Analysis on Temperature Distribution in a Semiconductor Wafer during Rapid Thermal Annealing with Lamp Heaters

Transient and steady radial temperature distribution in a wafer heated with halogen lamps was numerically calculated. Unsteady conduction in the wafer was combined with two-dimensional radiation heat transfer between the specular wafer and the lamps. As radiative properties of a quartz tube changed from transparent to opaque at a wavelength of 4.5μm, the band-energy approximation was used. When the lamps were divided into center and side lamp groups and their power ratio was controlled to remain in the 1.4 to 1.6 range, the steady temperature distribution in the wafer was minimized. The mimimum temperature distribution was 1.1°C when the wafer diameter was less than the width of the center lamp group. In order to minimize temperature distribution in the wafer at temperature rising or cooling periods, it was necessary to change lamp power ratio at each temperature level.