8. (6 points) Diffusion is an important process in many aspects of materials science, including the fabrication of semiconductor devices. Semiconductor devices are of- ten prepared by first crystallizing one material (for example, Si) and then diffusing impurities (such as P) into the crystal to act as "dopants". After diffusing P into the Si, the conductivity in this region increases. (a) Suppose we start with a Si wafer (typically hundreds of micrometers thick) that initially contains no Phosphorus (P) atoms. The surface concentration is held at 1020 atoms/cm³ of P, and the reaction proceeds at 1100°C. The diffusion coefficient Do is 10.5 cm²/s, and Qd = 3.6881 eV. What is D at 1100°C in cm²/s? (b) The reaction proceeds for 3 hours. At what depth (in μm) will the concen- tration of P be 1018 atoms/cm³? (c) Many devices include thermal oxide layers of SiO2, patterned on top of the Si wafer. Suppose the diffusion coefficient D for P in SiO2 is 2.9 × 10-16 cm²/s. Why do you think this might be useful for the fabrication of transistors and other semiconductor devices on Si?