A model for rapid thermal processing: achieving uniformity throughlamp control

A first-principles approach to the modeling of a rapid thermal processing (RTP) system to obtain temperature uniformity is described. RTP systems are single wafer and typically have a bank of heating lamps which can be individually controlled. Temperature uniformity across a wafer is difficult to obtain in RTP systems. A temperature gradient exists outward from the center of the wafer due to cooling for a uniform heat flux density on the surface of the wafer from the lamps. Experiments have shown that the nonuniform temperature of a wafer in an RTP system can be counteracted by adjusting the relative power of the individual lamps, which alters the heat flux density at the wafer. The model is composed of two components. The first predicts a wafer's temperature profile given the individual lamp powers. The second determines the relative lamp power necessary to achieve uniform temperature everywhere but at the outermost edge of the wafer (cooling at the edge is always present). The model has been verified experimentally by rapid thermal chemical vapor deposition of polycrystalline silicon with a prototype LEISK RTP system. The wafer temperature profile is inferred from the poly-Si thickness. Results showed a temperature uniformity of ±1%, an average absolute temperature variation of 5.5°C, and a worst-case absolute temperature variation of 6.5°C for several wafers processed at different temperatures