2009.04.20-ECE659-L37-notes

2009.04.20-ECE659-L3 - r A P m φ = ⋅ a a a a a 29 29 1 2 P dr r p r a a a a a If both the levels are s levels the integral gives a 0

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ECE 659 Quantum Transport: Atom to Transistor Lecture 37: Inelastic transport Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H s Σ 2 Σ 1 Σ [ ] 1 n in G EI H G G G - + = - - Σ = Σ 1 2 s Σ + Σ + Σ in f + Γ + Σ ( 29 ( 29 ( 29 1 2 1 2 B s k T I D n p D p n D e ε - - + - = 1 Σ 2 Σ 1 2 1 1 2 2 s f Γ s in n s DG DG Σ = Σ = ( 29 D + Let us consider only an absorption process: E ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 p n n p s p n G A G G E G E I E D G E G E = - - + - + ( 29 ( 29 ( 29 ( 29 ( 29 in n s s s q I E Trace E A E E G E = Σ - Γ We can write: p n G A G = - Then by comparison: ( 29 ( 29 ( 29 ( 29 ( 29 in n s p n s D G E D G E G E Σ = + - Γ = + + + -
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μ Broadening occurs even if the level is completely filled Slope given by quantum of conductance 2 iEt t e e γ - Interaction with light: 1 Σ 2 Σ 1 ε 2 ( 29 2 2 2 2 2 2 p qA p q q A p A A m m m m + = + + a a a a a a v * s s s D G U U Σ = Strength of a scattering potential This means we have a source term: v v v * * * in n s U ss UU D G ψ ψψ = = Σ In terms of matrix elements: * k ki i ij kl s U U U = So D is a rank 4 tensor Interaction term Negligible 1 1 1 2 2 2 * * q U A p m E =   =   a a Goes into off-diagonal terms ( 29 ( 29 * * 1 2 q dr r U
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Unformatted text preview: r A P m φ = ⋅ ∫ a a a a a ( 29 ( 29 * * 1 2 P dr r p r ≡ ∫ a a a a a If both the levels are s levels, the integral gives a 0 due to spherical symmetry which converts the integral into anti-symmetric function. So we would get absorption between s and p levels. If the level is p x then the absorption occurs for photons with vector potential A in x direction and so on. Due to S-O coupling in valence band: HH up spin: p x +ip y HH down spin: p x-ip y So we obtain circularly polarized light. If we can preferentially fill up spins in a particular orientation we get a net polarization, which is the primary way to measure spin polarization p x , p y , p z p z p x , p y E s p x p y p z s s...
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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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2009.04.20-ECE659-L3 - r A P m φ = ⋅ a a a a a 29 29 1 2 P dr r p r a a a a a If both the levels are s levels the integral gives a 0

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