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# hw9_solutions - ECE 440 Homework IX Solution to be posted...

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ECE 440 Homework IX Spring 2008 Solution to be posted by Wednesday, March 12, 2008 1. An abrupt Si p-n junction has the following properties at 300 K: p-side n-side A = 10 -4 cm 2 N a = 1x10 17 /cm 3 N d = 1x10 16 /cm 3 τ n = 1 µs τ p = 10 µs µ p = 220 cm 2 /V-s µ n = 1080 cm 2 /V-s µ n = 700 cm 2 /V-s µ p = 400 cm 2 /V-s (a) Determine the contact potential V o of the junction, and the depletion widths at equilibrium, under a forward bias of V o /2 and under a reverse bias of 4V o . At equilibrium conditions: V n N N q kT V i d a 754 . 0 ) 10 5 . 1 ( ) 10 1 ( ) 10 1 ( ln 0259 . ln 2 10 16 17 2 0 = × × × = = m N N q V W a d μ ε 329 . 10 1 10 1 10 6 . 1 754 . 0 10 85 . 8 8 . 11 2 1 1 2 17 16 19 14 0 = + = + = - - To calculate the depletion width under various biases use one of the following (equivalent) expressions: 0 0 0 0 ) ( 1 1 ) ( 2 ) ( V V V V V W N N q V V V V W f a d f f - = = + - = = ε In this case, I use the second. m V V V V V W V V W μ 233 . 2 ) ( ) 2 ( 0 0 0 0 0 = - = = = m V V V V V W V V W μ 736 . 4 ) ( ) 4 ( 0 0 0 0 0 = + = = - = (b) Draw the band diagrams qualitatively at equilibrium and under forward and reverse bias showing the varying depletion widths, Fermi level and the quasi-Fermi levels. Equilibrium :

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The Fermi level is always flat in an equilibrium band diagram. Forward Bias : When the junction is forward biased, the depletion width and the barrier height are reduced. The system is no longer in equilibrium and quasi Fermi level splitting on both sides of the junction occurs. Since there is no recombination in the depletion width, the quasi Fermi levels remain flat in this region and then begin to decrease as we move further into each side of the junction (due to recombination of minority carriers).
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hw9_solutions - ECE 440 Homework IX Solution to be posted...

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