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First principles simulations of

electron transport at the

molecule-solid interface

Hao Ren

School of Biotechnology

Royal Institute of Technology

Stockholm 2010

c⃝ Hao Ren, 2010

ISBN 978-91-7415-629-4

ISSN 1654-2312

TRITA-BIO-Report 2010:8

Printed by Universitetsservice US-AB,

Stockholm, Sweden, 2010

To my wife Xuan and to my parents.

Abstract

In this thesis I concentrate on the description of electron transport properties of

microscopic objects, including molecular junctions and nano junctions, in partic-

ular, inelastic electron tunneling in surface-adsorbate systems are examined with

more contemplations. Boosted by the rapid advance in experimental techniques

at the microscopic scale, various electric experiments and measurements sprung

up in the last decade. Electric devices, such as transistors, switches, wires, etc.

are expected to be integrated into circuit and performing like traditional semi-

conductor integrated circuit (IC). On the other hand, detailed information about

transport properties also provides new physical observable quantities to charac-

terize the systems. For molecular electronics, which is in the state of growing up,

its further applications demands more thorough understanding of the underlying

mechanism, for instance, the effects of molecular configuration and conformation,

inter- or intra-molecular interactions, molecular-substrate interactions, and so on.

Inelastic electron tunneling spectroscopy (IETS), which reflects vibration features

of the system, is also a finger print property, and can thus be employed to afford the

responsibility of single molecular identification with the help of other experimental

techniques and theoretical simulations.

There are two parts of work presented in this thesis, the first one is devoted to

the calculation of electron transport properties of molecular or nano junctions: we

have designed a negative differential resistance (NDR) device based on graphene

nanoribbons (GNRs), where the latter is a star material in scientific committee

since its birth; The transport properties of DNA base-pair junctions are also exam-

ined by theoretical calculation, relevant experimental results on DNA sequencing

have been explained and detailed issues are suggested. The second part focused on

the simulation of scanning tunneling microscope mediated IETS (STM-IETS). We

have implemented a numerical scheme to calculate the inelastic tunneling intensity

based on Tersoff-Hamann approximation and finite difference method, benchmark

results agree well with experimental and previous theoretical ones; Two applica-

tions of single molecular chemical identification are also presented following bench-

marking.

v

Preface

The work presented in this thesis has been carried out at the Department of The-

oretical Chemistry, School of Biotechnology, Royal Institute of Technology, Stock-

holm, Sweden and National Laboratory for Physical Sciences at the Microscale,

University of Science and Technology of China, Hefei, China.

List of papers included in the thesis

Paper I Graphene nanoribbons as a negative differential resistance device

Hao Ren, Qunxiang Li, Yi Luo, and Jinlong Yang

Appl. Phys. Lett. 94, 173110(2009).

Paper II Important structural factors controlling the conductance of DNA pairs

in molecular junctions

Xiaofei Li, Hao Ren, Ling-Ling Wang, Ke-Qiu Chen, Jinlong Yang, and Yi Luo

J. Phys. Chem. C, submitted.

Paper III Simulation of inelastic electronic tunneling spectra of adsorbates from

first principles

Hao Ren, Jinlong Yang, and Yi Luo

J. Chem. Phys. 130, 134707(2009).

Paper IV Identifying configuration and orientation of adsorbed molecules by

inelastic electron tunneling spectra

Hao Ren, Jinlong Yang, and Yi Luo

J. Chem. Phys., submitted.

Paper V Determining tautomer structures of a melamine molecule adsorbed on

Cu(001) by inelastic electron tunneling spectroscopy

Shuan Pan, Hao Ren, Aidi Zhao, Bing Wang, Yi Luo, Jinlong Yang, and J. G.

Hou

in manuscript.

List of papers not included in the thesis

Paper I Quantum dot based on Z-shaped graphene nanoribbon: First-principles

study

Hao Ren, Qunxiang Li, Qinwei Shi, and Jinlong Yang, Chin. J. Chem. Phys. 20,

489(2007).

Paper II Edge effects on the electronic structures of chemically modified arm-

chair graphene nanoribbons

Hao Ren, Qunxiang Li, Haibin Su, Qinwei Shi, and Jinlong Yang

arXiv:0711.1700 [Cond-mat.matrl-sci](2007).

Paper III Strain effect on electronic structures of graphene nanoribbons: a first-

principles study

Lian Sun, Qunxiang Li, Hao Ren, Haibin Su, Qinwei Shi, and Jinlong Yang

J. Chem. Phys. 129, 074704(2009).

Paper IV Switching mechanism of photochromic diarylethene derivatives molec-

ular junctions

Jing Huang, Qunxiang Li, Hao Ren, Haibin Su, Qinwei Shi, and Jinlong Yang

J. Chem. Phys. 127, 094705(2007).

Paper V Single quintuple bond [PhCrCrPh] molecule as a possible molecular

switch

Jing Huang, Qunxiang Li, Hao Ren, Haibin Su, and Jinlong Yang

J. Chem. Phys. 125, 184713(2006).

Paper VI Theoretical study on the CF3CH3 + OH reaction

Huanjie Wang, Hao Ren, Dacheng Feng, and Yueshu Gu

Chem. J. Chin. Univ. 26, 1682(2005).

Paper VII Tunneling the electronic structures of graphene nanoribbons through

chemical edge modification: A theoretical study

Zhengfei Wang, Qunxiang Li, Huaixiu Zheng, Hao Ren, Haibing Su, Qinwei Shi,

and Jie Chen

Phys. Rev. B 75, 113406(2007).

vii

Comments on my contribution to the papers included

• I was responsible for the ideas, calculation and writing of the manuscripts of

paper I and IV;

• I was responsible for the formula derivation, calculation and writing of the

manuscript of paper III;

• I was responsible for part of the calculations and assist in the writing of the

manuscript of paper II;

• In paper V, I was responsible for the theoretical modeling and analysis, I

also assisted the writing of the manuscript.

viii

Acknowledgments

It is a pleasure to have this chance to express my gratitude and appreciation to

the people who helped me.

My supervisor Prof. Yi Luo played the most important role in the shaping of this

thesis. It was three years ago Prof. Luo gave me the chance to study in Sweden

and hold me from then on. I appreciate Prof. Luo introduced me a more fruitful

work style and his constant encouragement and enthusiasm. His breezy, optimistic

and surefooted attitude impressed me a lot and will affect me in my future life.

I would like to thank my supervisor in China, Prof. Jinlong Yang in University

of Science and Technology of China (USTC). He opened me a window to the

exciting academic life and provided the chance to study in Stockholm. His superior

knowledge, discerning intuition, rigorous attitude, and wide spectrum of research

interests set me an example that I intend following.

I would also like to thank Prof. Qunxiang Li in USTC, who accelerated my pace

to the fantasying field of nano-science and technology. My gratitude to Profs.

Dacheng Feng, Chengbu Liu, and Dongju Zhang in Shandong Unversity, China,

for their guidance when I was a undergraduate. Also thank Prof Haibin Su in

Nanyang Technological University, Singapore, for his guidance and encouragement.

Dr. Jun Jiang, Dr. Hongjun Xiang (USTC) and Dr. Bin Li (USTC) helped me a

lot in the early stage of implementation of our code. Great importance should also

be addressed of which fruitful discussions in experimental details and techniques

with Prof. Bing Wang (USTC) and Dr. Shuan Pan (USTC).

Frequently occurred discussions with Drs. Wenhua Zhang, Erjun Kan, Zhenpeng

Hu, Shuanglin Hu, Mrs. Keyan Lian, Misters Qiang Fu, Xiaofei Li, Ying Zhang, Sai

Duan, Weijie Hua, Guangjun Tian occasionally inspire me new ideas and enjoyed

me a lot. Lili Lin and Xin Li (DLUST) assisted me to prepare some figures of this

thesis.

Thanks to Drs. Zhenyu Li, Lanfeng Yuan, Xiaojun Wu, and Jing Huang for their

guidance and help.

The active and dynamic environment in Dept. of Theoretical Chemistry is exciting

and lead to high efficiency and happy working. I really appreciate the head of our

department — Prof. Hans Agren, and I’m sincerely thanks to all the people in the

department.

Thanks to the countless guys we live together in the last three years, without whom

I can not imagine the complete of the present thesis and how I can tide over the

ix

lonely days. I am glad to give my thanks to all of them: Bin Gao, Hui Cao, Kai

Fu, Na Lin, Tiantian Han, Kai Liu, Feng Zhang, Jicai Liu, Shilu Chen, Yuejie Ai,

Qiong Zhang, Zhijun Ning, Xing Chen, Xiao Cheng, Yuping Sun, Xiuneng Song,

Xin Li (ECUST), Fuming Ying, Jiayuan Qi, Zhihui Chen, Ke Zhao, Qun Zhang,

Ke Lin, Chunze Yuan, Qiu Fang, and many other friends in our group. Also thanks

to all the members in Prof. Yang’s group in USTC.

Thanks to China Scholarship Council (CSC) for the two years’ financial support

during 2007-2009.

Finally, my gratitude to my wife Xuan for her sweet love, unconditional under-

standing and support, immense patience; And to my parents, for their sincerely,

warmest and totally paying out.

x

Contents

1 Introduction 1

2 Electronic Structure Methods 5

2.1 Quantum theory and electronic structure . . . . . . . . . . . . . . . 5

2.2 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Non-relativity approximation . . . . . . . . . . . . . . . . . 7

2.2.2 Born-Oppenheimer Approximation . . . . . . . . . . . . . . 7

2.2.3 Independent-electron approximation . . . . . . . . . . . . . 8

2.3 Hartree-Fock approximation and self-consistent method . . . . . . . 9

2.4 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 Thomas-Fermi-Dirac Approximation . . . . . . . . . . . . . 11

2.4.2 Hohenberg-Kohn Theorem . . . . . . . . . . . . . . . . . . . 11

2.4.3 Kohn-Sham equation . . . . . . . . . . . . . . . . . . . . . . 12

2.4.4 Exchange-Correlation functionals . . . . . . . . . . . . . . . 14

2.5 Non-equilibrium Green’s function . . . . . . . . . . . . . . . . . . . 15

2.5.1 System and models . . . . . . . . . . . . . . . . . . . . . . . 15

2.5.2 Current Calculation . . . . . . . . . . . . . . . . . . . . . . . 17

3 Nano and Moleculear Electronics 19

3.1 Progress in molecular electronics . . . . . . . . . . . . . . . . . . . . 20

3.2 Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Scanning tunneling techniques . . . . . . . . . . . . . . . . . 22

3.2.2 Molecular junctions . . . . . . . . . . . . . . . . . . . . . . . 24

xi

CONTENTS

4 Graphene related materials 27

4.1 Geometric and electronic structures of graphene . . . . . . . . . . . 27

4.2 Preparation and characterization . . . . . . . . . . . . . . . . . . . 30

4.2.1 Physical approaches . . . . . . . . . . . . . . . . . . . . . . 31

4.2.2 Chemical approaches . . . . . . . . . . . . . . . . . . . . . . 31

4.2.3 Characterization of graphene . . . . . . . . . . . . . . . . . . 33

4.3 Graphene nanoribbons . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3.1 Fabrication of GNRs . . . . . . . . . . . . . . . . . . . . . . 34

4.3.2 Structural and electronic properties of GNRs . . . . . . . . . 35

5 Inelastic Electron Tunneling in Surface-Adsorbate Systems 39

5.1 Surface science and STM . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 STM mediated inelastic tunneling spectra . . . . . . . . . . . . . . 41

5.3 Simulation of STM-IETS . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3.1 Calculation of Tunneling Current . . . . . . . . . . . . . . . 43

5.3.2 Inelastic electron tunneling . . . . . . . . . . . . . . . . . . . 44

6 Summary of papers 49

6.1 Molecular electronics . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.1.1 AGNR as a NDR device . . . . . . . . . . . . . . . . . . . . 49

6.1.2 Structural factors controlling the conductance of DNA pairs

junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.2 Inelastic tunneling spectra . . . . . . . . . . . . . . . . . . . . . . . 51

6.2.1 Method implementation and benchmarks . . . . . . . . . . . 51

6.2.2 Identifying adsorption configuration and orientation of cis-

2-butene adsorbed on Pd(110) surface . . . . . . . . . . . . . 53

6.2.3 Melamine tautomers adsorbed on Cu(100) surface . . . . . . 54

References 57

xii

1

Introduction

野马也，尘埃也，生物之以息相吹也；天之苍苍，其正色邪？其远而无

所至极也。

Zhuang-Zi(《庄子·逍遥游》, ∼ 369 B.C. — 286 B.C.)

Human’s cognition of nature evolves with the developments in science and tech-

nology. Probably the most familiar examples to the nowadays people are the

revolutions at the beginning of the last century that gave birth to the new physics:

relativity and quantum mechanics. It is commonly accepted that quantum the-

ory is suitable to describe microscopic processes occur in atoms, molecules or the

so-called nano-scale objects with dimensions from few angstroms to hundreds of

nanometers. The more interesting is, even in such a narrow area, starkly contrasted

viewpoints appears from time to time. In the early 1950s, Erwin Schrodinger be-

lieved that it is not possible to perform experiments to manipulate microscopic

particles such as electrons, atoms, or molecules [1]. However, only seven year lat-

ter, in 1959, Richard Feynman made his famous speech “There’s Plenty of Room

at the Bottom” [2], where he claimed that there is no physical principles that

restrict such microscopic manipulations, and different laws, different phenomena,

and different applications were expected in the virtue of pronounced quantum ef-

fects introduced by the small sizes. In fact, many of the phenomena Feynman

mentioned have been realized and are well known. For instance, high resolution

microscopes and minimized electric devices are not at all surprising and are playing

important roles in the daily life.

In order to reveal the underlying physics and chemistry of the emerging new phe-

nomena, theoretical investigations are inevitable and with great importance. On

the other hand side, just as described in the above paragraph, both predictions

1

1 Introduction

proposed from a theoretical point of view and theoretical studies will still play an

important role in the future evolution of science and technology.

As the most appropriate theory framework to describe atomic-scale objects and

phenomena [3], quantum theory has been the primary tools in the theoretical in-

vestigation of atoms, molecules and condensed matter. Atoms, consist of nuclei

and electrons, are the fundamental particles in chemistry, determines the prop-

erties of substance. Both the dynamics of nuclei and electrons can be described

by quantum theory, and in this context, the physical and chemical properties of

molecules, solids or even more complicated systems can be explained or predicted

in terms of quantum theory, at least in principle.

There seems a beautiful future when quantum mechanics is applied in the de-

scription of microscopic systems. Just as the famous proposition by P. A. M.

Dirac eighty years ago, that we had got almost all the desired rules to describe

the world, and the only questions left were the complexity of equations and the

lack of adequate mathematical skills to solve them [4]. The optimistic estima-

tion continued many years, much effort has been devoted into the development of

mathematical skills and numerical methods, such as the self-consistent field (SCF)

method [5], density functional theory (DFT) [6], quantum Monte Carlo methods

[7], and so on. However, the equations are so complex due to the so many degrees

of freedom. As a consequence, there is no exact analytic solutions for almost all

the systems encountered in practice except extremely simple systems.

Just as described in the quotation at the beginning of this chapter, all the living

and non-living objects in the world are interacting with each other by some kind

of breath, in such a manner, the sky is blue. Yet is blue the true color of the sky?

It is so far that beyond human’s scope. The key problem of electronic structure

theory is how to take into account of electron correlations, which appears when

more than one electron exists. The number of electrons in normal condensed

systems concerned is usually has the order of magnitude of 1023, in this context, the

only practical approach is to calculate the properties approximately, by employing

various approximations to models with accessible dimensions reduced by means of

consideration of symmetry, sacrifice of precision of less important part, etc.

Dissenting opinion to the reductionist hypothesis that everything can be reduced

to the few set of fundamental laws, however, was proposed by P. W. Anderson,

who believes that there would be new properties at each level of complexity, and

research of new rules under which new behaviors appear is also required [8]. Thus

in this constructionist context, chemistry is such a discipline obey the laws of many-

body physics, and the theoretical aspect of chemistry mainly concerns many-body

problem and its expression in systems consist of atoms, molecules and condensed

2

matter.

In this thesis, I will concentrate on the electronic structure theory and its applica-

tions at molecule-surface interfaces, both the electronic and transport properties of

such systems are investigated by using state-of-the-art simulation methods based

on electronic structure theory.

One of my topics is the simulation of electronic transport in molecular electronics.

Molecular electronics can be attributed to a growing point of Feynman’s speech

[2], and the first theoretical prediction is made by Aviram and Ratner, in 1974 [9],

where the authors proposed specific electric characteristics could be achieved by

constructing specific molecular devices and integrate into electric circuits. Thanks

to the advances in microscopic technologies such as scanning probe microscopy

[10, 11], molecule junction technique [12–14], people were able to construct such

devices at single molecular level in the recent years. Corresponding theoretical

simulation is desired in the further development of the new area, aimed to un-

derstanding of new behaviors observed in experiments, to gathering up new rules

from practical work, to predicting new phenomena would appear in specific sys-

tems, and to designing new devices. At present, the most widely used simula-

tion method in molecular electronics is non-equilibrium Green’s function (NEGF)

technique combined with DFT, several simulation schemes have been implemented

[15–21] and contributed a lot to the advance of this area. By employing the NEGF-

DFT scheme, we designed a negative differential resistance (NDR) device based

on graphene nanoribbons (GNRs), which exhibit robust NDR characteristics for

various systems with different sizes. We also re-examined an experimental work

devoted to DNA sequencing [22, 23], in which different DNA base pairs can be

identified by measuring their difference in conductance due to different number

of hydrogen bonds in the junctions. By performing first principles calculations,

we approved the possibility of such a electric approach to sequencing DNA pairs,

although the measurements in experiments was not exact enough to do so.

The other topic is devoted to the simulation of inelastic electron tunneling spec-

tra (IETS) in surface-adsorbate systems. IETS reflects the vibration features of

system, new tunneling channels would be opened when the injecting energy of

electrons is large enough to excite corresponding vibration mode. Usually these

inelastic contribution is considered to be small compared with its elastic coun-

terpart, and is omitted in many current or conductance oriented measurements.

However, IET would prominent in the quadratic differential of current respect to

voltage (d2I/dV 2), which can be directly measured or calculated numerically from

current-voltage characteristics. Due to its vibrational nature, IETS is a finger

print properties of the system, thus is powerful in the characterization of chemical

3

1 Introduction

species, geometry configuration or conformation, inter- or intra-molecular inter-

actions, molecule-surface interactions, and so on. Experimentally, IETS measure-

ment could be carried out by using molecular junction techniques or scanning tun-

neling technique. We implemented a scheme based on the finite difference method

proposed by Lorente and Persson [24, 25] to simulate IETS in surface-adsorbate

systems at first-principles level, the scheme is employed combined with the latest

experimental work, chemical identifications at single molecular level is achieved.

4

2

Electronic Structure Methods

The biggest difficulty in the modern electronic structure theory is to find an ap-

propriate approach to describe electron correlation interaction. In this point of

view, the developing of first principles calculation can be regarded as a journey

for further approximation about electron correlation along with the improvement

of calculation ability, for both hardware and software. Following this thread, in

this chapter, I briefly introduced the history of electronic structure theory and

first-principles calculations and then a concise description of Hartree-Fock approx-

imation and self-consistent method is presented, followed by a superficial depiction

of the widely used density functional theory and non-equilibrium Green’s function

method, where the later is employed in the calculation of electron transport prop-

erties in molecular devices.

2.1 Quantum theory and electronic structure

Most of the systems in practice we concerned are many-body systems, especially

for condensed matter systems, where the number of electrons possesses an order

of magnitude of Avogadro constant (NA ∼ 6.02×1023). As a result of the massive

degrees of freedom, we should adopt a statistical physics point of view to handle

electronic structure problems. In 1925, W. Pauli proposed the famous exclusion

principle, which claimed it is not possible that two electrons occupy a same quan-

tum state simultaneously [26]. Exclusion principle could be further employed in the

explanation of the periodic table of chemical elements. Hereafter, E. Fermi gener-

alized Pauli’s exclusion principle into a statistical rule of non-interacting particles,

5

2 Electronic Structure Methods

e.g. Fermi-Dirac statistics:

fi =1

eβ(εi−µ) + 1(2.1)

where, fi is the occupation number of electrons on the i-th energy level, β = 1/kBT ,

relates to Boltzmann constant kB and temperature T , εi is the i-th eigenenergy,

µ is the chemical potential of system. Fermi-Dirac statistics and its counterpart

Bose-Einstein statistics are the fundamental rules for microscopic particles, corre-

sponding to fermions and bosons, respectively, and guarantee the wave functions

are antisymmetric or symmetric during exchanging two of N identical fermions or

bosons.

The procedure of simulating physical properties of system by using quantum me-

chanics is just the procedure of solving many-body Schrodinger equation of the

system. We must construct the Hamiltonian of the system first, for example, the

Hamiltonian of a typical many particle system can be written as the following

without any difficulty:

H = He +HI +HeI (2.2)

where

He =∑

i

pi2

2me

+∑

i<j

Vee(ri − rj)

HI =∑

I

pI2

2MI

+∑

I<J

VII(RI −RJ)

HeI =∑

iI

VeI(RI − ri)

(2.3)

here, ri and RI are the coordinates of the i-th electron and the I-th nucleus,

Vee, VII and VeI represent the interactions between electrons, nuclei and electron-

nucleus, respectively. Further consideration about other boundary conditions, such

as relativistic effects, spin, or electromagnetic filed, could be added as terms of

Hamiltonian.

Owing to the complexity of the problem, it is obvious that considering all the

degrees of freedom equally from an “ab-initio” manner is impossible. Thus various

approximations is necessary to reduce the calculation into a acceptable level.

6

2.2 Approximations

2.2 Approximations

The most rudimental approximations in quantum chemistry are non-relativity

approximation, Born-Oppenheimer approximation, and independent-electron ap-

proximation (Hartree approximation). These three approximations greatly reduced

the complexity of the problems we faced, thus forming the foundation of the whole

quantum chemistry. I will briefly describe these important ideas in the following.

2.2.1 Non-relativity approximation

As we all know that, the dynamics of massive body or objects with speed com-

parable with that of light could only be described properly in the framework of

relativity. In first principles calculations, thanks to the small mass of electrons and

most of the atoms, a non-relativity description should be exact enough. However,

consideration of relativistic effects is essential for heavy atoms, due to the high

speed of their core electrons [27].

There are several approaches to include relativistic effects into first-principles cal-

culation. For instance, relativistic effects can be directly included in the aug-

mentation method by using pure spin functions as basis[28–30], where these spin

functions are generated by solving relativistic radial equation. Or the relativis-

tic effects can be included in the building of pseudopotentials, during which the

relativistic Dirac equation is employed to carrying out atomic calculations, and

these relativistic pseudopotentials can be directly used to construct Hamiltonian

in following calculations[31, 32]. We use the pseudopotential approach to include

relativistic effects in our calculation if necessary in this thesis.

2.2.2 Born-Oppenheimer Approximation

Born-Oppenheimer approximation is also called adiabatic approximation. In the

Hamiltonian Eq. (2.3), there is only one term, of which the value is small enough

to be omitted in an accrual calculation: the kinetic energy term of nuclei∑

Ip2

I

2MI.

Compared with the mass of electrons, that of nuclei is immensely large. Even for

the lightest hydrogen atom, the ratio between the masses of nucleus and electron is

at the magnitude of order 103. Hence, we can approximate the masses of nuclei are

infinity, thus all the kinetic terms of nuclei can be omitted, then the Hamiltonian

can be written as:

H = T + Vext + Vint + EII (2.4)

7


For simplicity, Hartree atomic unit is usually used in the deductions and calcula-

tions, where h = me = e = 4π/ϵ0 = 1. The terms in the above equation can thus

be expressed as: Kinetic energy T ,

T =∑

i

−1

2∇2

i , (2.5)

where ∇2 = ∂2

∂x2 + ∂2

∂y2 + ∂2

∂z2 is Laplace operator.

The external potential of electrons from nuclei Vext,

Vext =∑

i,I

VI(|ri −RI |) (2.6)

the Coulomb interactions among electrons Vint,

Vint =1

2

∑

i=j

1

|ri − rj|(2.7)

and the last term EII , represents the classical Coulomb interactions between nuclei,

is an constant for a specific configuration.

With the help of Born-Oppenheimer approximation, the number of degrees of free-

dom of the system is further reduced, all the contribution from nuclei interactions

is nothing but a constant.

2.2.3 Independent-electron approximation

In fact, the so-called independent-electron approximation can be classified as two

approaches [33], they are Hartree approximation and Hartree-Fock approximation,

where the latter takes into account the antisymmetric wave functions under ex-

changing particles for fermions systems. I will only describe Hartree approximation

in this section, and leave its further development in the next, combined with the

self-consistent method.

Hartree approximation was proposed in 1928, by D. R. Hartree [5], in which the

complex interactions among electrons can be approximated as a single electron

moving in an effective field composed by the other electrons and all the nuclei,

therefore, the many electron problem is simplified as a spherical potential system.

The inter-electron Coulomb interactions in Eq. (2.7) can be expressed as

Vint =∑

i

vHi (2.8)

where the Hartree potential vHi is the average potential that the i-th electron

experiences.

8

2.3 Hartree-Fock approximation and self-consistent method

2.3 Hartree-Fock approximation and self-consistent

method

There is no consideration of the antisymmetric nature of electron wave functions

in the original Hartree approximations [5]. In 1930, Fock used an antisymmetrized

determinant wave function to solve the time-independent Schrodinger equation

HeffΨσi (r) =

[− h2

2me

∇2 + V σeff (r)

]Ψσ

i (r) = ϵσi Ψσi (r) (2.9)

where V σeff (r) is the effective potential experienced by electron with spin σ at

position r. For N-electron system, the single Slater determinant can be written as

[34]:

Ψ =1

(N !)1/2

∣∣∣∣∣∣∣∣∣

ϕ1(r1, σ1) ϕ1(r2, σ2) ϕ1(r3, σ3) · · ·ϕ2(r1, σ1) ϕ2(r2, σ2) ϕ2(r3, σ3) · · ·ϕ3(r1, σ1) ϕ3(r2, σ2) ϕ3(r3, σ3) · · ·

......

.... . .

∣∣∣∣∣∣∣∣∣(2.10)

where ϕi(rj, σj) is the single-electron spin orbital, it’s the product of position

component ψi(ri) and spin component αi(σi).

According to the variational method, the ground state energy of system has the

following form [34, 35]:

E = ⟨Ψ|H|Ψ⟩ =∑

i,σ

∫drψσ∗

i (r)

[−1

2∇2 + Vext(r)

]ψσ

i (r) + EII

+1

2

∑

i,j,σi,σj

∫drdr′ψσi∗

i (r)ψσj∗j (r′)

1

|r− r′|ψσii (r)ψ

σj

j (r′)

− 1

2

∑

i,j,σ

∫drdr′ψσ∗

i (r)ψσ∗j (r′)

1

|r− r′|ψσj (r)ψσ

i (r′)

(2.11)

the first term in Eq (2.11) is single particle energy, the second and third terms

are Coulomb interaction and exchange interaction between electrons, respectively.

The Coulomb term is also called Hartree term:

EHartree =1

2

∫drdr′

n(r)n(r′)

|r− r′| (2.12)

where n(r) is the electron density at position r. Since the spin orbitals of different

spin degree of freedoms mutually orthogonal to each other, only exchange among

electrons with same spin contributes.

9


Variate energy respect to all the variables, we then get the Hartree-Fock equation

−1

2∇2 + Vext(r) +

∑

j,σj

∫dr′ψ

σj∗j (r′)ψ

σj∗j (r′)

1

|r− r′|

ψσ

i (r)

−∑

j

∫dr′ψσ∗

j (r′)ψσi (r′)

1

|r− r′|ψσi (r) = ϵσi ψ

σi (r)

(2.13)

the above equation can be written into a single particle equation in the following

form:

Heffi ψi,σ(r) =

[−1

2∇2 + V eff

i,σ (r)

]ψi,σ(r) = ϵi,σψi,σ(r) (2.14)

It is obvious in Eq. (2.13) that each of the spin orbitals depend on the others,

hence Eq. (2.13) is a nonlinear equation and can only be solved by self-consistent

method. Indeed, the numerical method employed in solving Hartree-Fock equation

is named “self-consistent field” (SCF) method.

SCF method initializes with a set of guess spin orbitals and thus the Hamiltonian

can be constructed, by substituting into Hartree-Fock equation (2.13), a new set

of spin orbitals would be generated, from these new orbitals new Hamiltonian can

be constructed, and another new set of spin orbitals can be obtained, such loop

revolves until convergence is achieved.

Hartree-Fock approximation and SCF method are cornerstones of electronic struc-

ture calculations. It is difficult to bypass them in most of the modern calculation

approaches. However, there is no consideration of electron correlation in Hartree-

Fock approximation, which largely restrict its application in various areas. Electron

correlation amounts for about 1% of the system total energy, hence Hartree-Fock

is a good approximation for energy calculations. Whereas for many cases, such as

calculations of bond energy, excitation energy, barrier in chemical reactions, ad-

sorbe/desorbe energy etc., where the energy difference between different systems is

essential, Hartree-Fock can hardly provide a reasonable result. To resolve the cor-

relation nightmare, various methods have been proposed based on Hartree-Fock

method, such as configuration interaction (CI) [34], Møller-Plesset perturbation

method (MPn) [34, 36], and so on.

2.4 Density functional theory

The most intolerable defect of traditional quantum chemistry calculation method,

including Hartree-Fock and its further development — post Hartree-Fock (CI,

10


MPn, etc.), is the tremendous calculational complexity. For example, O(N4) for

Hartree-Fock, O(N5) for MP2, and especially for full configuration interaction

method, the complexity exponential increases with the number of particles. Indeed,

the application of these methods is usually limited for systems with moderate

sizes. On the other hand, there is only one variable — electron density — in

density functional theory (DFT), where any physical quantity can be expressed as

a functional of electron density n(r). The calculational complexity of DFT is only

at the order of O(N2) ∼ O(N3).

2.4.1 Thomas-Fermi-Dirac Approximation

The original ideas of DFT were proposed by Thomas [37] and Fermi [38] in 1927,

where they expressed the kinetic energy term with a explicit functional of electron

density [33]. In 1930, Dirac took into account the local approximation of electron

exchange and correlation interactions, which was omitted in Thomas-Fermi ap-

proximation, derived Thomas-Fermi-Dirac approximation [39], where the energy

functional is expressed as:

ETF [n] =C1

∫drn(r)5/3 +

∫drVext(r)n(r)

+ C2

∫drn(r)4/3 +

1

2

∫drdr′

n(r)n(r′)

|r− r′|

(2.15)

where the first and third terms are the local approximation of electron kinetic

energy and exchange energy, respectively. The last term is classical Hartree energy.

Despite Thomas-Fermi-Dirac approximation proposed a heuristic method to han-

dle the degrees of freedom of many electron systems, its lack in detailed physical

and chemical information restricts its application in actual calculations.

2.4.2 Hohenberg-Kohn Theorem

It is commonly accepted that the two theorems proposed by Hohenberg and Kohn

in 1964 [6] are the onset of modern DFT. These two Hohenberg-Kohn (HK) the-

orems constituted the foundation of modern density functional theory, and I shall

retail them in the following [33, 40, 41]:

HK Theorem I: For any systems of N-interacting electrons, any of its physical

properties are completely determined by the ground state electron density n(r).

11


HK Theorem II: The global minimum of energy functional is the ground state

energy, and the corresponding electron density is the ground state density.

We can write the Hamiltonian of any many-electron system as

H = −1

2

∑

i

∇2 +∑

i

Vext(r) +1

2

∑

i =j

1

|ri − rj|(2.16)

and the energy functional can be expressed as

EHK [n] = T [n] + Eint[n] +

∫drVext(r)n(r) + EII

= FHK [n] +

∫drVext(r)n(r) + EII

(2.17)

where EII is nucleus-nucleus interaction, FHK [n] is system internal energy, includ-

ing electron kinetic energy, potential energy and interaction energy.

2.4.3 Kohn-Sham equation

The HK theorems ensure that all the physical properties are determined by ground

state density on the premise of we have got the explicit energy functional of density.

However, it is so difficult that there is no such exact functional so far. In 1965,

Kohn and Sham proposed that the many-electron system can be replaced by a

fictitious non-interacting many particle system with the same external potential,

all the interactions between electrons are classified into a exchange-correlation

(XC) term. The ground state density and other properties can be obtained by

solving the non-interacting system, and the precision only depends on the quality

of XC functional.

We can write the Hamiltonian of the auxiliary fictitious system as

Hσaux = −1

2∇2 + Vσ(r) (2.18)

and the electron density

n(r) =∑

σ

n(r, σ) =∑

σ

Nσ∑

i=1

|ψσi (r)| (2.19)

where ψσi is the i-th single particle orbital with spin component σ. Thus the kinetic

term is

Ts = −1

2

∑

σ

Nσ∑

i=1

⟨ψσi (r)|∇2|ψσ

i (r)⟩ =1

2

∑

σ

Nσ∑

i=1

∫dr|∇ψσ

i (r)|2 (2.20)

12


and the classical Coulomb term can defined as the interaction between electron

density with itself:

EHartree =1

2

∫drdr′

n(r)n(r′)

|r− r′| (2.21)

In this way, we can write out the energy functional as the following:

EKS = Ts[n] +

∫drVext(r)n(r) + EHartree[n] + EII + EXC [n] (2.22)

where all the many body effects are included in EXC term.

Subject to the orthonormal constraint of orbitals

⟨ψσi |ψσ′

j ⟩ = δi,jδσ,σ′ (2.23)

we have the variational equation of energy functional at ground state

δEKS

δψσ∗i (r)

=δTs

δψσ∗i (r)

+

[δEext

δn(r, σ)+δEHartree

δn(r, σ)+

δEXC

δn(r, σ)

]δn(r, σ)

δψσ∗i (r)

= 0 (2.24)

and then a Schrodinger-like equation

(HσKS − ϵσi )ψσ

i (r) = 0 (2.25)

is obtained, which is called Kohn-Sham (KS) equation, where ϵσi is the i-th eigenen-

ergy for spin σ, and KS effective Hamiltonian

HσKS(r) = −1

2∇2 + V σ

KS(r) (2.26)

here, V σKS is KS potential

V σKS(r) = Vext(r) +

δEHartree

δn(r, σ)+

δEXC

δn(r, σ)

= Vext(r) + VHartree(r) + V σXC(r)

(2.27)

Equations (2.25) – (2.27) are KS equations. It is obvious that we should have

resorts to SCF method to solve KS equations. Moreover, the KS scheme is inde-

pendent of the selection of exchange-correlation approximations.

The KS orbitals are usually described as linear combinations of a set of functions,

which is called basis set. The basis set should be infinite dimensional in principle,

which is evidently impossible to be implemented in practice. In most of the cases,

a cutoff is used to truncate the number of dimensions. There are many kinds

of basis set are widely used in calculations, such as Salter type orbitals (STO)

[42], Gaussian type orbitals (GTO) [43], plane waves [33], Wannier functions [44],

13


wavelets [45], and so on. Among these kinds of basis sets, STO and GTO are

widely used in traditional quantum chemistry calculations, due to the ease to

describe atomic orbitals. On the other hand, plane wave basis is the most natural

way to do calculations under periodic conditions, and most of the widely used solid

state simulation packages adopt plane wave basis.

2.4.4 Exchange-Correlation functionals

KS scheme transforms the quantum many-electron problem into a effective single

electron problem, and dumps all the un-exact part into exchange-correlation term,

thus, a EX functional with high quality is essential for our calculation. Moreover,

the explicit separation of kinetic and Hartree term from the total energy implies

that the EX functional would be localized [33]. Despite the exact expression of

EX potentials should certainly be very complex, we still have some clews from

its various boundary conditions. Some kinds of widely used XC functionals are

present in the following.

local (spin) density approximations, L(S)DA

The exchange and correlation interactions is localized in homogenous electron gas,

thus the XC functional only depends on electron density [33, 41]

ELDAXC [n↑, n↓] =

∫drn(r)ϵhom

XC (n↑(r), n↓(r))

=

∫drn(r)

[ϵhomX (n↑(r), n↓(r)) + ϵhom

C (n↑(r), n↓(r))] (2.28)

LSDA performs very well in metallic system, as a result of most of the electron

states near Fermi energy are delocalized, thus is a good approximation to homoge-

nous electron gas.

Generalized gradient approximations, GGA

In addition to the dependence on electron density, GGA also takes into account of

the dependence on gradient of electron density [33, 41]

EGGAXC [n↑, n↓] =

∫drn(r)ϵXC(n↑(r), n↓(r), |∇n↑|, |∇n↓|, . . . )

=

∫drn(r)ϵhom

X (n)FXC(n↑(r), n↓(r), |∇n↑|, |∇n↓ |, . . . )(2.29)

14

2.5 Non-equilibrium Green’s function

where FXC is a dimensionless quantity, ϵhomX (n) is the exchange of non-polarized

homogenous electron gas.

GGA improves the performance in complex chemical environments, especially for

binding energy calculation of molecules and solids, where chemical precision is

achieved [40]. As a result, GGA greatly extended the application of DFT. There

are many GGA functionals so far, such as Becke88 [46], PW91 [47], PBE [48] etc.,

all these functionals are widely used in the nowadays calculations.

Hybridized functions

As we all know that the description of exchange interaction is exact in Hartree-

Fock method, if we take the exact exchange and linearly combined with exchange

or correlation taken from LSDA or GGA, the constructed new functional is called

hybridized exchange-correlation functional. Usually these functionals are better

approximations for specific systems [33, 40, 49].


First-principles calculation brought a reliable approach which is popularized and

applied in many areas in the recent decades [33, 41, 50–53]. However, traditional

first-principles methods also possesses its limitations, for example, only finite-sized

systems or infinite systems with internal periodicity can be calculated, in addition,

these systems must be in equilibrium. In this context, systems in molecular elec-

tronics, which are non-equilibrium, non-periodic, and infinite with open boundary

conditions could not be treated properly by using these traditional methods. The

good thing is creativeness never cower away when demands appear. In this sec-

tion, I would like to briefly describe the framework of non-equilibrium Green’s

function (NEGF) technique and how to calculate the electron transport properties

numerically by employing NEGF combined with DFT [54–57].

2.5.1 System and models

A typical open system in molecular electronics can be simplified into a model shown

in Figure 2.1, where C, L and R represents the central region (usually constructed

by molecules), the left and right electrodes. Both the electrodes are semi-infinite

and extend periodically to left and right, respectively. It is commonly assumed

that there is no direct interaction between left and right electrodes, which can be

15


Figure 2.1: Schematic model of tunneling junctions. The central region (C) coupledwith left (L) and right (R) leads. Both left and right leads are only periodic in thedirection away the central region.

assured by including sufficient large number of layers from each electrodes into the

central region. In this context, the model consists of three parts, the central one

is a finite system, and the others are periodic systems.

The Hamiltonian of the model also include contributions from the three part

H =

HLL HLC 0

H†LC HCC HCR

0 H†CR HRR

(2.30)

substitute the above Hamiltonian into Green’s function equation,

ESLL −HLL ESLC −HLC 0

ES†LC −H†

LC ESCC −HCC ESCR −HCR

0 ES†CR −H†

CR ESRR −HRR

×

GLL GLC GLR

GCL GCC GCR

GRL GRC GRR

=

ILL 0 0

0 ICC 0

0 0 IRR

(2.31)

where S is overlap matrix and I is unit matrix. It is easy to obtain the Green’s

function of the central region by solving the above equation,

GCC(E) = ESCC − [HCC + ΣL(E) + ΣR(E)]−1 (2.32)

here, ΣL(E) and ΣR(E) are the self energies of left and right semi-infinite elec-

trodes, and can be calculated by the following equations, respectively,

ΣL(E) = (ESLC −HLC)† G0LL(E) (ESLC −HLC)

ΣR(E) = (ESCR −HCR)† G0RR(E) (ESCR −HCR)

(2.33)

16


Figure 2.2: Schematic of contour integral path of during solving density matrix fromGreen’s function. EB is the bottom energy, whose value is lower than that of any elec-tronic states in the calculation.

where G0LL(RR) is the retarded Green’s function of the left(right) electrode, which

can be directly calculated from

G0LL(E) = (zSLL −HLL)−1 ,

z = E + iη(2.34)

a typical value for η is about 1 meV [19].

2.5.2 Current Calculation

According to Landauer type view point on the electron transport process through

tunneling junctions [54, 55, 57–59], there are two kinds of scattering states in the

scattering region, each comes from the left and right electrode, respectively. The

scattering states with energy below µL from the left electrode are occupied and

similar for states from right. The chemical potentials of each electrode are the

same in equilibrium, thus the contributions from these two kinds of states coun-

teracts each other, leading to zero net current. When a bias is imposed across

the junction, the above equilibrium would be broken and there would be non-zero

current. Thinking about the process a little detailed, we note that the occupations

of each scattering states would be affected by the non-equilibrium boundary con-

dition, and thus self-consistent method is necessary for exactly evaluation of the

current.

17


Following Landauer’s type formula, the current under steady state approximation

is

I(Vb) = −2e2

h

∫ +∞

−∞T (E, Vb)[f(E − µL)− f(E − µR)]dE, (2.35)

where µL(R) is the chemical potential of left(right) electrode, f is Fermi-Dirac

distribution function, T (E, Vb) is the transmission probability of injecting electrons

with energy E when a bias Vb is imposed. Transmission function can be calculated

directly from the Green’s function of the scattering region

T (E, Vb) = Tr[ΓL(E)GCC(E)ΓR(E)G†CC(E)] (2.36)

Here, the self energy

ΓL(R)(E) = i(ΣL(R)(E)− [ΣL(R)(E)]†

)(2.37)

reflects the coupling between electrodes and central region at energy E.

The density matrix of the system can also relate to the Green’s function [18–20, 60]

DCC =1

2π

∫ +∞

−∞dE

[GCC(E)ΓL(E)G†

CC(E)f(E − µL)

+ GCC(E)ΓR(E)G†CC(E)f(E − µR)

]

=− 1

π

∫ +∞

−∞dEℑ [GCC(E)f(E − µL)]

+1

2π

∫ +∞

−∞dE

[GCC(E)ΓR(E)G†

CC(E)][f(E − µR)− f(E − µL)] .

(2.38)

the first term is analytical thus can be evaluated by using contour integral approach

(see Figure 2.2) with high efficiency. On the other hand, there exists singular points

in the second term, thus a dense mesh grid is necessary for the calculation.

The density matrix can be feed back to DFT modules to generate new ground

state density,

ρ(r) =∑

µ,ν

ϕ∗µ(r)ℜ [(DCC)µ,νϕν(r)] , (2.39)

and Hamiltonian

(HCC)µ,ν = ⟨µ|T + Vext(r) + VH [ρ(r)] + VXC [ρ(r)]|ν⟩, (2.40)

thus a new iteration starts from the calculation of new Green’s function, and

iterates until convergence is achieved. Then the current can be calculated by using

Eq. (2.36) and Eq. (2.35). For non-zero bias calculations, the above scheme can

be used followed by shifting the chemical potentials of left and right electrode by

eVb/2 upwards and downwards, respectively.

18

3

Nano and Moleculear Electronics

Despite the prediction of manipulating objects at atomic scale by Feynman is as

early as at the end of 1950s [2], the actual implementation is after 1982, when

Binnig and Rohrer invented scanning tunneling microscope (STM) in Zurich [10].

STM based on the quantum tunneling phenomena, and the first time supply a

practical approach to observe objects and processes at atomic scale. The pristine

STM use tunneling current or conductance as indication in the measurements,

thus it is necessary that the tunneling system is conductive, which restricts its

application in insulating or liquid phase systems. Four years latter, in 1986, Binnig

and coworkers invented atomic force microscope (AFM) [11], greatly expanded

the scope of scanning probe techniques. Besides, other spectroscopy [61–63] or

illuminating techniques [62, 64, 65], high resolution spectroscopic methods [66–

68] and nano-scale preparation and manufacture [12–14] etc. also boost the rapid

growth of this area.

The terminology nano-materials implies that materials with at least one of its

dimensions is at nanometer scale [69], for example, molecules and clusters are zero-

dimensional, nanotubes and nanowires are one-dimensional, few-layered graphene

and atomically thin bismuth telluride are two-dimensional. Nano-electronics is

the study of electric circuits composed by nano-materials, and in this context,

molecular electronics is just a special case of nano-electronics, where the circuits

consist of various molecules. Owing to the small sizes, especially for cases that one

of the system dimension is comparable with the characteristic length of microscopic

particles in it, we must seek help from quantum mechanics; On the other hand, the

ratio of surface atoms increases as the system size decreases. These two issues are

responsible for the new behaviors emerged, which are highly dependent on the size,

shape, chirality, composition etc. of the system. Furthermore, such dependencies

lead to versatile properties and thus provide potential applications in the future

19

3 Nano and Moleculear Electronics

Figure 3.1: A schematic view of Moore’s Law. The number of transistors in a singleprocessor and the manufacture process are presented as green and red curves, respectively.All the data take from the website of Intel R⃝corporation [71].

mechanics, electrics, magnetics, and chemistry [70].

3.1 Progress in molecular electronics

The size of electronic devices in silicon industry is approaching its physical limit in

the recent years, the revenue production of 32 nm products has begun and 22 nm

technologies is in development, and will appear on the market in middle 2010 [71].

According to Moore’s Law (though seems being invalidate recently, see Figure 3.1),

the number of transistors on unit area doubles every 18 months [72], the actual size

of a single transistor will down to atomic scale, and the traditional semiconductor

techniques will no longer work owing to two issues: Firstly, the resolution of light

etching technique will reach its limit due to the finite wave length; secondly, silicon

dioxide, the widely used insulating layer in traditional metal-oxide-semiconductor

field-effect transistor (MOSFET), would be conductive when its thickness down to

0.7 nm [16]. Seeking for new devices with smaller sizes, higher performance and

lower energy consumption becomes an urgent problem.

We usually trace back to Aviram and Ratner’s proposal of molecular rectifier [9]

as the origin of the concept of molecular electronics. In the work nearly 40 years

ago, the authors proposed that rectification can be implemented by a two probe

molecular junction in which the molecule consist of an acceptor-donor pair. This

kind of approaches to construct devices from single molecules or clusters are called

20

3.1 Progress in molecular electronics

“bottom-up” method, compared with the traditional “top-down” methods, molec-

ular devices would be much smaller and be much easier to tune their functions.

Molecular electronics became popular just in the latest twenty years, by the virtue

of the advancements in chemical synthesis and microscopic characterization. To

realize electronic chips at molecular level, the electron transport properties of single

molecules must be characterized at first. At present, most of the studies in this area

are in the early stage. As the result of the complexity and diversity of composition

and configuration of molecules, single molecular junctions exhibit versatile electric

characteristics, such as rectification [73–75], amplification [76], filed modulation

[77], giant magnetic resistance [78, 79], Coulomb blockage [80], Kondo effects [79–

81], and so on.

The advances in experimental techniques brought great challenges and opportuni-

ties to the theoretical aspect. In most of the experiments, the detailed configuration

and conformation of molecules under the influence of electrodes, the structure of

electrodes, or the effects of electrode-molecule interactions will strongly affect the

transport properties of the junctions. However, these factors could not be com-

pletely characterized so far. Identifying the correspondence between experimental

measurements and detailed compositional and structural information of the molec-

ular junction is indispensable for the further development of molecular electronics.

Theoretical simulation is the most effective approach to achieve this goal, not only

because of its high cost effective, we can also perform ideal experiments and design

molecular devices with specific electric functionalities.

Electron transport through molecular junctions is a non-equilibrium process with

open and non-periodic boundary conditions, thus new theoretical framework/method

is needed to describe these new behaviors. The first first-principles electron trans-

port calculation was carried out by Di Ventra and co-workers, where the authors

using muffin-tin model to describe the metal electrodes and employing Lippman-

Schwinger equation to calculate the conductance [15]. However, as a consequence

of the using of plane wave basis, the dimensions of matrices in the calculation is

tremendously large, which prevented its popularization in the simulation commu-

nity. Taylor et al. combined the non-equilibrium Green’s function technique and

density functional theory (NEGF-DFT) to calculate the conductance of molecular

junctions, localized atomic orbital basis set is used in the calculation, for its effi-

ciency [17, 18]. NEGF-DFT is the most popular approach for electron transport

calculation so far [16, 19, 20].

21


3.2 Experimental techniques

Because of the close contact of the works in this thesis with the experimental

developments, I shall briefly introduce some of the related experimental techniques

in this section.

3.2.1 Scanning tunneling techniques

For a long time, there are mainly two kinds of approaches to collect microscopic

structural information of materials. One is diffraction techniques which employing

the wave character of light or microscopic particles to diffract with the periodic

structure of material, information about the reciprocal lattice can be character-

ized. X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), low en-

ergy electron diffraction (LEED) etc. are some examples of these techniques, which

concentrate on the periodic information of materials. However, these techniques

are limited by the purity of light or particles and their inability in real space char-

acterization. The other one is high resolution microscopy that detects the local

structural information in real space, including high resolution optical microscopy,

scanning electron microscopy (SEM) [82], transmission electron microscopy (TEM)

[83], field ion microscopy (FIM) [84] and so on. The applicabilities of these methods

are also restricted by the wave length of light or particles.

The invention of STM, AFM and a series of other scanning probe microscopes

provide the possibility to detect local structural information in real space at the

mean time with an atomic resolution. The lateral and vertical resolution of STM is

about 1 A and 0.1 A, respectively [85, 86]. STM works with the quantum tunneling

principle, upon which electrons probably tunneling through a classically forbidden

barrier with energy higher than itself. A schematic view of STM is presented in

Figure 3.2, in which the sample adsorbed on conductive substrate plus the STM

tip constitute a circuit, and the vacuum region between tip and sample can be

viewed as the tunneling barrier. The probability of electrons tunneling between

tip and sample depends on the imposed bias voltage, the physical and chemical

properties of substrate, sample and STM tip.

Constant current mode and constant height mode are the commonest among the

scanning modes of STM [88]. In constant current mode, the tunneling current is

fixed and thus the tip height changes according to the change of density of states

(DOS), a topographic mapping of the sample DOS is obtained after scanning;

Whereas in constant height mode, the tip height and bias voltage are fixed and

the scanned map reflects the spatial distribution of sample DOS in the cross plane

22


Figure 3.2: Schematic drawing of STM. Created by Michael Schmid, TU, Wein. Alsoavailable at Wikimedia commons [87].

on which tip moves. Besides, scanning tunneling spectroscopy (STS) is often used

in measurement, in which the tip position is fixed and the bias voltage gradually

changes, by recording the change in current, a current-voltage curve is obtained. In

a STM measurement, a typical bias voltage is about 0.1 V and a typical tunneling

current is about 1 nA, usually the vacuum barrier is about 5 ∼ 7 A in length [88].

In most of the cases, the measured tunneling current and STM images depend on

the geometrical configuration and electronic structures of the sample, the STM tip

can also effect experimental results [86, 89].

Abundant information about the electronic states of the sample, especially local

properties can be obtained by numerous repeatable STS measurements, where the

current-voltage (I-V), differential I-V (dI/dV ), and quadratic differential (d2I/dV 2)

characteristics reflect the distribution of electronic and vibrational states in energy

space. Due to these properties strongly dependent on the chemical composition,

geometry configuration and conformation, sample-substrate interaction, and intra-

or inter-molecular interactions (if any), STM is capable of detailed characterizing

the sample-substrate systems.

The contributions to tunneling conductance can be classified as elastic and in-

elastic part, elastic tunneling usually dominate the tunneling process, in which

electrons experience elastic scattering and their energy conserves. The resonant

tunneling model can be used to describe elastic tunneling processes: The Fermi

levels of electrodes shift in opposite direction when a bias V is imposed, hence

there would be a energy window with width eV . If there are delocalized states

23


in the junction with energy in the range covered by the energy window, electrons

with corresponding energy in the electrode would tunneling through the junction

to the unoccupied states at the other side. In this context, tunneling current

and thus conductance appear, and the delocalized states in the junction is called

tunneling channel that provides a pathway for the injected electrons [54, 55, 57].

The requirement of electrons experience elastic tunneling delimits that tunneling

occurs only there exists occupied and empty states with energy matches tunneling

channels. This is only a simplified description of the actual tunneling process, in

which various other factors effects. The most obvious is the inelastic scattering

between tunneling electrons and vibration modes (phonons) of the sample, where

injecting electrons exchange energy with the vibration modes of nuclei. Inelastic

tunneling occurs when the injecting electrons possess large enough energy to ex-

cite a specific vibration mode, thus it can be viewed as a new tunneling channel

is opened by inelastic electron excitation. The inelastic contributions lead to a

suddenly change in tunneling conductance, and can be characterized by the peaks

in differential conductance (d2I/dV 2) spectrum, which is called inelastic electron

tunneling spectra (IETS), and is a powerful tool in microscopic characterization. In

addition, inelastic electron can induce changes of the chemical bonding of samples,

which is also a practical approach to manipulate chemical reactions [90].

Despite STM has advantages over many other techniques, there are still many

limitations in practice. The complexity of the mechanism of STM measurement

and the ambiguity in tunneling junction construction brought great difficulties

in chemical characterization of the system. Signals detected by STM directly

reflect electronic states, but not geometric configuration, i.e. STM does not work

with a “what you see is what you get” way. As a result, theoretical simulations

are necessary to explain experimental results and to guide further investigations.

Besides, most of STM measurements are tunneling current based, which restricted

this technique could only be used in conductive systems.

3.2.2 Molecular junctions

Molecular junctions is a circuit constructed by a molecule sandwiched between two

electrodes, as shown in Figure 3.3. Although the concept was proposed as early as

in 1974 [9], actual molecular junctions appear in 1990s, thanks to the advancement

of experimental technologies. There are several techniques to construct molecular

junctions, such as:

• Scanning tunneling microscopy

As described above, a tunneling junction appears in a typical STM mea-

24


Figure 3.3: Schematic of a molecular junction consists of two gold electrode and ap-aminophenyl. Golden, gray, blue and light white ball represent gold, carbon, nitrogenand hydrogen atoms.

surement, which is constructed by the sample and tip and substrate as two

electrodes. Hence a scanning tunneling spectrum is just the I-V character-

istics of a specific configuration which depends on the tip position. As long

ago as in 1995, Joachim et al. implemented a molecular amplifier using

C60 molecules in STM [76]. Recently, Lindsay’s group proposed that DNA

sequencing could be achieved by measuring the conductance difference be-

tween base-pair junctions constructed by STM [22, 23]. Our group have also

investigated these junctions based DNA pairs, first-principles calculations

demonstrated that it is possible to identify different junctions by comparing

the conductance, although the measurements in the experiments were not

exactly enough.

• Break junctions

There are many members in the family of the break junction techniques, such

as mechanically controllable break junction (MCBJ) [12, 14], electromigration-

induced break junction (EIBJ) [80], etc. MCBJ is invented in 1992, by

Muller and coworkers, where molecules are bridged between a gap between

metal electrodes with width controllable in a mechanical manner [12]. The

first measurement of single-molecular conductance was performed by Reed’s

group in 1997, in which the conductance of a 1,4-benzendithiol molecule

sandwiched between gold electrode was measured [14].

• Other techniques

Besides the above two kinds of approaches, molecular junctions can also be

constructed using other methods, such as crossed-wire tunneling junction

[91, 92] and magnetic-bead junction [93, 94]. Both of the methods using self-

25


assembling techniques, for example, in the former case, two wires crossed

with one of them is modified by a molecular self-assembling monolayer, thus

construct molecular junctions between these wires. In the later case, gold

and nickel layers are deposited on a silica bead, and then move the bead to

bridge a metallic electrode gap using magnetic assembling techniques.

26

4

Graphene related materials

Graphene, the single atomic thick monolayer carbon allotrope, has attracted tremen-

dous research interests since its birth in 2004 [95]. Both fundamental and applied

scientists have paid great attention to this star material not only because of its

intrinsic “big physics” governed by its peculiar electronic properties [96–98], but

also as a consequence of its versatile potential applications in physics, chemistry,

material science and micro-electronics.

It is more than sixty years since the first theoretical work of graphene in which

it is considered as the starting point to calculate the band structure of graphite

[99–101]. However, there is not so much attention has been paid to this material

before its first successfully isolation by using micromechanical cleavage method

[95, 102]. This issue can be ascribed to two reasons: In the first place, it is in

1930s that Landau and Peierls have proved that strictly two-dimensional crystals

are not stable at any finite temperature as the consequence of thermal vibration

[103, 104]; In the next place, even with the hindsight of the existence of graphene,

it is quite difficult to find out graphene from a haystack of graphite segments nei-

ther by optical microscopy [105] nor by scanning probe techniques. The existence

of graphene sheets can be reconciled with the theoretical prediction by Peierls

and Landau by taking into account of the ripples in the normal direction [106]

thus destroys the strick two-dimensional lattice symmetry and the strong C-C sp2

bonding suppresses out-of-plane vibration.

4.1 Geometric and electronic structures of graphene

Graphene adopts a two-dimensional honeycomb lattice which consist of two irre-

ducible carbon atoms as shown in Figure 4.1 (a). In the chemist’s point of view,

27

4 Graphene related materials

Figure 4.1: Two dimensional lattice of graphene in real (a) and reciprocal (b) space.The two non-equivalent carbon atoms are labeled as “A” and “B” in (a), respectively. Byusing Wigner-Seitz cell method, the reciprocal lattice also adopts a honeycomb symmetry,the three high symmetry points in the first Brillouin zone are labeled as “Γ”, “K”, and“M” in (b).

graphene was made out of carbon hexagons which can be viewed as spliced dehy-

drogenated benzene rings. In this context, all the carbon atoms bear a sp2 type

hybridization between the carbon 2s orbital and two of its 2p orbitals, thus every

carbon atom bonding with each of its three nearest neighbors with a σ bond in

addition to the π bonds among the whole plane. Moreover, graphene can act as

the starting point in the study of its zero, one, and three dimensional counterparts:

Fullerenes (0D) are obtained by introducing pentagon defects into two-dimensional

graphene sheets and wrapping it up; Carbon nanotubes (CNT, 1D) are obtained

by rolling graphene in a specific direction; and graphite (3D) can also be made out

of graphene by stacking layer-by-layer.

on the other hand, in a physicist’s point of view, graphene is a two-dimensional

crystal with a honeycomb symmetry. The two lattice vectors in Figure 4.1 (a) can

be expressed as

a1 = a(

√3

2,1

2), a2 = a(

√3

2,−1

2) (4.1)

where a = dC−C ×√

3 = 2.46 A is the lattice constant, and dC−C is the C–C bond

length, which is about 1.42 A. The reciprocal lattice vectors can be calculated as

b1 =2π

a(

1√3, 1), b2 =

2π

a(

1√3,−1) (4.2)

28

4.1 Geometric and electronic structures of graphene

Figure 4.2: Band structure of graphene along Γ−K, K−M, and M−Γ. Data collectedfrom first-principles calculation carried out by using VASP package [121, 122], PBEfunctional [48] and ultra-soft pseudopotentials [123] are employed in the calculation.

thus the first Brillouin zone can be constructed by using a Wigner-Seitz cell method

[107], and also adopts a honeycomb lattice, as shown in Figure 4.1 (b). The band

dispersion along high-symmetry directions in the first Brillouin zone is presented

in Figure 4.2, we can see that the honeycomb lattice symmetry lead to a peculiar

band structure, where the conduction band and valence band degenerate at K

and K ′ point thus graphene is a zero-gap semiconductor. It is also notable that

the linear dispersion relation near Fermi level brings Fermi velocities of charge

carriers the value 300 times less than the light speed c. These carriers should

be viewed as quasiparticles called massless Dirac fermions described by Dirac’s

equation [96, 108–113]. It was in 1980s Semenoff realized that graphene pro-

vides a perfect platform for a condensed matter simulation of (2+1)-dimensional

quantum electrodynamics (QED) [114]. The much smaller carrier speed dramat-

ically enhances many QED effects inversely proportional to the speed of light.

Indeed, many QED specific phenomena predicted in theory have been observed in

graphene systems, such as chiral quantum Hall effects [96, 108, 115], Klein paradox

[96, 97, 116], quantum Hall ferromagnetism [117, 118], and so on. Recently, Tza-

lenchuk and coworkers performed very accurate measurements of quantum Hall

effect in graphene sheets, which could help the improvement of standard for elec-

trical resistance and mass, although it is somewhat mordant to set the standard

of mass using massless Dirac fermions [119, 120].

29


A question rise naturally when we considered graphene as a two-dimensional crys-

tal? Or how thin does the system is thin enough to become two-dimensional?

Evidently, a graphene monolayer with thickness of one atom is two-dimensional.

Partoens and Peeters have demostrated that the band structure of systems with

eleven or more graphene layers only diverged from that of bulk grahite by 10%,

and the band structure of graphene from monolayer to trilayer evolves from zero-

gap semiconductor to semimetals with evident band overlap [124]. Furthermore,

since the screening length in the normal direction of layers in graphite is about 5

A [125, 126], and the inter-layer distance in graphite is 3.4 A, therefore, graphene

systems with only 5 layers should be discriminated into surface and bulk layers

[96].

Except for the intriguing QED specific nature and usefulness in fundamental

physics, one of the most interesting properties of graphene might be the high charge

carrier concentration even at room temperature and insensitive to the existence

of defects [95, 102, 108, 127]. Accordingly, graphene is a good candidate for the

next generation micro-electronics applications [96, 128]. In fact, many electronic

devices have been predicted or implemented on the basis of graphene, such as filed

effect transistors [129–138], quantum dots [134, 139–141], negative differential re-

sistance (NDR) devices [142, 143], single molecular detector [144, 145], etc. To

take advantages of the nowadays semiconductor technology, the zero-gap graphene

sheets should be tunned to behave as semiconductors and further tuning of the size

of electronic gaps is inevitable. This can be realized by many approaches, includ-

ing spacial confinement [146–150], imposing extra boundary conditions [149–153],

chemical modifications [154–156] and so on.

4.2 Preparation and characterization

Despite graphene has definitely been produced occasionally in the more than 500

years’ history of using graphite as a marking tool or solid lubricant, the first ev-

idence of its existence is the successful exfoliation in 2004, when Geim’s group

repeatedly peel highly oriented pyrolytic graphite (HOPG) mesas, using optical

microscope and atomic force microscope (AFM) to characterize the generated

graphene films [95]. From then on, various approaches have been developed to

prepare graphene, aimed to higher quality, higher throughput and higher yield

[96, 157]. According to whether the preparation procedure involves chemical reac-

tions, we can roughly classify the emerging methods into two kinds, say, chemical

approaches and physical approaches.

30


4.2.1 Physical approaches

Until now, the highest quality graphene sheets available were prepared by using

the original “micromechanical cleavage” method [95, 102]. Even in their earliest

report, few-layer graphene sheets with dimensions up to 10 µm and thicker flakes

with dimensions up to 100 µm were fabricated successfully. However, the cleavage

method is low yield and low throughput. Another approach is demonstrated by

Coleman’s group, in which graphite powder was first dissolved in organic solvent by

sonication, and then drop the dispersion onto holey carbon. This method results

in a monolayer yield of ∼1 wt%, and potentially be improved to 7-12 wt% [158].

4.2.2 Chemical approaches

The low throughput and yield critically restrict the expansion and development

of graphene investigation and application. Chemists are calling for help to seek-

ing large-scale, cost effective, high yield preparation methods. Be worthy of the

accumulated experiences in carbon chemistry, expecially in the recent decades’ re-

search in graphite, fullerenes and CNTs, various chemical approaches have been

put forward to satisfy the scientific and engineering demands [159].

Chemical exfoliation via redox process

There are also liquid-phase exfoliation methods based on chemical reactions, es-

pecially redox reactions. The first solution based exfoliation approach is demon-

strated by Ruoff’s group in 2006 [160, 161], by molecular-level dispersion of these

chemically modified graphene sheets into solution, followed by mixing with polystyrene

and reduction. The produced graphite oxide is high hydrophilic due to the attached

hydroxyl, epoxide, carbonyl and carboxyl functional groups. In order to prevent

aggregation due to less hydrophilic induced by reduction, electrostatic-stabilization

can be introduced by rasing the pH of the solution [162].

The most conspicuous advantages of solution-phase redox exfoliation methods are

its low cost and high throughput. However, the solubility of graphene sheets often

decreases with the increasing molecular weight, hence limits the produce of large

scale graphene. Moreover, the oxidation and reduction of graphite always destroy

the two-dimensional crystal symmetry of graphene. These two issues should be

addressed in the further investigation [157, 159].

31


Epitaxial growth and chemical vapor deposition

Graphene can also be prepared by epitaxial growth or chemical vapor deposition

(CVD) methods. One of the earliest transport measurements on few-layer graphene

sheets was performed by de Heer’s group in 2004, where the graphene samples were

grown epitaxially on Si-terminated (0001) surface of 6H-SiC [163, 164]. Depending

on the surface on which graphene grown is terminated by silicon or carbon atoms,

there are two types of graphene prepared by SiC surface epitaxial growth. Usually

graphene monolayer or bilayer is obtained in the former case, moreover, the band

gaps opens as a consequence of graphene-substrate interactions and substrate in-

duced doping and disorder, while the linear dispersion relation retains away Fermi

level [165–167]. In the case of carbon terminated face, multilayer graphene is

preferable to be thermally decomposed on SiC substrate, in which the interlayer

spacing is slightly larger that in bulk crystalline graphite [168, 169]. As a result

of relatively weak electronic coupling between inner layers and strong screening

by surface layers, these samples exhibit electronic properties like free-standing

graphene [166, 169–171].

An alternative route for the epitaxial growth is the use of transition metal substrate

instead of SiC wafer. Epitaxial growth of graphene monolayer or few-layers on Pt

[172], Ir [173], Ni [174–176], and Ru [177, 178] surfaces combined with chemical va-

por deposition (CVD) have been intensively studied in the recent five years. These

CVD approaches rely on the temperature-dependent solubility of interstitial car-

bon atoms in transition metal substrates. Usually hydrocarbons such as methane,

propylene or gas mixtures are decomposed at high temperature and the generated

carbon atoms dispersed in substrate with high solubility, followed by programmed

cooling of the system, carbon atoms would separate out. In this sense, graphene

with wafer sizes might be prepared, indeed, large scale epitaxial graphene with

dimension up to 200 µm has been grown on Ru(0001) surface [178].

bottom-up approach via organic synthesis

The most pronouncing disadvantages of the above mentioned method is the uncon-

trollable character in the preparation process. From the organic chemistry point

of view, graphene possesses a “macromolecue” structure in which sp2 bonding is

distributed homogeneously among carbon frameworks. Hence the development of

a controllable method to prepare graphene sheets could has recourse to an organic

synthesis route.

Mullen’s group demonstrated that graphene nanoribbon-like polyacyclic hydro-

carbons (PAHs) could be synthesized in a bottom-up manner from 1,4-diiodo-

32


2,3,5,6-tetraphenylbenzene and 4-bromophenylboronic acid [179]. UV/vis adsorp-

tion spectroscopy and mass spectrometry revealed the formation of graphene nanorib-

bon up to 12 nm in length. SEM and STM measurements showed a high self-

assemble tendency of these reactions. However, it is well known that the solubility

decreases and the probability of occurrence of side reactions increases as the molec-

ular weight of reaction product increases, thus extending the size of produced PAHs

remains a big challenge for chemists [157, 179].

4.2.3 Characterization of graphene

One of the most critical reason for the delayed discovery of graphene single or

few-layer sheets is the difficulty in characterizing them. In order to examine the

stack of graphite thin films to find graphene monolayer sheets, an effective approach

works at the micrometer scale should be used. Obviously, the modern visualization

technique depends on scanning probes can not afford this task since their low

throughput. Further more, since the opacity of suspended graphene monolayers is

only 2.3% [105, 180] and is transparent on most substrate, it is difficult to recourse

to optical microscopy. Indeed, AFM has been the only tool to identify graphene

monolayer and few layers, even AFM is only able to distinguish monolayer and

bilayer sheets when the films contain folds or wrinkles [95, 102]. Raman spectra

dawned this issue in 2006 [181], where Raman fingerprints of graphene monolayer,

bilayer and few-layer sheets allow high-throughput, unambiguous identification of

graphene layers. However, Raman spectra still does not allow locating graphene

crystallites in real space. Blake et al. studied the visiblity of graphene monolayer

on SiO2 substrate exposed in visible light with various wavelengths [105]. They

found that graphene on SiO2 can be detected by monochromatic illumination for

any substrate thickness, in addition to 300 nm and ∼100 nm thick SiO2 substrate

are the most effective.

Many other techniques are also used in the characterization of graphene and related

materials, such as X-ray photoelectron spectroscopy (XPS) [182–186], , Fourier

transform infrared resonance (FTIR) [162, 186–190], electron diffraction (ED)

[184], AFM [162, 188, 191], STM [192, 193], TEM [184, 186], nuclear magnetic

resonance (NMR) [183, 184, 186, 188, 194], electron spin resonance (ESR) [186]

and so on. All these techniques play important roles in the characterization of the

structural and electronic properties of graphene.

33


4.3 Graphene nanoribbons

The high carrier mobility, long phase coherence length of graphene combined with

its two-dimensional planar structure with mechanically stiffness and flexibility open

a new window of potential applications in micro-electronics [96, 128]. However,

the zero-gap character of graphene does not compatible with the mature semi-

conductor technology, where the band gap is necessary with great significance.

Various route seems probable to open band gaps in graphene materials, such as

introducing configurational defects or chemical modification. Among these pro-

posed approaches, spatial confinements realized by cutting two-dimensional sheet

into one-dimensional graphene nanoribbons (GNRs) with specific width, shape,

and edge chirality is the most straightforward way.

4.3.1 Fabrication of GNRs

Owing to the dependence of electronic structure of GNR on its size, shape, chiral-

ity and chemical environment, GNR is expected to be one of the most probable

material to continue Moore’s Law in the next decade [72, 195]. Nevertheless, most

of the applications of graphene in practice relies on the fabrication of GNR in a

controllable manner. So far, a number of approaches have been proposed in the

recent years.

Since the planar structures and the possibility of move or grow graphene onto

traditional wafers, the fully-fledged microlithography technique is expected to be

suit to etching GNRs. Oxygen plasma [196] and electron beam [197] have used

to etch graphene on SiO2 wafers, where hydrogen silsesquioxane (HSQ) was used

as etching mask. However, due to the limit in spacial resolution, lithographic

techniques is unable to fabricate narrow GNRs (less than 10 nm in width) with

smooth edges [196–198]. STM can also be used to tailor graphene sheets into

nanoribbons in a well defined manner. Taking advantage of the atomic resolution

of STM, armchair edged GNRs with width 2.5 nm and energy gap 0.5 eV have

been etched [199]. Yet the low throughput and low yield restrict the application of

STM tailoring technique again. Metallic nanoparticles can also be used as scissors

in the lithographic-etching procedure. Fe [200] and Ni [201] nanoparticles have

been thermally generated and used to cut down graphene into GNRs.

Chemical vapor deposition method can also be used to fabricate GNRs directly.

Campos-Delgado et al. showed that bulk production (grams per day) can be

achieved by pyrolyzing ethanol aerosol containing ferrocene and thiophene in quartz

tubes. GNRs with width 20 ∼ 300 nm and thickness with 2 ∼ 40 layers is obtained

34


[202]. This single-step CVD approach can only fabricate mixtures of few-layer

GNRs with various kinds of edge chirality, further exfoliation is needed to obtain

individual GNR sheets.

There are also solution-phase based approaches in the fabrication of GNRs. Li et al.

demonstrated by dispersing exfoliated graphite in noncovalent polymer solution,

ultrasmooth edged GNRs with width from 50 nm down to sub-10 nm can be

fabricated. Field-effect transistor-like devices can be constructed based on these

solution-phase derived GNRs, and an on-off ratio of about 107 is obtained at room

temperature [203].

Carbon nanotubes can be stated as rolled-up graphene sheets with corresponding

C-C bonds rejoined, inversely, CNTs can also be unzipped forming GNRs. Jiao et

al demonstrate that multi-walled carbon nanotubes (MWCNTs) can be unzipped

into GNRs with smooth edges, controllable width and more importantly, high

yield. MWCNTs were embedded in poly(methyl methacrylate) (PMMA) layer

mask, and leaving a side exposed to Ar plasma. Hence the exposed side would

be etched faster than the others and result in unzipped CNTs [204]. The most

pronouncing advantage of the CNT unzipping approach are its controllable width

and edge chirality, in addition to high yield. However, using CNT as raw material

lead to low cost-effectiveness compared with other fabrication methods.

4.3.2 Structural and electronic properties of GNRs

Depending on the crystallographic direction of edges (edge chirality), there are two

kinds of typical GNRs as shown in Fig. 4.3: GNRs with armchair edges (AGNR)

and zigzag edges (ZGNR). The width W of GNRs can be defined as the number

of C–C dimers or zigzag chains in the transverse direction of AGNR or ZGNR,

respectively. Thus the GNRs in Fig. 4.3 can be noted as 15-AGNR (a) and 8-

ZGNR (b), respectively, where the numbers 15 and 8 denote the width of system.

Since the carbons in pristine graphene are sp2 hybridized, there is one dangling

bond for each carbon atom at the edges of GNRs. Hydrogen atoms are usually

used to saturate these dangling bonds of edge carbon atoms in real calculations

[146–150, 152–155, 205].

It was 1996, ten years before the successful fabrication of GNRs, Fujita et al.

investigated the electronic structures of ZGNRs and AGNRs based on nearest

neighboring tight-binding (TB) method [206, 207]. First principles calculation of

the band structures of ZGNRs that confirmed the TB results of ZGNRs at density

functional theory (DFT) level using localized density approximation (LDA) [205].

In the nearest neighboring TB simulations, only two parameters, the on-site energy

35


Figure 4.3: Schematic of structures of GNRs. (a) Armchair edged GNR with widthW=15, 15-AGNR; (b) Zigzag edged GNR with width W=8, (8-ZGNR).

and the hoping integrals, are considered, where the later corresponding to the sp2

interactions between two neighboring carbon atoms. All the ZGNRs are predicted

as metallic due to the two edge states from each edge degenerate when k ≥ 2π/3a

in the first Brillouin zone. On the other hand, the energy gaps of AGNRs change

with the width and behaves a family behavior with width period of 3: systems

with width W = 3p + 2 are metallic and others are semiconductor, where p is an

integer [206].

Son et al. thoroughly examined the electronic structures of GNRs with hydrogen

saturated edges by performing first principles calculations. They found that all the

AGNRs are semiconductors with energy gaps inversely scales with system width

[146, 147], nevertheless, the family behavior of the tendency of energy gaps change

with system width reserves, except AGNRs with width W = 3p + 2 and 3p + 1

possess the smallest and largest energy gaps among a period, respectively. Fur-

ther GW quasiparticle calculations demonstrated that the energy gaps are about

three times larger than those from LDA calculation [148], by the virtue of treating

electron correlation more carefully [31, 33].

More interestingly is the case of ZGNRs, the metallic state was reproduced by

a spin-unpolarized calculation with two edge states degenerated at Fermi level.

However, this paramagnetic state is not the ground state with 20 meV per edge

36


carbon atom higher than that of the antiferromagnetic state for 8-ZGNR. More-

over, the spin degeneration would be removed by introducing a transverse electric

field perpendicular with the periodic direction in system plane, where one of the

valence band and conductance band of one spin orientation would overlap and left

the other semiconducting, leading to a half-metallic character [149, 149]. The ex-

ternal transverse electric field can be generalized to an internal one introduced by

chemical functionalization of carbon atoms at each edge with electron withdrawing

and donating groups. ZGNRs with one side decorated by NO2 and the other by

CH3 groups were predicted to be half-metallic [155].

Chemical modification [156, 208] and strain effects [153] to the electronic properties

of GNRs have also been examined theoretically.

37

5

Inelastic Electron Tunneling in

Surface-Adsorbate Systems

As a sub-discipline of physics or an inter-discipline of physics, chemistry, material

science and biology, surface and interface science attracted tremendous interests

in the recent decades, and plays more and more important roles both in the fun-

damental and applied research. In fact, surface science is already a fundamen-

tal discipline in the research activities in, for example, semiconductor technology,

catalysis, epitaxial growth, life science, and so on [84, 209]. Indeed, the thoroughly

understanding of growth mechanisms at a microscopic scale is essential for the de-

sign and application of novel materials; Adsorption and desorption, the elementary

processes in surface science, are the basis of heterocatalysis; A substrate is also

inevitable in the integrating of molecular devices into circuits. All this kind of

demands in frontier researches boomed the rapid growth of surface and interface

science [209].

5.1 Surface science and STM

Researchers have made colossal progresses in the studies of surface and interface

systems, especially at a microscopic level: In the experiment aspect, there are a

number of powerful microscopy technologies have been invented and applied in

daily research. Scanning tunneling microscope (STM) is the most notable exam-

ple, by which single atom or single molecule and its trace on the surface can be

characterized in a real-time manner, moreover, chemical bonding can also be ma-

nipulated by using STM [90]; In the simulation aspect, the progress in calculation

ability and the spring up of solid and efficient computational methods provides

39

5 Inelastic Electron Tunneling in Surface-Adsorbate Systems

Figure 5.1: Simulated STM constant current image of HOPG. The carbon lattice of thetopmost layer is placed underneath the image to mark the positions in real space. LDOSdata collected from first-principles calculation carried by VASP package [121, 122], PBEfunctional [48] and ultra-soft pseudopotential are used in the calculation. The LDOS isintegrated from density of states in the energy range [0,0.25] eV respect to Fermi energy.

the possibility of full-quantum mechanical description or dynamics simulation of

interested systems.

The exact characterization system is a prerequisite for any investigations, however,

it is not a trivial work in surface and interface science, as a result of the large surface

atom ratio, the existence of dangling bond, surface sates, geometric reconstruction,

and chemical modification, etc. The invention of STM overcame many of these

difficulties. In 1983, Binnig and coworkers scanned the first STM image of the

reconstructed Si(111)-7×7 surface in real space [10], and thus resolved the Si(111)

surface reconstruction puzzle perplexed people for more than twenty years since its

discovery [210]. However, as mentioned in Chapter 3.2.1, the STM images reflect

spatial distribution of density of electronic states, but not the surface topography.

As a result, there is no direct correspondence between STM images and positions

of atoms on surface. One of the most famous examples might be the STM constant

current images of highly oriented pyrolytic graphite (HOPG) surface as shown in

Figure 5.1, in which only three protrusions are observable in an area corresponding

to a hexagonal ring [211].

By means of the ultimate high resolution and the ability to provide structural

information in real space, STM made enormous contributions to the investigation

of surface systems. The atomic resolution in real space brought the possibility of

performing single atomic or single molecular experiments, which is very significant

in the following aspects: First, atoms and molecules are elementary particles in

chemistry, which preserve the chemical properties of substance; Next, there is no

ensemble average in single molecular experiments, which is significant in macro-

40

5.2 STM mediated inelastic tunneling spectra

scopic experiments; Third, the effects of environment that system experienced are

relatively largely enough to be detected in experiments; Fourth, the observation of

quantum objects such as atoms or molecules implies that it is possible to manipu-

late them or their interactions – chemical bonding [90]. On the other hand, these

features bring trouble to the understanding of single molecular phenomena: As

the consequence of the absence of ensemble average, fluctuations between different

measurements are evident and numerous repeatedly measurements are necessary

for a reliable result, this is just the cases for STS experiments in which most of the

reported results are averaged among a number of repeated experiments; The sys-

tem is so small that some of its properties are sensitive to perturbations from the

environment, sometimes even qualitatively. One example is the system melamine

tautomers adsorbed on Cu(100) surface, in which the orientation of top N-H bond

varies when electron pulse is imposed, however, this change in orientation of a

single chemical bond lead to distinct current-voltage characteristics [73]. In this

aspect, theoretical simulation is able to eliminate the ambiguities introduced by

random perturbation, and plays an important role to reveal the underlying physics

and chemistry of surface phenomena.

5.2 STM mediated inelastic tunneling spectra

STM mediated inelastic tunneling spectra (STM-IETS) becomes more and more

important in the recent several years. IETS reflects the vibration features of sys-

tem, which is sensitive to the chemical composition, structural configuration, and

conformation of system. The first IETS experiment was performed by Jaklevic

and Lambe in 1966 [212], where the authors buried molecules into the interface

of a metal-oxide-metal tunneling junction, and measured its I-V characteristics.

A suddenly change in conductance occurs when the injection energy of electrons

(say, the bias voltage) is large enough to overcome the excitation energy of a spe-

cific vibration mode of the molecules. This change in conductance arises from

inelastic electron tunneling process, in which extra tunneling channels opened by

electron-phonon scattering. However, the first single molecular IETS experiment

was conducted only eleven years ago, by W. Ho’s group, where a STM is employed

to excite the vibration modes of acetylene molecules and measure the conductance

change [213, 214].

Since the vibration features are fingerprint properties of molecules, functional

groups, clusters, and even more complex systems, such as surface-adsorbate sys-

tems, in this aspect, at a single molecular level, STM-IETS relies heavily on the

reconstruction of substrate surface, the chemical composition of adsorbates, the

41


adsorption site, configuration, conformation and orientation, the molecule — sur-

face interactions, and inter- or intra-molecular interactions (if any), etc [215]. In

addition, the tunneling current would definitely effect the system in an STM ex-

periment, exciting electrons [62, 64, 65] or phonons [24, 216, 217] or leading to

adsorption/desorption processes [218, 219], combined with the disability to obtain-

ing surface topography. Usually it is difficult to characterize the system merely by

STM images and STS. STM-IETS then undertakes the mission to eliminate these

ambiguities and performs chemical characterization at single molecular level.

For a concrete impression for the efficiency and power of STM-IETS in chem-

ical characterization at atomic level, I would like to cite the experimental and

theoretical works about the identification of the products by benzene molecules

dehydrogenation on Cu(100) surface [220, 221]. The STM induced benzene de-

hydrogenation experiment was performed by L. J. Lauhon and W. Ho in 2000,

where the STM topographic images and IETS of benzene molecule and its dehy-

drogenated products on Cu(100) surface were measured, and then those results

were compared with that of pyridine (C5H5N) on the same surface. Based on

the similarity between the symmetry of STM images and C-H(D) peak locations

in STM-IETS, the authors non-conclusively proposed that the reaction products

might be benzyne fragment (C6H4) with two hydrogen atoms dissociated [220].

However, thoroughly theoretical simulations of the topographic images and STM-

IETS by Bocquet, Lesnard and Lorente demonstrated that the topographic images

of a benzene molecule lying on Cu(100) surface, and a phenyl (C6H5) or benzyne

fragments stand upon the bridge site of Cu(100) surface are hardly distinguish-

able due to their similar symmetry. However, the IETS features corresponds to

C-H stretching modes of each of these adsorbates is distinctive. By comparing

with the simulated STM-IETS with the measured ones, the authors conclude that

the benzene dehydrogenation product is a phenyl fragment rather than a benzyne

fragment [221].

5.3 Simulation of STM-IETS

Many approaches aimed to describe the tunneling process in STM measurement

emerged since the invention of this revolutionary instrument [88, 222]. Depending

on how to treat the tip-sample interactions, these approaches can be classified as

semi-classical or quantum mechanical. For the semi-classical approaches, the vac-

uum gap between tip and sample is considered as a slowly varying potential through

which electrons tunneling between tip and sample. This method is firstly proposed

by J. Bardeen and was named Bardeen approximation, where the tip electronic

42


structure should also be considered quantum mechanically [223]. Tersoff-Hamann

approach is a further approximation based on Bardeen approach, where the tun-

neling current is proportional to the local density of states (LDOS) at Fermi level

[224, 225]. The tip-sample-substrate in an STM experiments can also be viewed as

a tunneling junction and thus the description of tunneling processes in molecular

electronics is applicable in STM systems. In this context, electrons experience

scattering during tunneling, and the conductance can be directly calculated by

employing Landauer-Butticker formula, in which the conductance is proportional

to the transmission probability [226]. Moreover, the non-equilibrium Green’s func-

tion method can also be used in the calculation of tunneling conductance [227], and

the inelastic contribution can be incorporated in a straightforward way [217, 228].

5.3.1 Calculation of Tunneling Current

Bardeen approximation was proposed in 1961, much earlier than the invention of

STM. In the original formulation to describe the superconducting tunneling junc-

tions, Bardeen adopted WKB approximation, that the tunneling electrons move in

a slowly varying potential [223]. In particular, the wave functions ψi and ψj, each

from one side of the tunneling junction, fulfils the Schrodinger equations in the

corresponding part of space with appropriate boundary conditions, and overlaps in

the vacuum barrier region. Thus the transmission probability of electron tunneling

from state i to state j can be calculation by using Fermi golden rule:

Wij =2π

h|Mij|2δ(Ei − Ej) (5.1)

where the tunneling matrix element Mij can be expressed as

Mij =h2

2m

∫

S

dr2[ψ∗

i (r)∇ψj(r)− ψ∗j (r)∇ψi(r)

](5.2)

here, S is a cross section between tip and sample, so the tunneling matrix Mij

is just a surface integral of the current density. For a better description of STM

systems, C. J. Chen et al. further developed the tunneling theory on the basis of

Bardeen approximation [88], where the tunneling current can be written as

I =4πe

h

∫ +∞

−∞[f(EF − eV + ϵ)− f(EF + ϵ)] ρS(EF − eV + ϵ)ρT (EF + ϵ)|Mµν |2dϵ

(5.3)

here, f(E) is Fermi function, ρS and ρT are the density of states (DOS) of sample

and STM tip, respectively. If the temperature is low enough that kBT is smaller

43


than the energy resolution in measurement, the tunneling current can be approxi-

mated as

I =4πe

h

∫ eV

0

ρS(EF − eV + ϵ)ρT (EF + ϵ)d|Mµν |2ϵ (5.4)

by approximating the value of Fermi functions for occupied and unoccupied states

are 1 and 0, respectively. We can further approximate that the tunneling matrix

elements Mij varies only slightly in the experimental energy range, then we have

I ∝ 4πe

h

∫ eV

0

ρS(EF − eV + ϵ)ρT (EF + ϵ)dϵ (5.5)

that is to say, the tunneling current is just the convolution of the DOS of two

subsystems, which implies the measured physical quantity in STM experiment is

DOS.

The effects of STM tip to the measurements were usually found to be neglectable

in many experiments, which is also expected by people that the deviation from

different tips can be omitted. Tersoff and Hamann proposed a simple STM tip

model of which the wave functions are spherical symmetric s-type states [224, 225],

they use Sommerfeld model for metals to simulate the spherical tip, as shown in

Figure 5.2. The tunneling matrix element Mij at low bias can then be calculated

by subject the analytical expression of s-type orbitals

Mij =2πh2

mκΩ−1/2tip κR exp(κR)ψj(r0) (5.6)

where Ωtip is the normalized volume of STM tip, r0 is the radius of curvature of

tip, κ =√

2m(U − E)/h is the inverse decay length of wave functions. Thus the

tunneling current at bias V is

I ∝∫ EF +eV

EF

ρS(r, E)dϵ (5.7)

Differentiating tunneling current respect to bias voltage, the tunneling conductance

is obtaineddI

dV∝ ρS(r, EF ) (5.8)

Eq. 5.8 is Tersoff-Hamann approximation. From Eq. (5.7) and Eq. (5.8), we can

see that the constant current STM images reflect the contour LDOS of sample at

Fermi level. With the help of Tersoff-Hamann approximation, it is easy to explain

STM measurements qualitatively, and has been used in various systems, such as

semiconductor surfaces, surface-adsorbate systems, tunneling heterojunctions, and

so on [229].

44


Figure 5.2: Schematic of tunneling junction in STM experiments. The STM tip mightadopt various shapes, except for the lowest part is a hemisphere with radius of curvatureR.

5.3.2 Inelastic electron tunneling

Boosted by the rapid growth in STM-IETS experiments, there have been several

theoretical works concentrate on the simulation of inelastic tunneling process in

STM systems. Lorente and coworkers developed a scheme to calculate the elastic

and inelastic contributions to tunneling conductance based on Tersoff-Hamann ap-

proximation and Bardeen approximation [24, 230, 231], and revealed the symmetry

selection rules in STM-IETS [232]. A unified description of propensity rules for

IETS has also been proposed by Paulsson et al. [228]. Mingo and Makoshi devel-

oped a Green’s function based method to calculate the inelastic electron tunneling

[217], NEGF methods appropriate for molecular junctions can also be used in STM

systems[233–236]. In addition, many works combined theoretical simulation and

experimental measurement also emerged [221, 237–242].

In the following, I shall describe the scheme to calculate STM-IETS we imple-

mented based on Tersoff-Hamann approximation using finite difference method.

Most of the formula were derivated along the original work by Lorente et al.

[24, 25, 230, 231].

In Tersoff-Hamann approximation [224, 225], the tunneling conductance is propor-

tional to the LDOS of sample at Fermi level,

dI

dV(r) ∝ ρ(r, EF ) =

∑

n,k

|⟨r|Ψn,k⟩|2 δ(εn,k − EF ) (5.9)

45


here, ρ(r, EF ) is the LDOS at Fermi energy at position r, Ψn,k is the n-th wave

function with k-vector k whose eigenenergy is εn,k. The Delta function is substi-

tuted by a Gaussian in practical calculations, the broadening parameter could be

selected by considering practical experimental parameters, such as temperature,

energy resolution, etc.

Since STM-IETS originated from the vibrational excitation induced by inelas-

tic tunneling electrons, in the framework of Tersoff-Hamann approximation, the

change in tunneling conductance would be proportional to the change in the LDOS

induced by the corresponding vibration mode,

d2I

dV 2

∣∣∣∣Qi

∝ |δρ(r, EF )|2

=∑

n,k

[2ℜ⟨Ψn,k|r⟩⟨r|δΨn,k(Qi)⟩+ |⟨r|δΨn,k(Qi)⟩|2

]δ(εn,k−EF

)

= δρI + δρII

(5.10)

where δρ(r, EF ) is the change in LDOS at Fermi level at position r, |δΨn,k(Qi)⟩ is

the change in wave function |Ψn,k(Qi)⟩ induced by the ith vibration mode Qi.

From Eq. (5.10), we note that the intensity of IETS is contributed by two terms,

i.e. the first and second terms generated by finite difference, and are odd and even

parities, respectively. Taking into account of the arbitrariness in the assigning of

positive direction of vibration modes, combined with the same weight of positive

and negative directions, the contributions from the first order term vanishes, and

only δρII is needed in our calculation.

By using finite difference method, the changes in wave functions are linearly de-

pendent on the small displacement of ions’ positions, thus we can write out the

wave functions of systems experienced small configurational distortions [231],

|Ψ+n,k(fQi)⟩ = |Ψ0

n,k⟩+ fQi|Ψ0n,k⟩

= |Ψ0n,k⟩+ f |δΨn,k(Qi)⟩

|Ψ−n,k(fQi)⟩ = |Ψ0

n,k⟩ − fQi|Ψ0n,k⟩

= |Ψ0n,k⟩ − f |δΨn,k(Qi)⟩

(5.11)

where |Ψ0⟩ is the wave functions of the equilibrium configuration, and |δΨ(Qi)⟩is its change along Qi. The parameter f is introduced to ensure the validity of

harmonic approximation. Benchmark calculations using f = 0.1, 0.2, 0.5, and 1.0

demonstrated that there is no qualitative difference between these tests [243].

46


The change in wave functions can then be obtained by combining the equations in

Eq. (5.11):

|δΨn,k⟩ =1

2f

[|Ψ+

n,k(fQi)⟩ −|Ψ−

n,k(fQi)⟩⟨Ψ+

n,k(fQi)|Ψ−n,k(fQi)⟩

](5.12)

here, |Ψ−n,k⟩ is projected on the direction of |Ψ+

n,k⟩ to eliminate the phase difference

between wave functions in different systems.

47

6

Summary of papers

In this chapter, I would like to give a brief summary of the listed papers in this

thesis. All the works are classified into two part, the first is molecular electron-

ics, including device design and theoretical simulation of DNA sequencing using

conductance difference; The second part is inelastic electron tunneling spectra in

surface-adsorbate systems. I shall introduce our benchmark results first, and fol-

lowed by the performance of our STM-IETS code in two typical surface-adsorbate

systems, carbon oxide adsorbed on Cu(100) surface and acetylene adsorbed on

Cu(1000), which have been widely studied both by experiments and theoretical

simulation. Then two applications combined with the latest STM-IETS experi-

ments will be presented.

6.1 Molecular electronics

There are two works in this section, one is the theoretically design of negative

differential resistance (NDR) device based on armchair edged graphene nanorib-

bons (AGNR); the other is a theoretical study of the electron transport of DNA

base pairs based molecular junctions, in the latter study, we concentrate on the

structural effects on transport properties.

6.1.1 AGNR as a NDR device

All the AGNRs are semiconductors with energy gaps inversely proportional to its

width [146, 148, 244]. Combined with the high carrier mobility and long phase

coherence length [96, 157], it is expected that ballistic transport would occur in a

considerable large device constructed by graphene.

49

6 Summary of papers

In paper I, we designed a NDR device based on selectively doped AGNRs. The

doped nitrogen atoms introduce doping states in the energy gap of the electrodes,

and lead to sharp DOS peaks in the corresponding energy range. On the other

hand, in the scattering region, discrete energy levels appear due to the finite size.

In the resonant tunneling regime, the DOS peaks in the left and right electrodes

shit up and down with a value eV/2 when a bias voltage V is applied across the de-

vice. In consequence, the tunneling channel would be constructed or destructed at

different bias, and there would be a bias range that the channels are constructed at

lower bias and are destructed when the bias increases, which will lead to a decrease

in tunneling current, and exhibits as negative differential resistance phenomenon.

We have investigated devices consists of AGNRs with various widths and of various

lengths of scattering region, the results shows the larger of the energy gap of

undoped electrode, and the shorter the scattering region, the more evident the

NDR peak. This can be easily understood that from one side, the doping DOS

peak would be sharper when the gap of undoped system is larger; from the other

side, the energy intervals between discrete electronic states in the scattering region

would be larger when the size is smaller. Both of these issues contribute to a more

dramatic change in tunneling channel construction, and lead to a more evident

NDR peak.

6.1.2 Structural factors controlling the conductance of DNA

pairs junctions

The widely use of DNA technique in life science and medicine industrial demands

a cost-effective DNA sequencing method, the well established electric/electronic

techniques seems and is expected to be an effective approach in this aspect. Re-

cently, Lindsay’s groups proposed a method to sequencing DNA base pairs by using

STM to measure the conductance decay respect to tip-substrate distance [22, 23].

Molecular junctions composed by STM tip, DNA base pair (AT or GC), and

substrate are constructed in the experiments. At the mean time, the tunneling

currents were recorded as stretching the STM tip. Since the number of hydrogen

bonds (H-bonds) between base pairs in AT and GC are two and three, respectively,

thus AT pairs might be more flexible than GC pairs. In the experiment, the authors

self-assembled one of the base group on gold surface and held the other with STM

tip, the current decay curves evolves from the largest current to about zero last

more than and less than 2 nanometers, for 3-H-bonds and 2-H-bonds junctions,

respectively. Thus the number of H-bonds can be identified by comparing the

50

6.2 Inelastic tunneling spectra

current-distance decay curves between different base pairs, and DNA sequencing

is achieved by electric measurement [22, 23].

However, it is well known that the effective distance of H-bonds is about 0.25 nm,

which is much smaller than the decay lengths in the experiments (about 2 nm),

hence we believe that the difference between decay curves in the experiment is

not a consequence of the different number of H-bonds, other causes of this phe-

nomenon should be addressed. In paper II, by performing first-principles geometry

relaxation and transport calculation, we conclude that the experimentally observed

distance dependent tunneling current difference between DNA base pair junctions

are not caused by different number of H-bonds but by the different stacking struc-

tures. Furthermore, we found that this electrical read-out technique is probably

useful although the experimental measurements are not exact enough.


I shall briefly describe three of my works in this section, at first I’d like to introduce

the method implementation and benchmarks, and then two applications of our code

followed, both of them are combined with the latest experimental works.

6.2.1 Method implementation and benchmarks

We implemented the simulation method described in Section 5.3 on the basis of

converged electronic structures of VASP package [121, 122], in which the wave

functions is expanded in a plane wave basis set with a sufficient large energy

cutoff, projector augmented wave (PAW) [245] is used to describe the electron-ion

interactions in the calculations. The dynamic matrix is constructed by “selective

dynamics” supplied by VASP by confining positions of ions in lower layers.

In the plane wave representation, the wave functions is linear combinations of a

set of plane waves,

|Ψn,k⟩ =

Nk∑

i

ci,n,k|k + Gi⟩ (6.1)

where ci,n,k is the linear combination coefficients, Gi is the i-th wave vector of a

plane wave, it is an integer multiple of reciprocal lattice vectors

Gi = nxib1 + nyib2 + nzib3 (6.2)

51

6 Summary of papers

here, nσi is the i-th integer multiples in direction σ, and the reciprocal lattice

vectors can be calculated from lattice vectors in real space

aibj = 2πδij (6.3)

Nk in Eq. (6.1) is the number of plane waves at a specific k of the k-sampling in

the first Brillouin zone, and depends on the energy cutoff Ec

h2|k + GNk|2

2me

≤ Ec (6.4)

Since the plane waves are mutually orthonormal, only the coefficients need to be

operated in the calculation of STM-IETS in our code.

We have tested our code in two typical surface-adsorbate systems, which have

been widely investigated by experimental and theoretical means. Indeed, these

two system are also the earliest studied in the single molecular IETS area [213,

214, 246, 247].

CO molecule adsorbed on Cu(100) surface

The single molecular STM-IETS measurement of CO was first carried out by L.

Lauhon and W. Ho in 1999 [246], in which CO and its isotopic substitute adsorbed

on Cu(100) and Cu(110) surfaces. There are three peaks in the STM-IETS of

various isotopic substituted CO molecules adsorbed on both surfaces, which are

located at ∼20 meV, 36.3(33.2) meV, and 256 meV, and corresponding to Cu

surface vibration, two degenerated hindered rotation modes, and C-O stretching

mode, respectively. The CO-Cu stretching mode is not detectable in STM-IETS

experiments, which can be explained by the symmetry selection rules proposed

by Lorente et al. [232]. The spatial distribution of IET signals from hindered

rotation modes has also been scanned, and appeared as a protrusion centered at

the molecular axis [246].

In our benchmark calculations, we reproduced the STM-IETS and spatial distribu-

tions of IET signals induced by the hindered rotations and C-O stretching mode,

our results agreed very well with the experimental ones and previous theoretical

simulations [231].

Acetylene molecule adsorbed on Cu(100) surface

Acetylene (C2H2) and its deuterates (C2D2 and C2HD) adsorbed on Cu(100) and

Ni(100) surface are also widely studied both by experimental and theoretical tech-

52


niques [24, 213, 214, 217, 232, 247]. We used a series of acetylene molecules ad-

sorbed on Cu(100) surface as another typical system to benchmark our code.

It is found experimentally only peaks corresponding to C-H or C-D stretching

modes are detectable in the STM-IETS measurement. There is one peak in

C2H2@Cu(100) and C2D2@Cu(100), and two peaks in C2HD@Cu(100), where the

degeneracy between symmetric and antisymmetric C-H or C-D stretching modes

is eliminated by isotope effect [214]. In the meantime, IET signals only appear

when the injecting electrons possess energy just enough to excite a observable vi-

bration mode of the system [214]. Reversible rotation of the adsorption orientation

can also be achieved by inelastic electron excitation, where energy transfer from

C-H (C-D) stretching mode to the hindered rotation mode [213]. The IET sig-

nals were found to be spatially localized to the bonds which are responsible to the

corresponding vibration modes, this phenomenon can be verified by scanning the

spatial distribution of C-D stretching signals in C2HD@Cu(100) [247]. Further-

more, the C-H (C-D) stretching peak for C2H2 (C2D2) is mainly contributed by

the antisymmetric stretching mode, which is a consequence of the selection rules

[232].

Our benchmark simulations reproduced all the STM-IETS spectra and IET spa-

tial maps, all of our results are in good agreement with the previous theoretical

works[24, 217, 232].

6.2.2 Identifying adsorption configuration and orientation

of cis-2-butene adsorbed on Pd(110) surface

There are four equivalent adsorption orientations for the system cis-2-butene molecule

adsorbed on Pd(110) surface, as a result of both the symmetry of adsorbate and

substrate as shown in Figure 6.1. Sainoo and coworkers obtained the STM im-

ages of this system with each orientation, and found that these STM images can

be mutually transformed to each other under STM induced inelastic excitation,

which implies that the adsorption orientation can be reversibly varied [248].

The STM image of cis-2-butene molecule adsorbed on Pd(110) surface consists of

two parts: a head with a larger bright spot and a tail with a smaller and less bright

spot [248, 249]. By assuming the head corresponds to the two higher CH3 groups

and the tail corresponds to the relatively lower C=C double bond bonding to a Pd

atom at on-top site, the dynamics of orientation transformation induced by STM

inelastic excitation was revealed. Two vibration features are observable in STM-

IETS, i.e. C-H (C-D) stretching modes at 358 (268) meV and molecule-surface

stretching modes at 36 (32) meV for C4H8 (C4D8), both features are responsible

53

6 Summary of papers

Figure 6.1: Schematic view of the structure of one of the four equivalent adsorptionorientations of cis-2-butene molecule adsorbed on Pd(110) surface.

to the suddenly increase in the yield in orientation transformation recorded as

increasing bias voltage [248].

However, our calculation gives a different topographic image versus adsorption

orientation relations. In our simulation, the head of topographic image corresponds

to the CH3 group protrude along the Pd line of Pd(110) surface [(110) direction],

and the tail corresponds to the other CH3 group protrude normal to the Pd line

[(001) direction]. To verify our results, we carried out STM-IETS simulations and

compared with the experimental ones. STM-IETS were measured at the center of

the head in topographic images. According to claimed by experimenters, IETS was

measured at the midpoint of the line joining up the highest hydrogen atoms belong

to each CH3 groups. According to our simulation, IETS was measured above the

hydrogen atom of the CH3 group in (110) direction. By comparing the calculated

IETS at these two positions with the measured ones, the actual image-orientation

correspondence can be verified.

6.2.3 Melamine tautomers adsorbed on Cu(100) surface

Controlling the electron transport properties at single molecular level is inevitable

for the practical application of molecular electronics. Pan and Fu et al. demon-

54


strated that the transport properties of melamine tautomers adsorbed on Cu(100)

surface can be controlled by imposing current pulse by using STM [73]. When

melamine molecule is adsorbed on Cu(100) surface, two of its attached hydrogen

atoms at the same side of the triangular would be dissociated, and the molecule

would stand upon the bridge site of Cu surface with two N-Cu bonds for each nitro-

gen atoms at the dehydrogenated side. The adsorption configuration is presented

in Figure 6.2 D and E, and its topographic image exhibit a symmetric “dumbbell”

shape as shown in Figure 6.2 A and B (molecule 2). One of the top hydrogen

atoms can be transferred to the shoulder site of the adsorbed molecule by impos-

ing further pulse, and the orientation of the left top N-H bond is free to change

under electron pulse. These two melamine tautomers, named as melamine-C1 and

melamine-C2, whose adsorption configurations are presented in Figure 6.2 F and H,

respectively. The topographic images of C1 and C2 exhibit as asymmetric “cashew

nut” with different opening direction [73]. Furthermore, the I-V curves for C1 and

C2 evidently differ to each other, where for the one hand, C2 possesses a rectifier

character in which electrons tunneling from sample to STM tip is preferable, in

addition, the tautomers behave like a switch with on and off states corresponding

to C1 (C2) and C2 (C1) for positive (negative) bias, respectively [73].

Despite the manifold distinctions between melamine-C1 and C2, especially in the

I-V characteristics, it is difficult to identify these two states merely by STM topo-

graphic images, in which the shapes are exactly the same, and only the opening

directions are different. STM-IETS measurements were carried out towards single

molecular chemical identification. As a result of the difference in relative orien-

tations of N-H bonds on the top and shoulder site of melamine tautomers, the

out-of-plane swinging mode redshifted from 105 meV in melamine-C1 to 97 meV

in melamine-C2. This difference can be directly reflected by STM-IETS, by per-

forming IETS simulations, the proposed mechanism for melamine tautomerization

induced single molecular rectifying and switching in Ref. [73] is verified.

55

6 Summary of papers

Figure 6.2: Rectifying and switching behavior of a modified single melamine molecule.(A and B) STM topographic images of the same area (V = 0.2 V, I = 0.5 nA) inwhich molecules 1 and 3 are activate by applying a +2.4 V pulse on each of them. Theblack dots marked on the images give the STM tip position at where all conductancemeasurements are taken. Inset, STM images acquired with a sample bias of -0.8 V. Thescale for apparent high of the molecule is given. (C) I-V curves measured for Cu (black),melamine (red), and melamine-C (blue). Fluctuation features are shown in the inserts.(D and E) top and side views, respectively, of the computational model for the melamineadsorbed on Cu(100). The dashed line represents the unit cell. Calculated STM imagesof the optimized structures of melamine-C1 (F) and melamine-C2 (H) are given in Gand I, respectively (at V = - 0.6 V and height of 7 A from metal substrate). (J) Thecalculated I-V curves for dehydrogenated melamine, melamine-C1, and melamine-C2 onCu(100). Reprinted with permission from Ref. [73]. Copyright (2009) National Academyof Sciences, U.S.A.

56

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