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 electron-electron 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.
We begin with a brief critical discussion of the existing definitions of melting and damage thresholds and the different kinds of experimental determinations of the thresholds. Then we investigate the thermal and athermal melting of a wide-band gap semiconductor (SiO<sub>2</sub>) and of silicon by two different methods consisting of a rate equation for the excited electrons and of a complete self-consistent solution of a coupled system of differential equations for the electron density and for the electron and phonon temperatures. In particular, we focus on the role of the critical electron density in the case of athermal melting. Our calculations suggest that this is determined by the critical plasma density. Finally, we conclude with a discussion of the benefits and drawbacks of the two approaches.
We begin with a short discussion of existing approaches to the description of nonequilibrium processes and the possibility of how to overcome the problem of the definition of temperature in this case. Next, we explain why the equations of fluxes and conductivities as derived in standard solid state theory have to be reconsidered. Starting from the Boltzmann equation then we derive expressions for the thermal and electrical conductivity with new qualitative and quantitative properties. These results are supported by comparison with experiments.
First, we give a briefly critically discuss the existing definitions of melting and damage thresholds and the different kinds of experimental determinations of the thresholds. Then we investigate the thermal and athermal melting of oxides (wide-band gap semiconductors) and of silicon by solving a rate equation for the excited electrons and a by complete self-consistent solution of a coupled system of differential equations for the electron density and for the electron and phonon temperatures. In particular, we direct our attention to the still open question about the value for the critical electron density in the case of athermal melting.
An experimental and theoretical investigation of ultrashort pulse damage thresholds of Si and Ge semiconductors has been carried out. As the source of laser radiation, a commercial sub picosecond Ti:Sapphire laser system has been used. It produces laser pulses of 0.5 mJ pulse energy at 1 kHz repetition rate, providing a Gaussian-like beam profile. Compressor tuning allowed for varying the pulse duration from 150 fs to 5.5 ps. The laser damage thresholds were measured in air and for this pulse duration range. The damage morphologies were investigated with various microscopic inspection techniques like Nomarski DIC, atomic force and white light interference microscopy.
From both a theoretical and an experimental point of view, the properties of fs laser pulses are fascinating. For a deeper understanding and for the prediction of the experimental results, the knowledge is necessary of absorption and of the optical penetration depth on the fs scale. For the description of the interaction of a fs-laser pulse with a solid, the stan-dard values of the properties of a solid are not suited because they have been experimentally determined or theoretically derived under the assumptions of a steady state and local thermal equilibrium. Depending on the property considered and the laser pulse duration either one or both of these conditions may be violated. In this paper, we derive equations for the optical properties of metals in the case of local thermal nonequilibrium be-tween the electron and phonon system. For a given laser intensity, we calculate, as an example, the absorption and opti-cal penetration depth for gold. For this purpose, we need the time dependent temperatures of the electrons and phonons. They are evaluated by means of our extended two temperature model. Finally, we compare the results with the standard equilibrium behavior as well as with the experimental findings and close with a short discussion.
The nonequilibrium properties of the electrical and thermal currents in metals in the transient regime are investigated. The transition range, by definition, lies between the time necessary for establishing the electron temperature and the time that justifies a description by the standard steady state equations. Using a second order expansion of the Boltzmann equation, we derive the relaxation functions for the electrical and thermal cases and determine the relaxation times related to them. It is shown that the relaxation time for the electrical transport corresponds to Drude's momentum scattering time whereas the corresponding time for the heat flow is identified as the electron temperature relaxation time. Consequently, Ohm's law should remain a good approximation in most cases whereas the Fourier equation must be supplemented by a relaxation term leading to the hyperbolic heat conduction equation. In addition, we discuss the changed properties of the electrical and thermal conductivity on short time scales and show that both quantities becomes explicit functions of time. Moreover, the thermal conductivity shows a dependence on the laser frequency.
Practical high precise and efficient micromachining can be realized with computer controlled ultrashort laser pulses suppressing the thermal diffusion effect inside the material to be ablated. A direct translation from solid to the vapor state takes place at sufficient intensity levels. Experimental results of micromachining of different materials with femtosecond laser pulses at wavelengths of 800 nm and 267 nm from a commercial Ti:sapphire laser are presented. Holes down to a diameter below 1 micron have been drilled with 800 nm pulses into aluminum as an interesting metal with an absorption peak in the IR-range nearby 800 nm. Because of their low energy band gap semiconductors have a strong absorption at UV wavelengths. Arrays of holes down to 1 micrometer in diameter have been drilled into silicon and InP using 267 nm pulses. Results of fused silica as an example for transparent insulator materials are compared to result of semiconductors. The hole array manufacturing process takes only a few seconds. Precision can be improved by matching laser parameters to the processed material.
Recently, several groups have demonstrated that the spatial and temporal temperature distribution inside metals resulting from femtosecond laser pulses cannot be fully explained 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 electron-phonon 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.