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Page 1: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Computational Nanoelectronics

A. A. FarajianInstitute for Materials Research, Tohoku University, Sendai 980-8577,

Japan

In collaboration with

K. Esfarjani, K. Sasaki, T.M. Briere, R.V. Belosludov, H. Mizuseki, M. Mikami, Y.Kawazoe, and B.I. Yakobson

Page 2: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Overview: Molecular electronics insertion strategy; Active atom wire interconnects

Keeping the initial target application simple, cheap and unsophisticated: passive interconnects

Initial products will be silicon complements with response time of the order of second: sensors

Moving on to active devices, with novel function, form, or cost advantage

Finally; introducing entirely new generation of products: commercial delivery time of more than one decade

Molecular ElectronicsJ.M. Tour, World Scientific (2003)

Page 3: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Nanotube molecular quantum wiresCredit: C. Dekker

Page 4: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Nanotube nanotransistor Credit: C. Dekker

Page 5: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Nanotube logic nanogate Credit: C. Dekker

Page 6: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Doped nanotube bundle Credit: R. Smalley

Page 7: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Doping with C60- and Cs+

Credit: G.-H. Jeong

2 nm

4 nm

(b)

(a)

Page 8: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Formation of junction between empty and Cs+ –doped parts

Credit: G.-H. Jeong

Page 9: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Conductance of a single benzene moleculeCredit: J.M. Tour

Page 10: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

DNA conductance along axis D. Porath et al.

Page 11: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Specific systems within the prescribed scheme:

Shielded, passive/active, molecular wires: polythiophene/polyaniline inside cyclodextrines

Building upon the existing silicon base: Bi line on Si surface

Active (rectifying) device: doped nanotube junction

How good is DNA? Cheking DNA’s transport

Page 12: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Doped nanotube junction

Page 13: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Negative differential resistance

Page 14: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Rectifying effect

Page 15: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Doped Nanotube Junctions

Page 16: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Ab initio calculation:inside doping is favored by ~ 0.2 eV

Page 17: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Ab initio calculation:energetics of light and heavy dopings

Page 18: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Ab initio calculation:band structures of light and heavy dopings

Page 19: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Ab initio calculation:density of states of light and heavy dopings

Page 20: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Junction and Bulk Geometries

Page 21: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Surface Green’s Function Matching

Page 22: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Screening charge pattern for doped metallic junction

(initial shifts of chemical potentials: 2.5 eV)

Page 23: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Screening charge pattern for doped semiconducting junction (initial shifts of chemical potentials: 2.5 eV)

Page 24: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Metallic nanotube doped by a charged dopant

Page 25: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Screening charge pattern of (5,5) for an external point charge 1.0 e

Page 26: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Bi line on Si(001): relatively stable

Page 27: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Bi line on Si(001): stable

Page 28: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Hamiltonian and overlap

Using the above-mentioned basis, the Hamiltonian of the system is obtained using Gaussian 98 program

Moreover, as the basis is non-orthogonal, the overlap matrix is also obtained

The Hamiltonian and overlap matrices are then used in calculating the conductance of the system using the Green’s function approach

Page 29: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Reflected and Transmitted Amplitudes; Transmission Matrix

1,;,

;1

,;,1;11

1,;

;1

,;,1;11

1,;

),(S

)(

nnAnABA

nB

BAnn

nAnnAnAABABnBtn

nBnnBnBBBBBBnBrn

GSTVE

GGG

GGG

G

GGG

GGGG

Page 30: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Junction and Bulk Geometries

Page 31: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Conductance

2;,;

,

2

2

||),(S||)(2

),(T2

),(

nA

BAnnnB

nn

VEv

v

h

e

VEh

eVE

Page 32: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Conductance, alternative derivation

Conductance [2e2/h]:

With

Being the Green’s function of the molecule (junction part of the system)

)(Tr ),( 12 GGVE MOLMOL

)( 211

HESG MOLMOL

Page 33: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Surface Green’s functions

And

With Σ1(2) being the surface terms describing the semi-infinite parts attached to the junction part

Finally)]()()[,()( 12 EfEfVEdEVI

)(i 2)1()2(1)2(1

Page 34: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

PT attached to gold contacts

Page 35: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

PT in cross-linked Alpha CD

Page 36: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

PT in Beta CD

Page 37: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Molecular wire:transport through shielded polythiophene

Page 38: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

HOMO-LUMO energies(Hartree)

PT in ACD non-

interacting

PT in BCD interacting

PT in BCD non-

interacting

PT

LUMO -0.1288 -0.1355 -0.1273 -0.1290

HOMO -0.1366 -0.1431 -0.1378 -0.1381

Page 39: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Density of States

Page 40: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Conductance

Page 41: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Spatial Extension of MOs (n~80; E~0.3)

LUMO

HOMO

LUMO+n

Page 42: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

DNA conductance perpendicular to axis in collaboration with T.M. Briere

Au(111) STM Tip

Au(111) Substrate

Page 43: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

AT Base Pair

Page 44: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

CG Base Pair

Page 45: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Bulk Gold Contact

Page 46: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Density of States (Fermi energy ~ -0.1)

Page 47: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Conductance

Page 48: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

AT: Spatial distribution of HOMO (E ~ -0.154)

Page 49: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

AT: Spatial distribution of LUMO+n (E ~ 0.570)

Page 50: Computational Nanoelectronics A. A. Farajian Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan In collaboration with K. Esfarjani,

Conclusions:

Two stable positions for Cs along diagonal direction

Rectifying effect New nearly flat bands

via doping Alignment of Frmi

energy and van Hofe singularity: possibility of superconductivity

In DNA transport, dominant current-carrying states are localized on the hydrogen bonds

A high density of states does not necesserarily mean high conductance

AT and CG have different conductance due to differently localized states