Bärbel Rethfeld

Effective energy gap of semiconductors under irradiation with an ultrashort VUV laser pulse

We study theoretically the electronic excitation within semiconductors under irradiation with an ultrashort VUV laser pulse as provided by the new free-electron laser FLASH in Hamburg, Germany. Applying Monte Carlo technique we obtain the transient distribution of the excited electrons within solid silicon. We find the statistical nature of an effective energy gap for multiple electronic excitation, providing the fundamental understanding of the experimentally accessible pair creation energy measured as a long time limit. Considering photoabsorbtion, impact ionizations and Coster-Kroning transitions, we estimate the pair creation energy and give a general formula to calculate the effective energy gap for semiconductors.

Heat transport in nanoscale heterosystems: a numerical and analytical study

The numerical integration of the heat diffusion equation applied to the Bi/Si-heterosystem is presented for times larger than the characteristic time of electron-phonon coupling. By comparing the numerical results to experimental data, it is shown that the thermal boundary resistance of the interface can be directly determined from the characteristic decay time of the observed surface cooling, and an elaborate simulation of the temporal surface temperature evolution can be omitted. Additionally, the numerical solution shows that the substrate temperature only negligibly varies with time and can be considered constant. In this case, an analytical solution can be found. A thorough examination of the analytical solution shows that the surface cooling behavior strongly depends on the initial temperature distribution which can be used to study energy transport properties at short delays after the excitation.

Electron kinetics in semiconductors and metals irradiated with VUV-XUV femtosecond laser pulses

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, Paulis 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.

Excitation and relaxation dynamics in dielectrics irradiated by an intense ultrashort laser pulse

When transparent dielectrics are irradiated by an intense, ultrashort laser pulse, the electron density in the conduction band is increased tremendously. Simultaneously, valence band states become unoccupied and the electron–phonon coupling strength is increased. In this paper, we present our work on modeling the ultrafast nonequilibrium dynamics of laser-excited transparent dielectrics with Boltzmann collision integrals. We track the distribution function of conduction and valence band electrons and discuss the effects of Auger recombination in relation to impact ionization and multiphoton/tunnel ionization on the femtosecond timescale. Finally, we investigate the electron–phonon coupling strength in highly excited dielectrics and calculate the electron–phonon coupling parameter for silicon dioxide-like material.

Electron dynamics in transparent materials under high-intensity laser irradiation

Abstract. 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.

A split-step method to include electron-electron collisions via Monte Carlo in multiple rate equation simulations

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron-phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron-electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron-electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.

Electron kinetics in liquid water excited by a femtosecond VUV laser pulse

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.

Dynamics of electrons in liquid water excited with an ultrashort VUV laser pulse

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.

Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy

Understanding the transfer of spin angular momentum is essential in modern magnetism research. A model case is the generation of magnons in magnetic insulators by heating an adjacent metal film. Here, we reveal the initial steps of this spin Seebeck effect with <27 fs time resolution using terahertz spectroscopy on bilayers of ferrimagnetic yttrium iron garnet and platinum. Upon exciting the metal with an infrared laser pulse, a spin Seebeck current js arises on the same ~100 fs time scale on which the metal electrons thermalize. This observation highlights that efficient spin transfer critically relies on carrier multiplication and is driven by conduction electrons scattering off the metal–insulator interface. Analytical modeling shows that the electrons’ dynamics are almost instantaneously imprinted onto js because their spins have a correlation time of only ~4 fs and deflect the ferrimagnetic moments without inertia. Applications in material characterization, interface probing, spin-noise spectroscopy and terahertz spin pumping emerge.Probing spin pumping in the terahertz regime allows one to reveal its initial elementary steps. Here, the authors show that the formation of the spin Seebeck current in YIG/Pt critically relies on hot thermalized metal electrons because they impinge on the metal-insulator interface with maximum noise.

Modeling energy transfer and transport in laser-excited dielectrics

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.