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Unformatted text preview: Lecture 12 Monday February 21 EE 332 Semiconductor Devices Problem Assignment Monday 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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- Spring '08