A boron diffusion is used to form a p$-$region on a $1-$cm n$-$type silicon wafer. The following sequence of diffusion was performed.

$1$st step$)$ solubility$-$limited B pre$-$deposition: $15$ min at $1000$C $2$nd step$)$ drive$-$in: $5$ hrs at $1100$C

$($a$)$ Find the junction depth Xj and the surface concentration of B after the $1$st step.

$($b$)$ Find the junction depth Xj and the surface concentration of B after both $1$st and $2$nd steps.

$($c$)$ After the drive$-$in step, the above Si wafer was subjected to an additional thermal annealing at $1150$C for $2$ hours during other thermal process. Find the newly formed junction depth Xj and the surface concentration of B$.$