The numbers in parentheses next to each problem are point values for that problem. Tungsten (W) is used as an interconnect in the manufacture of integrated circuits. Low-pressure chemical vapor deposition (CVD) of tungsten can be earned out via the reaction of tungsten hexafluoride with hydrogen: WF_6 + 3 H_2 rightarrow W + 6 HF Ideally, this reaction takes place only on the solid surface onto which W is being deposited. WF_6, H_2, and HF are gases: The metallic tungsten that is found remains on the solid surface, and the tungsten of the tungsten layer increases with time. The w deposition rate is given (park, J, -H., Korean J. chem. Eng., 19(3), 391 (2002)]: t_w = exp[-8300/T]p^2.5_Hz P_wF6/1 + 450p_wr6 Where r_w = rate of W deposition (mol cm^-2 5^-1), P_WE6 = partial pressure of WF_6 (mm h_g), P_H2 = partial pressure of H_2 (mm H_g), and T = temperature (K) A disk of silicon with diameter of 5.5 cm is placed inside a reactor. The temperature of the silicon disk is kept at 673k. The feed to the reactor is continuous is consists of a mixture of WF_6, H_2 and argon (Ar), which is inert. The total gas rate is 660 standard cnm^3/min (SCCM). The inlet mole fractions are: ywy_6 = 0.045 y_Hz = 0.864 y_Ar = 0.091 The total absolute pressure in the reactor is 1 mm Hg (i.e., 1 Torr). Assume that W deposits only on one side (the top side) of the silicon wafer. Assume that the mixing of the gas in the reactor is so vigorous that the gas composition is the same everywhere in the reactor. Further assume that the gas composition in the reactor has reached steady state, and that transport resistances are negligible. Derive expressions for P_WF6 and P_H2 in terms of the fractional conversion of WF_6. Calculate the liner growth rate of the tungsten layer, in A/min and the mole fraction of WF_6 in the outer gas stream.