Theoretical modeling of short pulse laser interaction with condensed matter Tzveta Apostolova Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences ELI Nuclear Physics Workshop’2010

Short pulse nanostructuring Nanostructures in Si – Lebedev Physical Institute 2009 – unbuplished Number of incident pulses ~103 Energy density ~50-300 mJ/cm2 Wavelength 744 nm Pulse duration (FWHM) ~100 fs Pulse energy <0.5 mJ Pulse repetition rate 10 Hz

Formation of filaments Single pulse filaments in PMMA, energy density 0.50-25 mJ/cm2– Lebedev Physical Institute 2009 Similar could be obtained for Si if irradiated with mid-IR

GaAs Laser radiation parameters Wavelength Pulse duration Conduction band Pulse duration electron Repetition rate Laser radiation Forbidden band Intensity The damage of materials can be described by a critical density of photo-excited electrons in the conduction band hole Valence band Laser radiation GaAs semiconductor

Non-uniform laser radiation spatially and temporally dependent laser field inside the material Optical damage Electrical damage for GaAs Structural damage

Theoretical model mean traveling length of electron in one period of laser radiation induced energy due to the interaction of electrons with the laser field

Energy loss to phonons term Conduction-Electron Energy Joule Heating Current Spontaneous Phonon Emission Current Diffusion Current Distribution Function Terms: Photon ionization Impact ionization Auger recombination Ionization due to Coulomb Scattering Recombination due to Phonon Scattering Pumping due to Photon Absorption The distribution function is a product of the density-of-states and the state-occupation probability Electrons can flow to higher energies by gaining power from an incident pulsed laser field Electrons can also flow to lower energies by emitting spontaneous phonons The competition between different currents in the energy space can be described by a Fokker-Planck equation

local fluctuation of electron kinetic energy is included in the kinetic Fokker-Planck equation under the condition but Drude ac conductivity

dependence on magnitude and frequency of the field Single photon excitation

Effects of thermal emission and recombination scattering-in scattering-out scattering-in scattering-out

Effects of lattice temperature

Time dependence of the electron density and average kinetic energy for different intensities and different bandgap widths

WL

Effects of joule heating

Effects of joule heating

Conclusions We derive quantum-mechanically a generalized Fokker-Planck type equation in energy space for conduction electrons in semiconductors irradiated by laser field in which the effect of the laser field treated classically is included via -energy drift term for conduction electrons-joule heating effect -renormalization of the electron-phonon scattering by the field- effect of free carrier absorption We include source and sink terms (up to 2nd order in perturbation theory) We investigate numerically the factors influencing the laser-induced damage to semiconductors

Results For , in GaAs we obtain The calculations show that for the chosen parameters the semiconductor GaAs is electrically damaged but not optically damaged. We find out that the average conduction electron kinetic energy is smaller than the bangap energy at all times which means that for the given parameters of the laser field the semiconductor GaAs is structurally stable.

at the United States Air Force Research Laboratory Work was done in collaboration with Dr. Danhong Huang Dr. David Cardimona Dr. Paul Alsing at the United States Air Force Research Laboratory

Spatial dependence of Source terms In the final result include the spatial dependence by taking the envelope of the electric field as a function of the spatial coordinates regarded as parameters. Spatial dependence of Source terms Single photon excitation

Generalized non-local Fokker Planck equation Following E. Bringuier J. Appl. Phys 86, 6847, (1999) we can augment the energy –space equation by adding the spatially dependent currents on the LHS

energy change before any collision occurs is Spectral drift velocity and diffusion coefficient at energy in coordinate space electron with at energy change before any collision occurs is the probability for the electron starting from not to experience collisions between 0 and t is first order expansion E.Bringuier Phys. Rev. B 52, 1995

averages over a collision free flight The average energy gained over a flight is (to order ) is Number of states in a surface element in space ensemble average over a constant energy surface

The drift velocity in real space is related to the field induced drift velocity in energy space by The position-space diffusion coefficient is related to the field dependent diffusion coefficient in energy space by