2009.01.14-ECE659-L2-notes

2009.01.14-ECE659-L2-notes - S D L Vd Vg 1 f ( 29 T E h dD...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 2: Molecular Ballistic & Diffusive Transport Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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S D L Vd Vg 0.1 mm 10 µm 1 µ m 0.1 µm 10 nm 1 nm 0.1 nm Macroscopic dimensions - - Atomic dimensions Traditionally : q G qn m τ = τ,n,m -> not clear for small conductors ( 29 2 q G D h π γ = E μ1 μ 1-μ2=qVd I V <--- L ---> D(E) μ2 f1(E) f2(E) ( 29 ( 29 1 1 E kT f E e μ - = + ( 29 ( 29 ( 29 ( 29 1 2 I dED E f E f E -
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( 29 ( 29 ( 29 ( 29 1 2 2 I q dED E f E f E γ = - Factor of 2 : twice the time taken to travel from one contact to the other occupancy in the channel is average of the two contacts ( 29 1 2 1 1 2 2 2 f f f f f + - = - ( 29 ( 29 ( 29 ( 29 1 2 q I dE D f E f E π = - 2 ( ) I q T E V h = Ballistic Channel:
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Unformatted text preview: S D L Vd Vg 1 f ( 29 T E h dD ( 29 ( 29 ( 29 ( 29 1 2 qV q I T E dE f E f E h =- dhhhDhhh f1(E) f2(E) qV 2 f ( 29( 29 1 2 q I dET E f f h =- 1 ( ) ( ) 2 dED E I q vf E L = vt I qnv = ( 29 1 2 ( ) 2 D E I q dE v f f L =- ( 29 1 2 ( ) ( ) 2 q hD E v E I dE f f h L =- ( 29 1 2 ( ) M E q Dv I dE f f h L =- dD 1 2 ( ) mfp f f f f mfp L +--=-+ For diffusive transport modes: ( ) mfp M E mfp L + Diffusive Transport: 1 f 2 f ( 29 f x + ( 29 f x-( 29 ( ) 2 D E I q dE v f f L +-=- If L&gt;&gt;mfp , we get Ohms law...
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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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2009.01.14-ECE659-L2-notes - S D L Vd Vg 1 f ( 29 T E h dD...

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