4. (25 pts) The formation of the semiconducting thin film is controlled by the molecular diffusion of the dopant atoms crystalline-silicon matrix. Chemical vapor deposition method uses to deliver phosphorous atoms to the silicon wafer surface. In the process, phosphorous oxychloride (POCl3) is vaporized. The POCl3 vapors are fed into a chemical vapor deposition (CVD) reactor at elevated temperature and reduced pressure, where POCl3 decomposes on the silicon surface according to the reaction: - Consider the P-doping of crystalline silicon at 1150C to promote P-diffusion. - P atom concentration is constant at the interface (diffusion coefficient of P atoms in crystalline silicon is very low), and only a thin film of SI-P is needed in the process, P-atoms do not penetrate far into the silicon. - Surface concentration of P-atom in the silicon =1.251020 atoms P/cm3 solid Si (which is dilute) - P-rich coating is considered as an infinite source of P(CAS constant ) - Pure solid silicon =51022 atoms Si/cm3 solid. a) According to the given assumptions/problem statements, determine the variables of concentration profile CA(A : phosphorus \& B:Silicon), b) Find the initial and boundary conditions. c) Determine the depth of the Si-P thin film after 30min, if the target concentration is 10% of the surface value