Using the prototype model $($i$.$e$.,$ ignore the apparent emitter band$-$gap narrowing reduction on the injection efficiency$),$ find and for an npn BJT with N$$DE $=1019$ cm$3,$ N$$AB $=21017$ cm$3,$ and N$$DC $=1017$ cm$3.$ Indicate clearly all your steps. Let VBE $=0\mathrm{.}8$ V and VCB $=2\mathrm{.}0$ V$.$ The metallurgical widths are WEM $=0\mathrm{.}2$m and WBM $=0\mathrm{.}2$m$.$