2009.01.23-ECE659-L5-notes

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

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Unformatted text preview: ECE 659 Quantum Transport: Atom Atom to Transistor Lecture 5: Where is the resistance? Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly A G =σ L+λ R= L S Vg γℏ Vd D ρ A (L + λ) d D vx λ dE AL 2 σ = q 2 ∫ dEf ( E ) E γℏ μ1 μ 1-μ2=qVd μ2 σ = qnµn I= f1 f1 hDvz + q − dE ∫ 2L ( f − f ) h f1(E) D(E) f2(E) f2 f2 (f − f df df = =− dz dz λ + − + − ) In ballistic: df + df − = =0 dz dz In non-ballistic: (f + − f − ) = ( f1 − f 2 ) λ λ+L Fermi function? In general NO (at T = 0K) (at large T ) df af1 ≃ f 0 + − ( µ1 − µ2 ) dE df (1 − a ) f1 ≃ f 0 + − ( µ1 − µ2 ) dE df ≃ f0 + − ( aµ1 + (1 − a ) µ 2 ) dE μ1 μ+ μ- μ2 ( f + − f − ) ⇒ dµ+ = dµ− = − (µ+ − µ− ) df + df − = =− λ λ dz dz dz dz I= hDvz q dE 2L h∫ M df + − − (µ − µ ) dE λ λ+L ( µ1 − µ 2 ) μ+ 104 10 μ- L L+λ λ L+λ 104 I= q λ M ( µ1 − µ2 ) h L+λ (µ + −µ − ) 10 µ + − µ − R= channel = 104 µ + − µ − L+λ contact μ1 μ+ h qM 2 λ μ- μ2 Rc = Rd q2 λ µ1 − µ 2 I= M h L+λ q h qM h = 2 qM 2 L λ q2 λ G= M h L+λ h = 25k Ω q2 h 12.5k Ω = 2q 2 M M ...
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2009.01.23-ECE659-L5-notes - ECE 659 Quantum Transport:...

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