cqt-datta-l3-slides - nanoHUB.org online simulations and...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
nano HUB .org Supriyo Datta 1 online simulations and more Network for Computational Nanotechnology CQT Lecture #3 Unified Model for Quantum Transport Far from Equilibrium CQT, Lecture#3: Probabilities, Wavefunctions and Green Functions Objectives: To extend the simple model from Lecture 2 into the full-blown model shown opposite that combines the NEGF (Non-Equilibrium Green Function) method with the Landauer approach. Model based on (1)Datta, Phys.Rev.B40, 5830 (1989);J.Phys.Cond.Matt.2, 8023(1990). (2)Meir and Wingreen, Phys.Rev.Lett.68, 2512(1992). Reference: QTAT, Chapters 8-11. “QTAT” Datta, Quantum Transport: Atom to Transistor, Cambridge (2005) H Σ 1 Σ 2 μ 1 2 Σ s
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
nano HUB .org Supriyo Datta 2 online simulations and more Network for Computational Nanotechnology Probabilities, wavefunctions, Green functions H Σ 1 Σ 2 μ 1 2 Σ s Unified Model for Quantum Transport Far from Equilibrium 1 2 1 γ 2 s D(E-U) Simple quantitative model For Transport Far from Equilibrium 1 2 1 2
Background image of page 2
nano HUB .org Supriyo Datta 3 online simulations and more Network for Computational Nanotechnology Probabilities, wavefunctions, Green functions H Σ 1 Σ 2 μ 1 2 Σ s Unified Model for Quantum Transport Far from Equilibrium 1 2 1 γ 2 <--- L --> 0.1 mm 10 μm 1 μm 0.1 μm 10 nm 1 nm 0.1 nm Macroscopic dimensions Atomic dimensions Diffusion equation Boltzmann equation “NEGF”
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
nano HUB .org Supriyo Datta 4 online simulations and more Network for Computational Nanotechnology Summary: 1-grid point model I 1 = q γ 1 = dE D ( E ) F f 1 [] I 2 = q 1 = dE D ( E ) f 2 F 21 () 2 qK E Id E ff h ⇒= 12 1 2 Ff f F −= ⇒− = Transmission E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 1 ( E ) E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 2 ( E ) 1 / = μ 1 1 / = μ 2 qV D K ( E ) 2 π D ( E ) 1 CHANNEL D R A I N S O U R C E I V F
Background image of page 4
nano HUB .org Supriyo Datta 5 online simulations and more Network for Computational Nanotechnology <--- L --> 0.1 mm 10 μm 1 μm 0.1 μm 10 nm 1 nm 0.1 nm Macroscopic dimensions Atomic dimensions R 1 : R 2 > R 1 R 2 = R 1 R 2 can even be less than R 1 = / 1 γ μ 1 2 / = μ 2 qV 2 / = μ 2 qV R 2 : = / 1 μ 1 Introducing a Grid
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
nano HUB .org Supriyo Datta 6 online simulations and more Network for Computational Nanotechnology Energy -resolved current () 12 2 qK E I dE f f h =− Transmission E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 1 ( E ) E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 2 ( E ) = / 1 γ μ 1 2 / = μ 2 qV q h qV T 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 --- E ---> --- T(E) ---> T ( E ) = K ( E ) /2 K ( E ) 2 π D ( E ) 1 1-grid point model
Background image of page 6
nano HUB .org Supriyo Datta 7 online simulations and more Network for Computational Nanotechnology 2-grid point diffusive model E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 1 ( E ) E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 2 ( E ) qV 2 / γ = μ 2 = / 1 μ 1 I 2 = K ( E ) f 2 F 2 [ ] K ( E ) 2 πγ 1 D ( E ) I 12 = K ( E ) F 1 F 2 [ ] ( Currents normalized to q dE/h ) 11 2 1 2 2 21 3 Ff FF fF f f −= ⇒− = [] 12 () 3 KE I ff ⇒= F 2 F 1 --- E ---> --- T(E) ---> 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1-point 2-point I 1 = K ( E ) F 1 f 1 [ ]
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
nano HUB .org Supriyo Datta 8 online simulations and more Network for Computational Nanotechnology Equivalent circuit E -0.2 0 0.2 0.4 0.6 0.8 1 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 f 1 ( E ) E -0.2 0 0.2 0.4 0.6
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/30/2010 for the course EE 495 taught by Professor S.datta during the Spring '10 term at Indiana University-Purdue University Fort Wayne.

Page1 / 30

cqt-datta-l3-slides - nanoHUB.org online simulations and...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online