CAR Saturday, October 10, 2015 Modeling Narrow Channel Textured Networks Meg Noah and Young-Kyun...

CAR Friday, April 21, 2023

Modeling Narrow Channel Modeling Narrow Channel Textured NetworksTextured Networks

Meg Noah and Young-Kyun KwonMeg Noah and Young-Kyun KwonDepartment of Physics and Applied Physics, Department of Physics and Applied Physics, University of Massachusetts, LowellUniversity of Massachusetts, LowellNanomanufacturing Center of ExcellenceNanomanufacturing Center of ExcellenceCenter for High-rate NanomanufacturingCenter for High-rate NanomanufacturingIn collaboration with Seunghun Hong at Seoul National University, In collaboration with Seunghun Hong at Seoul National University, KoreaKorea

[email protected][email protected]

Meg Noah

ABSTRACTWe present a statistical model for networks of nanotubes applied to simulations of thin film CNFET conductivity. The network is modeled as a two dimensional diffusion of nanotubes on a rectangular flat surface of user-specified dimensions. The connectivity of the ensemble of randomly assigned lengths, positions, orientations, and conductance is found by creating an equivalent grid of resistors. The model classifies each as being a semiconducting device, a metallic device, or a defective device. For a set of user specified manufacturing parameters, Monte Carlo techniques are used to derive an analytical expression to estimate the probability density function of a creating a semiconducting device.

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This work was supported under the Nanoscale Science and Engineering Centers Program of the National Science Foundation (Award # NSF-0425826)

2

2

4.26

th

SL

Not Connected Semiconductor

Metallic

Classification of ChannelsClassification of ChannelsSemiconductorsMetallic

Nanotube Properties-2

NT.64NTμm for =3μm L

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MotivationMotivation Traditional isotropic models

present manufacturing showstoppers!

Modeling community has not yet Modeling community has not yet produced statistical simulations of produced statistical simulations of anisotropic nanotube networks.anisotropic nanotube networks.

Affordable solutions of nanotubes are mixed chiralty, and when the density is too high, the channels are conductors.

Even when the channel is semiconducting, the on-off ratio is poor due to the presence of metallic NT.

Reported values of short channel width randomly-oriented SWNT networks ~ w1.53 pose manufacturing problems.

0 1 2 3 4 5 60

0.2

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0.8


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Semiconductor

Channel Properties

MetallicNot Conducting

Behnam, et al APL 2006

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ObjectivesObjectives

Model electronic properties of Model electronic properties of anisotropic nanotube networks.anisotropic nanotube networks.

Determine the feasibility of using Determine the feasibility of using mixed chirality nanotubes.mixed chirality nanotubes.

Model ensembles of nanotube Model ensembles of nanotube networks from a statistical networks from a statistical characterization of a nanotube characterization of a nanotube mixture.mixture.

Extend NTFET model to sensor model.Extend NTFET model to sensor model.

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MethodologyMethodology Represent the device as a 2D random network of Represent the device as a 2D random network of

nanotubes of specified length, Ls, and conductivity, nanotubes of specified length, Ls, and conductivity, G, dispersed in a channel of length, L, and width, W.G, dispersed in a channel of length, L, and width, W.

Represent the system as a network of nodes and Represent the system as a network of nodes and resistorsresistors

[Reduce the grid using Kirchhoff’s Laws][Reduce the grid using Kirchhoff’s Laws] Compute electronic propertiesCompute electronic properties Monte Carlo simulationsMonte Carlo simulations Model the distribution functions of each class Model the distribution functions of each class

(eg metallic, semiconducting, defective) as a (eg metallic, semiconducting, defective) as a function of CNT density.function of CNT density.

An analytical expression derived from model output An analytical expression derived from model output provides a fast estimation of probability of success provides a fast estimation of probability of success for a give manufacturing parameter set.for a give manufacturing parameter set.

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OverviewOverview We present a model of nanotube network channels and its We present a model of nanotube network channels and its

application to high-performance nanoscale transistors.application to high-performance nanoscale transistors. The model predicts electronic properties of single The model predicts electronic properties of single

channels, and statistical metrics of ensembles of channels.channels, and statistical metrics of ensembles of channels.

Semiconductor

Channel Properties

Metallic

Not Conducting

-4 -2 0 2 40

0.5

1

1.5

2

2.5

3

3.5

4

VG [V]

I SD [

nA

]

Length = 4 mWidth = 2 m

Density = 1 NT/ m2

Fraction Metallic = 0.3333

Semiconducting Network

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Take-Home MessageTake-Home Message Both experimental and simulation results show that the Both experimental and simulation results show that the

conductivity and mobility of textured network devices conductivity and mobility of textured network devices increased with reduced channel width, unlike random increased with reduced channel width, unlike random network-based or conventional silicon-based devices.network-based or conventional silicon-based devices.

Our model answers many ‘what if’ questions:Our model answers many ‘what if’ questions:– Do textured networks offer advantages over traditional Do textured networks offer advantages over traditional

percolations as environmental sensors? percolations as environmental sensors?

– Can the properties of a network in an environment be predicted if Can the properties of a network in an environment be predicted if the NT properties are statistically known?the NT properties are statistically known?

– What manufacturing parameters would result in feasible mass What manufacturing parameters would result in feasible mass production of such an environmental sensor?production of such an environmental sensor?

– What strategies, including logical combinations of sensors, work for What strategies, including logical combinations of sensors, work for optimizing selectivity? Sensitivity? optimizing selectivity? Sensitivity?

– Is it better to have optimal semiconducting properties, or better to Is it better to have optimal semiconducting properties, or better to have more NT even if the channel is more metallic?have more NT even if the channel is more metallic?

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PublicationsPublications Journal ArticlesJournal Articles

– Hahm, Noah, Kwon, Jung, Diameter Selective Growth of Vertically Hahm, Noah, Kwon, Jung, Diameter Selective Growth of Vertically Aligned Single Walled Carbon Nanotubes by Ethanol Flow Control, Aligned Single Walled Carbon Nanotubes by Ethanol Flow Control, Nanotech 2008 Vol. 1Nanotech 2008 Vol. 1

– Lee, Noah, Park, Seong, Kwon, and Hong, “Textured” Network Lee, Noah, Park, Seong, Kwon, and Hong, “Textured” Network Devices: Overcoming Fundamental Limitations of Devices: Overcoming Fundamental Limitations of Nanotube/Nanowire Network-Based Devices, Small (2009)Nanotube/Nanowire Network-Based Devices, Small (2009)

– Lee, Baik, Noah, Kwon, Lee, and Hong, Nanowire and Nanotube Lee, Baik, Noah, Kwon, Lee, and Hong, Nanowire and Nanotube transistors for lab-on-a-chip applications, Lab on a Chip, Issue 16 transistors for lab-on-a-chip applications, Lab on a Chip, Issue 16 (2009)(2009)

APS PresentationsAPS Presentations– Noah and Kwon, Toward 100% Semiconducting Devices From Noah and Kwon, Toward 100% Semiconducting Devices From

Mixed Chirality Nanotube Networks (2007)Mixed Chirality Nanotube Networks (2007)– Lee, Im, Lee, Myung, Kang, and Hong, Large-Scale Array of Pristine Lee, Im, Lee, Myung, Kang, and Hong, Large-Scale Array of Pristine

Carbon Nanotube Transistors (2007)Carbon Nanotube Transistors (2007)– Noah and Kwon, Modeling Narrow Channel Textured Networks Noah and Kwon, Modeling Narrow Channel Textured Networks

(2008)(2008)– Lee, Hong, Noah, Kwon, Park, and Seong, Fabrication of Long Lee, Hong, Noah, Kwon, Park, and Seong, Fabrication of Long

Channel Carbon Nanotube Network Transistor Arrays (2008)Channel Carbon Nanotube Network Transistor Arrays (2008)– Park, Lee, Lee, Hong, Kwon, Noah, Park, Seong, Structural Control Park, Lee, Lee, Hong, Kwon, Noah, Park, Seong, Structural Control

of Carbon Nanotube Networks for High-Performance Devices (2010)of Carbon Nanotube Networks for High-Performance Devices (2010) CHN Poster PapersCHN Poster Papers

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Traditional Percolating SystemsTraditional Percolating Systems Derivation of percolation threshold, the critical density of Derivation of percolation threshold, the critical density of

stickssticksof a given length to percolate. Pike and Seager of a given length to percolate. Pike and Seager PRBPRB 1974 1974

Define critical stick length Define critical stick length LLSS for given density of sticks. for given density of sticks. Derivation of percolation critical exponents. Derivation of percolation critical exponents. ‘Conductivity’ exponent (‘Conductivity’ exponent (LLSS / L / LTHTH ) )22 shown to be t=1.24±0.03. shown to be t=1.24±0.03. Define anisotropy metric. Define anisotropy metric. Balberg, Binenbaum, & Anderson Balberg, Binenbaum, & Anderson PRLPRL 1983 1983

Conductivity is a power of the channel length. Conductivity is a power of the channel length. ~ ~ LLCC..

Relations of Relations of IISDSD to to LLSS for isotropic systems. for isotropic systems.Pimparker, Guo, Alam Pimparker, Guo, Alam NCNNCN at NanoHUB.org 2006 at NanoHUB.org 2006

Conductivity is a power of the average NT bundle length. Conductivity is a power of the average NT bundle length. ~ ~ LLSS

Hecht, Hu, Grüner Hecht, Hu, Grüner APLAPL 2006 2006

Conductivity is a power of the channel width for NT networks.Conductivity is a power of the channel width for NT networks. ~ ~ LLWW

. Behnam, et al . Behnam, et al APLAPL 2006 2006

2

2

4.26th

SL

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SNU New Process, Anisotropic SNU New Process, Anisotropic NetworkNetwork

1. Pattern an Alignment Key onto a substrate.

2. Assemble the CNT onto the substrate.

3. Pattern the electrodes onto the CNT channels.

4. Deposit a SiO2 film over the electrodes, CNT channel, and substrate.5. Pattern on the Gate after selective burning Back-Gate.

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IV CharacteristicsIV Characteristics

Equivalent CircuitsEquivalent Circuits

Probability Distribution of each device class (metallic, not connected, semiconductor, success, false alarm, missed detection)

Probability Distribution of each device class (metallic, not connected, semiconductor, success, false alarm, missed detection)

NTNetworkModel

Model DescriptionModel Description

WinSpice

Length/Type DistributionNanotube ConductivityContact ResistancesMeasured and ModeledEnvironmental SensitivityFunctionalized Variations

Nanotube Properties

NTNetworkSensorModel

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Populate ChannelPopulate Channel

Find NT-ElectrodeIntersections

Find NT-ElectrodeIntersections

Find NT-NT CrossingsFind NT-NT Crossings

Table of Nodes/ResistorsFor Equivalent Circuit

Table of Nodes/ResistorsFor Equivalent Circuit

Compute IV CurveCompute IV Curve

Read User InputsRead User Inputs

Loop for nTrialsLoop for nTrials

Model Single NanotubeNetwork Channel

Model Single NanotubeNetwork Channel

Assign ClassificationTabulate Results

Assign ClassificationTabulate Results

Model DescriptionModel Description

Probability DistributionsFor Different Classes

IV Curves

Loop for nEnvironmentsLoop for nEnvironments

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0 1 2

0

0.5

1

1.5

2

2.5

3

3.5

4

Width [m]

Length

[ m

] 1.0 NT/ m2

Metallic SWNT Model Value = 4 kΩ/m McEuen, P. and Ji-Yong Park,

'Electron Transport in Single-Walled Carbon Nanotubes', MRS Bulletin, April 2004

Predicting Predicting I-V Curves for Curves for EnsembleEnsemble

McEuen, P. and Ji-Yong Park, 'Electron Transport in Single-Walled Carbon Nanotubes', MRS BUlletin, April 2004

Burke, PJ 'An RF Circuit Model for Carbon Nanotubes' IEEE-NANO 2002

Ilani, et. al, 'Measurement of the quantum capacitance of interacting electrons in carbon nanotubes', Nature Physics, Vol 2, Oct. 2006

Semiconducting Nanotubes

G=C(Vg0-Vg)/L C ~ 60 aF ranges from 1000

to 20000 cm2/V s

CNT Contact Electrode

Model Value = 50 kΩ

-4 -2 0 2 40

0.5

1

1.5

2

2.5

3

3.5

4

VG [V]

I SD [

nA

]


Density = 1 NT/ m2


Semiconducting Network

Contact Points at CNT Junctions.1 to .3 Go (43 to 129 kΩ)

Model Value = 40 kΩ Yoon, et. al., Physical

Review Letters Vol. 86, No. 4, 2001

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Database – NT Length, LDatabase – NT Length, LSS

1) Input length allowed to vary up to +/- input standard deviation value from a Gaussian random number. Most of our results were LS

2) Measured Lengths for 0.1 mg/mL o-dichlorobenzene SWNT suspensions

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Component Model Value ReferenceNT Length Distribution

Ave=m Measurement from Seunghun Hong at Seoul National University, Korea

NT Junctions 40 kΩ 1 to .3 Go (43 to 129 kΩ) Yoon, et. al., Physical Review Letters Vol. 86, No. 4, 2001

Metal/Metal orSemi/Semi

200–400 kΩ Hecht

Metal/Semi 20000–40000 kΩ Hecht

NT Contact Electrode

50 kΩ Kwon

Metallic SWNT 4 kΩ/m McEuen, P., MRS Bulletin, April 2004

SemiconductingSWNT

G=C(Vg0-Vg)/LC ~ 60 aF~1000 to 20000 cm2/V s

McEuen, P., MRS Bulletin, April 2004Burke, PJ IEEE-NANO 2002Ilani, et. Al, Nature Physics, Vol 2,

2006

Database SummaryDatabase Summary

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Nanotube Molecular Wires as Chemical SensorsJing Kong, et al., Science 287, 622 (2000)

Component Model Value Reference

Environment Parameters

Semiconducting NTG=CeC(Vg0-Vg-Ve)/L

Ve=f(gas,P,T,time,n,m)

Ce=f(gas,P,T,time,n,m)

G = f(Contact Force (nN), diameter of tubes, Landauer-Buttiker formula)

Various experimental & theoretical papers.O2, P.G. Collins, 2000NH3, NO2 J.Li, 2003 cnt networks NH2-R J.Kong, 2001HO-R T.Someya, 2003

Yoon, Mazzoni, Choi, Ihm, Louie PRL, 2001

DatabaseDatabase

Yoon, Mazzoni, Choi, Ihm, Louie PRL, 2001

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Metallic10-8 A > ISD

Classification as a TransistorClassification as a Transistor

Failure in Manufacturing

Not ConnectedISD < 10-10 A

Semiconductor

IOFF < 10-10 AISD > 10-8 A

SemiconductorsMetallic

Nanotube Properties

Manufacturing

Success

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Classification as a TextureClassification as a Texture

Histogram , Bundling

sin

cos

S D S D

ii

ii

L L L L

PAnisotropy

P

Anisotropic Channels

Anisotropy≠1

Isotropic Channels

Anisotropy ~ 1

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Increasing Channel Length, Increasing Channel Length, LL

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Semiconductor

Channel Properties

Metallic

Not Conducting

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Increasing Channel Width, Increasing Channel Width, WW

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Increasing Fraction of Metallic Increasing Fraction of Metallic NTNT

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Model Output AnalysisModel Output Analysis

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ln(L)/W

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SC C M( ) ( ) ( )P P P

NC 0

1( ) 1 tanh

2P A

Analytical ExpressionAnalytical Expression

0 = Density at which 50% of devices are connected = f(L,W)μ = Asymmetry factor, value fit as 0.0404γ = Slope factor = 0.2848β = Scaling factor = 25.9704

M C( ) ( )P P f C NC( ) 1 ( )P P

f = fraction of nanotubes that are metallic

Note: Values for dimensions greater than nanotube length.

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General Result: Balberg, Binenbaum, Anderson PRL 1983 General Result: Balberg, Binenbaum, Anderson PRL 1983 ~ ~ LLSS

Validation: Scaling with NT Validation: Scaling with NT LengthLength

Note: When the tubes in the network approach 20–30 microns, the resistancealong the tube itself becomes comparable to the resistance of the junction

Hecht, APL (89) 2006Hecht, APL (89) 2006 ~ ~ LLSSa a 0 < a < 20 < a < 2Our modelOur model

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Validation: Scaling Channel Validation: Scaling Channel LengthLength

Pimparkar, Guo, Alam NCN NanoHUB, 2006

Our model.

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4.5Semiconducting Networks

VG [V]

I SD [

nA

]


Density = 1 NT/ m2


Validation: I-V Curves of Individual Validation: I-V Curves of Individual DevicesDevices

Long Channel Low Density of

CNT

ModeledModeled MeasuredMeasured

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I SD [

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Metallic Networks

Validation: I-V Curves of Individual Validation: I-V Curves of Individual DevicesDevices

Long ChannelHigh Density of CNT


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Validation: Probability of Validation: Probability of SuccessSuccess

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Channel: 20 m x 3 m


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Channel: 20 m x 16 m


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ModeledModeled

Validation: Ensemble Validation: Ensemble ConductivityConductivity

MeasuredMeasured

-1conductivity S cm

length [micron] model input

channel width [micron] model input

source-drain voltage V model input

effective channel thickness cm

source-drain

SD

SD

SD

SD

L IV W t

L

W

V

t

I

current (computed) A

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Validation: Ensemble MobilityValidation: Ensemble Mobility

0

2 -1 -1

0

mobility cm V s

length [micron] model input

channel width [micron] model input

source-drain voltage V model input

capacitance per unit

channel area V

SD

SD G

SD

dIL

C V W dV

L

W

V

C

-1 -2 8 C cm fit at 1.65 10

source-drain current (computed) A

gate voltage V model input

SD

G

I

V


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Modeling NT Network SensorsModeling NT Network Sensors Performance MetricsPerformance Metrics

– sensitivitysensitivity– stabilitystability– selectivityselectivity

ClassificationClassification– SuccessSuccess– Missed DetectionMissed Detection– False Alarm (ID)False Alarm (ID)– False Alarm (Quantity)False Alarm (Quantity)

Sensor SuitesSensor Suites– Evaluating Selective Evaluating Selective

StrategiesStrategies Two channels with Two channels with

different responses to different responses to same gas used to same gas used to logically logically

– VotingVoting– Dynamic Range and Dynamic Range and

SensitivitySensitivity– Improved samplingImproved sampling– Dynamic FlowDynamic Flow

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Success in Sensing

Failure in Sensing

Classification as a SensorClassification as a Sensor

Missed Detection False Alarm(Identify)

PositiveDetection

Sensitivity, Stability, Response Time

vs

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Sensor Model ResultsSensor Model Results

4 micron x 1 micron, 1/3 metallic NT, ‘saturated’

A=4.0 E=6.4 Scm-1

@ Vg=-0.75 V

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A=11.7 E=17 Scm-1

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A=94.8 E=105.3 Scm-1

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Concept for an AccelerometerConcept for an Accelerometerfor microgravityfor microgravity

Structural relaxation of a (5,5) Structural relaxation of a (5,5) crossed SWNT junction with a 15 crossed SWNT junction with a 15 nN contact force.nN contact force.

Contact distance (.25 nm) Contact distance (.25 nm) reduced by 20% from the van der reduced by 20% from the van der Waals distance.Waals distance.

Center-to-center distance is 0.74 Center-to-center distance is 0.74 nm. (Free space distance would nm. (Free space distance would be about 1.01 nm)be about 1.01 nm)

Tried a 4x1 (very anisotropic) Tried a 4x1 (very anisotropic) channel:channel:20 20 junction = 2.94 µA at V junction = 2.94 µA at VGG=-6V=-6V40 40 junction = 2.87 µA junction = 2.87 µA

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SummarySummary

We have developed a model for estimating We have developed a model for estimating the probability of successful and defective the probability of successful and defective semiconductors resulting from a set of semiconductors resulting from a set of manufacturing parameters.manufacturing parameters.– For example, over 90% of an ensemble of 40x2 µm For example, over 90% of an ensemble of 40x2 µm

nanotube networks, of nanotube networks, of 11//33 metallic content and 4 metallic content and 4 NT/µmNT/µm22, will have semiconductor properties. , will have semiconductor properties.

– An analytical function was fit to model output.An analytical function was fit to model output. We can predict the We can predict the II--VV Curves of the Curves of the

nanotube networks by finding an equivalent nanotube networks by finding an equivalent circuit of resistors and nodes.circuit of resistors and nodes.

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ConclusionsConclusions

Our results:Our results:

Explain why measurements of textured Explain why measurements of textured networks show improved conductivity with networks show improved conductivity with narrow channels.narrow channels.

Show that traditional percolation models are Show that traditional percolation models are insufficient for textured networks.insufficient for textured networks.

Characterize nanotube network ensembles.Characterize nanotube network ensembles.

Model the network Model the network II--VV, , , , in different in different environments.environments.

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Future WorkFuture Work

Expand database of nanotube parametersExpand database of nanotube parameters– Dispersions with bundlingDispersions with bundling– Substrate dependenceSubstrate dependence– Environmental factors Environmental factors – Model SWNT transmissionModel SWNT transmission– Different nanotubes – Nickel or Gold Different nanotubes – Nickel or Gold

Model ensemble statistics ofModel ensemble statistics of II--VV curves and curves and values quantifying production parameters in values quantifying production parameters in terms of mobility, dynamic range, etc.terms of mobility, dynamic range, etc.

Connection to percolation modelsConnection to percolation models Verification and validation with Verification and validation with

experimental dataexperimental data

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Future WorkFuture Work

DeDefect Analysisfect Analysis Additional V&VAdditional V&V Model nanotube network Model nanotube network

performance as a sensor performance as a sensor Functionalization forFunctionalization for

selectivity:selectivity:Ara h 1 moleculeAra h 1 molecule

Maleki, Soheila J., et. al, The Journal of Immunology, 2000

CAR Saturday, October 10, 2015 Modeling Narrow Channel Textured Networks Meg Noah and Young-Kyun...

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