Lecture 7 DFT Applications 武晓君 xjwu@ustc.edu.cn 江俊 jiangj1@ustc.edu.cn

Why DFT

DFT Application

DFT Application

DFT Application

DFT Application EA IP WF Strict in DFT theory, but not strict in DFT computations.

DFT Application For Solid State Physics

DFT Application For Molecular Electronics

Quantized electron energy Extended π systems Elegance The problems of chemistry and biology can be greatly helped if our ability to see what we are doing, and to do things on an atomic level, is ultimately developed — a development which I think cannot be avoided. Richard Feynman Molecular Electronics: Use molecule to conduct electrons and thereby perform electronic processing Size: scale from 1 to 100 nm Given the same amount of space, many times faster and more powerful than silicon based devices Manufacturing: fabricated identically and defect-free in enormous numbers Self-assembly Manufactured molecular synthesis tools highly developed Quantized electron energy Extended π systems Provides thermodynamically favorable electron conduction π Conjugation acts conduction switch Elegance Elegant solutions to non-volatile and inherently digital storage

FET SWCNT across Pt Electrodes (C. Dekker, Delft)

Electron transport in molecular device HOMO

Theoretical Modelling for Molecular Electronics Quantum Chemistry Most cost-effective way to treat molecular system Solid State Physics Bulk Materials Molecular Device ? Different Effects Huge Success Green Functional theory. Still Difficult !!! S D Surface adsorber + non-equilibrium Green’s function M

Landauer Formula Landauer Formula DOS Ef - Treat the “extended molecule” with Quantum Chemistry - Describe the electrode with Density of States (DOS) - The extended molecule is in equilibrium with the source and drain by lining up the effective Fermi level Tunneling Current Density from Source to Drain:

Quantum Chemistry approach based on Green’s Function Theory

Quantum Chemistry approach based on Green’s Function Theory

Quantum Chemistry approach based on Green’s Function Theory Based on Elastic-Scattering Green’s Function Theory Transition operator: Transition Probability:

Landauer Formula Tunneling Current Density from Source to Drain: DOS Ef

Electronic transport in Gold-Benzenedithiol-Gold Simulation Results Current vs. Voltage and Conductance vs. Voltage

Conjugated Polymer Increasing of size, Density of State(DOS) increases Biggest one: 3200 atoms 13440 electrons 20000 Basis functions(6-31G) Increasing of size, Density of State(DOS) increases Discrete molecular orbital to continuous band HOMO-LUMO gap remains constant as 2.78eV Energy structure analogous to inorganic Semiconductor

Conjugated Polymer Semiconducting behaviour, verified by Experiments.

poly 24 = 18.3 nm i(Ei) =i(0)(1+ Ei)  is the dephasing factor Poly10, Charging effect poly 24 = 18.3 nm i(Ei) =i(0)(1+ Ei)  is the dephasing factor A: =3, B: =10

Electronic transportation in (5, 5) CNT

Electronic transportation in (5, 5) CNT PNAS, 101,13408,2004

Molecular Field Effect Transistor Gate Bias (Vg) Modulate the transportation of electrons

Current-Voltage characteristics, IETS Simulation of Carbon Nanotube (CNT), DNA, ... Structure determination, DNA sequence identification, Bio-molecular devices

Vd Vd IETS: Inelastic Electron Tunneling Spectroscopy The Fingerprint of Molecular Devices Vibration of molecule leads to transition peak Vd Vd

IETS Measure The Fingerprint of DNA Vibration of DNA leads to transition peaks

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