In microprocessors, thin metal circuitry lines are connected vertically using cylindrical "vias."

These metal vias are surrounded by oxide to prevent short circuits; the oxide is deposited first and

the vias are filled in afterwards. We have an oxide layer with empty vias that need to be filled with

tungsten metal using chemical vapor deposition (CVD) through the instantaneous reaction below:

WF:(g) + 3H-(g) → W(s) + 6HF(g)

The oxide walls are "I" deep (z = 0 is at the top, z = L at the bottom) and the empty vias are 0.5

um in diameter. The tungsten does not coat the side walls; it is only deposited on the base of each

via. The mole fractions of WF6 at the top of via is ywrs, and the system is not dilute. There is no

forced convection.

A. Draw a diagram of the process, showing the movement of the various species. State all

assumptions.

B. Develop mathematical expressions that relate the flux of tungsten hexafluoride (Nws) to the

fluxes of the other pertinent species. Okay to drop the subscript z to simplify the notation.

C. Simplify the general equation for NwFs (Fick's law) and the continuity equation to derive one

differential equation that can be integrated to determine ywF6 (2). Assume steady state and

constant T, P, and DAB-

D. State the boundary conditions for this process (instantaneous reaction).

E. Integrate your equation in Part C with your boundary conditions in Part D to derive an

expression of the form ywrs = ....

F. Derive an expression for the flux of WF, in the gas film, NwF6-