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EE 338_HW7_Solutions

# EE 338_HW7_Solutions - EE 338 Fall 2007 HW#7 Solutions...

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10/29/2007 EE 338 Fall 2007 HW#7 Solutions 5.5 (a) n-side: E E kT N n F Fi d i = F H G I K J ln = ( ) F H G I K J 0 0259 5 10 15 10 15 10 . ln . x x or E E eV F Fi = 0 3294 . p-side: E E kT N n Fi F a i = F H G I K J ln = ( ) F H G I K J 0 0259 10 15 10 17 10 . ln . x or E E eV Fi F = 0 4070 . (b) V bi = + 0 3294 0 4070 . . or V V bi = 0 7364 . (c) V V N N n bi t a d i = F H G I K J ln 2 = ( ) L N M M O Q P P 0 0259 10 5 10 15 10 17 15 10 2 . ln . b gb g b g x x or V V bi = 0 7363 . (d) x V e N N N N n bi a d a d = + F H G I K J F H G I K J L N M O Q P 2 1 1 2 / = ( ) ( L N M 2 117 8 85 10 0 736 16 10 14 19 . . . . x x b g × + F H G I K J F H I K O Q P 10 5 10 1 10 5 10 17 15 17 15 1 2 x x / or x m n = 0 426 . μ Now x x x p = ( ) ( ) L N M 2 117 8 85 10 0 736 16 10 14 19 . . . . b g × + F H G I K J F H I K O Q P 5 10 10 1 10 5 10 15 17 17 15 1 2 x x / x m p = 0 0213 . μ We have ε max = eN x d n = ( ) 16 10 5 10 0 426 10 117 8 85 10 19 15 4 14 . . . . x x x x b gb gb b g g or ε max . / = 3 29 10 4 x V cm 5.7 ) (b) n N E E kT O C C F = L N M O Q P exp a f = F H I K 2.8 10 0 21 0 0259 19 x exp . . or n N x cm O d = = 8 43 10 15 3 . (n-region) p N E E kT O V F V = L N M O Q P exp a f = F H I K 104 10 018 0 0259 19 . exp . . x or 1

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