As starting material we have $99\mathrm{.}999999$ at$.\%$ Si $(=8$ nines or $8N).$ The only dopant is Aluminium

and we call this $8N-Si(Al)($see periodic table$).$ At room temperature the electron mobility in $Si$ is

${}_e=0\mathrm{.}25\frac{m^2}{Vs},$ the hole mobility ${}_h=0\mathrm{.}05\frac{m^2}{Vs},$ unit of charge $1\mathrm{.}6{10}^{-19}C,$ the density of $Si$

$=2\mathrm{.}33\frac{g}{c}{m}^3,$ the atomic mass of Si $28\mathrm{.}08$ and Avogadro's number $6\mathrm{.}022{10}^{23}.$

a$)$ What is the electrical conductivity of this material at room temperature $($where conduction can be

considered in the pure extrinsic exhaustion$/$saturation regime$)?$

Apart from the starting material, also the auxiliary materials $8N-Si(Ga)$ and $8N-Si(As)$ are in stock.

b$)$ We want to make an intrinsic semiconductor by melting the starting material together with one

of the auxiliary materials. Which auxiliary material we have to choose and in what ratio we have

to melt the two materials together?

c$)$ With which one of the two auxiliary materials together with the starting material can we make a

semiconductor with a conductivity $($at room temperature$)$ of $=8\mathrm{.}0(m{)}^{-1}?$ What is then the

type of semiconductor we have? What is then the required ratio for melting together the starting

material with the auxiliary material?

Given hints: $,=n|e|{}_e+p|e|{}_h$