1. 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

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

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

4. 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

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

6. 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

7. 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

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

9. dependence on magnitude and frequency of the field
Single photon excitation

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

11. Effects of lattice temperature

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

13. WL

14. Effects of joule heating

15. Effects of joule heating

16. 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

17. 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.

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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