2009.02.04-ECE659-L10-notes

2009.02.04-ECE659-L1 - 1 1 2 2 M T M T = i S M S μ = dhDh± 1 1 1 1 2 2 2 2 1 1 1 2 2 2 i M R M T i M T M R = = 1 2 = = In equilibrium 1 1 i i = 1

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ECE 659 Quantum Transport: Atom to Transistor Lecture 10: Two probe/Four probe Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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1 2 3 4 a=(1,2) b=(3,4) S D I 1 i + 3 i + 4 i + 3 i - 4 i - 2 q i M h q μ + + = { } [ ] { } i S i - + = { } [ ][ ] { } i S M S - + = dhDh± For 2 terminal : { } [ ] { } { } { } { } i S i i i i S i - + + - + = = - - 1 i - 2 i - 2 i + [ ] { } [ ] { } { } I I S M M S + + = = - = - [ ][ ] Y I S M M S = - = - [ ] [ ] 1 1 2 2 2 2 i i I S i i i i I S + - + + - - + + = + + = + [ ][ ] 1 conductance of channel 2 2 i i I S I S M + - - + - + - = - + dhhhDhhh± [ ] 1 1 1 channel Y M S M I S M M S M S M - - - = - +   = - +  
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a a b b a b i Ai Ci i Di Bi - + + - + + = + = + Four probe : b b i i + - = [ ] [ ] 1 1 b a b a b I B i Di i I B Di i D I B i + + - + + + - + - = = - = - { } { } { } [ ] [ ] { } { } [ ] [ ][ ] { } 1 1 a a b B b i i i I P D I B i i I P D I B M μ + - - + - + - = = - - = - - M1 M2 R T T R [ ][ ] [ ][ ] 1 4 pt A B Y I P M D I B M - - = - - [ ] a [ ] 1 a a i A C I B D i P - - + = + - d h hhD h h h± [ ][ ] 2 pt A Y I P M - = - a a i Pi - + = { } { } { } [ ] { } [ ][ ] a a a A i i i I P i I P M + - + + = - = - = - 1 2 1 2 R T S T R = Row need not add to 1 1 2 1 1 1 2 2 1 2 2 1 1 2 2 0 0 R T M M R M T S T R M M T M R   = =     Now, rows also add to M1 and M2
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Unformatted text preview: 1 1 2 2 M T M T = { } [ ][ ] { } i S M S μ-+ = dhDh± 1 1 1 1 2 2 2 2 1 1 1 2 2 2 i M R M T i M T M R-+ +-+ + = + = + 1 2 + + = = In equilibrium: 1 1 i i-+ = 1 M-S D L 1 1 k a L λ = + 1 i = 1 1 2 2 1 1 1 2 2 M R M T M M T M T + = = ' ' ' ' ' t a c t b d S SM a b c d × × = = × × If a magnetic field is present a and a’ are unequal In a two terminal device they are equal even in presence of magnetic field due to sum rule Sum rule...
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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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2009.02.04-ECE659-L1 - 1 1 2 2 M T M T = i S M S μ = dhDh± 1 1 1 1 2 2 2 2 1 1 1 2 2 2 i M R M T i M T M R = = 1 2 = = In equilibrium 1 1 i i = 1

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