Temperature distribution in semiconductor wafers heated in a vertical diffusion furnace

The transient temperature distribution in a row of wafers in a vertical diffusion furnace was calculated as the heating power of the furnace was PID (proportional-integral-derivative)-controlled. Radiative heat transfer was combined with axisymmetric unsteady conduction in wafers and the furnace. With feedforward control of the heating power (which means that when wafers are inserted into the furnace, heater temperature is set higher than the desired heating temperature), the temperature of the wafers reached the heating temperature rapidly. The radiative properties of silicon wafers changed from semitransparent to opaque at 500°C, and the effect of this change on the temperature distribution in the wafers was calculated. It was found that thermoplastic deformation of the wafers is more likely to occur during withdrawal than during insertion