence of impact ionization into account. This averaging approach can reproduce the evolution of free electron density in SiO2 with reasonable accuracy.
The distribution function of free electron gas in metals and insulators for the case of irradiation with a laser pulse of moderate intensity is calculated. A microscopical description on the basis of time-dependent Boltzmann equations is used. For the metal, photon absorption by free electrons, electron-electron collisions and electron-phonon collisions are considered each by a corresponding collision integral. In dielectrics, additional terms for two ionization processes (strong-electric-field ionization and impact ionization) are included. We choose aluminum as a representative of a metal and SiO2 for modeling an insulator. The results show the sequence of excitation and relaxation of the electron gas. Due to photon absorption the occupation number of electron gas differs significantly from Fermi distribution. For metals we show that electron thermalization to a Fermi distribution occurs rapidly within less than hundred femtosecond after irradiation ended. For dielectrics we find that for pulses shorter than about 100 fs, impact ionization is negligible in comparison with strong-electric-field ionization. We shown that in this case impact ionization can not be described by simple rate equations.
Irradiation of metals and dielectrics with subpicosecond laser pulses reveals a variety of different microscopic processes compared to longer pulses. We choose a transport theoretical description of electrons and phonons, which allows us to investigate the contribution of particular collision processes on macroscopic material response, even for highly nonequilibrium subsystems where a hydrodynamic description fails. The absorption of laser energy is described by photon- absorption of free electrons with assistance of phonon collisions. We considered relaxation of the electron gas by electron-electron and electron-phonon collisions. In the case of a dielectric, terms for multiphoton ionization and impact ionization are included. A resulting system of coupled time- dependent Boltzmann equations is solved numerically. For SiO2 as an example of dielectrics we calculate changes in occupation numbers of electrons and phonons, respectively, determining the sequence of excitation and relaxation of the subsystems under ultrashort laser pulse irradiation. It is shown that the essential process of free-electron generation is multiphoton ionization. Additionally, we investigate polarization effects for the case of irradiation of metals. Using parameters for gold we find anisotropic absorption of laser energy, which depends on polarization of the electric field and material parameters as well as on photon energy of irradiating laser light.
The interaction of subpicosecond laser pulses with metals is studied theoretically using phenomenological two-temperature model. Wide-range approximations for electron thermal conductivity and electron-ion energy exchange rate are proposed. Effects of temperature dependence of the thermophysical characteristics on lattice heating dynamics are discussed. Melting and evaporation kinetics are incorporated into the model to describe the metal ablation. Damage threshold and ablated layer thickness are calculated.
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