(Solved): Suppose that it is desired to diffuse Al into pure Si such that Al concentration at a depth of ...

Suppose that it is desired to diffuse $\mathrm{Al}$ into pure $\mathrm{Si}$ such that $\mathrm{Al}$ concentration at a depth of $10^{-3}\mathrm{cm}$ from the surface will be just half of the surface concentration. How long should a silicon piece would be heated in Al-vapor at $1327^{\circ }\mathrm{C}$ ? Assume: 1. $\mathrm{erf}(\mathrm{z})\cong \mathrm{z}$ 2. Diffusivity of $\mathrm{Al}$ in $\mathrm{Si}$ at $1327^{\circ }\mathrm{C}$ is $8\times 10^{-12}{\mathrm{cm}}^2/\mathrm{s}$.