$(20$ points$)$ Show the bias polarities and depletion regions of an n$-$p$-$n BJT in the normal active, saturation, and cutoff modes of operation on the simplified diagram of the BJT as used in the class.

$(\backslash (5\backslash$times $3=15\backslash )$ points$)$ Draw the three sketches one below the other to $($qualitatively$)$ reflect the depletion widths for these biases.

The BIT has a base transport factor of $1\mathrm{.}0$ and an emitter injection efficiency of $0\mathrm{.}5.(5$ points$)$ Roughly calculate by what factor would increasing emitter doping by $\backslash (5$ x $\backslash )$ would increase, decrease, or leave unchanged the emitter injection efficiency and base transport factor? Assume other $\backslash ($ B J T $\backslash )$ parameters remain unchanged.