One integrated circuit design calls for the diffusion of arsenic into silicon wafers; the background concentration of As in $Si$ is

$2\mathrm{.}5{10}^{20}$ atoms $\frac{?}{m^3}.$ The predeposition heat treatment is to be conducted at $1000C$ for $45$ minutes, with a constant

surface concentration of $8{10}^{26}As$ atoms $\frac{?}{m^3}.$ At a drive$-$in temperature of $1100C,$ determine the diffusion time required

for a junction depth of $1\mathrm{.}2m.$ For this system, values of $Q_d$ and $D_0$ are $4\mathrm{.}10eV$ and $2\mathrm{.}29{10}^{-3}\frac{m^2}{s},$ respectively.