The thermal condition of a silicon substrate in a rapid thermal processing system using circular infrared lamps and specular reflectors is systematically studied based on the direct approach model using a ray trace simulation with resolving the number of reflections, for the first time, in order to clarify the mechanism that the thermal condition for the silicon substrate is not sensitive to the distance between the circular infrared lamp and the reflector base plate forming the region behind the circular infrared lamp. Since total reflection from the specular reflectors behind the circular infrared lamp causes no energy loss on their surface, the intensity of the ray emitted from the infrared lamp toward the reflector base plate can be maintained and transported to the silicon substrate surface, even if the distance between the circular infrared lamp and the reflector base plate influences the path of the rays which are approaching the silicon substrate. Therefore, it is concluded that the thermal condition of the silicon substrate can be robust to the geometry of the specular reflectors behind the circular infrared lamp.Temperature of materials is a key parameter for controlling any chemical process, chemical kinetics, product quality, and productivity. For obtaining both a reasonable throughput and quality, rapid thermal processing ͑RTP͒ 1-18 is widely used in semiconductor device manufacturing processes. Further improvement in the RTP system for various aspects, 15 such as uniformity, reproducibility, and the ramp rate of the substrate temperature, requires advanced and appropriate theoretical calculation models 19,20 which can optimize the entire heat radiation from the heat source accounting for entirely and exactly the complicated three-dimensional geometry of the RTP system. Since the rays from tungsten/halogen filament lamps to a mirror-polished silicon substrate surface surrounded by reflectors have extremely complicated paths, the usual theoretical models 16,17,19,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] are insufficient to describe the RTP system. Therefore, the direct approach model using ray trace simulation ͑DARTS͒ 36-38 has been developed and evaluated as an extension of the ray tracing method. 19,[31][32][33][34][35] The DARTS model has, experimentally, been shown to be valid 36 and capable of evaluating in detail the temperature and its profile in the RTP system. [36][37][38] The RTP system using an arrangement of circular infrared lamps 39 with various diameters is expected as an industrial application due to its high flexibility in adjusting the temperature profile in the radial direction of the silicon substrate. Our previous studies 37,38 showed that the thermal condition of the silicon substrate was very sensitive to the distance between the circular infrared lamp and the silicon substrate surface. However, we simultaneously showed that the distance between the circular infrared lamp and the reflector base plate forming the region behind the circular infrared lamp was in...