Modeling of heat transport and wafer heating effects during plasma etching

Uniformity of plasma etching and deposition processes critically depends on the wafer temperature and its spatial variation across the wafer. The goal of this work is to use mathematical modeling to investigate the key factors that determine the wafer temperature and its radial uniformity during plasma etching. Toward this end, a mathematical model of energy transport in and out of a Si wafer in a plasma etching reactor that employs a substrate platen with a He back side cooling arrangement was developed. The possibility of wafer bowing due to high He back side pressure was considered and the effects of ion bombardment flux uniformity, He back side pressure, and different wafer clamping arrangements were studied. While an increase in He back side pressure increases the rate of heat transfer from the wafer to the electrode, excessive He pressure causes the wafer to bow. Bowing increases the electrode-wafer gap, decreases the heat transfer rate, and adversely affects the temperature uniformity. These effects are most pronounced for large diameter wafers (>200 mm) and are predicted to be very important in the processing of 300 and 400 mm substrates. The manner in which the wafer is clamped to the cooled electrode is another key factor that determines the heat transport at the wafer edge and the radial temperature profile across the wafer. The uniformity of the wafer temperature depends on the heat transport at the wafer edges. Poor thermal contact at the wafer edge leads to a high but uniform wafer temperature; on the other hand, if a good thermal contact is made at the wafer edge, the average temperature is lower but less uniform. Model predictions compared well with the available experimental data.