Three-dimensional transient thermal analysis for laser chemical vapor deposition on uniformly moving finite slabs

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Abstract
A mathematical model for heat transfer in the substrate during laser chemical vapor deposition (LCVD) is presented. The results of this study are applicable to the LCVD of pure titanium obtained from the thermal decomposition of titanium tetrabromide on stainless steel (S.S. 304), because the absorptivity of the substrate is determined from the optical properties of titanium tetrabromide, pure titanium, and S.S. 304. The three-dimensional and transient heat conduction equation is solved for a slab of finite dimension by considering both convective and radiative losses of energy at the surfaces of the slab. Thermal analysis such as this can provide information on the variation of film width with laser power and scanning speed, and the upper and lower limits of the operating scanning speed for LCVD processes. It is found that for a given laser power, the peak temperature varies linearly with the operating scanning speed of the laser beam on the log-log scale. Also, the peak temperature is found to vary linearly with the laser power on the linear scale for a given scanning speed of the laser beam. Finally a method of determining the optical properties at high temperatures from the low-temperature data is presented.