Seminario J.M. Molecular and Nano Electronics. Analysis, Design and Simulation

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THEORETICAL AND COMPUTATIONAL CHEMISTRY

Molecular and Nano Electronics

THEORETICAL AND COMPUTATIONAL CHEMISTRY

SERIES EDITORS

Professor P. Politzer

Department of Chemistry

University of New Orleans

New Orleans, LA 70148,U.S.A.

VOLUME 1

Quantitative Treatments of Solute/Solvent

Interactions

P. Politzer and J.S. Murray (Editors)

VOLUME 2

Modern Density Functional Theory: ATool

for Chemistry

J.M. Seminario and P. Politzer (Editors)

VOLUME 3

Molecular Electrostatic Potentials: Concepts

and Applications

J.S. Murray and K. Sen (Editors)

VOLUME 4

Recent Developments and Applications of Modern

Density FunctionalTheory

J.M. Seminario (Editor)

VOLUME 5

Theoretical Organic Chemistry

C. Párkányi (Editor)

VOLUME 6

Pauling’s Legacy: Modern Modelling of the

Chemical Bond

Z.B. Maksic andW.J. Orville-Thomas (Editors)

VOLUME 7

Molecular Dynamics: From Classical to Quantum

Methods

P.B. Balbuena and J.M. Seminario (Editors)

VOLUME 8

Computational Molecular Biology

J. Leszczynski (Editor)

VOLUME 9

Theoretical Biochemistry: Processes and Properties

of Biological Systems

L.A. Eriksson (Editor)

Professor Z.B. Maksi´c

Rudjer Boškovi´c Institute

P.O. Box 1016,

10001 Zagreb, Croatia

VOLUME 10

Valence Bond Theory

D.L. Cooper (Editor)

VOLUME 11

Relativistic Electronic StructureTheory, Part 1.

Fundamentals

P. Schwerdtfeger (Editor)

VOLUME 12

Energetic Materials, Part 1. Decomposition, Crystal

and Molecular Properties

P. Politzer and J.S. Murray (Editors)

VOLUME 13

Energetic Materials, Part 2. Detonation,

Combustion

P. Politzer and J.S. Murray (Editors)

VOLUME 14

Relativistic Electronic StructureTheory,

Part 2. Applications

P. Schwerdtfeger (Editor)

VOLUME 15

Computational Materials Science

J. Leszczynski (Editor)

VOLUME 16

Computational Photochemistry

M. Olivucci (Editor)

VOLUME 17

Molecular and Nano Electronics:

Analysis, Design and Simulation

J.M. Seminario (Editor)

VOLUME 18

Nanomaterials: Design and

Simulation

P.B. Balbuena and J.M. Seminario (Editors)

THEORETICAL AND COMPUTATIONAL CHEMISTRY

Molecular and Nano Electronics:Analysis,

Design and Simulation

Edited by

J. M. Seminario

Department of Chemical Engineering

and Department of Electrical and Computer Engineering

Texas A&M University

College Station, Texas, USA.

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Contents

Preface vi

1 Metal–molecule–semiconductor junctions: an ab initio analysis 1

Luis A. Agapito and Jorge M. Seminario

2 Bio-molecular devices for terahertz frequency sensing 55

Ying Luo, Boris L. Gelmont, and Dwight L. Woolard

3 Charge delocalization in (n, 0) model carbon nanotubes 82

Peter Politzer, Jane S. Murray and Monica C. Concha

4 Analysis of programmable molecular electronic systems 96

Yuefei Ma and Jorge M. Seminario

5 Modeling molecular switches: A flexible molecule anchored to a surface 141

Bidisa Das and Shuji Abe

6 Semi-empirical simulations of carbon nanotube properties under electronic

perturbations 163

Yan Li and Umberto Ravaioli

7 Nonequilibrium Green’s function modeling of the quantum transport of

molecular electronic devices 187

Pawel Pomorski, Khorgolkhuu Odbadrakh, Celeste Sagui, and Christopher Roland

8 The gDFTB tool for molecular electronics 205

A. Pecchia, L. Latessa, A. Gagliardi,Th. Frauenheim and A. Di Carlo

9 Theory of quantum electron transport through molecules as the bases of

molecular devices 233

M. Tsukada, K. Mitsutake and K. Tagami

10 Time-dependent transport phenomena 247

G. Stefanucci, S. Kurth, E. K. U. Gross and A. Rubio

Index 285

Preface

The new field of molecular and nano-electronics brings possible solutions for a post-

microelectronics era. Microelectronics is dominated by the use of silicon as the preferred

material and photo-lithography as the fabrication technique to build binary devices

(transistors). Properly building such devices yields gates, able to perform Boolean

operations and to be combined yielding computational systems capable of storing,

processing, and transmitting digital signals encoded as electron currents and charges.

Since the invention of the integrated circuits, microelectronics has reached increasing

performances by decreasing strategically the size of its devices and systems, an approach

known as scaling-down, which simultaneously allow the devices to operate at higher

speeds. However, as devices become faster and smaller, major problems have arisen

related to removal of heat dissipated by the transistors and physical limitations to keep

two well-defined binary states; these problems have triggered research into new alter-

natives using components fabricated by different procedures (self-assembly, chemical

deposition, etc.), which may encode information using lower energetic means.

The goal of this book is to bring together the most active researchers in this new

field, from the entire world. These researchers illustrate what is probably the only way

for success of molecular and nano-electronics: a theory guided approach to the design

of molecular- and nano-electronics. The editor thanks all the contributors for their kind

collaboration, effort, and patience to put together this volume, and acknowledges the

dedication of Ms Mery Diaz who helped compiling this camera-ready volume. The editor

also thanks the continuous support of the US Army Research Office to the development

of this new field.

Jorge M. Seminario

Texas A&M University

Molecular and Nano Electronics: Analysis, Design and Simulation

J. M. Seminario (Editor)

Chapter 1

Metal–molecule–semiconductor junctions:

An ab initio analysis

Luis A. Agapito and Jorge M. Seminario

Department of Chemical Engineering and Department of Electrical and Computer

Engineering, Texas A&M University, 3122 TAMU, College Station, TX 77843, USA.

seminario@tamu.edu

1. Introduction

The ability to calculate the current–voltage characteristics through a single molecule is

essential for the engineering of molecular electronic devices [1, 2]. Because quantum-

mechanical effects prevail at atomistic sizes, there is a need to implement and develop

precise ab initio quantum chemistry techniques rather than using those originally devel-

oped for microscopic and mesoscopic systems.

In order to evaluate experimentally the use of single molecules as electronic devices,

the usual approach is to attach them to macroscopic contacts to be able to measure their

electrical properties. However, this is not a direct requirement for the design but just to

help us to understand their electrical behavior and to make sure that we have the correct

tools to model their behavior. In practice, molecular devices should not be connected to

macroscopic contacts when they are components of a circuit. The whole advantage of

having nanosized devices would be lost if they are connected to macroscopic or even

microscopic contacts. Nevertheless, the presence of macroscopic contacts influences

greatly the electrical properties of a single molecule [3–5]; thus our community tries to

test the metal–molecule–metal junction as an independent unit instead of evaluating the

isolated molecule. Experimentally, it has been challenging to measure metal–molecule–

metal junctions with metallic contacts separated by a distance of ∼20 Å or less. Only

few experiments until now have claimed to have been able to address a single molecule

between two macroscopic gold contacts [6].

Fortunately, quantum-chemistry techniques can be used to study precisely

isolated [7, 8] and interconnected molecules. We use the Density Functional Theory

(DFT) of a quantum-chemistry flavor [9] to determine the electronic properties of

molecules; a mathematical formalism based on the Green function (GF) is used then

2 Luis A. Agapito and Jorge M. Seminario

to account for the effect of the contacts on the molecule keeping the realistic chemical

nature of the sandwiched molecule. These techniques can also be used to study scenarios

where the information is not coded in electron currents [10–12].

The electron transport in quantum chemistry is studied as a chemical reaction or as a

state transition through junctions of atomic sizes and can also be approximately described

in terms of mesoscopic physics models in a coherent regime, where the electrons travel

with a given probability, sequentially one after the other through the molecule without

electron–electron or phonon–electron interactions. This kind of transport is described

by the Landauer formalism [13]. Here, we use our DFT-GF technique [14] to make an

atomistic adaptation of the Landauer formalism for the calculation of current through

molecular junctions.

Specifically, we focus our study on an oligo-phenylene-ethynylene (OPE) molecule,

which has been proposed as a candidate for a molecular electronic device [15]. Similar

OPE molecules, attached to gold contacts, have shown two distinctive states of con-

ductance, namely a high- and a low- conductance state. Those states can be used to

encode information as logic “0” and “1,” hence, their importance. Switching between

the two states of the molecule is mainly attributed to two different mechanisms: changes

in charge state [15] and changes in conformational states [16].

We use our DFT-GF formalism to calculate the conductance through metal–nitroOPE–

metal junctions in several charge and conformational states. Two different metallic

materials are evaluated in this work: the commonly used gold and the promising carbon

nanotube (CNT).

2. Electron transport at interfaces

From the computational viewpoint, primarily two types of molecular systems are

involved in the work presented here: finite and extended systems. Finite systems refer

to molecules or nanoclusters with a finite number of atoms whereas an extended system

refers to a crystalline such as the contacts. The tools to study both types of systems

are well-established in the computational chemistry field [1, 2, 17–20]. The Gaussian

03 [21] is capable of performing calculations of systems with periodic boundary con-

ditions in one, two and three dimensions. However, systems that combine both a finite

and an extended character represent a new and challenging area of research; this is the

case for the study of a single molecule (finite) adsorbed to contact tips (modeled as an

infinite crystal material).

The discrete electronic states of an isolate molecule are obtained by solving the

Schrödinger equation; we solve that equation following a DFT approach. When the

molecule is adsorbed on a contact tip, the continuous electronic states of bulk material

modify the discrete electronic states of the molecule. In other words, electrons from the

contacts leak into the molecule, modifying its electronic properties. A mathematical for-

malism based on the Green function is used to account for the effect of the bulk contacts.

2.1. Electronic properties of molecules and clusters

The electronic properties of a molecular system can be calculated from its auxiliary

wavefunction, which is built as a determinant of molecular orbitals (MOs). MOs are

Metal–molecule–semiconductor junctions 3

linear combinations of atomic orbitals (AOs) from all the atoms composing the system.

In other words, the atomic orbitals are the basis functions, , used to expand the MOs

shown in Eq. (1).

2.1.1. Basis functions

Practical procedures represent the AO using linear combination of Gaussian functions

also called primitives. Gaussian-type functions (GTFs) or primitives, which form a

complete set of functions, are defined in their Cartesian form as:

ijk

=Kx

−r

(1)

where i j k are nonnegative integers,  is a positive orbital exponent, x

y

z

, are

Cartesian coordinates and r

is the radial coordinate. The subscript b indicates that the

origin of the coordinates is at the nucleus b. K is a normalization constant.

The sum l = x +y +z determines the angular momentum of an atomic orbital.

Depending on whether l equals 0, 1, 2, , the GTF is called s-, p-, d-,  type

respectively. The principal quantum number n determines the range of the exponents

for a particular function.

A basis function 

, also referred to as contracted Gaussian-type orbitals (GTOs), is

defined as a normalized linear combination of GTFs (g

) or primitives:



(2)

where d

are called contraction coefficients. Basis sets published in the literature

provide the values of , Eq. (1), and d

, Eq. (2). A basis function is constructed to

resemble a given AO. Throughout this work, two basis sets are used: the LANL2DZ,

which includes an effective core potential and the 6-31G(d) also represented as 6-31G

∗

in the specialized literature.

For instance, in the 6-31G(d) basis set, the inner shell 1s atomic orbital of carbon is

formed by contracting six GTFs, as follows:



u=1



 (3)

where the contraction coefficients d

and the Gaussian exponents 

are given in

Table 1. For an s-type function, the GTF given in Eq. (1) simplifies to

 = e

−x



(4)

where the normalization constant K, defined in Eq. (1), has been included in the

contraction coefficients.

2.1.2. Density functional theory

For a polyatomic molecular system, the electronic non-relativistic Hamiltonian can be

written as

=−







j>i

(5)