A crystalline silicon wafer of 10 cm diameter and 1.0 mm thickness is coated with a thin film of elemental arsenic metal (As), which is a semiconductor dopant. The As-coated silicon wafer is “baked” in a diffusion furnace at 1050^oC to allow the arsenic molecules to diffuse into the silicon. At this high temperature, the solubility of arsenic in silicon is 2.3 × 10²¹ atoms As/cm³, and the diffusion coefficient of As in solid silicon still is 5.0 × 10-3 cm²/s. Initially, there is a uniform background impurity of arsenic in the silicon of 2.3 × 10¹⁷ atoms As/cm³. To obtain a desired semiconductor property and microelectronic device structure, the target concentration of arsenic atoms in the silicon must be least 2.065 × 10²⁰ atoms As/cm³ at a junction depth of 0.5 µm(l.0 × 10⁴ µm = 1.0 cm). 

a. What is the diffusion time required, and how many total As atoms will be loaded into the silicon? 

b. Make a plot of the square root junction depth (z^1/2) vs. time t from z = 0.5 µm to 1.0 µm. 

c. What is the calculated flux of As atoms into the silicon at 5 min and 10 min into the process? Why is it not possible to estimate the flux at t = 0?