2009.03.06-ECE656-L23-notes

2009.03.06-ECE656-L23-notes - ECE 659 Quantum Transport:...

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Unformatted text preview: ECE 659 Quantum Transport: Atom Atom to Transistor Lecture 23: Transverse Modes Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly µ1 µ2 ε E ε −t k ɶ I (E) ε −t E 4t −t −t α = −t 4t ⋱ β = ⋱ ⋱ α β * H = −t ⋱ α β α ɶ I (E) β αβ β * α ⋱ ⋱ ⋱ [V,D]=eig(alpha) V + = V −1 V +αV = D α = VDV + ε1 ε2 ε3 ε −t ⋱ ⋱ −t 4t −t α = −t 4t −t −t ⋱ ⋱ αν = 4t − 2t cos ka 2πν N Eψ n = εψ n − tψ n −1 − tψ n+1 ψ n = ψ 0 eikna = ψ 0 eik ( n+ N )a kNa = 2πν For box boundary condition: k ψ n = ψ 0 sin kna Eν ( k ) = αν − 2t cos ka ky ( E − ε ) sin kna = −t sin k ( n − 1) a + sin k ( n + 1) a 2sin kna cos ka kν ( N + 1) a = πν 2π W 2π L kx For periodic boundary: kν a = 2πν N π k2 k2 f f N= = LW 2π 2π 2π ns = LW k2 f 2π 1012 / cm2 For box boundary: kν a = πν N +1 2π Eν ( 0 ) = αν − 2t = 4t − 2t cos kν a − 2t = 2t (1 − cos kν a ) ≃ ta 2 kν2 2πν πν , N N +1 λf kfω = πv ...
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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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2009.03.06-ECE656-L23-notes - ECE 659 Quantum Transport:...

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