A FE-FD hybrid scheme for solving parabolic two-step micro heat transport equations in irregularly shaped three dimensional double-layered thin films exposed to ultrashort-pulse lasers.

摘要

Multi-layer thin films are important components in many micro-electronic devices. These films are often used when a single film layer is insufficient to meet devices specifications. The continued reduction in component size has the side effect of increasing the thermal stress on these films and consequently the devices they comprise. Understanding the transfer of heat-energy at the micro-scale is important for thermal processing using a pulse-laser. Often, micro-voids may be found in processed devices. This is due to thermal expansion. Such defects may cause an amplification of neighboring defects resulting in severe damage and consequently the failure of the device. Thus a complete understanding of thermal dissipation and defects is necessary to avoid damage and to increase the efficiency of thermal processing.; A hybrid finite element - finite difference (FE-FD) method has been developed for solving three dimensional parabolic two-step heat transport in irregular double-layered thin film exposed to ultrashort pulsed lasers. This scheme first discretizes the thin film system along the xy-plane by a finite element method. Then the z-direction is discretized via a weighted finite difference scheme. The two are combined into a numerical scheme which is then coded into a computer simulation. It is shown that the scheme is unconditionally stable with respect to the initial condition and the heat source. Three distinct numerical examples are studied. The first being a 0.05 mum gold thin film disk, with 1 mm diameter, atop a same-dimensioned chromium padding layer. This disk is exposed to an ultra-fast laser burst and the thermal properties are demonstrated. Secondly, the same thin-film disk array is exposed to a double burst laser pulse and the thermal properties examined. Finally the ultrashort laser is moved in a complete circle about the center of the double-layered thin disk and the thermal properties are examined.; The outcome of this study provides an efficient and reliable numerical method for solving micro-scale heat transport equations, and gives a better understanding of the nature of heat transport in such a system. Also, the hybridization procedure offers a new way to examine three dimensional heat transport systems---one that utilizes the strengths of both the finite element and the finite difference methodologies. The research results have a significant impact on the development of short-pulse laser applications in structural monitoring of thin metal films, laser patterning of such films and laser synthesis and processing of thin film deposition.