Abstract：Wafer cooling/heating by gas flow along the backside of the wafer is a key part of the plasma-etching process. The rarefied gas heat transfer across the gap between the wafer and the electrostatic chuck is modeled in this article with an analytical equation developed for the entire pressure range whose predictions are verified by direct simulation Monte Carlo results. The model is then used to investigate the effects of the gas pressure, gap size, accommodation coefficient and gas temperature on the heat transfer coefficient. The gap size and gas temperature have little influence, so the etching temperature and the surface profiles like the height have little effect on the heat transfer between the wafer and the electrostatic chuck. However, the gas pressure and the accommodation coefficient significantly impact the heat transfer coefficient. Therefore, changes in the gas pressure during the etching process will significantly affect the heat transfer between the wafer and the electrostatic chuck.
孙钰淳, 程嘉, 路益嘉, 侯悦民, 季林红. 静电卡盘与晶圆之间稀薄气体传热的影响因素[J]. 清华大学学报（自然科学版）, 2015, 55(7): 756-760.
SUN Yuchun, CHENG Jia, LU Yijia, HOU Yuemin, JI Linhong. Factors influcing rarefied gas heat transfer between a wafer and an electrostatic chuck. Journal of Tsinghua University(Science and Technology), 2015, 55(7): 756-760.
 Brezmes A O, Breitkopf C. Simulation of inductively coupled plasma with applied bias voltage using COMSOL [J]. Vacuum, 2014, 109: 52-60.
 Woo J C, Kim S H, Kim C I. Etch characteristics of TiN/Al2O3 thin film by using a Cl2/Ar adaptive coupled plasma [J]. Vacuum, 2011, 86(4): 403-408.
 Kanno S, Edamura M, Yoshioka K, et al. High-temperature electrostatic chuck for nonvolatile materials dry etch [J]. J Vac Sci Technol B, 2005, 23(1): 113-118.
 Nojiri K. Dry Etching Technology for Semiconductors [M]. Cham, Switzerland: Springer International Publishing, 2015.
 Springer G. Heat transfer in rarefied gases [J]. Advances in Heat Transfer, 1971, 7: 163-218.
 Song S, Yovanovich M, Nho K. Thermal gap conductance: Effects of gas pressure and mechanical load [J]. J Thermophysics and Heat Transfer, 1992, 6(1): 62-68.
 Klick M, Bernt M. Microscopic approach to an equation for the heat flow between wafer and E-chuck [J]. J Vac Sci Technol B, 2006, 24(6): 2509-2517.
 Samir T. Improving Wafer Temperature Uniformity for Etch Application [D]. Lubbock: Texas Technology University, 2003.
 刘静. 刻蚀工艺静电卡盘温度仿真及真空测温技术研究[D]. 北京: 北京工业大学, 2012. LIU Jing. Temperature Simulation on ESC in Etching Process and Study on Measurement Method with Vacuum System [D]. Beijing: Beijing University of Technology, 2012. (in Chinese)
 Moon M D, Gambino J P, Adderly S A, et al. The effect of backside roughness on Al interconnect dimensions for RF CMOS SOI devices [C]//Proc Advanced Semiconductor Manufacturing Conference (ASMC) 25th Annual SEMI. New York, 2014: 384-388.
 Kennard E. Kinetic Theory of Gases [M]. New York: McGraw-Hill, 1938.
 Dushman S, Lafferty J M, Brown S C. Scientific foundations of vacuum technique [J]. American Journal of Physics, 1962, 30(8): 612.
 Bird G A. DS1V Program [R/OL]. [2014-12-30]. http://www.gab.com.au/.