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

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)

Nanotube molecular quantum wiresCredit: C. Dekker

Nanotube nanotransistor Credit: C. Dekker

Nanotube logic nanogate Credit: C. Dekker

Doped nanotube bundle Credit: R. Smalley

Doping with C60- and Cs+

Credit: G.-H. Jeong

2 nm

4 nm

(b)

(a)

Formation of junction between empty and Cs+ –doped parts

Credit: G.-H. Jeong

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

DNA conductance along axis D. Porath et al.

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

Doped nanotube junction

Negative differential resistance

Rectifying effect

Doped Nanotube Junctions

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

Ab initio calculation:energetics of light and heavy dopings

Ab initio calculation:band structures of light and heavy dopings

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

Junction and Bulk Geometries

Surface Green’s Function Matching

Screening charge pattern for doped metallic junction

(initial shifts of chemical potentials: 2.5 eV)

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

Metallic nanotube doped by a charged dopant

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

Bi line on Si(001): relatively stable

Bi line on Si(001): stable

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

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

Junction and Bulk Geometries

Conductance

2;,;

,

2

2

||),(S||)(2

),(T2

),(

nA

BAnnnB

nn

VEv

v

h

e

VEh

eVE

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

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

PT attached to gold contacts

PT in cross-linked Alpha CD

PT in Beta CD

Molecular wire:transport through shielded polythiophene

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

Density of States

Conductance

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

LUMO

HOMO

LUMO+n

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

Au(111) STM Tip

Au(111) Substrate

AT Base Pair

CG Base Pair

Bulk Gold Contact

Density of States (Fermi energy ~ -0.1)

Conductance

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

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

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