Transcript bair_thesis_presenta..

COMPUTATIONAL MODELING
OF THE ELECTRICAL SENSING
PROPERTIES OF SINGLE WALL
CARBON NANOTUBES
By: Shawn Bair
Organization

Introduction

Carbon Nanotubes





Electrical Background
Field Effect Transistors






Literature Experimentation
Modeling


Preparation
Properties
Applications
Overview
Non-equillibrium Green’s Functions
Poisson Equation
Density Functional Tight Binding
Results
Conclusions
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 deposition
Formed in various single and multi-walled
arrangements.
CNT Types and Naming Convention




CNT structure
described using two
numbers (n,m)
A graphene sheet is
cut along C
C = na + mb
This divides CNTs into
three groups:
armchair, zigzag, and
chiral.
n=m
m=0
n≠m
Carbon Nanotube Properties

Mechanical Properties:


Young’s modulus of up to 1000 GPa (5x steel)
Tensile strength of 63 GPa (50x steel)



Weak under compression
High diameter (nm) to length (up to cm) ratio
Electrical 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 CNTs
Applications



Strong physical properties
lead to applications in
polymers and materials.
Use as tips for atomic
force microscopes
Conducting bridges in
nanoscale electrical
systems

Appealing due to changes
in CNT conductivity
resulting from applied
forces or exposure to
molecules.
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/rgeme/teaching-notes/introduction-403
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.
N-Type CNTFET
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 NO2 and NH3.
CNTs appeared to behave as
p-type semiconductors

Note: CNTs were exposed to
air.
Past Experimental Data

Avouris et al discovered that p-type behavior was not
intrinsic, but a product of exposure to O2.



Annealing at 200 C in vacuum for 10 hours converted CNTs to n
type behavior.
3 min exposure to O2 caused reversion to p-type
PMMA would protect the n-type qualities from low O2 exposure
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 experiments
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
by
e
= Electron charge, h = Planck’s constant
 T(E)= Transmission probability
 fS ,fD = Fermi function of source and drain electrode

Need method to find T(E), fS ,fD
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 calculated
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.
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.
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
Poisson Equation

The electron density from NEGF is expanded into
neutral atomic reference densities (ni0) and density
fluctuations.
 Fi00
represents s-orbital like radial function
 Δqi represent Mulliken charges, which are related to
the electron population on each atom as determined
by basis functions.
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 gate


This potential is then used in another NEGF loop
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 handle
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 equation
T represents the kinetic energy term
 Vext represents electron-ion interactions
 Vxc represents exchange and correlation potential

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 distance
 Each 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 calculations
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 effects
Single SWCNT Modeling Settings






An (8,0) zigzag SWCNT was modeled in DFTB+ to examine the effects of NO2
and NH3 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 A
Distance of molecules from CNT surface
 NO2 = 2.18 A
NH3 = 3.67
Single 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
molecule
Results – Gate Variation
Gate Variation Effect on Current flow
0.1 V Bias
4.50E-007
4.00E-007
Current (Amps)
3.50E-007
3.00E-007
2.50E-007
Hole
Conduction
2.00E-007
1.50E-007
Electron
Conduction
1.00E-007
5.00E-008
0.00E+000
-25
-20
-15
-10
-5
Gate Voltage (V)
0
5
NO2 Doped CNT
NH3 Doped CNT
10
Results – Bias Variation
I-V Curve at -7 V Gate Voltage
0
0.5
1
1.5
2
2.5
3
1.00E+000
Current (Amps)
1.00E-001
1.00E-002
1.00E-003
1.00E-004
1.00E-005
1.00E-006
1.00E-007
1.00E-008
Bias Voltage (V)
NO2 Doped CNT
NH3 Doped CNT
3.5
Results – NO2 Distance
Current at 1 V Bias with Varying NO2
Distance
7.20E-008
Current (A)
7.10E-008
7.00E-008
6.90E-008
6.80E-008
6.70E-008
6.60E-008
0
0.5
1
1.5
2
2.5
NO2 Distance from CNT Surface (A)
3
3.5
4
4.5
5
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.
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 region
Simulating exposure to air and O2 groups.
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/transistors
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, 1998
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: 978-953307-054-4, InTech, DOI: 10.5772/39424. Available from:
http://www.intechopen.com/books/carbon-nanotubes/fundamentalphysical-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).
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