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Computational Modeling of the Electrical Sensing Properties of Single Wall Carbon Computational Modeling of the Electrical Sensing Properties of Single Wall Carbon

Computational Modeling of the Electrical Sensing Properties of Single Wall Carbon - PowerPoint Presentation

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Computational Modeling of the Electrical Sensing Properties of Single Wall Carbon - PPT Presentation

Nanotubes By Shawn Bair Organization Introduction Carbon Nanotubes Preparation Properties Applications Electrical Background Field Effect Transistors Literature Experimentation Modeling ID: 756776

carbon density charge cnt density carbon cnt charge cnts properties electron type system dftb negf represents contacts exposure functional

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Slide1

Computational Modeling of the Electrical Sensing Properties of Single Wall Carbon Nanotubes

By: Shawn BairSlide2

Organization

Introduction

Carbon

Nanotubes

Preparation

Properties

Applications

Electrical Background

Field Effect Transistors

Literature Experimentation

Modeling

Overview

Non-

equillibrium

Green’s Functions

Poisson Equation

Density Functional Tight Binding

Results

ConclusionsSlide3

What are Carbon Nanotubes (CNTs)

Discovered by

Iijima

in 1991.

Structure of rolled

graphene. Diameter range of 0.4 to 2.0 nm.Synthesis methods include: arc discharge, laser ablation, chemical vapor depositionFormed in various single and multi-walled arrangements.Slide4

CNT Types and Naming Convention

CNT structure described using two numbers (

n,m

)

A

graphene sheet is cut along CC = na + m

b

This divides CNTs into three groups: armchair, zigzag, and

chiral.

n=m

m

=0

n≠mSlide5

Carbon Nanotube Properties

Mechanical Properties:

Young’s modulus of up to 1000

GPa

(5x steel)

Tensile strength of 63 GPa (50x steel)Weak under compressionHigh diameter (nm) to length (up to cm) ratioElectrical Properties:

Enhanced reactive surface

Varying properties depending on

nanotube type and exposure to molecules

Armchair CNTs are always metallic, zigzag and chiral tend to be semiconducting.Metallic conduction occuring when allowed wave vectors pass through region where valence and conduction bands are degenerate

High theoretical current density for metallic CNTsSlide6

Applications

Strong physical properties lead to applications in polymers and materials.

Use as tips for atomic force microscopes

Conducting bridges in

nanoscale

electrical systemsAppealing due to changes in CNT conductivity resulting from applied forces or exposure to molecules. Slide7

Electrical Background

Current is the flow of charge carriers.

Majority charge carriers can be electrons or holes.

Charge transfer from a source contact to a drain.

Absorption of

dopant molecules on the bridging material can alter the number of charge carriers.

Images:

http://www.eng.umd.edu/~dilli/courses/enee313_spr09/files/supplement

http://www.ceb.cam.ac.uk/research/groups/rg-eme/teaching-notes/introduction-403Slide8

CNT Field Effect Transistor (CNTFET)

A CNTFET consists of

Source and Drain contacts

CNT conducting bridge

Gate,

seperated from system by a dielectric

Gate affects energy levels of nearby bands

A positive voltage lowers band energy levels.

The effect of this depends on the contact fermi

level and the material.Slide9

N-Type CNTFETSlide10

Past Experimental Data

Kong et al published one of the most often cited examples of CNTs being used as sensors.

They measured large changes in conductance upon exposure to NO

2

and NH

3.CNTs appeared to behave as p-type semiconductorsNote: CNTs were exposed to air.Slide11

Past Experimental Data

Avouris

et al discovered that p-type behavior was not intrinsic, but a product of exposure to O

2

.

Annealing at 200 C in vacuum for 10 hours converted CNTs to n type behavior.3 min exposure to O2 caused reversion to p-typePMMA would protect the n-type qualities from low O2

exposureSlide12

Thesis Objectives

Model CNTFET system, investigating use as a sensor for gases.

Why use modeling?

Purchase of CNTs expensive (618$/g), especially for specific types (928$/g).

Producing single CNT FETs can be difficult due to the scale

Easier to alter conditions then in experimentsSlide13

How to model the current flow

Goal is to find the current flow,

I

, across the semiconducting CNT bridge at various voltage bias and differing gate voltages

Landaur-Buttiker

formula states that current is found bye = Electron charge, h = Planck’s constantT(E)= Transmission probabilityfS ,

f

D

= Fermi function of source and drain electrodeNeed method to find T(E), f

S ,fD Slide14

Non-Equillbrium Green’s Functions (NEGF) Overview

Most common system for examining transport at a molecular level.

Consists of an iterative process where, given a self consistent potential, Green’s functions are used to calculate charge density

ρ

.

Poisson equation, using charge density of system, calculates self consistent potential, UH ,which represents electron-electron and electron-ion interactions

Once converged, T(E) able to be calculatedSlide15

NEGF Setup

System first divided into three sections.

Source and drain contacts, and extended device region

Regions further divided into layers

Each layer only interacts with those adjacent to it

Contacts assumed to be bulk properties.Slide16

NEGF Calculations

The goal of the NEGF equations is to find the charge density matrix

G

<

represents the electron-electron correlation matrix, and is equal to

The broadening functions, represent the broadened density of states in the device.Slide17

NEGF Calculation

represents the contacts self energy, which includes effects from the contact. Along with Gr and Ga contains Hamiltonian and overlap terms, which are calculated using density functional tight-binding theory.

Once converged Slide18

Poisson Equation

The electron density from NEGF is expanded into neutral atomic reference densities (n

i

0

) and density fluctuations.

Fi00 represents s-orbital like radial functionΔqi represent

Mulliken

charges, which are related to the electron population on each atom as determined by basis functions.Slide19

Poisson Equation

Poisson equation for mean field electrostatic potential is

A three dimensional version of this equation is used in finding the potential throughout the device space

Boundary conditions include

Potential falling to zero at large distance

Potentials reach bulk set value at contacts or gateThis potential is then used in another NEGF loopSlide20

Density Functional Tight Binding (DFTB)

NEGF and Poisson calculations require a basis set and calculated Hamiltonian (H) and Overlap(S) matrices.

These are calculated using Density Functional Tight Binding (DFTB) theory, first proposed by Slater and

Koster

.

Useful due to having good accuraccy and being able to calculate more than the ~100 atoms DFT can reasonably handleSlide21

Basic DFTB

Linear combinations of atomic

orbitals

that are orthogonal to

orbitals

on other atoms are created and used as a basis set.Leads to Kohn Sham equationT represents the kinetic energy termVext represents electron-ion interactions

V

xc

represents exchange and correlation potentialSlide22

Basic DFTB

With the

orbitals

calculated, Hamiltonian matrix elements can be evaluated

Two center Approximation made to reduce the computational difficulty

Hμv set to 0 beyond a certain distanceEach calculation is broken into smaller pieces, dependent on the type of orbitals and distance.

These smaller pieces, once solved, can ideally be used again elsewhere in the calculationsSlide23

Basic DFTB Energy equation

First term represents energies of

orbitals

Second terms eliminate excess energy from double counting

Third term adds energy from exchange and correlation

Final term adds ion-ion effectsSlide24

Single SWCNT Modeling Settings

An (8,0) zigzag SWCNT was modeled in DFTB+ to examine the effects of NO

2

and NH

3

on its conductivity.Modeled system consisted of 224 Carbon atoms, 96 in the central device region and 64 in each contact region. Diameter of 6.27 ADistance of molecules from CNT surfaceNO

2

= 2.18 A NH

3 = 3.67Single Molecule placed approximately 0.714 A from CNT length midpoint

Planar Gate, when used, 7 A from center, 7 A long. Placed on opposite side of moleculeSlide25

Results – Gate VariationSlide26

Results – Bias VariationSlide27

Results – NO2 DistanceSlide28

Conclusions

Results appear to be qualitatively as expected, with CNT performing as an n-type semiconductor, and molecules as appropriate

dopants

.

Conduction of CNT able to be modified using gate.

Noticible change observed in single NT from just one molecule (3-4 atoms) added to 96 atom device region.Not as large change in two CNT system.Quick calculation times at low bias and gate voltage.Some difficulty with convergence at high values, large systems, more atom types.Slide29

Conclusions-Further Applications

Modeling metal contacts into system

Chosen metal for contacts in

nanoscale

electronics can have very large effects

More heavily doping the device regionSimulating exposure to air and O2 groups.Slide30

References

Iijima

, S. Helical microtubules of graphitic carbon.

Nature.

1991, 354, 56–58.Koskinen, P. Computational Modeling of Carbon Nanotubes. [Online] Carbon

Nanotube

Hierachial Composites for Interlaminar

Strengthening. Aerospace Engineering Blog. [Online] May 11, 2012.Lieber

, C. Carbon nanotube atomic force microscopy tips: Direct growth by chemical vapor deposition and application to high-resolution imaging. PNAS

.

2000

,

vol

.97, no.8, 3809-3813

Field effect Transistors.

Nanointegris

. [Online]

http://www.nanointegris.com/en/transistorsSlide31

References

M K

Achuthan

K N

Bhat

(2007). "Chapter 10: Metal semiconductor contacts: Metal semiconductor and junction field effect transistors". Fundamentals of semiconductor devices. Tata McGraw-Hill. pp. 475 ff. ISBN 007061220X.B. Aradi, B.

Hourahine

, and Th.

Frauenheim. DFTB+, a sparse matrix-based implementation of the DFTB method. J. Phys. Chem. A, 111(26):5678, 2007.

M. Elstner, D. Porezag, G.

Jungnickel, J. Elsner, M. Haugk

, T.

Frauenheim

, S.

Suhai

, and G. Seifert. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B, 58:7260, 1998Slide32

References

A

Pecchia

, L

Salvucci

, G Penazzi, and A Di Carlo. Non-equilibrium green’s functions in density functional tight binding: method and applications. New J Phys, 10:065022, 2008.Zoheir Kordrostami and Mohammad Hossein Sheikhi

(2010). Fundamental Physical Aspects of Carbon

Nanotube

Transistors, Carbon Nanotubes, Jose Mauricio

Marulanda (Ed.), ISBN: 978-953-307-054-4, InTech, DOI: 10.5772/39424. Available from: http://www.intechopen.com/books/carbon-nanotubes/fundamental-physical-aspects-of-carbon-nanotube-transistors

F. Bloch, Z. Physik 52, 555 (1928)Lowdin

, P-O. On the Non-

Orthogonality

Problem Connected with the Use of Atomic Wave Functions in the Theory of

MOlecules

and Crystals. J. Chem. Phys.

18

, 365(1950).Slide33

References

Frauenheim

, TH. et al. A Self-Consistent Charge Density-Functional Based Tight-Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology. Phys. stat. sol. (b)

217

, 41 (200). 41-61