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Fakultät Maschinenwesen, Professur Materialwissenschaft und Nanotechnik

Berlin, 20.03.2015 11:45 – 12:00

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Ab-initio model of extended CNT-metal contacts

Artem Fediai, Dmitry Ryndyk and Gianaurelio Cuniberti

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General information

Method: Nonequilibrium Green function formalism + DFT

Basis: All Hamiltonians are Konh-Sham Hamiltonians given in atomic orbital basis

DFT details: Peudopotentials approximation: Goedecker-Teter-Hutter (GTH)

XC energy: generalized gradient approximations (GGA), type: Perdew-Burke-Ernzerhof (PBE)

Basis: Carbon: single-ζmetals: double-ζ

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Geometry of extended CNT-metal contacts

…… …Local contact

A A-A

…… …Extended contactREALISTIC

A

A

A

NOT REALISTIC

A-A

metalCNT

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Extended vs. local contact

Inflow DISTRIBUTED

Inflow localized

! (concept of internal / external contact)

Local contact

Extended contact

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Extended CNT-metal contact: experimental evidence

*[A. D. Franklin and Z. Chen, Nature Nanotechnology. Vol. 5, 858 (2010)]

One ballistic CNT Several CNT-FET with different contact length Lc

Contact length has a strong influence on the contact resistance Output characteristics for

different contact lengths*

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Idea of the method

… …Initial system

Its tight-binding representation( is a Hamiltonian of the CNT unit cell)

Metal implies to modify:- on-cite (by self-energy se)- hopping matrices (by self-energy st)of the CNT unit cells

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Quantities to be computed

HC*

HC

SMe

e †, 1 1,C i ij i i j i i ji H j t t

e s sS s Me , 1 1

†

,( ) ( ) () )( ij i j i jt tE E Ei E j

+

=

Graphical representation of

is an effective Hamiltonian of the CNT-metal system

HC*

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Approximations for practical realization

HC* = HC + SMe

HC

SMe

PBC

the rest of the algorithm is done rigorously

For the relevant CNTs neglecting of the curvature effects gives not more than 10% error

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Systems to be DFT-simulatedHC is to be found in practice by DFT simulation System 1 as follows:

System 1: 4 (embedded)– 22 (free) – 4 (embedded) periods of the (16,0) ** From this simulation we take only HC

576 metallic atoms and 1920 C atomsz

xy

System 2 System 3

By defining the elements of the Systems 2,3 we construct the Hamiltonian of the system “graphene on the metal”(infinite in all direction to exclude quantization effects)

z

xy

810 metallic atoms and 240 C atoms

810 metallic atoms

** From this simulations we take only S(E)

S(E) is to be found in practice by DFT simulation System 2 and 3:

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Metal: FCC lattice [111]; lattice constant is close to 4 Å supercell to obtain common periodicity by metal and honeycomb lattice (rectangular version of supercell):

(a) One common supercell of the metal and graphene

x

z. y

x

z. y

z

x. y

(b) Top view on Systems 1,2 in terms of the common supercell

principal layer(slice)

Going to k-space is natural as we deal with periodical system

3 33 3

! for Pd and Al stretching/ compression is < 3% to fit with Carbon

Special tricks to find S(E)

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Explanation for 2-D simple system

TB chains inz-direction are

bounded

TB chains in z-direction are separated, but depend on

Self-energy in space (for each )

Real space self-energy (within one supercell)

( ) ( )s SE a E a

InfiniteFinite, has a size of the supercell

||k

||k

||k

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Self-energies: to which extend?

given atomnearest neighbor (n.n.) next nearest neighbor (n.n.n.)next next nearest neighbor (n.n.n.n.)

Self-energy due to the metal taken into account:

S

S

S

S

on-cite matrix

n.n. hopping matrix

n.n.n. hopping matrix

n.n.n.n. hopping matrix

Results show that p orbitals remainseparated from s-like orbitals in S.Hereafter we consider only p-orbitals, as they are relevant within the energy range of interest

(E)

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Self-energies: individuality of the metal

Imaginary part (diagonal) of Sdescribes strength of coupling

Real part (diagonal) of Sdescribes band banding

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Local density of states along the tube

d Pd-C= 3.5 A d Al-C= 3.75 A

Pd AlPd Al

p-type FET embedded CNT segment preserves a bandgap Ohmic contact for holes

ambipolar FET (closer to n-type) embedded CNT segment is metalized inside Al ambipolar Schottky contacts

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Dispersion relation in the embedded CNT segment

embedded CNT is doped, but preserves its band structure, incl. the gap

embedded CNT changes its band structure dramatically it slightly resembles metallic tube or graphene

Pd Al

-1 0 1-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

K [pi/a]

E [

eV

]

-1 0 1-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

K [pi/a]

E,

[eV

]

All energy levels are more or less broadened (self-energies are complex inside the tube)

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Transmission coefficient for different contact lengths

Long Pd contacts are ballistic As Pd contacts become shorter than ~50 nm, transmission falls down exponentially

Transmission is significantly suppressed for any contact length of Al contact Transmission for holes is stronger suppressed than for electrons in Al contacts

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Pd-CNT contacts: comparison with the experiment

*[Franklin et. al. ACS Nano, 2014, 8 (7), pp 7333–7339]

Contact resistance increases as contact length Lc decreases:

Model vs. experimentExperiment*

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Al/CNT vs. Pd/CNT contacts (simulation)

CNTFET polarity is definedby the contact material:Al/CNT ambipolar;Pd/CNT p-type

Scaling of Rc(Lc) differs muchdepending on metal type

Pd

Al

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Conclusion

Our model predicts correctly:- polarity of the CNTFET (n- or p-type), - contact resistance and its dependence on the contact lengthbased solely on ab-initio based transport calculations.

Particular results:Al yields bad n-type FET, whereas Pd yields good p-type FET for long contacts.Experimental and theoretical results for Pd are in good qualitative agreement.

Thank you for your attention!