lecture15 - Lecture 15 Monday February 28 EE 332...

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Lecture 15 Monday February 28 EE 332 Semiconductor Devices Problem Assignment Monday ! 5.9 omit parts d , h ,and i Contact Potential = = = 2 2 ln / ln ln i d a d i a n p bi n N N q kT N n N q kT p p q kT V The built-in potential was shown to be: Raising both sides to the power e yields: kT bi qV e p p n p = p n n p n n e p p kT bi qV = = p n n p p n i n p n n p p n p n n p = = = 2 Because Then Finding the Concentration Ration in the Presence of an Applied Field ( ) ( ) ( ) ( ) kT E E kT E E kT E E kT E E Vn Vp fp fn fp Vp Vn fn e e e e / / / / = = ( ) () kT E E V kT E E V n p Vn fn Vp fp e N e N p p / / = E fn -E fp =-qV a in steady state, and qV bi =E Vp -E Vn E Vp =valance band energy on p-side N V cancels out () ( )( ) kT V q kT V q kT V V q n p bi a a bi e e e p p / / / = = Minority Carrier Enhancement At equilibrium kT qV p n n p bi e n n p p = = 0 0 0 0 () () kT qV kT qV kT V V q n n p p a bi a bi e e e x p x p / / / ) ( = = kT qV n p a e p p / 0 0 = For a steady state bias p p0 and p n0 are equilibrium values and p p (x p ) and p n (x n ) are steady state values. replacing
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Minority Carrier Injection () kT qV n p n n p p a e p p x p x p / 0 0 ) ( = kT qV n n kT qV n n a a e p x p e x p p / / ) ( or ) ( = = ! Greatly enhanced minority
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lecture15 - Lecture 15 Monday February 28 EE 332...

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