Nanotubes By Shawn Bair Organization Introduction Carbon Nanotubes Preparation Properties Applications Electrical Background Field Effect Transistors Literature Experimentation Modeling ID: 756776
Download Presentation The PPT/PDF document "Computational Modeling of the Electrical..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
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