Temperature distribution in semiconductor wafers heated in a vertical diffusion furnace

The transient temperature distribution in a row of wafers heating in a vertical diffusion furnace was calculated as the heating power of the furnace was PID (proportional plus integral plus 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, the 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 degrees C, and the effect of this change on the temperature distribution in the wafers was calculated. Thermoplastic deformation of the wafers is more likely to occur during withdrawal than during insertion. >