4.+pn+junctions

# 4.+pn+junctions - MATSCI 302 April 9 2008 pn junctions...

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MATSCI 302 April 9, 2008 pn junctions Please submit your project preference forms to Craig on Friday. Email him if you are an off-campus student. Reading: Chapter 5 from Streetman’s text

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Review of notation i E T k E E i o B i F e n n ) ( - = F E C E V E ) ln( i o B i F n n T k E E = - D i o D o N n p N n 2 = = T k E E i o B F i e n p ) ( - = ) ln( i o B F i n p T k E E = - ; ; For an n-type doped material:
10 8 6 4 2 0 -2 -4 -6 -8 0.0 0.2 0.4 0.6 0.8 1.0 What happens when p and n-type semiconductors come together? Fp E Fn E p-type n-type 1 Fermi-Dirac Distribution ) ( E f T k E E B F e E f ) ( 1 1 ) ( - + = The Fermi Level must be constant at equilibrium. If it weren’t, there would be a flow of carriers.

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A pn junction at equilibrium o qV F E o V C E V E = contact potential T k qV n p p n B o e p p n n = = ) ln( ) ln( ) ln( ) ln( ) ln( ) ( ) ( 2 n p p n i p n o i p i n o Fp ip in Fn o p p q T k n n q T k n p n q T k V n p q T k n n q T k V q E E q E E V B B B B B = = = + = - + - = What is ? o V E in E ip
Another derivation of the contact potential 0 ] ) ( ) ( ) ( [ ) ( = - = dx x dp D x E x p q x J p p p μ T k q D dx x dp x p x E D B p p = = ) ( ) ( 1 ) ( dx dV x E - = ) ( (Potential energy of electron = ) qV -

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4.+pn+junctions - MATSCI 302 April 9 2008 pn junctions...

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