In manufacturing semiconductors, rapid thermal processing (RTP) is used to rapidly heat a silicon wafer to an elevated temperature in order to induce effects such as ion diffusion, annealing, and oxidation. One type of RTP device consists of a cylindrical enclosure with a coaxially positioned wafer. The top side of the wafer experiences uniform irradiation from a lamp bank, G_lamp. The enclosure lateral (A₂) and bottom (A₃) surfaces have a low emissivity ε₂ = ε₃ = 0.07 and are maintained at 300 K by coolant passages. The wafer (A₁) diameter is D = 300 mm and the height of the enclosure is L = 300 mm. The aperture (A₄) diameter is D_a = 30 mm and provides for optical access to the wafer.

(a) What lamp irradiation, Clamp, is required to maintain the wafer at 1300 K if the wafer emissivity is E₁ = 0.8? What is the heat removal rate by the cooling coil? Assume there are no heat losses from the top side of the wafer.

(b) If the enclosure were perfectly reflecting, the radiosity of the wafer, J₁, would be equal to its blackbody emissive power. E_b1, As such, the radiosity would be independent of the wafer emissivity, thereby minimizing effects due to variation of that property from wafer-to-wafer. For wafer emissivities of ε₁ = 0.75, 0.8, and 0.85, plot the fractional difference, (E_b1 – J₁)/E _b1, as a function of the aspect ratio for 0.5 < L/D < 2.5. How sensitive is this parameter to the enclosure surface emissivity, ε₂?

10 m 58 4 m 6 m 5A