$($a$)$ The doping in the emitter, base and collector of is ${10}^{19}c{m}^{-3},{10}^{17}c{m}^{-}{?}^3$ and ${10}^{16}c{m}^{-3},$ respectively, in a Silicon npn transistor. State the approximate minority carrier concentrations in each of these regions.

$[3$ marks$]$

$($b$)$ If the emitter$-$base junction is forward biased, will the minority carrier concentration increase or decrease at emitter$-$base junction?

$[1$ mark$]$

$($c$)$ Write the equation showing how the minority carrier concentration varies with applied bias in a pn junction.

$[1$ mark$]$

$($d$)$ If a forward bias of $0\mathrm{.}3$ V is applied to the emitter$-$base junction, what is the new minority carrier concentration in the base?

$[2$ marks$]$

$($e$)$ Write the equation relating the diffusion coefficient to carrier mobility. $[1$ mark$]$

$($f$)$ Calculate the diffusion coefficient for minority carriers in the base region at room temperature.

$[2$ marks$]$

$($g$)$ Using the diffusion current equation, show how the collector current relates to the minority carrier concentration in the base region.

$[2$ marks$]$