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hw10_solutions

# hw10_solutions - ECE 440 Homework X Solution to be posted...

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ECE 440 Homework X Spring 2008 Solution to be posted by Saturday, March 15, 2008 1. An n + -p Si junction with a long p-region has the following properties: N a =2x10 16 /cm 3 ; µ n = 1000 cm 2 /V-s; µ p = 360 cm 2 /V-s; τ n =1 µs. If we apply 0.65 V forward bias to the junction at 300 K, what is the electric field in the p-region far from the junction? Draw a band diagram in the p-region far from the junction assuming that the junction is at x=0 and the p- side is in x>0. Since this is a n + -p junction, we can ignore the contribution of holes to the diffusion current. s cm u q kT D n p n / 9 . 25 2 = = cm D L p n p n p n 00509 . = = τ 3 2 250 , 11 - = = cm p n n p i p so 0.7263A/cm 1 e n L D q 0) (x J J kT qV p p n p n p diff n = - = = . On the p side, far from the junction, the contribution of diffusion current approaches zero while the drift current due to holes is dominant. Since current must be continuous along the x-direction we know the drift current far from the junction will be equal to the diffusion current near the junction. ) ( ) ( ) ( ) 0 ( x E x p q x J x J p p n drift p p diff n μ = = cm V x p q x J x E p p p diff n / 6305 . 0 10 2 360 10 6 . 1 7263 . 0 ) ( ) 0 ( ) ( 16 19 = = = = - μ Once we have an equation for E(x) we can construct the band diagram. Notice that the electric field points in the same direction as the electric field in the depletion region.

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