You are the engineer in charge of a doping process that introduces boron into silicon that is initially

pure. The boron surface concentration is maintained at $5wt\%$ and the diffusivity parameters for boron

diffusing in silicon are: $Q_d=3\mathrm{.}87e\frac{V}{?}$ atom and $D_0=2\mathrm{.}4{10}^{-3}\frac{m^2}{s}.$

a$.$ Compute the diffusion coefficient of boron in silicon at $1,272C.$

b$.$ The microprocessor you are currently working on requires a dopant concentration of $0\mathrm{.}5wt\%$

$($weight percent$)$ at a depth of $8$ microns from the exposed surface of the silicon wafer.

Compute the diffusion length required to achieve this doping.

c$.$ Compute the time, in minutes, required to achieve this doping level if the process is carried

out at $1,272C.$

d$.$ We want to achieve the same concentration specified in part b$.,$ but in one hour instead of the

time you computed in part c$.$ Calculate the temperature we should use. Hint: the diffusion

length stays constant here so the product of diffusion coefficient and time $D^{**}t$ also has to

stay the same in parts $c.$ and d$.$