Recently, several groups have demonstrated that the spatial and temporal temperature distribution inside metals resulting from femtosecond laser pulses cannot be fully exp'ained by the two-temperature model for the electrons and phonons. Since these short pulse lengths may be comparable to the electron temperature relaxation time, we introduce a heat flow which is nonlocal in time. By this way we are taking into account in first order a non-equilibrium distribution of the electrons. As a consequence, three additional terms appear in the differential equation for the electron temperature. Furthermore, we offer an explanation for the different response of metals to the laser radiation on the basis of the electronphonon coupling constant and the average phonon frequencies squared, well-known quantities in McMillan's theory on superconductivity.Using a double temperature model with nonlocal heat flow and a laser pulse length of 1 ps, the calculated surface temperatures of the electron and phonon subsystems are presented for Cu, Nb, and Pb. This is compared with the results of a local heat flow approach and with the conventional theory as well. Additionally we present calculations of the electron surface temperature of a thin Au film. We find that our model is capable of describing the new measurements on Au films more consistently than the standard double temperature model. . INTRODUCTIONPicosecond and especially femtosecond lasers are becoming a universal tool for surface processing because they possess some advantages in comparison to lasers with longer pulses. First, the whole energy of the laser pulse is absorbed by the material and not partially by a plasma produced above the surface. Second, heat conduction by phonons does not occur during the time of the laser target interaction allowing a more localized storage of energy. It should be emphasized that this is in contrast to the physics prevailing at longer pulse lengths where the process essentially is governed by the thermodynamics of phonons. This may be applied for the production of structures with sharper edges due to a direct evaporation without melting.On the other side, an estimate of the penetration depth of the heat is no longer possible with L(Kt)112, where ic is the heat diffusion coefficient and t is the pulse length, because it is dominated initially by the temperature relaxation time of the electrons and their Fermi velocity, as we will show below. Not surprisingly also the surface temperature and the temperature distribution inside the metal may be very different from that calculated according to the standard heat conduction approach (Fourier), well suited for ns-pulses. However, with decreasing laser pulse length and the smaller the heat exchange coefficient of the investigated metal is, distinctions between the results of the two temperature model1 (TTM) and our proposed extended two temperature model 2(ETTM) become more obvious.Furthermore, we will work out the crucial importance of the heat exchange coefficient between the electron and phono...
We start with a short introduction of some newer thermodynamical approaches to the description of nonequilibrium processes related to the interaction of short laser pulses with matter. Then we shall use the example of electronic thermal conductivity to show why the equations usually derived in standard solid state theory have to be reconsidered. This is mandated by the loss of local thermal equilibrium, the nonstationarity, and the enhanced contribution from electronelectron scattering. Based on Boltzmann's equation we derive an expression for the thermal conductivity with new qualitative and quantitative properties. These results are supported by comparison with experiments.
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