Pressurized liquid Tin finds application in the generation of Extreme Ultra-Violet light for semiconductor lithography. In order to improve the throughput of the lithography systems, tin must be pressurized to higher levels, and in turn, new pressurization methods are needed.

A phase change tin pump is an innovative system that pressurizes and pumps liquid Tin by harnessing the expansion and contraction during phase changes, without the need for any moving parts. The pump needs to pressurize liquid tin up to 2000 bars, with a pumping capacity of 4 ml/hr. Since this system relies heavily on control over the temperatures of tin, this study is set up to address the thermal constraints in the system by investigating three aspects of temperature distribution in the system.

Firstly, the heaters in the pump are placed at discrete locations, but the working volume is continuous. Thus, it is challenging to define a temperature control function that can facilitate uniform melting and continuous flow of tin. The relation between rate of heat input to the pump and the rate of heat transfer in tin is estimated using an analytical model. From the analytical model, it is found that heating rates of the order of 0.1 K/s are required in order to melt tin in a reasonably uniform fashion over a zone length of 5 mm.

Secondly, the number of heaters are limited, and it is hard to achieve precise control over the temperature of tin at any given location. In order to establish a good basic control, the free design parameters are optimized so that a steady state gradient of 50 K is achieved between solid (200°C) and liquid (250°C) tin in the working volume. This is done by evaluating the thermal profile of the system for different combinations of the design variables, using Finite Element Analysis. The two objectives of this optimization problem (maximum temperature gain and minimum crosstalk) are seen to have contrasting requirements of the design variables. An optimal combination of the variables is found such that a gradient of 50 K is possible, but with a little trade-off on both the objectives.

Thirdly, a direct measurement of temperature of tin inside the pump is not feasible, and tin temperatures are estimated analytically. The accuracy of estimation is impacted by changes in local temperatures due to the non-linear properties of tin like absorption/release of latent heat, pressure-dependent melting point. The effect of non-linear tin properties on local temperature distribution is studied by setting up a finite difference model. It is seen that the absorption of latent heat during melting of tin results in a temperature that is 12 K lower than what would have been without the effect of latent heat.