Ultrafast Dynamics of laser-excited Solids

General Idea

High-energy laser pulses of subpicosecond duration irradiating metals or dielectrics are primarily absorbed by electrons within the solid. We study microscopic processes determining absorption, energy redistribution and the energy transfer to the crystal lattice. In particular, we model non-equilibrium electron distributions and discuss differences in material responses due to the ultrashort timescales as compared to longer timescales where usually a near-equilibrium condition can be assumed.

Motivation and relevant Timescales

Femtosecond laser-matter interaction is of significant interest to basic research and industrial applications. Ultrashort laser pulses offer great potential for material processing. In addition, femtosecond laser pulses have been extensively used to study fundamental physical processes in solids occurring on ultrashort time scales. The interaction of ultrashort laser pulses with materials involves a number of special features which are different from laser-matter interactions for longer pulses: For ultrashort pulse durations the fundamental physical processes like energy deposition, melting, and ablation are separated in time.

relevant processes for laser-matter interaction and corresponding timescales

Figure taken from:

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde and S. I. Anisimov.
Applied Physics A 79, 767, (2004)

The figure shows typical timescales and intensity ranges of phenomena and processes occurring during and after irradiation of a solid with an ultrashort laser pulse of about 100 fs duration. Depending on excitation strength, melting occurs roughly on a picosecond timescale. In semiconductors and dielectrics irradiated with high laser intensities the loss of crystalline order is possible within less than one picosecond. The state of the material after irradiation depends strongly on the type of material and on the laser properties such as intensity and wavelength. Expansion and ablation of the laser-excited material lasts up to the nanosecond regime.

The separation of the basic processes in time allows to investigate them separately, which generally simplifies the theoretical modeling. However, the challenge for such descriptions are strong effects of non-equilibrium which become important on these timescales. Averaged concepts like temperature may lose their meaning. Electron-lattice heating or heat transport into the bulk of the material may proceed differently for non-equilibrium energy distributions as compared to the equilibrium situation. Also rate equations describing the increase of absorption in initially transparent media may not be applicable on ultrashort timescales.

Our Interests

In our group we apply a large variety of kinetic approaches as Boltzmann equation, Monte Carlo simulation and systems of energy resolved rate equations to follow the excitation and relaxation dynamics within the material on femto- to picosecond timescales. So we can identify distinct effects of non-equilibrium energy distributions.

We are also concerned with subsequent processes, as for instance phase transitions which may proceed in a different way as known for longer pulses.

Moreover, apart from the processes shown in the figure above, we are also interested in ultrafast magnetization dynamics and electron dynamics in solids induced by swift heavy ions or VUV/XUV laser pulses.

Current projects as well as projects recently finished and/or to be continued are described below.

You may address questions on the projects either to the contacts given below or directly to Prof. Dr. Bärbel Rethfeld.

Current projects

Non-equilibrium conditions in laser excited metals

Contact: Sebastian Weber

Zeitaufgelöste Elektronenenergieverteilung nach anregung durch einen ultrakurzen Laserpuls We analyze theoretically the behavior of a metal which is excited by an ultrashort laser pulse. The irradiation process creates a non-equilibrium state in the electron system which causes that some properties vary drastically from their equilibrium state. In particular, the non-equilibrium energy transfer rate between the electrons and the lattice can differ significantly, which is important to estimate damage thresholds in material processing.

Current publication:
B. Y. Mueller and B. Rethfeld, Phys. Rev. B 87, 035139 (2013)

Ultrafast demagnetization dynamics

Contact: Sebastian Weber

spin resolved Boltzmann model Irradiating a ferromagnetic material by an ultrashort laser pulse leads to a demagnetization on a femtosecond time scale. Although this effect has been known for twenty years the fundamental mechanisms for this behavior are highly debated. To develop a theoretical explanation and to provide an experimental validation for the underlying mechanism of this ultrafast phenomenon, we collaborate with two other groups at Kaiserslautern (Prof. M. Aeschlimann and Prof. H. C. Schneider). In our theoretical approach we trace non-equilibrium electrons after a laser excitation. By assuming a spin-resolved model we find that the demagnetization effect can be explained by spin-flips in the electron system which evolves into a new equilibrium state with a lower magnetization.

Current publications:
B. Y. Mueller, A. Baral, S. Vollmar, M. Cinchetti, M. Aeschlimann, H. C. Schneider, and B. Rethfeld,
Phys. Rev. Lett. 111, 167204 (2013)
B. Y. Mueller, T. Roth, M. Cinchetti, M. Aeschlimann and B. Rethfeld, New Journal of Physics 13, 123010 (2011)

Kinetic description of electron- and phonondynamics in laser-irradiated dielectrics

Contact: Nils Brouwer

Electron distribution Transparent dielectrics, like quartz, become opaque when irradiated by intense ultrashort laser pulses. On the one hand, this leads to undesirable damage in optical setups, on the other hand, it can be used to process materials more precisely. For controlled applications, it is important to understand the underlying mechanisms.

While, in metals, conduction band electrons absorb visible laser light, these are not present in dielectrics at room temperature. A direct excitation of the electrons within the fully occupied valence band is impossible due to the Pauli principle. Unlike in semiconductors, single photons from the visible spectrum are not sufficient to overcome the band gap. Only with intense laser irradiation, the probability to absorb multiple photons at once is high enough and electrons can be excited from the valence band to the conduction band (multiphoton or tunnel ionization). Now, these new conduction band electrons can absorb single photons and gain even more energy. If they have sufficient energy, they can collide with valence band electrons and give them enough energy to excite them to the conduction band (impact ionization). Through the interplay of these processes, more and more energy is absorbed during the laser pulse. But whether impact ionization or multiphoton ionization make the major contribution to the generation of conduction band electrons depends strongly on pulse and material parameters. While, on the nanosecond timescale, impact ionization clearly dominates and multiphoton ionization only initiates the electron cascade, the last-mentioned process plays a more significant role on the femtosecond timescale.

Aside from the above-mentioned processes, there exist a couple of additional processes that can have an influence during the laser excitation of dielectrics as soon as electrons are excited to the conduction band: Electron-electron collisions lead to the thermalization of the electron distribution. Electron-phonon collisions transfer energy to the lattice, possibly leading to the melting of the material. Similar processes are possible in the valence band due to the holes left by the ionization processes. Auger recombination can counterbalance impact ionization and contributes to reaching the thermodynamic equilibrium between the bands.

In order to simulate all these processes, we use Boltzmann-type collision integrals to calculate the time-evolution of the distribution function of conduction and valence band electrons, respectively, as well as of acoustic and optical phonon modes. The efficient execution of the necessary numerical calculations require the use of strongly parallelized algorithms on high performance computing clusters. Currently, we are using the cluster Elwetritsch within the AHRP-project Lainel.

For further reading:
N. Brouwer and B. Rethfeld, JOSA B 31, C28 (2014)

Non-equilibrium phonon gas in laser-excited solids

Contact: Isabel Klett

Irradiation of metals with a femtosecond laser pulse leads to a hot electron gas, while the lattice stays nearly cold. Due to the excitation, the electronic system is out of thermal equilibrium, so after laser irradiation, two main processes occur: The first is the electron thermalization, the second is the energy transfer from the electrons to the lattice due to the electron-phonon-coupling. Both processes have been described by assuming a thermalized distribution function for the phononic system. However, due to the fact that only longitudinal phonon modes can absorb the energy of the electrons, this assumption does not hold. Besides, with THz-Lasers, different phonon modes can be excited directly, leading to a thermal non-equilibrium within the phononic system. Furthermore, in thin films phonon confinement effects have been observed, which is also an indication for a non-equilibrium distribution of the phonons. We describe the phonon-phonon interaction and phonon thermalization with a Boltzmann collision integral. Our aim is to model non-equilibrium phonon distributions and the resulting observable effects after ultrashort laser-matter interaction.

Our work is motivated by:
J.-M. Manceau, P.A. Loukakos, S. Tzortzakis, Appl. Phys. Lett. 97, 251904 (2010)
B. Krenzer, A. Hanisch-Blicharski, P. Schneider, Th. Payer, S. Möllenbeck, O. Osmani, M. Kammler, R. Meyer, and M. Horn-von Hoegen, Phys. Rev B 80, 024307 (2009)

Dynamics of electrons in liquid water excited with ultrashort XUV laser pulses

Contact: Bärbel Rethfeld

Electron distribution in water under VUV laser irradiation calculated with the Monte Carlo method The free–electron laser in Hamburg (FLASH) is able to produce ultrashort laser pulses in the extreme ultraviolet (XUV) spectral range. The peak energy approached 170 μJ and the average energy per pulse reached 70 μJ with a pulse duration of 10 fs. FLASH delivers ultrashort laserpulses at 13.7 nm, and also the third (4.6 nm) and the fifth harmonic (2.75 nm) are accessible.

We are working on the interaction of such new kind of irradiation with liquid water. In this process free electrons are created by photoionization, which we track by the use of the kinetic Monte Carlo method. We calculate the trajectory for these free electrons which can interact with the water molecules via ionization, elastic scattering or Auger recombination. Finally we are interested in time-, space and energetically resolved electron distributions.

This may serve as an initial condition to study further molecular movement, see e.g. Yaroslav Cherednikov.

The project is supported by Carl Zeiss Stiftung

Modeling laser irradiation of dielectrics

Contact: Oliver Brenk

Reflectivty in dependence of the free carrier density During irradiation with an intense ultrashort laser pulse breakdown of a transparent dielectric medium can occur. This effect is important for a wide range of applications: ranging from protecting optical elements to microstructuring and even surgery. Using the multiple rate equation, a simplified kinetic approach describing the temporal evolution of the conduction band electron density during irradiation, we investigate absorption and breakdown. Including optical parameters, dependent on electron density, we trace dielectric breakdown independent of the assumption of a critical density. This allows us to model the depths up to which material modification can occur. The flexibility of our model further enables us to create maps of breakdown for different laser and material parameters.

For further reading:
B. Rethfeld, Phys.Rev.Lett. 92, 187401, (2004)
B. Rethfeld, Phys. Rev. B 73, 035101 (2006)

Heat and carrier transport in semiconductors

Contact: Anika Rämer

Damage thresholds estimated with the nTTM using different optical parameters in comparison with experimental
							results. During the irradiation of semiconductors with an ultrashort laser pulse, electrons are excited from the valence band to the conduction band, thus creating electron-hole pairs. The excited electron-hole pairs interact with the phonon system, thereby heating the lattice.

When modeling heat relaxation and transport in semiconductors, it is therefore important to account for the transient free carrier density. This carrier density even strongly influences the optical parameters during the irradiation process.

By using a density-dependent two-temperature model (nTTM), we are able to model the temporal and spatial evolution of the free carrier density as well as the carrier and phonon temperature taking into account transient optical parameters. We are thereby able to make predictions on the damage thresholds for semiconductors that are in very good agreement with experimental data.

For further reading:
H. M. van Driel. Phys. Rev. B 35, 8166 (1987)
A. Rämer, O. Osmani and B. Rethfeld. J. Appl. Phys. 116, 053508 (2014)

Hydrodynamic models for pulsed laser irradiation of metals

Contact: Bärbel Rethfeld

Laser material removal, also known in the field as laser ablation, is nowadays used in a growing number of applications, such as micromachining, chemical analysis as well as pulsed laser deposition. Hence a better insight in the material evolution during short pulse laser irradiation can be helpful for the optimization of the related applications. Our aim is to develop hydrodynamic models for short pulsed laser irradiation of metals, ranging from the femtosecond to the nanosecond regime. Contrary to kinetic models, hydrocodes do not suffer from severe time- and length-scale limitations. Therefore they can provide a macroscopic description of material evolution during pulsed laser irradiation.

The present research focuses on the evolution of a metallic target under pulsed ns-laser irradiation. A typical experimental situation, as encountered in chemical analysis setups such as Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS), is modelled with an in-house developed hydrocode. A copper sample is placed in an ambient gas, such as argon. During ns-laser irradiation the copper target heats up, melts, evaporates and finally expands into the ambient gas. Here the laser pulse triggers breakdown in the expanding copper plume, resulting in a plasma that shields the target from the incoming laser light. Hence target dynamics will influence plume dynamics and vice versa.

Our aim is to calculate how the energy distributes between plasma and target.

Information on LA-ICP-MS:
A. Montaser, Inductively Coupled Plasma Mass Spectrometry, Wiley VCF, New York 1998, pp. 83-224

Nanostructuring of materials

Contact: Dimitry Ivanov

Nanostructuring of a 60 nm Au film Femto- and picosecond laser pulses are a powerful tool for generating surface structures on a sub-wavelength scale. Such structures are very reproducible and found promising applications in IT and Biotechnologies. The purpose of this project is to elaborate a model and to develop the related theory, which could be applicable in experimental data treatment on short pulse laser nanostructuring of materials. The main idea of our computational approach is to combine the advantages of several models to account for all possibly involved processes that additionally take place on different time and spatial scales. The model includes the description of laser-induced non-equilibrium phase transformation processes at the atomic level using molecular dynamics methods whereas the dynamics of the laser-excited free carriers is treated with help of continuum approaches. The results obtained with the combined atomistic-continuum model in super large scale parallel calculations look promising for the theoretical description of nanostructuring on metals (Au, Ni, Ag, Cu, and Al) and are directly comparable and in a very good agreement with experimental data. Further applications of the atomistic-continuum model will allow us to advance understanding of the fundamental mechanism of short pulse surface nanostructuring on semiconductors and insulators.

For further reading:
D. S. Ivanov and L. V. Zhigilei, Phys. Rev. B 68, 064114 (2003)
D. S. Ivanov, Z. Lin, B. Rethfeld, G. M. O’Connor, T. J. Glynn, and L. V. Zhigilei, J. Appl. Phys. 107, 013519 (2010)

Molecular Dynamics based development of non-equilibrium theory of phase transitions

Contact: Dimitry Ivanov

Results of calculations using a molecular dynamics approach The aim of this project is to elaborate the theory of nucleation for a continuum description of the kinetics of non-equilibrium phase transition processes induced in the solid by an ultrashort and localized energy deposition. Such energy deposition can be achieved by either a femto- or a picosecond laser pulse or by an ion beam focused on the material surface. A great number of concurrent and competing processes occur in the solid upon strong excitation.

Here, we apply a molecular dynamics (MD) approach to model the kinetics of the induced processes efficiently and with atomic precision. In the current project, we also include insights of other approaches by modelling the free carrier dynamics and induced changes of the interatomic potential. We expect to capture the kinetics of laser or ion beam induced phase transitions, such as homogeneous and heterogeneous melting (including influence of grain boundaries in polycrystals and non-thermal effects in semiconductors), spinodal decomposition, as well as spallation and evaporation. The long-term objective of this project is to develop a new model in a closed analytical form as a part of a non-equilibrium nucleation theory.

For further reading:
D. S. Ivanov, O. Osmani and B. Rethfeld
Computer Modeling of Nanostructuring on Materials with Tightly Focused Energy Deposition
Chapter in Laser Beams: Theory, Properties and Applications, Nova Science Publishers, New York (2009)