High- low junctions are common in bipolar devices. Consider the (majority ?electron) conduction properties of the abrupt n-n ⁺ junction shown below. The doping density is N _DL in the low side N _DH in the high side. The widths W _n and W of the low and high (quasi-neutral) sides are much wider than the width of the space-charge region at the metallurgical junction. Neglect electron degeneracy and energy-gap narrowing.

(a) For V >0, plot the variation of the electron quasi-Fermi level E _Fn across the n-n ⁺ junction. Ignore the space-charge region.

(b) Referring to (a) derive an expression for the current I. Assume a constant cross-sectional area A.

(c) How would electron degeneracy and energy-gap narrowing in the n ⁺ . Region affect 1?

n - W V (NOL) Fig. 1 n (NDH) w..