Chapter 1, Problem 1.56P

In the thermal processing of semiconductor materials,annealing ¡s accomplished by heating a silicon waferaccording to a temperature-time recipe and then maintaining a fixed elevated temperature for a prescribedperiod of time. For the process tool arrangement shownas follows,the water is in an evacuated chamberwhose walls are maintained at 27°C and within whichheating lamps maintain a radiant flux ${q^{″}}_s$ at its uppersurface. The wafer is 0.78 mm thick, has a thermal conductivity of $30{\text{W/m}}^{\text{2}}\cdot \text{K}$ , and an emissivity that equalsits absorptivity to the radiant flux $\left(\in ={\alpha }_1=0.65\right)$ . For ${q^{″}}_s=3.0\times {10}^5{\text{W/m}}^{\text{2}}$ , the temperature on its lower surface is measured by a radiation thermometer and foundto have a value of $T_{w,i}=997\text{°C}$ .

To avoid warping the wafer and inducing slip planes in the crystal structure, the temperature difference acrossthe thickness of the wafer must be less than 2°C. Is thiscondition being met?