Journal of Vacuum Science & Technology B, Vol.24, No.6, 2509-2517, 2006
Microscopic approach to an equation for the heat flow between wafer and E-chuck
Wafer cooling and heating by means of a gas at the wafer backside is a key technology in semiconductor manufacturing. A detailed understanding of the physical mechanisms is needed to yield the best process results. Besides the commonly used Smoluchowski interface condition, a microscopical approach is deduced describing the whole pressure range. Different thermal gas species and surface properties, as well as the velocity and angular distribution of the atoms, are basic features of the model. The angular distribution of the desorbed atoms is shown to have a significant influence on the wafer temperature. The heat transfer properties between the gas and two different surfaces are described by one value, the effective accommodation coefficient. The final wafer temperature is simulated as a function of the input power, the backside pressure, and the gas species. Helium has the best cooling properties of the inert gases, followed by neon. The influence of a pollution of the wafer surface on the uniformity of the wafer temperature has been determined. The surface roughness has no significant influence on the cooling abilities of an electrostatic chuck. (c) 2006 American Vacuum Society.