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2009.01.23-ECE659-L5-notes

2009.01.23-ECE659-L5-notes - ECE 659 Quantum Transport Atom...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 5: Where is the resistance? SupriyoDatta Spring 2009 Notes prepared by SamiranGanguly
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S D L Vd Vg D(E) E μ2 μ1 μ 1-μ2=qVd f1(E) f2(E) γ γ ( 29 A G L R L A σ λ ρ λ = + = + 2 ( ) 2 x v d D q dEf E dE AL λ σ = n qn σ μ = ( 29 2 z hDv q I dE f f h L - = - f1 f2 ( f f df df dz dz λ - + - - = = - 1 f 2 f 0 df df dz dz + - = = In ballistic: In non-ballistic: ( 29 1 2 ( ) f f f f L λ λ + - - = -
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Fermi function? In general NO (at T = 0K) (at large T ) ( 29 ( 29 ( 29 ( 29 ( 29 1 0 1 2 1 0 1 2 0 1 2 1 1 df af f dE df a f f dE df f a a dE μ μ μ μ μ μ + - - - + - - + - + - ( ( f f df df d d dz dz dz dz μ μ μ μ λ λ - + - + - + - - - = = - = = - μ1 μ2 μ+ μ-
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verticalbraceright ( 29 1 2 ( ) 2 z M L hDv q df I dE h L dE λ μ μ λ μ μ - - + = - - dncurlybracketlefthorizcurlybracketextdncurlybracketmidhorizcurlybracketextdncurlybracketright
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