Valencia Bernd Hüttner Folie 1 New Physics on the Femtosecond Time Scale Bernd Hüttner CphysFInstP DLR Stuttgart

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner 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)

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner 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

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

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

Valencia Bernd Hüttner 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.

Valencia Bernd Hüttner 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

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

Valencia Bernd Hüttner 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

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

Valencia Bernd Hüttner 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

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

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

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

Valencia Bernd Hüttner Folie Thermal diffusivity with the specific heat of NFE Few examples:

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Valencia Bernd Hüttner 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

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

Valencia Bernd Hüttner Folie 24 with the abbreviations The integration reads for the first order contribution

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner Folie 26 Surface temperature distributions of gold

Valencia Bernd Hüttner Folie 27 Optical penetration depth

Valencia Bernd Hüttner Folie 28 Absorption

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner Folie 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

Valencia Bernd Hüttner Folie 31 Cattaneo equation Energy conservation Extended two temperature model with

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner 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

Valencia Bernd Hüttner Folie 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

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