ECE495N-F08-HW_9

# ECE495N-F08-HW_9 - 1 ECE 495N Fall’08 ME118 MWF 1130A –...

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Unformatted text preview: 12/3/08 1 ECE 495N, Fall’08 ME118, MWF 1130A – 1220P HW#9: Due Wednesday Dec.10 in class. Basic equations of coherent transport 1 1 1 [ ] i + Γ = Σ − Σ , 2 2 2 [ ] i + Γ = Σ − Σ 1 1 2 ( ) [ ] G E EI H − = − − Σ − Σ , A ( E ) = i [ G − G + ] = G Γ 1 G + + G Γ 2 G + Density of states* 2 π 1 1 2 2 [ ( )] [ ] [ ] n G E G G f G G f + + = Γ + Γ Electron density* 2 π ( ) (( [ ]) [ ]) n i i i i q I E Trace A f Trace G h = Γ − Γ Current/energy 1 2 1 2 ( ) [ ]( ( ) ( )) q I E Trace G G f E f E h + = Γ Γ − 2-terminal current Simpler version introduced earlier: 1 1 2 2 1 2 ( ) ( ) ( ) ( ) f E f E n E D E γ γ γ γ + = + Electron density ( ) ( ) ( ) ( ) ( ) i i i q I E D E f E n E γ = − Current/energy 1 2 1 2 1 2 ( ) ( )( ( ) ( )) q I E D E f E f E γ γ γ γ = − + 2-terminal current In general H has to be replaced with H+U, and D(E) with D(E-U) where U has to be calculated self-consistently from an appropriate “Poisson”-like equation, but you can ignore this aspect in the following problems....
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ECE495N-F08-HW_9 - 1 ECE 495N Fall’08 ME118 MWF 1130A –...

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