Consider a 2 mm thick silicon wafer to doped using antimony (Sb). Assume that the dopant source (gas mixture of Antimony Chloride and other gases) provides a constant surface concentration of 6.4*10^22 atoms/m3. A heat treatment is desired such that the concentration of Sb at a depth of 1 micrometer is 0.2*10^22 atoms/m3. Assume that the silicon wafer to begin with contains no impurities or dopants. Assume the activation energy
for diffusion of Sb in Silicon is 380 kJ/mol and D{_{0}} for Sb diffusion in Silicon is 1.3 x 10^?3 m2/sec. Assume the heat treatment temperature will be 1100C.
a) Sketch the desired shape of the diffusion profile (i.e., the concentration of Sb as a function of position below the surface of the Silicon wafer) following the heat treatment.
b) What will be the required time at 1100C for the heat treatment?