One of the steps in semiconductor processing involves the placement of a stack of silicon

wafers into a tube through which a reactant gas is conveyed. The wafers are stacked coaxial

with the tube, and the interwafer spacing is $0\mathrm{.}5cm.$ The wafer radius is $7\mathrm{.}5cm.$

When the tube is loaded with a stack of waters, room air oceupies the interwafer space.

After the reactor has been loaded, an inert gas is pumped through the reactor. Exchange

between the flowing inet gas and the interwafer gas occurs only by diffusion in the

interwafer region.

The purpose of the inert gas llow is to assist the removal of water vapor from the interwaler

space. If the inert gas is dry, how long will it be before the water vapor concentration is

reduced to ${10}^{-2}$ of its initial value? Assume that operation is at amospheric pressure and

$300C.$ The diffusion coefficient of water in the inert gas is $0\mathrm{.}76c\frac{m^2}{s}.$ ssume that there is

no adsorbed water on the walers and that the wafers are impermeable to water.