# hw8_solutions - ECE 440 Homework VIII Solutions Spring 2006...

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ECE 440 Homework VIII Solutions Spring 2006 Due: Friday, March 03, 2006 1. An abrupt Si p-n junction is formed by alloying a uniformly doped n-type silicon bar of which N d = 4x10 16 /cm 3 . During the alloying process, a uniform counter doping of acceptors of N a = 1.5x10 17 /cm 3 is introduced in the region for x<0. For x>0, the doping remains to be N d = 4x10 16 /cm 3 . So, x<0 is the p-side and x>0 is the n-side. (a) Calculate the Fermi level positions at 300 K in the p and n regions. Treat each side separately (as if they were unconnected) to calculate the Fermi level positions far from the junction. p-side : eV n N N kT n p kT E E i d a i f i 409 . 0 10 5 . 1 10 4 10 5 . 1 ln 0259 . 0 ln ln 10 16 17 0 = × × × = = = n-side : eV n N kT n n kT E E i d i i f 383 . 0 10 5 . 1 10 4 ln 0259 . 0 ln ln 10 16 0 = × × = = = (b) Draw an equilibrium band diagram for the junction and determine the contact potential V o from the diagram. Looking at the band diagram we can calculate qV 0 geometrically. The contact potential is the difference between the Fermi level positions on the n and p sides of the junction. eV

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hw8_solutions - ECE 440 Homework VIII Solutions Spring 2006...

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