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ECE453Fall2010HW6[1]

ECE453Fall2010HW6[1] - Fall 2010 HW 6 ECE 453 HW#6 Due...

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Fall 2010 ECE 453 HW #6 Due 10/29 HW # 6 Due Friday, October 29, 2010 Problem 1 is based on QTAT, Sections 5.2 and 6.1. QTAT: S.Datta, Quantum Transport: Atom to Transistor, Cambridge (2005), ISBN 0- 521-63145-9, on reserve in Engineering Library and HKN lounge Central equation: [ h ( r k )] [ H nm ] exp( i r k .( r d m r d n )) m Bandstructure Problems 2,3 are based on Chapters 12-14 of notes (see Notes#4) Useful reference: QTAT, Chapter 8, Sect.9.1, 9.4-9.5 Central equations of coherent transport 1. 1 i [ 1 1 ] , 2 i [ 2 2 ] 2. G ( E ) [ EI H 1 2 ] 1 , 3. A ( E ) i [ G G ] G 1 G G 2 G Density of states / 2 4. [ G n ( E )] [ G 1 G ] f 1 [ G 2 G ] f 2 Electron density / 2 5. I i ( E ) q h ( ( Trace [ i A ]) f i Trace [ i G n ]) Current/energy 6. I ( E ) q h Trace [ 1 G 2 G ]( f 1 ( E ) f 2 ( E )) 2-terminal current In general H has to be replaced with H+U, just as D(E) is replaced with D(E-U) in the semiclassical model, where U has to be calculated self-consistently from an appropriate “Poisson” -like equation, but you can ignore this aspect in the HW problems.
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