Multiphysics Modeling and Analysis of Heat Transfer of Wafer on Electrostatic Chuck

The complete heat transfer path on the AlN and Al2O3 electrostatic chuck (ESC), which were utilized under the various operational conditions, is studied for the potential improvement on the temperature uniformity of the 12-inch wafer. In addition, an identical study on the expanded chuck (299mm) is also carried out for a comparison of the original chuck (293mm). An equivalent thermal circuit analogical to an electrical circuit was illustrated and formulated in terms of variables observed to offer a simple calculation toward a potential optimization. In addition, a good agreement with previous work was achieved and examined the reliability in this model system. The content of this study is divided in two parts: electrostatic force and wafer temperature. First, in order to optimize the functionality of the attractive force and in avoiding excessive “trial and error” chuck designs, a set of simulations were obtained under various conditions pertaining to the position of the electrode, material, finish and voltage, individually. Second, the ability of backside cooling plays a critical role in the need to control the wafer temperature and its uniformity. It demonstrates that helium exhibited the best performance among He, Ne and Ar, which shows a controllable function with a linear dependence on the pressure and insensitive to the environmental variation during the process. The histogram with a standard deviation (SD), as an indicator of the temperature uniformity, are used to illustrate a fraction of discrete values of the wafer temperature. It discovered the characteristics of the AlN chuck (293mm) exhibited an excellent ability for the wafer cooling on the edge, but unfavorable to the temperature uniformity which Al2O3 chuck (293mm) is capable without temperature oscillations while the backside pressure increases. In addition, it suggested that the characteristics of the different chucks (AlN and Al2O3 ) become more comparable with the increase of the level of the backside pressure. The AlN chuck (299mm) with a linearly dependent on SD and superior in the mean, is regarded as the best one among other chucks, one of which is the Al2O3 chuck (299mm) which SD becomes independent on the pressure and high mean.