1. Valencia Bernd Hüttner 3.-5.9.2008 Folie 1 New Physics on the Femtosecond Time Scale Bernd Hüttner CphysFInstP DLR Stuttgart

2. Valencia Bernd Hüttner 3.-5.9.2008 Folie 2 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary 3. Enhanced importance of electron-electron scattering time

3. Valencia Bernd Hüttner 3.-5.9.2008 Folie 3 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary 3. Enhanced importance of electron-electron scattering time

4. Valencia Bernd Hüttner 3.-5.9.2008 Folie 4 1. Local thermal equilibrium vs. Nonequilibrium, T el  T ph vs. T el >> T ph 1. What are the distinctions between ns and fs laser pulse interaction? 2. Electron-electron scattering time smaller than electron-phonon one 3. Changing of optical and thermal properties, e.g. time dependent 4. Relaxation time is in the order or above the laser pulse duration, PHCE HHCE or diffusive ballistic behavior 5. Intensity, ns: F = 1-10J/cm 2, fs: F = 1-10mJ/cm 2 → I 0 (fs)  10 3 ·I 0 (ns)

5. Valencia Bernd Hüttner 3.-5.9.2008 Folie 5 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 3. New thermal and optical properties 4. Hyperbolic heat conduction equation (HHCE) 5. Summary

6. Valencia Bernd Hüttner 3.-5.9.2008 Folie 6 2. Nonequilibrium of electron system Experimental result:  L =180fs, F abs =(300±90)  J/cm 2, E L =1.84eV, d=30nm≈2·d opt Figure 1: Experimental electron energy distribution function taken from Fann et al. FD Au

7. Valencia Bernd Hüttner 3.-5.9.2008 Folie 7 Theoretical approach Boltzmann equation with the photon operator for Gaussian laser pulse small parameter development

8. Valencia Bernd Hüttner 3.-5.9.2008 Folie 8 The first order reads and the 2 nd order For the one photon distribution function we find

9. Valencia Bernd Hüttner 3.-5.9.2008 Folie 9 Theoretical electron energy distribution function vs energy with 300 µJ/cm 2 absorbed laser fluence at five time delays. The dashed line is the Fermi-Dirac function and the corresponding electron temperature T e is shown.

10. Valencia Bernd Hüttner 3.-5.9.2008 Folie 10 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary 3. Enhanced importance of electron-electron scattering time

11. Valencia Bernd Hüttner 3.-5.9.2008 Folie 11 2. Enhanced importance of electron-electron scattering time Fermi liquid theory:  total  e-e T e (K)  (fs)  ph (300K)= 30fs Au

12. Valencia Bernd Hüttner 3.-5.9.2008 Folie 12 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary 3. Enhanced importance of electron-electron scattering time

13. Valencia Bernd Hüttner 3.-5.9.2008 Folie 13 3.1 Thermal conductivity 3. New thermal and optical properties where the scattering time is given as The integration yields

14. Valencia Bernd Hüttner 3.-5.9.2008 Folie 14 Thermal conductivity of Au for the case of nonlocal thermal equilibrium at fixed Tph=300K: Solid upper curve 1 + 2, dashed ~T e, dashed-dotted curve 2, and for the local thermal equilibrium T e =T ph =T: solid curve 1, dotted curve LTE, à experimental data taken from Weast λ 1 + λ 2 λ2λ2 λ e = λ 0 ·T e /T 0 Wiedemann-Franz

15. Valencia Bernd Hüttner 3.-5.9.2008 Folie 15 Time dependence of thermal conductivity t/  << 1: ballistic behavior t/  >> 1: diffusive behavior But there is more

16. Valencia Bernd Hüttner 3.-5.9.2008 Folie 16 Summary: Solid: Al Dasded-dotted: Ag  =  -1 Vertical lines: Electron temperature relaxation time  T AgAl

17. Valencia Bernd Hüttner 3.-5.9.2008 Folie 17 Volz – Physical Review Letters 87 (2001) 74301 Molecular dynamics and fluctuation-dissipation theorem

18. Valencia Bernd Hüttner 3.-5.9.2008 Folie 18 3.2 Thermal diffusivity with the specific heat of NFE Few examples:

19. Valencia Bernd Hüttner 3.-5.9.2008 Folie 19

20. Valencia Bernd Hüttner 3.-5.9.2008 Folie 20

21. Valencia Bernd Hüttner 3.-5.9.2008 Folie 21

22. Valencia Bernd Hüttner 3.-5.9.2008 Folie 22 What is with ballistic behavior? Einstein relation: Sample thickness vs time of flight for various Au films 50, 100, 150, 200, and 300nm thick. Brorson et al. – Phys. Rev. Lett. 59 (1987) 1962

23. Valencia Bernd Hüttner 3.-5.9.2008 Folie 23 Optical properties We find the electrical current by multiplying the BE with –e·v Dielectric function

24. Valencia Bernd Hüttner 3.-5.9.2008 Folie 24 with the abbreviations The integration reads for the first order contribution

25. Valencia Bernd Hüttner 3.-5.9.2008 Folie 25 Relations between the optical functions An example: hat-top profile with  =1eV,  L =500fs, I abs =10GW/cm 2, I abs =20GW/cm 2 Complex refractive index Optical penetration depth and absorption

26. Valencia Bernd Hüttner 3.-5.9.2008 Folie 26 Surface temperature distributions of gold

27. Valencia Bernd Hüttner 3.-5.9.2008 Folie 27 Optical penetration depth

28. Valencia Bernd Hüttner 3.-5.9.2008 Folie 28 Absorption

29. Valencia Bernd Hüttner 3.-5.9.2008 Folie 29 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary 3. Enhanced importance of electron-electron scattering time

30. Valencia Bernd Hüttner 3.-5.9.2008 Folie 30 4. Hyperbolic heat conduction equation (HHCE) Multiply BE by the product of the energy difference (E -  ) times the velocity Solving the integrals leads to Cattaneo’s equation with

31. Valencia Bernd Hüttner 3.-5.9.2008 Folie 31 Cattaneo equation Energy conservation Extended two temperature model with

32. Valencia Bernd Hüttner 3.-5.9.2008 Folie 32 Electron temperature as a function of time for a Au-film with thickness of d=30nm..\..\..\Mathematics\FlexPDE5\Files\Archiv\Different laser profiles.pg5

33. Valencia Bernd Hüttner 3.-5.9.2008 Folie 33 Overview 1. What are the distinctions between ns and fs laser pulse interaction? 2. Nonequilibrium of electron system 4. New thermal and optical properties 5. Hyperbolic heat conduction equation (HHCE) 6. Summary 3. Enhanced importance of electron-electron scattering time

34. Valencia Bernd Hüttner 3.-5.9.2008 Folie 34 5. Summary Nonequilibrium distribution of electrons – deviations from FD distribution Nonequilibrium between electrons and phonons – T e >> T ph Changed dependence of temperature of the thermal and electrical conductivity due to electron-electron scattering time Both conductivities become implicit and explicit time dependent Change of optical properties (partly drastic) Extended two temperature model (HHCE) must be used for the determination of the electron temperature leading to temperature waves Ballistic electron transport - The essential new points on the femtosecond time scale

35. Valencia Bernd Hüttner 3.-5.9.2008 Folie 35