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Unformatted text preview: Lecture 12 Monday February 21 EE 332 Semiconductor Devices Problem Assignment Monday Æ 4.1 and 4.5 The Fermi Levels of Two Conductors in Contact are Equal at Equilibrium Shown by equating the electron flow (flux) from conductor-1 to 2 for all energy states at equilibrium. At energy E, the rate from 1 to 2 is proportional to the number of electrons (occupied states) in conductor-1 with energy E, and to the number of empty states in conductor- 2, or (Note S(E) =density of states = states/cm-3 at E) [ ] [ ] ) ( 1 ) ( ) ( ) ( 1 to 2 from flow for likewise and ) ( 1 ) ( ) ( ) ( 1 1 2 2 2 2 1 1 E f E S E f E S E f E S E f E S − ∝ − ∝ Equating the Two Flow Rates at Equilibrium Yields ( ) ( ) 1 / 1 / 2 1 2 1 1 1 ) ( ) ( − − − − + = + = = kT E E kT E E f f e e E f E f Comparing the two sides of the equation yields: E f1 = E f2 , or the Fermi levels on the two sides are equal at equilibrium. [ ] [ ] ) ( 1 ) ( ) ( ) ( ) ( 1 ) ( ) ( ) ( 1...
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This note was uploaded on 06/30/2010 for the course EECE 332 taught by Professor Constable during the Spring '08 term at Binghamton.
- Spring '08