Question $3$

$($a$)$ A semiconductor specimen is fabricated by doping trivalent boron impurity into high$-$purity silicon with an impurity concentration of ${10}^{21}{m}^{-3}.$ The electron and hole mobilities are $0\mathrm{.}14$ and $0\mathrm{.}048\frac{m^2}{V}-$s$.$ Calculate the resistivity of the specimen at room temperature.

$(6$ marks$)$

$($b$)$ A laser beam from air shine on a transparent flat composite plate that consisting of a sheet of polystyrene and a sheet of glass. The laser path is air $$ polystyrene $$ glass $$ air. The incident laser beam is $10$ from the normal of the composite.

$($i$)$ Determine the angle of the beam with respect to the normal when it passes through to the polystyrene.

$(3$ marks$)$

$($ii$)$ Determine the angle of the beam with respect to the normal when it passes through to air on the opposite side of the composite.

$(6$ marks$)$

$\backslash$table$[[$Composite Materials,Index of Refraction$],[$polystyrene$,1\mathrm{.}53],[$glass$,1\mathrm{.}5],[$air$,1\mathrm{.}0]]$

$($c$)$ A cylindrical rod of steel with a diameter of $18$ mm and length of $250$ mm is deformed elastically in tension with a force of $48\mathrm{.}5$ kN $.$ Given that the modulus of elasticity of steel, $E,$ is $207$ GPa $.$ Determine change in length of the steel rod.

$(10$ marks$)$

$($Total: $25$ marks$)$