MSc project: Oblique impact of two droplets at high Weber number

MSc student: Y. Janssens

Project supervisors: Prof. dr. ir. J.F. Dijksman (ASML, TU/e), Prof. dr. ir. J. Westerweel (TU Delft), dr. ir. W.-P. Breugem (TU Delft)

Project start: mid February 2014

Project description:
ASML is the manufacturer of advanced lithographic projection equipment for making integrated circuits. The technology is driven by Moore's law which states that, once per 18 months the number of transistors per unit surface area is doubled. In order to cope with the timing of Moore's law ASML has made the choice to reduce the wave length of light used for projection from 138 nm (ultra violet light, UV) down to 13.5 nm (extreme ultra violet light, EUV).

To generate EUV a new concept is currently under investigation. The idea is to use a powerful laser for pulse wise heating of pancake-shaped droplets of molten tin in order to produce a gas of ionized tin atoms (tin plasma) that emits EUV. The pancake shape of the droplets is preferred over a spherical shape to optimize the conversion efficiency of laser power into EUV. Such pancake-shaped droplets can be continuously generated by colliding two droplet trains onto each other. For sufficiently high impact velocity two colliding droplets will merge with each other. Subsequently, the newly formed droplet will be severely stretched and will take the desired pancake shape for some time. For technical reasons it is desired that the droplet trains hit each other at a small angle (i.e., an oblique droplet impact). Furthermore, when a slight phase shift is present between the droplet trains, the droplets will hit each other off-center such that the newly formed droplets will rotate. This principle can be used to position the pancake-shaped droplets in the beam of the laser.

An important parameter that controls the dynamics of the head-on collision of two droplets in a gaseous environment is the so-called Weber (We) number. This number represents the ratio of droplet inertial forces to surface tension forces. A pancake-shaped droplet is formed for We > O(10-100). When the gaseous environment is at low pressure the colliding droplets will almost immediately coalesce upon impact. Subsequently, the newly formed droplet will be severely stretched towards a pancake-shaped droplet until the kinetic energy of the impacting droplets is converted into Gibbs free energy. Next, the pancake-shaped droplet will stretch back, which is followed by separation into 3 or more droplets. Most research on head-on binary droplet collisions has focused on the regime of We < 100. The goal of this MSc research project is to gain better understanding of oblique droplet collisions at low gas pressure (100-250 Pa) with We in the regime of O(100-1000) [1]. To this purpose numerical simulations will be conducted with a Coupled Level-Set/Volume-of-Fluid (CLSVOF) method [2] in which the flow within and around the colliding droplets is fully resolved on a fixed regular grid. The numerical results will be analyzed for the characteristic life time, thickness and diameter of the pancake-shaped droplet in relation to We and the impact angle, which are of importance for optimizing the conversion efficiency of laser power into EUV.

1. K.-L. Pan, P.-C. Chou and Y.-J. Tseng. Binary droplet collision at high Weber number. Phys. Rev. E, vol. 80, 036301, 2009.
2. M. Kwakkel, W.-P. Breugem and B.J. Boersma. Extension of the CLSVOF method for droplet-laden flows with a coalescence/breakup model. J. Comput. Phys., 253:166-188, 2013.