2009.04.15-ECE659-L36-notes

2009.04.15-ECE659-L36-notes - ECE 659 Quantum Transport:...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 36: Law of Equilibrium Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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( 29 ( 29 1 1 d u d u d u F f f I dE F f f - - - d F u F 2 μ 1 N impurities: 1 way 2 N ways 1 1 1 2 2 2 * * i t ψ ε   =   2 1 ln B S k W = 1 2 1 dS dE T = 1 2 E W 10 states 10 4 states
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( 29 ( 29 ( 29 ( 29 ( 29 ( 29 , B B B B S k S E S E k dS E dE k k D W E W e D W E e e e ε + - - + = = + = = = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 2 1 1 1 I D f E f E D f E f E - - - - + - - Density of States: 1 1 1 2 2 0 2 1 3 1 3 2 2 1 2 3 D E k E D E k E D E k E - hot loses energy and cold gains because total entropy goes up N electrons: 1 W 2 W 1 2 W W × E S hot cold ( 29 3 2 1 3 ln ln 1 ln 2 3 1 1 1 2 2 3 N B B W E S N W E k N dS E k dE E N α - = = = + - - = ( 29 3 2 1 3 2 dN N N dE E E - →
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Law of equilibrium: i B E k T i e P Z - = 1 E 2 E Occurs much less than the reverse process If the system can also lose particles, so as to have ifferent N at each different states: Fermi function: ε 1 0 ( 29 1 1 0 0 i i i kT E N P e Z Z μ - - ( 29
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This note was uploaded on 01/30/2011 for the course ECE 659 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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2009.04.15-ECE659-L36-notes - ECE 659 Quantum Transport:...

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