Temperature calculation for laser irradiation of sol-gel films on oxide substrates
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A model for estimating the temperature rise in a laser-irradiated oxide target is developed and applied to laser-firing of sol-gel films on oxide substrates. The model incorporates a continuous-wave (CW) Gaussian laser beam translated across a sol-gel film on a semi-infinite substrate. Heat effects due to phase changes are assumed to be absent. In addition, the laser energy is assumed to be absorbed primarily in the substrate material (since many sol-gel films are much thinner than the absorption depth of typical laser wavelengths). The model also takes into account the temperature dependence of the thermal properties of the substrate. The predictions from the model are compared to experimental data from various laser firing experiments. The temperatures predicted by the model are shown to agree well with experimental results.
I. INTRODUCTION Laser irradiation can be used to weld, drill, and cut metals; anneal crystals, ceramics, and glasses; dope semiconductors; and cure polymers and adhesives. One advantage of using lasers is the ability to heat localized regions preferentially. By matching wavelength and beam power to the optical and thermal properties of the target material, an appropriate heat treatment can be applied. In some cases surface heating may be desired without volume heating, requiring a high absorptivity of the incident radiation. On the other hand, it might be desirable to have a narrow beam that is absorbed deeply into the target (e.g., for laser scribing). Another characteristic of laser heating is that high heating and cooling rates can be achieved and tailored by rapid pulsing or scanning at high velocities. Having the ability to control all these parameters, lasers provide a versatile heating tool for materials scientists. When performing any sort of materials processing with lasers, it is useful to know the heat treatment of the material, including peak temperature, heating duration, and final cooling rates. During furnace heating of a material, the temperature, time-at-temperature, and heating/cooling rates are usually known and easily measured. However, with laser firing, heating occurs too rapidly to be measured by simple methods. Therefore, it is useful to be able to calculate sample temperatures and time profiles in laser-fired materials, rather than measuring temperature directly. However, when performing this calculation it is necessary to use accurate physical property data, including any strongly temperature dependent quantities. Solutions to the heat equation have been solved for many different types of laser heating. Depending on the J. Mater. Res., Vol. 10, No. 6, Jun 1995 http://journals.cambridge.org
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sample and the type of irradiation, assumptions can be made to simplify the calculations and still achieve an accurate solution. Solutions have been worked out for continuous wavelength (CW) irradiation1"11 and for pulsed irradiation.12 18 Most of these models give the temperature rise in material with a moving heat source,1>3i5"11>14"18 as well as for a
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