2009.02.02-ECE659-L9-notes

2009.02.02-ECE659-L9-notes - + +-= [ ] 1 b a i I B Di-+ +...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 9: Landauer-Buttiker Formalism Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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+ S D 1 i + 1 2 ( ) 2 z Dv df I q dE dE L L λ μ + - = - - + - dhhDhh± 1 2 ( ) 2 z Dv df I q dE f f dE L L f f + - = - - + - dhhDhh± 1 i - 2 i - 2 i + z=0 z=L q i M h q i M h + + - - = = 1 1 2 2 1 2 , L i Ri Ti T R L L i Ti Ri - + + - + + = + = = + + = + { } [ ] { } R T i S i S T R - + = =
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{ } { } { } [ ] { } { } { } { } [ ] { } i i i I S i i M i I S M μ + - + + + + = - = - = = - [ ] T T I S T T - - = - 1 1 i MT + - = 4 terminal measurements: + S D 1 2 3 4 a=(1,2) b=(3,4) { } { } 1 1 - ( 29 ( 29 1 1 2 2 1 2 i MT i MT = - = - - [ ][ ] Y I S M = - If we have defined voltages in terms Of average electrochemical potentials [ ][ ] [ ] 1 2 Y I S I S M - = - + a a b b a b i Ai Ci i Di Bi - + + - + + = + = + Each A, B, C, D are 2x2 matrices b b i i + - = Open circuit condition: 2 + - +
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[ ] b a I B i Di
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Unformatted text preview: + +-= [ ] 1 b a i I B Di-+ + =-[ ] 1 a a i A C I B D i P--+ = +- ≡ dhhhDhhh± Pi-+ To find voltages in b terminals, we need to express i in terms of i b { } [ ] { } 1 a b i D I B i--+ =-{ } [ ] [ ] { } { } [ ] [ ][ ] { } 1 1 b B b i I P D I B i i I P D I B M μ-+-+ =--=--a a i = { } { } { } [ ] { } a a a i i i I P i +-+ =-=-The voltage probes can be thought of as scatterers [ ] [ ][ ] 1 B Y I P D I B M-=--...
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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.

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2009.02.02-ECE659-L9-notes - + +-= [ ] 1 b a i I B Di-+ +...

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