cqt-datta-l2-slides - nanoHUB.org online simulations and...

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nano HUB .org 1 online simulations and more Network for Computational Nanotechnology D(E) 1 γ 2 μ 1 2 Σ s H Σ 1 Σ 2 1 2 Σ s CQT Lecture #2 Unified Model for Quantum Transport Far from Equilibrium CQT, Lecture#2: Electrical Resistance: A Simple Model Objective: To introduce a simple quantitative model for describing current flow in nanoscale structures and relate it to well-known large scale properties like Ohm’s Law. Model based on Datta, Nanotechnology,15, S433 (2004). Reference: QTAT, Chapter 1. “QTAT” Datta, Quantum Transport: Atom to Transistor, Cambridge (2005) Simple version D(E)
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nano HUB .org 2 online simulations and more Network for Computational Nanotechnology Equilibrium Energy Level Diagram V G V = 0 CHANNEL D S I <-- L --> Vacuum Level -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 E Fermi function f (E) Channel V G > 0 n-type V G < 0 p-type No states F I L E D M P T Y S D
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nano HUB .org 3 online simulations and more Network for Computational Nanotechnology What makes electrons flow? μ2 μ1 V G V D CHANNEL D S I μ1 μ2 V G V D CHANNEL D S I > 0
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nano HUB .org 4 online simulations and more Network for Computational Nanotechnology Escape rate μ1 μ2 = / 1 γ 2 / = Rate Escape : / = has dimensions of energy S Channel D 1 Small
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nano HUB .org 5 online simulations and more Network for Computational Nanotechnology Current through a very small conductor S Channel D V -0.2 0 0.2 0.4 0.6 -0.2 0 0.2 0.4 0.6 0.8 1 N o r m a li z ed C u en t V μ 1 μ 2 V I = / 1 γ 1 / = μ 1 2
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nano HUB .org 6 online simulations and more Network for Computational Nanotechnology -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.2 0 0.2 0.4 0.6 0.8 1 What is Conductance ? N o r m a li z ed C u en t V -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.2 0 0.2 0.4 0.6 0.8 1 n d c e q γ 1 2 = q T k q V d I d / 4 2 / ~ 1 = = / 1 1 / = μ 1 2 0 0.2 0.4 0.6 0.8 1 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 0.8 1 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 empty full
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nano HUB .org 7 online simulations and more Network for Computational Nanotechnology -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.2 0 0.2 0.4 0.6 0.8 1 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.2 0 0.2 0.4 0.6 0.8 1 Conductance quantum N o r m a li z ed C u en t V n d c e = / 1 γ 1 / = μ 1 2 q T k q V d I d / ) 4 2 ( 2 / ~ 1 1 + = ~ q 2 /4 = if 1 >> kT 2
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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.

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cqt-datta-l2-slides - nanoHUB.org online simulations and...

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