First-principles Simulations of Nanomaterials for ... · Abstract Rapid developments of nanoelectronics and spintronics call for the design of new materials for building blocks of

First-principles Simulations of Nanomaterials for

Nanoelectronics and Spintronics

CAI YONGQING

(B.Sc., Northwestern Polytechnical University)

A THESIS SUBMITTED

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF PHYSICS

NATIONAL UNIVERSITY OF SINGAPORE

2011

Acknowledgements

First of all, I would like to thank my supervisor, Prof. Feng Yuan Ping. Prof.

Feng has given me lots of guidance and encouragement during the past years. I

am grateful to him for his word-by-word corrections of my manuscript and thesis,

and his support for me to attend the conference at ICTP.

I would like to thank my co-supervisor Dr. Zhang Chun, who has provided a lot

of help and suggestions on my research work. I got many insights from discussions

with his sharp mind and plenty of experience in the computational physics.

I would like to thank the previous and current members in the group. At the early

stage of my research, I got a lot of help from Wu Rongqin, Peng Guowen, and

Lu Yunhao. I had many useful discussions with them and other group members

including Ge MinYuan, Yang Ming, Zhou Miao, Sha Zhendong, Shen Lei, Bai

Zhaoqiang, Dai Zhenxiang, Zhang Aihua, and Yang Kesong.

At last, I would like to thank my parents, relatives and friends. Especially i thank

my parents for their support and love, and thanks Ke Qingqing for being patient

and enlightening with me in the past three years.

i

Table of Contents

Acknowledgements i

Abstract v

Publications vii

List of Tables x

List of Figures xi

1 Introduction 1

1.1 Quasi one-dimensional (1D) nanomaterials as building blocks of na-

noelectronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Molecular electronic devices: molecular diode and molecular switch 4

1.2.1 Molecular diode . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.2 Molecular switch . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Highly spin-polarized materials for spintronics . . . . . . . . . . . . 9

1.4 Objectives and scope of the thesis . . . . . . . . . . . . . . . . . . . 12

2 First-principles Methods 15

2.1 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . 16

ii

2.1.1 Hohenberg-Kohn theory and Kohn-Sham equation . . . . . . 17

2.1.2 LDA and GGA . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Implementation of density functional theory . . . . . . . . . . . . . 22

2.2.1 Pseudopotential . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.2 Planewave Basis . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Non-equilibrium Green’s function method . . . . . . . . . . . . . . 26

2.3.1 Green’s function . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.2 Open systems and NEGF . . . . . . . . . . . . . . . . . . . 28

2.3.3 Implementation of NEGF combined with DFT . . . . . . . . 30

3 Switching and rectification of a single light-sensitive diarylethene

molecule sandwiched between graphene nanoribbons 33

3.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Photochromic switching . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2.1 Molecular electronic structure . . . . . . . . . . . . . . . . . 37

3.2.2 Linear conductance and molecular switch . . . . . . . . . . . 38

3.3 Rectification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4 Functionalization of gold nanotubes and carbon nanotubes 54

4.1 Adsorbate and defect effects on electronic and transport properties

of gold nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.1.1 Computational details . . . . . . . . . . . . . . . . . . . . . 55

4.1.2 Structures and energetics of adsorbates on gold nanotubes . 55

4.1.3 Electronic structures of CO and O adsorbed gold nanotubes 60

4.1.4 Conductance of CO and O absorbed Au tubes . . . . . . . . 64

iii

4.1.5 Defect effects on conductance of Au tubes: Au adsorbate

and vacancy . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.2 Mechanically and chemically tuning of the work function of CNT . 68

4.2.1 Work function of CNT . . . . . . . . . . . . . . . . . . . . . 68

4.2.2 Computational details . . . . . . . . . . . . . . . . . . . . . 69

4.2.3 Strain effects on work function of pristine CNT . . . . . . . 71

4.2.4 Work function of potassium-adsorbed CNT . . . . . . . . . . 74

4.2.5 Strain effect on work function of potassium-decorated CNT . 75

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5 Strain effect on the spin injection and electronic tunneling of

Co2CrAl/NaNbO3/Co2CrAl 82

5.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.2 Energetics and electronic structure analysis . . . . . . . . . . . . . . 84

5.3 Strain effects on the spin injection and tunnel magnetoresistance . . 88

5.4 Strain effects on the tunnel magnetoresistance . . . . . . . . . . . . 91

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

6 Conclusions and perspectives 95

References 98

iv

Abstract

Rapid developments of nanoelectronics and spintronics call for the design of new

materials for building blocks of nanoscale electronic devices. In this thesis, first

principles calculations were carried out to study the physical properties of various

kinds of nanomaterials and investigate their potential applications in nanoelectron-

ics and spintronics.

Firstly, we studied coherent electronic transport through a single light sensitive di-

arylethene molecule sandwiched between two graphene nanoribbons (GNRs). The

“open” and “closed” isomers of the diarylethene molecule that can be converted

between each other upon photo-excitation were found to have drastically differ-

ent current-voltage characteristics. More importantly, when one GNR is metallic

and another one is semiconducting, strong rectification behavior of the “closed”

diarylethene isomer with the rectification ratio >103 was observed. The results

open possibilities for the design of a new class of molecular electronic devices.

Secondly, electronic and/or transport properties of gold nanotubes and carbon

nanotubes (CNTs) were studied. For gold nanotubes, effects of adsorbates (CO

molecule and O atom) and defects on the electronic and transport properties of

v

Au (5,3) and Au (5,5) nanotubes were investigated. After CO adsorption, the

conductance of Au (5,3) decreases by 0.9 G0, and the conductance of Au (5,5)

decreases by approximately 0.5 G0. For O adsorbed Au tubes, O atoms strongly

interact with Au tubes, leading to around 2 G0 of drop of conductance for both

Au tubes. When a monovacancy defect is present, the conductance decreases by

around 1 G0 for both tubes. For CNT, strain dependence of work functions of both

pristine and potassium doped CNTs was calculated. We found that for pristine

cases, the uniaxial strain has strong effects on the work functions of CNTs, and

the responses of work functions of CNT (5,5) and (9,0) to the strain are distinctly

different. When coated with potassium, for both CNTs, work functions can be

reduced by more than 2.0 eV, and the strain dependence of work functions changes

drastically.

Finally, effects of strain on transport properties of Co2CrAl/NaNbO3/Co2CrAl

magnetic tunneling junction (MTJ) were studied. Both spin polarization and tun-

nel magnetoresistance (TMR) of the MTJ were found to respond to positive (ten-

sile) and negative (compressive) strains asymmetrically. While a compressive strain

up to 4% causes slight increases in the spin polarization and small fluctuations in

TMR, a tensile strain of a few percent significantly reduces the TMR. This study

provides a theoretical understanding on relationship between transport properties

through a MTJ and interface atomic structural changes induced by an external

strain.

vi

Publications

[1] Yongqing Cai, Miao Zhou, Minggang Zeng, Chun Zhang, Yuan Ping Feng, “Ad-

sorbate and defect effects on electronic and transport properties of gold nanotubes”,

Nanotechnology 22, 215702 (2011).

[2] Yongqing Cai, Aihua Zhang, Yuan Ping Feng, Chun Zhang, Hao Fatt Teoh,

Ghim Wei Ho, “Strain effects on work functions of pristine and potassium-decorated

carbon nanotubes”, J. Chem. Phys., 131, 224701 (2009).

[3] M. G. Zeng, L. Shen, Y. Q. Cai, Z. D. Sha, Y. P. Feng, “Perfect spin-filter and

spin-valve in carbon atomic chains”, Appl. Phys. Lett. 96, 042104 (2010).

[4] M. Zhou, Y. Q. Cai, M. G. Zeng, C. Zhang, Y. P. Feng, “Mn-doped thiolated

Au-25 nanoclusters: Atomic configuration, magnetic properties, and a possible

high-performance spin filter”, Appl. Phys. Lett. 98, 143103 (2011).

[5] Yongqing Cai, Chun Zhang, Yuan Ping Feng, “Dielectric properties and lattice

dynamics of α-PbO2-type TiO2: The role of soft phonon modes in pressure-induced

phase transition to baddeleyite-type TiO2”, Phys. Rev. B 84, 094107 (2011).

[6] Yongqing Cai, et. al., “Strain effect on the spin injection and electronic con-

ductance of Co2CrAl/NaNbO3/Co2CrAl magnetic tunneling junction”, Manuscript

vii

finished for Phys. Rev. B submission.

[7] Yongqing Cai, Aihua Zhang, Yuan Ping Feng, and Chun Zhang, “Switching

and Rectification of a Single Light-sensitive Diarylethene Molecule Sandwiched

between Graphene Nanoribbons”, J. Chem. Phys. 135, 184703 (2011).

[8] Y. H. Lu, R. Q. Wu, L. Shen, M. Yang, Z. D. Sha, Y. Q. Cai, P. M. He, Y. P.

Feng, “Effects of edge passivation by hydrogen on electronic structure of armchair

graphene nanoribbon and band gap engineering”, Appl. Phys. Lett. 94, 122111

(2009).

[9] Z. D. Sha, R. Q. Wu, Y. H. Lu, L. Shen, M. Yang, Y. Q. Cai, Y. P. Feng, Y.

Li, “Glass forming abilities of binary Cu(100-x)Zr(x) (34, 35.5, and 38.2 at. %)

metallic glasses: A LAMMPS study”, J. Appl. Phys. 105, 043521 (2009).

[10] M. Yang, R. Q. Wu, W. S. Deng, L. Shen, Z. D. Sha, Y. Q. Cai, Y. P. Feng, J.

S. Wang, “Electronic structures of beta-Si(3)N(4)(0001)/Si(111) interfaces: Perfect

bonding and dangling bond effects”, J. Appl. Phys. 105, 024108 (2009).

[11] R. Q. Wu, L. Shen, M. Yang, Z. D. Sha, Y. Q. Cai, Y. P. Feng, Z. G. Huang,

Q. Y. Wu, “Enhancing hole concentration in AlN by Mg : O codoping: Ab initio

study”, Phys. Rev. B 77, 073203 (2008).

[12] R. Q. Wu, L. Shen, M. Yang, Z. D. Sha, Y. Q. Cai, Y. P. Feng, Z. G. Huang,

Q. Y. Wu, “Possible efficient p-type doping of AlN using Be: An ab initio study”,

Appl. Phys. Lett. 91, 152110 (2007).

[13] Zhaoqiang Bai, Yongqing Cai, Lei Shen, Ming Yang, Viloane Ko, Guchang

Han, and Yuanping Feng, Magnetic and transport properties of Mn3−xGa/MgO/Mn3−xGa

viii

magnetic tunnel junctions: A first-principles study, Appl. Phys. Lett. 100, 022408

(2012).

ix

List of Tables

4.1 Energetics and structures of adsorbates (CO, O, Au) on Au (5,3)

and Au (5,5) nanotubes. d is the shortest length of the bonds formed

by Au and adsorbates; δQx(x=CO, O, Au) and δQAu are the net

partial charge transfers of the adsorbates and the Au atom with the

shortest distance from the adsorbates. . . . . . . . . . . . . . . . . . 58

5.1 Calculated cohesive energies and interface bond lengths for various

CCA/NNO interfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 86

x

List of Figures

1.1 A molecular switch based on tuning the molecular orbital with elec-

tric field. Reprinted with permission from Ref.[56]. . . . . . . . . . 7

1.2 Switching cycle of diarylethenes. . . . . . . . . . . . . . . . . . . . . 8

1.3 Schematic pictures of density of states (DOS) of paramagnet, ferro-

magnet, and half metal. . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 Schematic illustration of the replacement of the all-electron wave-

function and core potential by a pseudo-wavefunction and pseudopo-

tential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1 Molecular structures and photochemical interconversion of the “closed”

and “open” diarylethene. The molecule can be divided into core,

spacer, and linker groups. . . . . . . . . . . . . . . . . . . . . . . . 34

xi

3.2 (a) Supercells of optimized 6-zGNR-“closed” diarylethene-6-zGNR

and 14-aGNR-“open” diarylethene-14-aGNR junctions. Red, blue,

violet and yellow lines denote bonds formed by O, N, C and S, re-

spectively. Note that hydrogen atoms are not shown in the figure.

The shadowed area denotes portions in the supercell chosen as elec-

trodes. (b) Band structures of 10-, 12-, and 14-aGNR and 6-zGNR.

The calculated band gaps are 1.21, 0.54, 0.22 eV for 10-aGNR, 12-

aGNR and 14-aGNR respectively. Ca and Cz are the lattice constant

of the unit cell of the aGNR and zGNR, respectively. . . . . . . . . 36

3.3 Lineup of orbitals for “open” (left) and “closed” (right) diarylethene. 38

3.4 Conductance spectra at zero bias of 6-zGNR-diarylethene-6-zGNR

(a) and 14-aGNR-diarylethene-14-aGNR (b) junctions with “closed”

(blue) and “open” (red) isomers. The short lines above the plots

show the HOMO/LUMO alignments with the electrode Fermi level.

(c) Isosurface plot of transmission eigenstates at EF for “closed”

(left) and “open” (right) isomers of diarylethene with 6-zGNR elec-

trodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.5 I-V characteristics of (a) aGNRs and (b) 6-zGNR diarylethene junc-

tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.6 Variation of logarithmic transmission curves with voltage logT(e,V)

for (a)10-aGNR, (b)12-aGNR, (c)14-aGNR and (d) 6-zGNR sym-

metrical junctions with diarylethene in the “closed” form. Evolu-

tions of HOMO-2 and HOMO-3 of the “closed” molecule as a func-

tion of voltage are shown by white points; . . . . . . . . . . . . . . 42

xii

3.7 Mulliken charge analysis for the “closed” diarylethene molecule em-

bedded in symmetric GNRs junctions. . . . . . . . . . . . . . . . . 44

3.8 (a) Optimized atomic configuration of the 6-zGNR-diarylethene (“closed”)-

10-aGNR junction. (b) Evolution of MPSH levels as a function

of voltage for the 6-zGNR-diarylethene-10-aGNR junction with the

“closed” diarylethene. Blue dotted lines indicate Fermi energy lev-

els of two electrodes. The shadowed area depicts the movement of

the band gap of 10-aGNR under biases. (c) I-V characteristics of

6-zGNR-(“closed”) diarylethene-x -aGNR (x=10, 12 and 14) junc-

tions. The inset shows the rectification ratio (RR) of these junctions

from 0.4 to 1.0 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.9 Variation of logarithmic transmission curves with voltage logT(e,V)

for asymmetrical junctions with (a)10-aGNR, (b)12-aGNR, (c)14-

aGNR as left electrode and 6-zGNR as right electrode and the di-

arylethene is in “closed” state. (d)logT(e,V) plot for “open” di-

arylethene with 14-aGNR and z6GNR electrodes. Dotted brown

lines indicate the range of current integration around the Fermi

level. Transmission peaks related to HOMO/LUMO are denoted

by yellow circles and yellow triangles. . . . . . . . . . . . . . . . . . 48

3.10 Mulliken charge analysis for the “closed” diarylethene molecule em-

bedded in asymmetric GNRs junctions . . . . . . . . . . . . . . . . 49

xiii

3.11 Spatially resolved local density of states along the transport axis for

(a) 6-zGNR-“closed” diarylethene-10-aGNR (b) 6-zGNR-“closed”

diarylethene-14-aGNR junctions at different bias voltages. The HOMO/LUMO

of diarylethene localized in the middle region and interface states

(ISs) localized at contacts can be clearly identified. . . . . . . . . . 50

4.1 Atomic structure of (n,m) gold SWNTs obtained by cylindrical fold-

ing of the 2D triangular lattice. Basis vectors of the 2D lattice are

a1 and a2 (Reprinted with permission from Ref. [133]). . . . . . . . 56

4.2 Geometric structures of (5,3) and (5,5) Au nanotubes and a schematic

description of possible adsorbing sites for adsorption: Top, B1 (Bridge

site 1), B2 (Bridge site 2), Center. . . . . . . . . . . . . . . . . . . . 57

4.3 Adsorption geometries for CO adsorption on Au (5,3) at top (a),

B1 (b), and Au (5,5) at B1 (c) sites, oxygen adsorption on Au (5,3)

at center (d), B1 (e), and Au (5,5) at center (f) sites, respectively.

The C, O, and Au atoms are depicted in grey, red, and yellow,

respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.4 LDOS and orbitals of CO adsorbed on Au (5,3) at top (a), B1 (b)

sites and Au (5,5) at B1 (c) site. The LDOS projected on the CO

molecule is shown in black and that projected on the gold atom

with the shortest distance from the C atom is colored yellow. The

populations of CO orbitals are calculated through integrating over

the relevant peaks. Included also are the vibrational frequencies of

stretching mode for different adsorption configurations. Notice that

the frequency of free CO molecule is calculated as 2128 cm−1 . . . . 62

xiv

4.5 Comparison of Au states after O atomic adhesion with those of the

pristine (5,3) (a) and (5,5) (b) Au tubes. For the adsorbed tubes,

LDOS is projected onto Au atom with the shortest distance from

the O atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.6 Quantum conductance spectrum for CO adsorbed Au (5,3)(a) and

Au (5,5) (b). The conductance spectra of pristine tubes (dashed

lines) are also given for comparison . . . . . . . . . . . . . . . . . . 64

4.7 Quantum conductance spectrum for oxygen adsorbed Au (5,3) (a)

and Au (5,5) (b). The conductance spectra of pristine tubes (dashed

lines) are also given for comparison . . . . . . . . . . . . . . . . . . 65

4.8 Conductance as a function of energy for defective Au (5,3) tube with

defects arising from Au adhesion (a) and monovacancy (b) on the

tube. The relaxed defective structures are given as the insets, where

the atoms around the defective site are highlighted by violet balls.

It can be seen that the Au adatom distorts the tube differently at

different adsorption sites. . . . . . . . . . . . . . . . . . . . . . . . . 66

4.9 Conductance as a function of energy for defective Au (5,5) tube with

defects arising from Au adhesion (blue line) and monovacancy (red

line) on the tube. The relaxed defective structures are given as the

insets, where the atoms around the defective site are highlighted by

violet balls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

xv

4.10 Supercells of CNT (9,0) (upper) and CNT (5,5) (bottom) employed

in calculations. Strains are applied by elongating or shortening the

length of tubes along the tube axis (z axis) with two outermost

layers (shadowed area) fixed to their bulk structures without strain.

In all calculations, the periodically replicated CNTs (in both x and

y directions) are separated by a vacumm region of 10 A. . . . . . . 70

4.11 Relation between work function (W) and potentials of CNT (5,5)

under -1% compressive strain . . . . . . . . . . . . . . . . . . . . . 71

4.12 Work functions of CNT (5,5) and CNT (9,0) Vs. strain. Tensile

strain is positive and compressive strain is negative. For CNT (5,5),

the work function changes monotonically when strain changes from

-10 % to +10 %. For CNT (9,0), when strain changes from -2% and

4%, the work function behaves similar to that of CNT (5,5). . . . . 72

4.13 Electron DOS as a function of energy for CNT (9,0) at different

compressive (a), and tensile (b) strains. Dashed lines denote Fermi

energies. Note: The electrostatic potential in the middle of vaccum

is set to be 0.0 eV. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.14 A schematic description of different adsorbing sites (purple circles)

of K atom on CNT (9,0) (left) and CNT (5,5) (right): Bridge sites

B1, B2 ; Hollow site H, and top site T. Binding energies for different

sites are calculated to be B1 : 1.58 eV, B2 : 1.62 eV, H : 1.73 eV, T :

1.59 eV for CNT (9,0), and B1 : 0.95 eV, B2 : 0.92 eV, H : 1.04 eV,

T : 0.92 eV for CNT (5,5),repectively. . . . . . . . . . . . . . . . . 76

xvi

4.15 Work function of potassium deposited CNT (9,0) and CNT (5,5) Vs.

deposition density (x in KxC). For CNT (9,0), the work function

reaches its minimum value of 2.2 eV at the coating density of 5.56%

(denoted as A in (a)), and the minimum work function of CNT (5,5)

is 1.98 eV occurring at the coating density of 6.25% (B in (a)). The

atomic structures of K-coated CNT (9,0) and (5,5) with minimum

work functions are shown in Fig. 5 (b) ( A: upper, and B: lower). . 77

4.16 Strain effects on adsorption energies of K@CNTs, and work func-

tions of K adsorbed CNTs: (a) Adsorption energy of a single K atom

on CNT (9,0) and (5,5) as a function of strain; (b) Strain depen-

dence of work functions of K coated CNT (9,0) as shown in Fig. 5

(b) (upper), and K coated CNT (5,5) (lower one in Fig. 5 (b)). . . . 78

4.17 (a) Calculated average charge transfer per K atom to CNT (5,5) and

CNT (9,0) at different strains. When strain changes from -10% to

10%, the charge transfer for two tubes monotonically increases. (b)

Isosurface of the differential charge density between isolated CNT

(5,5), K atoms, and K-coated CNT (5,5). . . . . . . . . . . . . . . . 79

5.1 Atomic structure of the CCA/NNO/CCA MTJ. The models are

built by stacking CCA directly on NNO along the [001] crystaline

direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2 LDOS for the majority (top panels) and minority (bottom panels)

spin electrons projeted to the O, Co and Nb atoms at the Co-NbO2

interface and in bulk region, respectively. The vertical dashed line

indicates the position of the Fermi level. . . . . . . . . . . . . . . . 87

xvii

5.3 Variation of the planar averaged SP along the interface normal di-

rection of the CCA/NNO/CCA MTJ, at various values of applied

strain. The position of the Co-NbO2 interface plane is indicated by

the vertical dashed line. The horizontal dashed line corresponds to

100% SP in each case. . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.4 In-plane wave vector k� = (kx, ky) dependence of majority-spin

(a) and minority-spin (b) transmissions at the Fermi level of the

CCA/NNO/CCA MTJ in the parallel magnetization configuration

without strain. (c) TMR ratio as a function of strain. . . . . . . . . 92

5.5 The differences between majority-spin transmissions at the Fermi

level in the parallel magnetization configuration in strained and

strain free CCA/NNO/CCA MTJ: (a) G↑↑(−4%)−G↑↑(0), (c) G↑↑(4%)−G↑↑(0). The transmission at zero strain is given in (b). The Fermi

surfaces corresponding to the two folded bands in the Brillouin zone

of the orthorhombic Co2CrAl are shown in (d) and (e), respectively. 93

xviii

Chapter 1

Introduction

In last decades, Si-based technology has witnessed a great success in microelec-

tronics. However, as the trend of miniaturization of the device sizes continues, new

phenomena and problems that are absent in microelectronics occurs. Thanks to

the development of nanotechnology, a variety of nanomaterials, such as nanowires

and nanotubes, have been successfully produced, which triggers the emergence of

nanoelectronics and provides new opportunities to achieve continuing performance

improvement in post-Si technology. Among all the produced nanomaterials, carbon

based nanomaterials such as carbon nanotubes (CNTs) and graphene are strong

candidates in replacing Si. In addition, molecular electronics which utilizes the ver-

satile characteristics of molecules may lead to new devices. Building an electronic

device on top of individual molecules is one of the ultimate goals in nanoelectronics.

Recently, spintronics is a particularly promising technology, where the spin states

1

Chapter 1. Introduction

of carriers are utilized as an additional degree of freedom for information process-

ing and storage. Combination of technologies in spintronics and nanoelectronics

could lead to a new generation of devices with novel functionalities and superior

performance.

1.1 Quasi one-dimensional (1D) nanomaterials as

building blocks of nanoelectronics

Quasi 1D nanomaterials such as metallic nanowires and nanotubes are quite promis-

ing in nanoelectronics due to their high current density and conductivity.[1–6] As

the dimension of materials reduces to nanoscale regime in which the mean free

path of electron is comparable to the size of the materials, conductance (G) of the

metallic 1D nanomaterials where the electrons transport ballistically is quantized

(G = NG0, G0 = 2e2/h).[7] Conductance quantization has been observed in a va-

riety of 1D Au, Pt, Cu, Ag nanowires.[1–4] More recently, helical single-wall gold

nanotubes were successfully synthesized in experiment.[8] Owning to their helical

structures, gold nanotubes have unique electronic and catalytic properties. It was

predicted by theoretical study that chiral current flowing through gold tubes may

induce strong magnetic field.[9, 10] For the metallic nanowires or nanotubes, ad-

sorption of even a single molecule on the surface of the materials can drastically

change the conductance.[11, 12] The effects of adsorption of atoms and molecules

on the surface of these quasi 1D nanomaterials are widely investigated to evaluate

the influences on potential nanoelectronics applications.[3, 13]

2


In addition, low-dimensional carbon-based nanomaterials, such as CNTs[14] and

graphene,[15, 16] have attracted great attentions for applications in nanoelectron-

ics due to their unique properties. Depending on chirality of the tube, CNTs can

be either metallic or semiconducting, and exhibit interesting physical properties in-

cluding long ballistic transport length,[17] high thermal conductivity,[18] and high

mechanical strength.[19] Single-wall CNTs have been considered as possible na-

noelectronic components such as diodes and field-effect transistors (FET).[20–23]

Since the first successful production of CNT-based FET in 1998,[23] single-wall

CNTs have been extensively investigated as a channel material for replacement of

Si to enhance the mobility and integration scale of electronic devices. The ability

of controlling the polarity of conduction carriers in CNT is highly important in na-

noelectronics applications. Normally, CNT devices present p-type behavior due to

oxygen molecules adsorbed on their surfaces.[24] n-type conduction in CNT-based

FET can be achieved by doping alkali atoms, which involves a charge transfer from

the alkali atoms to CNT.[25] In addition, annealing in vacuum[26] or contacting

with metallic electrode with a low work function such as Ca[27] and Sc[28] has also

been reported to be effective ways of producing n-type CNT devices.

Graphene is a planar network of carbon atoms connected by strong covalent C-C

bonds that exhibits linear energy-momentum (E -K ) relation in the band struc-

ture around Fermi energy. Velocities of electrons and holes in graphene are ∼108

cm/s and the mobilities are 15 000 cm2/Vs at room temperature,[15] which are

much higher than those of conventionally used semiconducting materials. These

properties make graphene a promising new material for applications in transistors

and integrated circuits. However, the lack of a bandgap in graphene sheets hinders

3


high ON/OFF current ratios in electronic devices. One way to create bandgaps

in graphene is to pattern graphene sheets into nanoribbons, which have attracted

great interest due to their potential applications in nanoelectronics.[29, 30]. A

graphene nanoribbon (GNR) can be either semiconducting or metallic depending

on its edge geometry. Ribbons with zigzag edges (zGNRs) were shown to be metal-

lic, whereas the armchair edged ribbons (aGNRs) are semiconducting with energy

gaps inversely scaling with the ribbon width.[31] They can be obtained either by

tailoring two-dimensional (2D) graphene or unzipping CNTs to 1D pattern.[32]

However, perfect edges on nanoribbons are difficult to achieve. Theoretical cal-

culations suggest that edge roughness will have a large impact on their electronic

properties.[33, 34] Besides the approach of making GNRs, other proposed methods

of tuning the electronic structure of graphene include applying external fields,[35]

chemical adsorption,[36, 37] exerting strain[38] and periodic potential,[39] or using

bilayer graphene.[40]

1.2 Molecular electronic devices: molecular diode

and molecular switch

1.2.1 Molecular diode

A diode or a rectifier, which allows an electric current to flow in one direction

but blocks it in the opposite direction, is an important component in electronic

circuits. The concept of a molecular diode was firstly proposed by Aviram and

4


Rater (A-R).[41] This molecular diode consists of a system with a donor group

and an acceptor group which are separated by a σ-bonded segment. The flow of

charges from cathode to anode can be described by a three-stage electron tunneling

process: cathode to acceptor, acceptor to donor, and donor to anode. The key to

obtain a large rectification ratio is to create a proper alignment of the acceptor

and donor levels, through which tunneling in the forward bias direction is strongly

favored.

The A-R type of molecular diode was fabricated for the first time using Langmuir-

Blodgett C16H33Q-3CNQ monolayer sandwiched between two planar Pt and Ag

electrodes, where the p-dodecyloxyphenyl group is the donor group, and the 3CNQ

moiety is the acceptor group.[42] Other experiment[43] using different electrodes

confirmed that the rectification observed in the above experiment[42] was due to the

molecule itself rather than the metallic interface. Rectification was also observed in

self-assembled monolayers of block copolymers in scanning probe experiments.[44]

While the above experiments were performed with a large number of molecules,

single molecule diode has been demonstrated in a molecule consisting of two weakly

coupled conjugated units, using a mechanically controlled break-junction (MCBJ)

method.[45] In this experiment, the two conjugated units in the molecule, with one

being fluorized and the other one not, are different and this breaks the symmetry

of the molecular junction. When sweeping the bias voltage, the energy levels of

both units are shifted relative to each other, and different currents for different

bias polarities lead to the diode behavior.

In addition to the Aviram and Rater’s approach, there are other proposals for

creation of molecular diodes based on different mechanisms, such as Coulomb

5


blockade,[46] multi-phonon suppression,[47] and intermolecular non-adiabatic elec-

tron transfer.[48] Asymmetric current-voltage (I-V ) curves may also be induced by

employing different molecule-electrode contacts on the two ends,[49] or by asym-

metrically placing a resonant level between the electrodes.[50] Theoretical calcu-

lation has shown that rectification may be realized in off-resonance regimes by

exploiting conformational changes in the molecule driven by an external electric

field.[51] However, previously reported molecular rectifiers usually have a small rec-

tification ratio in the order of 10,[52, 53] and recently, it has been concluded that

the rectification ratio originating from currently accepted rectification mechanisms

of single-molecule based devices generally has a limit of 100.[54] Although for some

single-molecule rectifiers, theoretical studies based on semi-empirical methods give

high rectification ratio (>>100), more reliable first principles calculations for the

same systems predicted a much lower ratio (<100).[55] Search for new mechanisms

of molecular junctions that can exceed the limit of rectification ratio, 100, is one

of the central issue of the field.[55]

1.2.2 Molecular switch

Single-molecule based switch holds great promise for the design of memory and

logic components in nanoelectronics. Two approaches to realize molecular switch-

ing have been proposed, including control of the orbital of the molecule through

electric field[56] and control of the conformation of the molecule in response to

external triggers.[57] For both approaches, the key is to translate the changes in

molecular orbital or molecular structure into changes in molecular conductivity to

6


Figure 1.1: A molecular switch based on tuning the molecular orbital with electric

field. Reprinted with permission from Ref.[56].

a measurable degree. Since molecular orbitals contain all quantum mechanical in-

formation of molecular electronic structures and offer spatial conduction channels

for electron transport, delicate modulation of the molecular orbitals is believed

to be an effective way to tune the performance of electron transport through the

molecule (Fig. 1.1).[56] For the latter approach, among various triggers, light is a

very attractive external stimulus because of ease of addressability, fast response

times, and compatibility with a wide range of condensed phases. Light-driven

switching of the so-called photochromic molecules has been carried out by several

experimental and theoretical groups.[57–59]

Photochromic molecules are compounds capable of undergoing a reversible photo

transformation between two stable states, and have attracted remarkable inter-

ests due to their potential applications in optoelectronic devices. Among them,

diarylethene is one of the most promising compounds due to its excellent thermal

stability and high fatigue resistance and has been widely exploited to reversibly

control the conductance connected with gold nanoparticles.[60, 61] The key idea

7


Figure 1.2: Switching cycle of diarylethenes.

underlying the diarylethene based switches is that two light convertible isomers

of the molecule, an “open” and a “closed” isomers (as shown in Fig. 1.2), have

dramatically different conductances when connected with metal leads. Structural

deformation between the “closed” and “open” states during photo transformation

leads to the reorganization of the π-conjugated backbone of the molecule, and junc-

tion based on the “closed” isomer with longer conjugation path-length has larger

conductance than that of the “open” isomer (Fig. 1.2). Metal-diarylethene junc-

tions have been extensively studied both theoretically and experimentally for their

applications in molecular switches.[61–63]

To make an optic switch by photochromic molecules such as diarylethene, one chal-

lenge is related to immobilization of the molecule to external bulk surface.[64] For

example, although switching between “open” and “closed” forms of the thiophene-

based diarylethene is reversible in solution, it can only be switched from the

“closed” to the “open” form once it is connected to gold via the Au-S bond.[62, 65]

The irreversibility is theoretically attributed to quenching of the excited states of

the “open” form associated with mixing with Au 3d orbitals. Density functional

theory calculations[66, 67] revealed that the quenching observed may result from

the alignment of the Fermi level of gold with the molecular frontier orbitals of the

“open” isomers. The deep-lying highest occupied molecular orbital level of the

8


“open” isomer locates at a high 3d density of states of the metallic electrode, thus

facilitating electron transfer events, and thereby reducing the lifetime of the hole

created after excitation. In contrast, the highest occupied molecular orbital of the

“closed” isomer is higher in energy and lies in a region of low density of states of

gold, hence ring opening can take place. Although a simple solution to preserve

the reversibility of the switch is to isolate the switching unit by non-conjugated

linker like CH2 group,[67] however, the electron transport would then be substan-

tially reduced and the ON/OFF ratio between the conductances of the “closed”

and “open” forms would be lowered. The use of carbon electrode like CNT or

GNR is believed to be an effective way to preserve the reversibility due to lack of

3d electrons.[64]

1.3 Highly spin-polarized materials for spintron-

ics

Spintronics exploits spin-dependent electronic properties of magnetic materials and

semiconductors in which information is encoded by electron spin. In 1933, F. Mott

firstly proposed a concept of spin dependent conduction in ferromagnetic met-

als where electrical current is a sum of two independent spin-minority and spin-

majority currents.[68] Experimental observation of a spin-polarized current was

reported by P. Tedrow and R. Meservey,[69] who investigated electron tunneling

from a ferromagnetic metal through an insulator into a superconductor. In 1975,

M. Julliere observed the effect of tunnel magnetoresistance (TMR) in a Fe/GeO/Co

9


magnetic tunneling junction (MTJ).[70] In 1988, A. Fert and P. A. Grunberg inde-

pendently discovered the giant magnetoresistance (GMR) in layered thin films of

ferromagnetic metal alternated to a non-magnetic metal.[71, 72] The discovery of

GMR stimulates tremendous interests in the field of spintronics and opens the door

to a wealth of new scientific and technological possibilities. To fabricate spintronics

devices, a highly spin-polarized current is strongly desired. Generally, there are

several promising ways to obtain highly spin-polarized carriers.

The first approach is to use a semiconducting or insulating barrier to selectively

filter carriers with one spin state from normal ferromagnetic metals such as Co or

Fe, as demonstrated in the Fe/MgO/Fe MTJ.[73] Considering the complex band

structure of the barrier, different electronic states have different symmetries, which

results in different tunneling probabilities for each spin direction and leads to spin

polarized current. Therefore, the ferromagnetic electrode and the tunneling barrier

play important roles in obtaining a highly spin polarized current. In addition,

theoretical calculation has shown that interface formed between the electrode and

barrier can strongly influence the spin polarization(SP) and TMR of MTJ.[74]

Recently, adoption of half metal as the spin source is widely investigated. Half-

metallic ferromagnets have a band gap at the Fermi energy (EF) for electrons

with one spin direction, whereas they are metallic with respect to electrons with

the opposite spin direction (Fig. 1.3). Therefore, a fully spin-polarized current

and a high spin injection efficiency are predicted for these compounds. Some half

metals have been theoretically predicted, including Fe3O4,[75] CrO2,[76] double

perovskites,[77] zinc-blende-type CrAs[78] and Heusler alloys.[79]

Among all the half-metallic ferromagnets, Heusler alloys are promising materials for

10


spintronics applications, due to their high Curie temperatures and large magnetic

moments per unit cell. Unfortunately, although a full SP is predicted for bulk

Heusler alloys, the measured SP is usually much lower. Most of the Heusler alloys

lose the high SP due to phase disorder and defects in bulk materials.[80] More

importantly, when a Heusler alloy is heterogeneously grown on another material,

the charge-discontinuity related interface states can dramatically weaken the SP

at the interface and reduce the TMR ratio.[81] In addition, interface strain due to

lattice mismatch may affect its SP. Theoretical calculation has shown that strain

can alter the width of the minority band gap and the position of the Fermi level in

the minority band gap.[82] It has been demonstrated that a 0.08% strain applied

to the NiMnSb half-Heusler alloy changes its magnetic anisotropy by 20%.[83] A

similar strain-induced effect was observed in Co2MnGa.[84]

The second method is the use of spin filtering layers where a nonmagnetic electrode

is combined with a ferromagnetic or ferrimagnetic insulating tunnel barrier.[85] In

the insulating magnetic layer, the conduction bands are spin polarized due to

exchange effect, which creates two different barrier heights for spin-up and spin-

down electrons from the nonmagnetic electrode. Since the tunneling probability

for the carrier is inversely related to the barrier height, electrons with one spin

direction can tunnel through the barrier much easier than electrons with the other

spin direction, which leads to a highly spin polarized current.

In addition, the recently developed ability to manipulate electron spin in molecules

offers a new route towards spintronics, and a new field of molecular spintronics that

combines spintronics and molecular electronics is emerging.[86, 87] Among all the

molecules, organic molecules are quite promising since they exhibit weak spin-orbit

11


Figure 1.3: Schematic pictures of density of states (DOS) of paramagnet, ferro-

magnet, and half metal.

and hyperfine interactions which are likely to preserve longer spin-coherence in time

and longer spin diffusive length than conventional metals or semiconductors.[86]

1.4 Objectives and scope of the thesis

Despite a great progress in nanotechnology such as in synthesizing nanomaterials

and fabricating nanoelectronics devices in recent years, understanding the under-

lying mechanisms of observed phenomena in nanoscale is still a great challenge.

This challenge originates from the quantum mechanical nature of the interactions

between atoms which can not be accurately treated with phenomenological or clas-

sical method used in microelectronics. The increase of complexity in nanoscale also

leads to difficulties in explaining the experiments from an atomic-scale perspective

which is important in understanding the growth of nanomaterials, interface struc-

ture, and measured properties of nanomaterials. In addition, there are many issues

needed to be clearly understood for fabricating high-performance nanoelectronics

and spintronics devices. Among all the factors, chemical adsorption and strain are

12


critically important and their effects should be analyzed since they are inevitable

during fabrication or operation. For CNTs, although chemical doping and strain

have been both widely investigated with respect to the electronic properties, their

effects on work function have less been explored. Similarly, for Au nanotubes, de-

tailed studies on the effects of chemical adsorption of molecules or atoms on the

conductance fell short. For spintronics devices, the strain induced effect on TMR

of MTJ is important from both technological side and physical side. Structural

deformations due to lattice mismatch of different materials in MTJs can strongly

alter the magnetic properties of the ferromagnet or the complex band structure of

the semiconducting or insulating layer. However, strain effect on spin polarization

and TMR of MTJ has not been systematically investigated.

Motivated by the above issues, the aim of this thesis is to study physical properties

of various kinds of nanomaterials for applications in nanoelectronics and spintron-

ics devices and to analyze new effects arising from variations such as strain and

chemical dopings through first principles calculations within the framework of den-

sity functional theory (DFT). The first-principles approach based on DFT has been

widely adopted to study materials in both micro- and nanoscale. In Chapter 2,

basic principles of DFT and non-equilibrium Green’s function technique (NEGF)

are presented. In Chapter 3, a molecular switch and diode made from diarylethene

molecule is discussed. Electronic structure and transport properties of a single

light sensitive diarylethene molecule sandwiched between two GNRs were investi-

gated. In Chapter 4, factors that influence the properties of two types of nanotube

(gold nanotube and CNT) are discussed. For the gold nanotube, the effects of ad-

sorbates (CO molecule and O atom) and defects on the electronic structures and

13


conductances of Au nanotubes are investigated. For CNTs, potential methods of

tuning of the work functions of CNT are presented, which is critically important

in designing CNT based devices as shown in Section 1.1. This study suggests that

combination of chemical coating and tuning of strain may be a powerful tool for

controlling work functions of CNTs, which in turn will be useful in future design

of CNT-based electronic devices. In Chapter 5, electronic structure and TMR of

MTJ of Co2CrAl/NaNbO3/Co2CrAl are studied. Variations of spin polarization

(SP) and spin injection across the interface with strain are presented. Finally,

Chapter 6 presents the summary of this thesis.

14

Chapter 2

First-principles Methods

Since the 30s of last century, physicists have come to realize that, in principle,

most of problems of materials can be explained by solving the time-dependent

Schrodinger equation of the many-body system. However, the complexity of the

macroscopic solid which comprises huge number of nucleus and electrons (∼1023)

makes the solving of the equation intractable. Although the Born-Oppenheimer

approximation[88] can reduce the problem to solve only the electrons moving in a

“frozen” field of nucleus, an accurate and affordable method of solving the elec-

tronic part of the equation is still a great challenge. In the first part of this

chapter, i will introduce the DFT which has been widely adopted to investigate

the electronic structure of many-body systems, in particular atoms, molecules, and

condensed phases. The pseudopotential technique, that makes the DFT based cal-

culations practical, is included in the second part. The non-equilibrium Green’s

function method which has been used to simulate the properties of open systems

15

Chapter 2. First-principles Methods

is briefly described in the last part of the chapter.

2.1 Density functional theory

In principle, most problems of materials can be explained by solving Schrodinger

equation of the many-body system comprised of electrons and nucleus. However,

lots of approximations have to be made to solve the problem. Based on the Born-

Oppenheimer approximation,[88] the Schrodinger equation of a many-body system

comprised of nucleus and electrons can be simplified to only consider the movement

of electrons, while the nucleus are treated as fixed particles which generate a static

potential. Most of the properties of the material depend on solving the many-

electron problem. The stationary Schrodinger equation for a system including N

electrons is:

HΨ(r1σ1, ..., rNσN) = EΨ(r1σ1, ..., rNσN) (2.1)

where ri(σi) is spatial (spin) coordinate of the electrons, and

H = T + Vee + V

= −1

2

N∑i=1

∇2i +

N∑i=1

N∑j>i

1

rij

+N∑

i=1

v(ri) (2.2)

is the Hamiltonian of the electronic system. T is the kinetic operator and V is the

external potential operator describing the Coulomb interaction between electrons

and nucleus. The Vee operator describes the electron-electron Coulomb interaction.

The difficulty in solving the above equation arises from the electron-electron in-

teraction. In the Hartree and Hartree-Fock approximations, the electron-electron

16


interaction is approximated by an effective potential, thus the many-electron in-

teracting problem becomes a single-electron non-interacting problem which can be

easily solved.

2.1.1 Hohenberg-Kohn theory and Kohn-Sham equation

In the original article in 1964,[89] Hohenberg and Kohn proved that the density

of electrons uniquely determines the external potential related to nuclei-electron

interaction up to a constant. Since the potential determines all ground state prop-

erties of the system, they suggested that the density can be used as the basic

variable of the problem. The density functional theory is based on the following

two theorems:

Theorem 1: The external potential is uniquely determined by the electronic density

(ρ(r)), except for a trivial additive constant.

This theorem shows that the ground state electron density can be served as the

fundamental quantity instead of the wave function. Since ρ(r) determines the

external potential and the number of electrons, it determines the electronic Hamil-

tonian and all the other ground state properties. The ground state energy E is a

functional of the density, thus:

E[ρ] = 〈ψ|T + Vee + V |ψ〉

= T [ρ] + Vee[ρ] +

∫ρ(r)V(r)dr

= FHK[ρ] +

∫ρ(r)V(r)dr (2.3)

17


The functional FHK[ρ] is the sum of kinetic and Coulomb energies and independent

of the external potential V (r).

Theorem 2: The true ground-state density ρ0 minimizes the energy functional,

E[ρ], subject only to the conservation of the total number of electrons.

The above two theorems show that the ground state properties can be determined

through a variational method by varying the electron density. However, there are

still several things which remain uncertain:

1) What is the form of this functional FHK[ρ]?

2) How to define the electron density for a many-body interacting system?

3) If the above two problems are solved, how to determine the ground state electron

density through the variational method?

Kohn and Sham[90] have introduced the idea of mapping many-body interacting

electrons into non-interacting electrons. The kinetic energy as well as potential

energy functionals can be divided into two parts: one of which can be calcu-

lated exactly under the assumption of non-interacting electrons (similar to the HF

method[91, 92]) and a correction term. They suggested the following separation of

F [ρ] for any interacting many-particle system:

F [ρ] = T [ρ] + Vee[ρ]

= Ts[ρ] + J[ρ] + Exc[ρ] (2.4)

where T [ρ] and Vee[ρ] are the exact kinetic energy functional and electron-electron

18


interacting potential for the N interacting electrons, respectively. Ts[ρ] is the non-

interacting approximation to the kinetic energy, and

Ts[ρ] =N∑

i=1

〈ψi| − h2

2m∇2

i |ψi〉 (2.5)

and

J [ρ] =1

2

∫drdr′

ρ(r)ρ(r′)|r− r′| (2.6)

is the classical Coulomb energy of Hartree, and

Exc[ρ] = T [ρ]− Ts[ρ] + Vee[ρ]− J[ρ] (2.7)

is the so-called exchange-correlation functional. The non-interacting electron den-

sity can be defined as:

ρ(r) =∑

σ=±1/2

N/2∑i=1

|ψi(r, σ)|2 (2.8)

Thus the ground state energy is determined by the minimum of the energy func-

tional, and a stationary condition has to satisfy:

δ{F [ρ] +

∫drV (r)ρ(r) + µ[N −

∫drρ(r)]} = 0 (2.9)

where µ is a Lagrange multiplier ensuring the variations δρ(r) are performed at

constant particle number N . If we plug the 2.4 into 2.9, we get

δTs

δρ(r)+

∫dr′

ρ(r′)|r− r′| +

δExc

δρ(r)+ V (r) = µ (2.10)

δTs

δρ(r)+ Veff(r) = µ (2.11)

where the Veff is the Kohn-Sham effective potential defined by

Veff =

∫dr′

ρ(r′)|r− r′| +

δExc

δρ(r)+ V (r)

= VH(r) + Vxc(r) + V(r) (2.12)

19


Moreover, since we are now dealing with the non-interacting cases, the equation

for the particle wave functions is just the Schrodinger equations:

[− h2

2m∇2

i + Veff(ri)]ψ(ri) = εiψ(ri), (i = 1, 2, ..., N) (2.13)

which are the so-called Kohn-Sham equation. Since the effective potential Veff(r)

requires the information of the electron density ρ(r) which in turn needs the Veff(r),

so the above equations need to be solved in a self-consistent manner.

Finally, the total energy of the interacting system can be written as

E =N∑

i=1

εi − 1

2

∫drdr′

ρ(r)ρ(r′)|r− r′| + Exc[ρ]−

∫dr

δExc

δρ(r)ρ(r) (2.14)

where

N∑i=1

εi =N∑

i=1

〈ψi| − h2

2m∇2

i + Veff(r)|ψi〉

= Ts[ρ] +

∫ρ(r)Veff(r)dr (2.15)

However, the above equations are still not in a tractable form because we have no

expression for Vxc.

2.1.2 LDA and GGA

The form of the exchange-correlation energy functional Exc[ρ], which depends on

a wave function or an electron density, is generally unknown. The effect of the

exchange and correlation on the electronic system can be vividly viewed from the

exchange-correlation (xc) hole picture.[93] A xc hole around a given point r is given

20


by

ρxc(r, r′) = g(r′, r)− ρ(r′) (2.16)

where g(r′, r) is the density at r′ given that one electron is at r. ρ(r′) is the normal

average density without including the electron at r. Thus ρxc(r, r′) describes the

hole dug into the average density ρ(r′) around the electron at r. This hole is

normalized

∫ρxc(r, r

′)dr′ = −1 (2.17)

which reflects a total screening of the electron at r due to the combined effect of

the Pauli principle between spin parallel electrons and the Coulomb interaction

between spin unparallel electrons, where the later can’t be treated in Hartree-Fock

method.

The difference among the DFT methods is the choice of the functional form of

exchange-correlation energy. In electronic structure calculations, the exchange-

correlation energy functional is often approximated by the local density approxi-

mation (LDA)[94, 95] or by the generalized-gradient approximation (GGA).[96, 97]

The LDA is the most common and straightforward approximation to the exchange-

correlation energy functional. Within the LDA, the Exc[ρ] is written as[94, 95]

Exc[ρ] =

∫εxc(ρ(r))ρ(r)d3r (2.18)

where εxc(ρ) is the exchange-correlation energy per unit volume of a homogeneous

electron gas with a density of ρ. The above form of the exchange-correlation energy

is similar to the treatment of kinetic energy in Thomas-Fermi theory.

21


The LDA has proven to be a good approach for the calculation of properties such

as structure, vibrational frequencies, elastic moduli and phase stability (of similar

structures). However, in computing energy differences between rather different

structures the LDA can have significant errors. For instance, the binding energy

of many systems is overestimated (typically by 20-30 %) and energy barriers in

diffusion or chemical reactions may be severely underestimated.

A natural extension of the LDA is the GGA in which the first order gradient terms

of the electron density in the expansion are included. A typical form for a GGA

functional is:[96, 97]

Exc[ρ] =

∫εxc(ρ(r),∇ρ(r))ρ(r)d3r (2.19)

GGA calculations have been performed for a wide variety of materials and the

adoption gradient correction on the density improves significantly on the LDA’s

description of the binding energy of molecules. Many properties of 3d transition

metals are greatly improved.

2.2 Implementation of density functional theory

2.2.1 Pseudopotential

Pseudopotential is an approximation which is based on the observation that the

most physical and chemical properties of materials are dependent on the valence

electrons to a much greater degree than that of the bound core electrons. Since the

valence wavefunctions must be orthogonal to the core states which are localized in

22


the vicinity of the nuclei, the valence states oscillate rapidly in the core region to

maintain this orthogonality. This rapid oscillation requires a lot of plane waves to

reproduce this character in the core region.[98]

In the pseudopotential approximation, the effect of the core electrons is treated

together with the nuclei. The strong core potential is replaced by a much weaker

pseudopotential which acts on a set of pseudo wavefunctions rather than the true

valence wavefunctions. In this way, both the core states and the orthogonalization

wiggles in the valence states are removed. The basic character of pseudopoten-

tial and pseudo wavefunctions compared with their true counterparts are shown

in Fig. 2.1.[98] The pseudopotential is introduced in such a way that there are no

radial nodes in the pseudo valence states in the core region while the pseudopoten-

tial and pseudo wavefunctions are identical to the true electron wavefunction and

potential outside a cut-off radius rc.

The most frequently used pseudopotential in first-principles calculations is the

norm-conserving pseudopotential technique developed by Bachelet et.al.[99] With

norm conserving pseudopotentials, inside rc , the pseudo-wavefunctions differ from

the true wavefunctions as stated above, but the norm is constrained to be the same

as the true valence states. That is,

∫drr2ϕps∗

l (r)ϕpsl (r) =

∫drr2ϕ∗l (r)ϕl(r) (2.20)

where the wavefunction and eigenvalues are different for different angular mo-

menta l, and this implies that the pseudopotential should also be l dependent.

Pseudopotentials of this type are often called semi-local. In 1990, Vanderbilt and

co-workers proposed another type of pseudopotential which is named as ultrasoft

23


Figure 2.1: Schematic illustration of the replacement of the all-electron wavefunc-

tion and core potential by a pseudo-wavefunction and pseudopotential.

pseudopotential.[100] In this scheme, the norm-conservation constraint is removed

and the pseudo-wavefunctions inside rc are required to be as soft as possible, which

greatly reduces the planewave cutoff needed in calculations. In 1994, Blochl de-

veloped the idea of “soft pseudopotential” in Vanderbilt’s scheme, and proposed

the “projector augmented-wave” (PAW) method[101] to accurately and efficiently

calculate the electronic structure of materials within the framework of density-

functional theory. The PAW pseudopotential retains the physics of all-electron

calculations, including the correct nodal behavior of the valence-electron wave func-

tions and the ability to include upper core states in addition to valence states in

the self-consistent iterations,[102] thus it is widely adopted to calculate systems

including 3d and 4f electrons.

24


2.2.2 Planewave Basis

As well known in quantum mechanics, the operator and the wavefunction have to

be “represented” in an appropriate space which is characterized with the different

basis. Popular basis includes the real space grids, the atomic orbital basis, the

wavelets, the planewave basis, and so on. The bases differentiate themselves in

the behaviors of obtaining the computational efficiency and the accuracy. The

DFT based electronic structure methods are usually classified according to the

representations that are used for the density, potential and, most importantly, the

KS orbitals. In this section, only the planewave basis will be discussed since the

planewave method due to its simplicity (just a fast Fourier transformation).

In a plane wave pseudopotential calculation, the single electron wavefunction ψj

and the potential Vj can be expanded using plane wave basis exp(iG · r):

ψj =∑G

Cj(G)exp(iG · r) (2.21)

Vj =∑G

Vj(G)exp(iG · r) (2.22)

The plane waves exp(iG · r) are confined within a sphere with radius Gcut defined

with a kinetic energy

Ecut =h2

2m|k + Gcut|2 (2.23)

One advantage of planewave basis is that the kinetic part of the KS equation can

be easily computed as

h2

2m∇2ψj =

h2

2m

∑G

|G|2Cj(G)exp(iG · r) (2.24)

25


Keeping in mind the above ideas, the Kohn-Sham equations are reduced to the

secular equation as:

∑

G′[h2

2m|k + G|2δGG′ + V PS(G−G′) + VH(G−G′) + Vxc(G−G′)]cn,k+G′ =

εn,kcn,k+G (2.25)

Thus, the Kohn-Sham equations can be solved through variationally computing

the matrix elements from the output charge density of the previous calculation.

2.3 Non-equilibrium Green’s function method

2.3.1 Green’s function

The NEGF formalism provides a computational approach for treating quantum

transport in nanodevices. In this section, we briefly review some basic definition

of the Green’s function. The Green’s function corresponding to the nonrelativistic,

one-particle, time-independent Schrodinger equation is defined as the solution of

the equation:

[E −H(r)]G(r, r′; E) = δ(r− r′), (2.26)

where the G(r, r′; E) satisfies the same boundary conditions as the wave function

ψ(r) of the Schrodinger equation:

[E −H(r)]ψ(r) = 0 (2.27)

26


According to the different time boundary condition of the above equation, we can

define the retarded and advanced Green’s function as

GR =1

E −H + iη(2.28)

GA =1

E −H − iη(2.29)

where η is a small positive infinitesimal. The spectral function A(E) can be defined

as

A(E) = 2πδ(E −H)

= i[GR(E)−GA(E)] (2.30)

Considering that the DOS, D(E), equals Trδ(E −H), thus

D(E) =1

2πTrA(E) (2.31)

Also, we can obtain the density matrix ρ of the system

ρ = f0(H − µ)

=

∫dEf0(E − µ)δ(E −H)

=

∫dE

2πf0(E − µ)A(E) (2.32)

Upon the calculation of Green’s function, we can obtain immediately the solution

of the general inhomogeneous equation satisfying the same boundary conditions as

G(r, r′)

[E −H(r)]ψ(r) = f(r) (2.33)

with the source f(r) as

ψ(r) =

∫G(r, r′)f(r′)dr (2.34)

27


2.3.2 Open systems and NEGF

If we are only interested in closed systems there would be little reason to use

Green’s functions. For open systems, adopting the Green’s function method allows

us to focus on the system of interest and replace the effect of all external contacts

and baths with self-energy functions Σ.[103]

For simplicity, we consider a device connected to a contact. There exist some

interactions between the two parts (the contact and the device), thus it is better

for us to establish similar inhomogeneous equations as 2.33 for both systems. Before

connecting to the device, the electrons in the contact have wavefunctions φR that

obey the following equation:

[E −HR + iη]φR = SR, (2.35)

where HR is the Hamiltonian for the contact and the term iηφR represents the

extraction of electrons from the contact while the term SR represents the reinjection

of electrons from external sources.

For the connected device, the objective is to obtain an equation of the following

form

(E −H − Σ)ψ = S, (2.36)

where Σ is the self energy accounting the influence from contacts to incorporate

the boundary conditions. H is the Hamiltonian of the isolated device. S is a source

term representing the excitation of the device by electron waves from the contact.

To obtain the above equation, we establish the composite Schrodinger equation for

28


the composite contact-device system, which can be divided into two blocks:

E −HR + iη −τ+

−τ E −H

φR + χ

ψ

=

SR

0

Using equation 2.35 to eliminate SR to write:

(E −HR + iη)χ− τ+ψ = 0 (2.37)

(E −HR)ψ − τχ = τφR (2.38)

We can make some matrix transformation to express χ in terms of ψ as

χ = GRτ+ψ (2.39)

where

GR = [E −HR + iη]−1 (2.40)

Substitute the above equation into the second equation to obtain

(E −H − Σ)ψ = S (2.41)

where

Σ = τGRτ+ (2.42)

S = τφR (2.43)

ψ = GS (2.44)

Thus we arrive at the form the we are trying to prove as 2.36. Simultaneously, we

obtain the Green’s function G = [E −H − Σ]−1 for the device.

29


For the two contact case, there is a current flow if there exists a difference in the

Fermi energies of the two contacts. The current at the two terminals is given by

I1 = − q

h

∫dETr[Γ1A(E)]f1(E)− Tr[Γ1G

n(E)] (2.45)

= − q

h

∫dETr[Γ1A2(E)(f1(E)− f2(E))] (2.46)

I2 = − q

h

∫dETr[Γ2A(E)]f2(E)− Tr[Γ2G

n(E)] (2.47)

= − q

h

∫dETr[Γ2A1(E)(f1(E)− f2(E))] (2.48)

where T = Tr[Γ2A1(E) = Tr[Γ1A2(E) is called transmission function. Form

multi-contacts, the current Ii at terminal i can be written in the form

Ii = − q

h

∫dEIi(E) (2.49)

Ii = Tr[Γi(A(E)fi(E)− Tr[ΓiGn]] (2.50)

2.3.3 Implementation of NEGF combined with DFT

If we only consider the Hartree potential in the Hamiltonian and neglect the

exchange-correlation effect, then the previous steps can be realized based on a

Schrodinger-Poisson solver[104] which is widely adopted by the device physicists

working in semiconductor field. However, to accurately study the transport in the

molecular electronic devices, the exchange correlation effect may play important

role and can not be excluded. The NEGF approach described above has now been

implemented in several software packages[105, 106] within the framework of DFT.

Upon modeling the two-probe structure and dividing the system into device and

electrode regions, the general solution procedure is illustrated elsewhere[107] and

can be summarized as the following steps:

30


Initialization: Perform independent calculations for the electrodes and determine

the effective potential and contact Green’s function for the subsequent calculation

of the self energies.

Self-consistent cycle:

1) Calculate electron density through Green’s function. Note that the calculation

of the electron density can be efficiently completed through a contour integral in

the complex plane due to the analytical nature of the Green’s function;

2) Obtain Hartree potential through solving the Poisson equation:

∇2VH(r) = −4πρ(r) (2.51)

Since the Poisson equation is a second-order differential equation, a boundary

condition is required to solve it. Note that the bulk boundary condition only

determines the Hartree potential up to an additative constant. For the central part

of the two-probe boundary conditions, since the electrodes Hartree potentials are

only determined up to additative constants, the left and right Hartree potentials are

floating relative to each other. However, the chemical potentials of the electrodes,

subjected to the constraint of µL−µR = eV (V is the external bias), are calculated

from their effective potentials, we can relate the Hartree potential to the chemical

potential and define a proper alignment of the Hartree potential in the left electrode

with that of the right electrode;

3) Calculate the Hamiltonian H and solve the KS equation;

4) Calculate the Green’s function.

31


The calculation is completed through a similar self-consistent cycle as solving the

KS equation, except adopting an approach of Green’s function to obtain the elec-

tron density ρ(r).

32

Chapter 3

Switching and rectification of a

single light-sensitive diarylethene

molecule sandwiched between

graphene nanoribbons

As the trend of miniaturization of electronic devices continues, the next genera-

tion of electronic devices will almost undoubtedly be composed of single molecules.

Among all kinds of single-molecule based electronic devices, molecular switch and

rectifier are mostly intensively investigated. In this chapter, rectification and

light-induced conductance switching of a single diarylethene molecule(Fig. 3.1)

connected with GNRs electrodes are presented. The “open” and “closed” iso-

mers of the diarylethene molecule that can be converted between each other upon

33

Chapter 3. Switching and rectification of a single light-sensitive diarylethenemolecule sandwiched between graphene nanoribbons

Figure 3.1: Molecular structures and photochemical interconversion of the “closed”

and “open” diarylethene. The molecule can be divided into core, spacer, and linker

groups.

photo-excitation were found to have drastically different I-V characteristics, sug-

gesting that the GNR-Diarylethene-GNR (G-D-G) junction can be used as a high-

performance light controllable molecular switch. In addition, when sandwiched

between metallic and semiconducting GNRs, strong rectification behavior of the

“closed” diarylethene isomer was observed.

34


3.1 Computational details

For structural optimization and electronic properties, DFT calculations were per-

formed with a plane wave basis set (cut-off energy 400 eV) and Perdew-Burke-

Ernzerhof (PBE)-GGA approximation[108] via the use of VASP.[109] The struc-

tures were relaxed until the force is less than 0.02 eV/A. To ensure a junction with

the central molecule free of strain, we also adjusted the molecule-lead separations

by fixing the outermost layers of electrodes (Fig. 3.2) and allowing other parts to

relax to obtain the lowest-energy structure. The transport properties of the G-D-

G junction were then calculated by the Atomistix ToolKit (ATK) code within the

NEGF formalism.[110]

Since it is well known that in 1D and 2D systems, the long-range magnetic order

does not exist at finite temperature,[111, 112] we stick to the non-magnetic case

of GNRs. In transport calculations, the aGNR (zGNR) electrode includes 2 (3)

unit cells of the pristine GNR as shown in the shadowed area of Fig. 3.2. 10 and

14 surface layers were included in contact regions of zGNR and aGNR junctions,

respectively, which have been tested to be large enough to screen the effects of

the scattering region. Double- polarized basis and a cutoff energy of 2040 eV for

the grid integration within the PBE-GGA approximation were adopted in all the

transport calculations.

35


Figure 3.2: (a) Supercells of optimized 6-zGNR-“closed” diarylethene-6-zGNR and

14-aGNR-“open” diarylethene-14-aGNR junctions. Red, blue, violet and yellow

lines denote bonds formed by O, N, C and S, respectively. Note that hydrogen

atoms are not shown in the figure. The shadowed area denotes portions in the

supercell chosen as electrodes. (b) Band structures of 10-, 12-, and 14-aGNR and

6-zGNR. The calculated band gaps are 1.21, 0.54, 0.22 eV for 10-aGNR, 12-aGNR

and 14-aGNR respectively. Ca and Cz are the lattice constant of the unit cell of

the aGNR and zGNR, respectively.

36


3.2 Photochromic switching

3.2.1 Molecular electronic structure

Understanding the arrangement of molecular electronic orbitals is normally a pre-

requisite to analyze the molecular electronic conducting results. The abrupt ad-

justment of the structures of the two isomers leads to a magnificent adjustment

of the frontier orbitals which are shown in Fig. 3.3. In addition to the highest

occupied molecular orbital (HOMO) and LUMO diagram, positions of orbitals in

adjacent to the frontier orbitals including three states beneath HOMO and one

state above LUMO are also presented for both isomers. The HOMO/LUMO gaps

of the “open” and “closed” structures are 2.81 and 1.14 eV respectively, where the

decrease of the gap for the “closed” state can be viewed as an increase of conjuga-

tion pathlength in the molecule through lowering the LUMO level and raising the

HOMO level. This change of gap is in accordance with experimental observation

of a blue or red shift in photo absorption spectrum of the compounds.[63] The

absolute changes of the HOMO and LUMO levels are critical to the understand-

ing of photochromic induced changes of the conductance through analyzing the

molecular resonant tunneling orbitals.

For both isomers, HOMO and LUMO mainly localized on phenyl and chromophore

parts and the shape and degree of delocalization between HOMO and LUMO are

distinctly different. According to Jorge M. Seminario, the spatial extent of orbital

which can be varied with voltage is a key factor for a quantitative and qualitative

prediction of the transport characteristics.[113] In this study, LUMO states for

37


Figure 3.3: Lineup of orbitals for “open” (left) and “closed” (right) diarylethene.

“open” and “closed” states are more extended than HOMO states which can be

predicted as the resonant channel entering the voltage window. Our following

analysis of the eigenstates of the molecular projected self-consistent Hamiltonian

(MPSH) at different voltages shows that the LUMO state indeed serves as the

main conducting channel while sweeping the chemical potentials of the electrodes.

3.2.2 Linear conductance and molecular switch

We next focus on the linear conductance of the probe at zero bias formed by

sandwiching diarylethene between the GNR electrodes (Fig. 3.4). The “closed”

structure of diarylethene presents an overall larger conductance than the “open”

form regardless of the electrode types. In the cases of aGNR junctions (Fig. 3.4),

38


Figure 3.4: Conductance spectra at zero bias of 6-zGNR-diarylethene-6-zGNR

(a) and 14-aGNR-diarylethene-14-aGNR (b) junctions with “closed” (blue) and

“open” (red) isomers. The short lines above the plots show the HOMO/LUMO

alignments with the electrode Fermi level. (c) Isosurface plot of transmission eigen-

states at EF for “closed” (left) and “open” (right) isomers of diarylethene with

6-zGNR electrodes.

transmission gaps near the Fermi energy, due to the absence of incidence electrons

(band gaps), are shown and the aGNR electrodes manifest their differences in con-

ductance spectrum in which different transmission gaps near the Fermi energies are

formed. These transmission gaps suggest a much smaller current at modest volt-

age than those of junctions made from zGNRs such as 6-zGNR in this study. For

6-zGNR junctions (Fig. 3.4), the conductance at the Fermi energy of the “closed”

form is 3 orders larger than that of the “open” isomer, which suggests a good

switching behavior of diarylethene. Another difference between diarylethene junc-

tions with aGNR and zGNR electrodes is related to the energetic alignment of the

39


Figure 3.5: I-V characteristics of (a) aGNRs and (b) 6-zGNR diarylethene junc-

tions.

diarylethene orbitals. Our results show that the Fermi energies are nearly located

at the middle of the HOMO/LUMO gaps for both isomers in the case of aGNR

and the positions of the frontier orbitals are independent of the width of aGNR.

This means that the orbital alignment is more sensitive to local environment in

regardless of the width of the ribbon. For zGNR, the Fermi energies are closer to

the LUMO than HOMO, and hybridization of surface states with molecular or-

bitals occur. These hybridized states are related to several resonances around the

Fermi energy in the transmission spectrum and serve as the largest contribution

of current at moderate bias (Fig. 3.4). Moreover, we will show that the variation

of the relative positions with LUMO and surface states can lead to the negative

differential resistance (NDR) phenomena when a bias is applied across the junction.

In order to confirm the possible switching behavior already suggested by the anal-

ysis of transmission probabilities at equilibrium, we have calculated the current-

voltage characteristics for the two different isomer conformations which are shown

in Fig. 3.5. Charge transport is strongly suppressed for “open” structure in all cases

40


and the ON/OFF current ratio is found to be 3 orders of magnitude among the

studied bias range. The ON/OFF ratio values are in good agreement with previ-

ous theoretical estimations and validated by experiments with Au-diarylethene-Au

junctions.[113, 114] For aGNR, threshold voltages are proportional to the band gap

values of the electrodes and increase with decrease of width of the ribbon. Cur-

rent fluctuation occurs during the resonant tunneling orbitals moving between the

two electrodes chemical potential window, which arises from the variability of the

coupling between LUMO and the localized tip states. Compared to the relatively

large threshold voltage (>1V) for aGNRs in our study, smaller threshold voltage

(0.2V) is needed for 6-zGNR. To investigate the influence of the type and width of

GNR on the electronic coherent transport properties, we plot bias dependence of

the transmission curves T(E,V) in Fig. 3.6. Since the currents are much smaller

for the “open” isomer in both aGNRs and zGNR junctions compared to those of

“closed” isomer in the whole voltage range, we are more interested in the latter case

and presents the plots for junctions with diarylethene “closed” form only. In the

figure, the voltage window is represented by dashed brown lines, and the current

is calculated by integrating the transmission coefficient within the voltage window

around the Fermi level. Variations of HOMO and LUMO under bias are calculated

through MPSH analysis and represented by yellow circle and triangles respectively.

As a clear indication of the sweeping of chemical potentials and electronic gaps of

the aGNR electrodes, transmission gaps are formed around the voltage window.

We can also observe that LUMO serves as the resonant tunneling channel for aGNR

junctions and the currents, as presented in Fig. 3.5, increase rapidly after LUMO

moving into the integration window and locating beneath valence band edges of

the source electrode. We can infer from the figures that both the gap value of

41


Figure 3.6: Variation of logarithmic transmission curves with voltage logT(e,V)

for (a)10-aGNR, (b)12-aGNR, (c)14-aGNR and (d) 6-zGNR symmetrical junctions

with diarylethene in the “closed” form. Evolutions of HOMO-2 and HOMO-3 of

the “closed” molecule as a function of voltage are shown by white points;

42


the electrodes and alignment of the LUMO to the Fermi energies of electrodes de-

termine the threshold voltage of the I-V characteristics of aGNR junctions where

contributions from interface state can be neglected.

In the case of 6-zGNR electrode (Fig. 3.6d), no gap exists for the zGNR electrodes

and the LUMO is located closer to Fermi energy (0.2eV) at equilibrium, thus lead-

ing to a smaller threshold voltage, compared to those of aGNR junctions. Another

feature in T(E,V) of 6-zGNR is the additional transmission peaks related to the

tunneling through the interface states as mentioned above (Fig. 3.4). These inter-

face states arising from hybridization between the molecule and zGNR dominate

the electron transmission through the junction at moderate bias (0.4V). However,

the interface states gradually shift down and diminish as the voltage increases, and

thus these channels are partly blocked for electronic tunneling at higher voltage

where LUMO moves into the window and resonant tunneling through this orbital

gives the largest transmission for the electrons.

Accordingly, the current flow through the molecule depends not only on the align-

ment of HOMO and LUMO relative to the Fermi levels of the electrodes at equi-

librium, but also on the shift induced by the external field. Orbital splittings

and crossings are found while bias sweeping across the junctions. For instance,

HOMO-2 and HOMO-3 which are degenerate for the isolated molecule at equi-

librium (Fig. 3.3) split when the bias exceeds 0.8, 0.4, 0.1 and 0V for 10-aGNR,

12-aGNR, 14-aGNR and 6-zGNR junctions, respectively. The different behaviors

of orbital movement and splitting can find their root in charge transfer between the

molecule and electrode. Such charge transfer changes the electrostatic potential

and therefore the molecular level structures. Our Mulliken population analysis of

43


-1 0 1153.40

153.45

153.50

153.55

153.60

Cha

rge

(e)

Voltage (V)

10-aGNR 12-aGNR 14-aGNR 6-zGNR

Figure 3.7: Mulliken charge analysis for the “closed” diarylethene molecule em-

bedded in symmetric GNRs junctions.

the central molecule (Fig. 3.7) shows approximately a transfer of 0.51 and 0.57 e

at zero voltage from the molecule to aGNRs and 6-zGNR, respectively. For the

6-zGNR, the larger charge transfer is expected due to a good match between the

π-characterized frontier orbitals and states at Fermi level, thus making the orbitals

even slightly split at zero voltage.

3.3 Rectification

Since the pioneering work of Aviram and Ratner in 1974,[41] several molecu-

lar rectifiers or diodes have been synthesized or designed based on a σ-bond-

segment separated donor-acceptor structure.[45, 115] It now is a common sense

44


that a non-symmetry of the junction, arising from asymmetric molecular struc-

ture such as Aviram and Ratner’s proposal,[45, 115, 116] asymmetrical positions

of HOMO and LUMO relative to the Fermi level of the electrodes,[116] or asym-

metry of the electrostatic potential (asymmetric coupling of the molecule to the

two electrodes),[117–119] is essential to design a molecular junction, although the

non-symmetry alone is not sufficient to achieve a large rectification effect if no

voltage drop occurs along the molecular bridge.[120]

In contrast to the widely used metal-molecule-metal junction, we use zGNR and

aGNR as right and left electrode respectively (Fig. 3.8), and demonstrate the possi-

bility that GNR based diarylethene junction behaves as a rectifier. The mechanism

behind the rectification differs from that of AR’s model and we will show that the

change of relative coupling strength at the two contacts with voltage leads to the

asymmetry of the I-V curve and makes the zGNR-diarylethene-aGNR junction eli-

gible for a rectifier. We only discuss the rectification of junctions with diarylethene

“closed” isomer since it gives larger current than the counterpart of diarylethene

“open” isomer, although rectification characteristic retains with the junction based

on “open” structure. In Fig. 3.8, we show the I-V behavior of our proposed rec-

tifier based on the asymmetric junctions with 10-aGNR, 12-aGNR and 14-aGNR

as the right electrode. It can be seen that threshold voltage remains constant

(-0.4V) for these different aGNR electrodes and is independent of the width of

aGNR electrode. Although the threshold voltage is independent of the width of

aGNR electrode, the rectification behavior is substantially different between these

junctions. The rectification ratio (RR) defined as the ratio of the current in the

forward and reversed bias directions at each voltage, for 10-aGNR, reaches at 7500

45


Figure 3.8: (a) Optimized atomic configuration of the 6-zGNR-diarylethene

(“closed”)-10-aGNR junction. (b) Evolution of MPSH levels as a function of volt-

age for the 6-zGNR-diarylethene-10-aGNR junction with the “closed” diarylethene.

Blue dotted lines indicate Fermi energy levels of two electrodes. The shadowed area

depicts the movement of the band gap of 10-aGNR under biases. (c) I-V charac-

teristics of 6-zGNR-(“closed”) diarylethene-x -aGNR (x=10, 12 and 14) junctions.

The inset shows the rectification ratio (RR) of these junctions from 0.4 to 1.0 V.

46


at 0.5V, and an average RR of 1635 between 0.4V and 1.0V suggests a potential

application in electronic devices. For 12-aGNR and 14-aGNR junctions, average

RRs between 0.4V and 1.0V of 34 and 11 are obtained, respectively. The inverse

dependence of the rectification ratio with the width of the electrode arises from the

variation of the band gaps of the electrodes and alignment of the frontier orbitals

of the molecule with the electrodes which can be clearly seen from T(E,V) plot

shown in Fig. 3.9. The asymmetry of the transmission with respect to voltage po-

larity leads to the asymmetry of the I-V curve. Only one transmission gap related

to the aGNR electrode exists compared with the previous symmetric aGNR junc-

tions (Fig. 3.6). Similar to the previous symmetric electrodes, only LUMO level

contributes to the electronic tunneling. As clearly shown in the figure, T(E,V)

of asymmetric junctions gives the same characteristics around the voltage window

edge as their correspondingly symmetric junctions. For instance, the LUMO res-

onance is blocked as in cases of symmetric aGNR junctions and the transmission

of the interface states between diarylethene and 6-zGNR are attenuated in reverse

voltage (positive voltage). In addition, the T(E,V) plot for diarylethene “open”

structure in Fig. 3.9 also demonstrates an asymmetry character and a much lower

transmission compared with diarylethene “closed” structure in Fig. 3.9, thus the

functionality of switch is retained for asymmetric junctions. This simultaneous re-

alization of functions of switch and rectification is a key advantage for application.

The behaviors of the molecular orbital level under voltage (Fig. 3.9) are also quite

different from those of the previous symmetric cases (Fig. 3.6). The asymmetry

of the levels with the voltage polarity is a direct indication of the different cou-

pling of the molecule with the electrodes. LUMO levels slightly tilt following the

47


Figure 3.9: Variation of logarithmic transmission curves with voltage logT(e,V)

for asymmetrical junctions with (a)10-aGNR, (b)12-aGNR, (c)14-aGNR as left

electrode and 6-zGNR as right electrode and the diarylethene is in “closed” state.

(d)logT(e,V) plot for “open” diarylethene with 14-aGNR and z6GNR electrodes.

Dotted brown lines indicate the range of current integration around the Fermi level.

Transmission peaks related to HOMO/LUMO are denoted by yellow circles and

yellow triangles.48


-1 0 1 2153.40

153.45

153.50

153.55

153.60

Cha

rge

(e)

Voltage (V)

6-zGNR-14-aGNR 6-zGNR-12-aGNR 6-zGNR-10-aGNR

Figure 3.10: Mulliken charge analysis for the “closed” diarylethene molecule em-

bedded in asymmetric GNRs junctions

movement of the 6-zGNR electrochemical potentials, thus a stronger coupling of

the molecule with 6-zGNR than binding with aGNRs can be predicted. The slopes

of the evolution of the molecular eigenenergies with the bias can been rationalized

in terms of the polarizability of molecular eigenstates.[45, 121] The same trend of

the LUMO and HOMO as shown in the figure means a similar polarizability of

the two orbitals. Mulliken charge analysis for the “closed” diarylethene molecule

embedded in asymmetric GNRs junctions is plotted in Fig. 3.10.

The local density of states (LDOS) of the junctions with 10-aGNR and 14-aGNR

as right electrode at -0.8V, 0V, +0.8V and +1.4V, representing different situations

of the molecular energy alignment with electrodes, is plotted in Fig. 3.11. For the

10-aGNR junction, we can clearly distinguish hybridized LUMO and interface state

(denoted by IS1) formed at 6-zGNR side for zero voltage, both of which locate in

49


Figure 3.11: Spatially resolved local density of states along the transport axis for

(a) 6-zGNR-“closed” diarylethene-10-aGNR (b) 6-zGNR-“closed” diarylethene-14-

aGNR junctions at different bias voltages. The HOMO/LUMO of diarylethene

localized in the middle region and interface states (ISs) localized at contacts can

be clearly identified.

the gap of the semiconductor. Such hybridized interface states are absent at the

armchair ribbon side, therefore, the molecule is relatively weakly coupled to 10-

aGNR at equilibrium. At +0.8V, they are still in the band gap but near the valence

band edge of 10-aGNR and a low transmission and conductance is still expected.

When the voltage increases to +1.4V, LUMO comes into resonance with valance

band and the occupancy of the orbital will change. Charge transfer between the

orbital and electrodes enables a slower speed of the orbital movement. At the same

time, IS1 shifts down with 6-zGNR electrode and an apparent splitting of LUMO

and IS1 occurs. Both states locate between the 6-zGNR electrochemical potential

and valence band edge of 10-aGNR, therefore, increasing the probability of the

carrier transfer between the electrodes. However, the coupling of LUMO between

6-zGNR at this voltage decreases, and the width of LUMO becomes narrower as

50


shown in the figure. In addition, the extension of IS1 into the diarylethene also

decreases, thus the tunneling channel through IS1 is also suppressed. In contrast

to the case of positive voltage, the coupling between LUMO and 6-zGNR remains

strong in the whole negative voltage range, a larger current is consequently found

at negative voltage. According to Hosein Cheraghchi,[122] asymmetry in LDOS

gives rise to an asymmetry in the couplings of the central region to electrodes. On

the side with weaker coupling screening would be less effective and potential drop

would be more pronounced.

The scenario of rectification process for 14-aGNR asymmetric junction is similar

to that of 10-aGNR junction except for a smaller band gap of 14-aGNR electrode.

In both cases, we can see a strong localization of the ISs at the tip of source

electrode. The variability of these ISs gives rise to nonlinear I-V characteristics of

the junction. For instance, the peak around +1.4V in the I-V curve (Fig. 3.8) is

related to the emergence of IS2 for 10-aGNR junction (Fig. 3.11). The attenuation

and shift of ISs at positive voltage are clearly reflected by the change of transmission

in T(E,V) plot (Fig. 3.9).

3.4 Summary

This study demonstrates the design of a photo switch and rectifier based on a com-

bination of GNR and diarylethene, which hopes to take advantage of recent ad-

vancement of creating GNR with different shapes, sizes and edges structures,[123,

124] and the adoption of carbon electrode in photochromic molecular switches is

51


believed to suppress the effect of movement of tip atoms due to strong polarization

field under bias compared with using traditional metallic electrodes.[64, 125–127]

The current ratio of ON/OFF states (corresponding to “closed” and “open” states

of diarylethene) of GNR-diarylethene-GNR junctions can reach 3 orders between

-2 and +2V. We find that the alignments of HOMO and LUMO of diarylethene

with aGNR electrodes are nearly independent of width of aGNRs. Moreover, the

pseudo-gaps forming at the source tip of 6-zGNR electrode give rise to remarkable

non-linear I-V characteristics. For aGNR electrodes, the presence of an energic

gap of the incident carriers from the semiconductor electrode induces significant

negative differential resistance affects due to the sharp changes of density of states

near the band gap edge.

Rectification is shown for 6-zGNR-diarylethene(“closed”)-x -aGNR junctions (x=10,

12, 14) with average rectification ratios of 1635, 34 and 11 for 10-aGNR and 12-

aGNR and 14-aGNR junctions between 0.4 and 1V respectively. The design of a

molecular rectifier normally needs to consider the following factors: work function

of the leads, the affinity of the molecule, the orbital alignment with electrochem-

ical potential of the electrodes and bond formation of the contact. In contrast

to the previous molecular diodes where the rectifications are proved to be due to

donor-acceptor mechanism ,[41, 45, 115] or an asymmetric alignment of the fron-

tier orbitals to the Fermi levels of the electrodes,[116] or different couplings of the

molecule with the two sides,[117–119] the rectification arises from the variability

of the coupling of the contact under different voltages. This asymmetry of the

coupling with bias polarity has less been notified before, although the effect of the

barrier length ratio and height ratio has been investigated by a tunneling barrier

52


model.[54] These findings help to the development of novel molecular electronic

devices based on GNR.

53

Chapter 4

Functionalization of gold

nanotubes and carbon nanotubes

Functionalization of nanotubes through chemical adsorption of molecules or atoms,

which offers a possible way to modify the electronic and chemical properties of the

nanotubes, is highly important for nanoelectronics applications. In this chapter,

functionalization of gold nanotubes and CNTs is described. For the gold nanotubes,

effects of adsorbates (CO molecule and O atom) and defects on electronic structures

and transport properties of Au nanotubes (Au (5,3) and Au (5,5)) were studied.

For the CNTs, variations of work function with uniaxial strain for both pristine

and potassium doped CNTs are presented. The results suggest that combination

of chemical coating and tuning of strain may be an effective way to control work

functions of CNTs, which is critical in future design of CNT-based nanoelectronic

devices.

54

Chapter 4. Functionalization of gold nanotubes and carbon nanotubes

4.1 Adsorbate and defect effects on electronic

and transport properties of gold nanotubes

4.1.1 Computational details

For structural optimization and electronic structure calculations, the first principles

method based on DFT was employed via the computational package VASP.[109,

128] A plane wave basis set with the cut-off energy 396 eV was used. The structures

were relaxed until the forces on atoms are less than 0.02 eV/A. Transport properties

were calculated by ATK code within the NEGF formalism.[110, 129, 130] Double-ζ

polarized basis and a cutoff energy of 150 Ry for the grid integration were adopted

in transport calculations. In all calculations, the PBE format of GGA pseudopo-

tential was included.[108] Vibrational analysis was done using DMol3,[131, 132]

and the effective core potential (ECP) and a double numerical basis set including

a d -polarization function (DND) were adopted.

4.1.2 Structures and energetics of adsorbates on gold nan-

otubes

Since theoretical studies have shown that Au (5,5) is the most stable one among all

freestanding gold tubes (Fig. 4.1) and Au (5,3) is the most energetically favored for

tubes when suspended between two gold electrodes,[133] we stick to the two tubes

in the study. Relaxations of structures of CO molecule, O and Au atoms on Au

55


Figure 4.1: Atomic structure of (n,m) gold SWNTs obtained by cylindrical folding

of the 2D triangular lattice. Basis vectors of the 2D lattice are a1 and a2 (Reprinted

with permission from Ref. [133]).

tubes have been performed through choosing various starting geometries to explore

all possible adsorption sites. Figure 4.2 shows atomic structures of Au (5,3) and

(5,5) tubes, and possible adsorption sites (top, center and two inequivalent bridge

sites, B1, B2) of CO molecule or O, Au atoms. In Table. 4.1, we list the adsorption

energy, bonding length defined as the shortest distance between the adsorbate (CO,

O and Au) and the nearest Au atom, and the change of net charge of the adsorbates

and the bonded Au atoms, for the most stable adsorption configurations of different

cases. The adsorption energy ∆E is calculated by subtracting the energy of the

total system from the sum of energies of the nanotubes and the adsorbates. In

the case of Au (5,3), for each adsorbate, we found that the difference between the

binding energy of the lowest-energy configuration (top site adsorption) and that of

the second lowest one (B1 site adsorption) is around 0.03 eV. These two adsorption

56


Figure 4.2: Geometric structures of (5,3) and (5,5) Au nanotubes and a schematic

description of possible adsorbing sites for adsorption: Top, B1 (Bridge site 1), B2

(Bridge site 2), Center.

configurations may co-exist in experiments. We therefore show both of them in

the table. Other adsorption configurations (not shown in the table) have binding

energies at least 0.4 eV smaller than the most stable one.

The side views of optimized geometries of CO or O adsorbed Au (5,3) and (5,5)

tubes are shown in Fig. 4.3. For the case of CO adsorbed Au (5,3), two nearly

degenerate stable adsorption configurations are found as above mentioned: The

top site adsorption (Fig. 4.3a) where the C atom directly binds to the Au atom,

and the B1 adsorption (Fig. 4.3b) where the CO is on the bridge site of Au chains

along the direction parallel to the tube axis. For the top site adsorption, the C-Au

bonding length is 1.99 A comparable to that of CO adsorption on Au chain (C-Au

bond length 1.96 A) on NiAl surface.[13] As shown in Fig. 4.3a, the Au (5,3) tube

undergoes a significant distortion upon CO adsorption, clearly suggesting strong

57


Table 4.1: Energetics and structures of adsorbates (CO, O, Au) on Au (5,3) and

Au (5,5) nanotubes. d is the shortest length of the bonds formed by Au and

adsorbates; δQx(x=CO, O, Au) and δQAu are the net partial charge transfers of

the adsorbates and the Au atom with the shortest distance from the adsorbates.

Adsorbate ∆E(eV)(site) d(A) δQx δQAu

Au (5,3)

CO 0.57(top) 1.99 0.389 -0.090

0.54(B1) 2.12 0.399 -0.045

O 4.66(center) 2.12 -0.522 0.150

4.65(B1) 2.03 -0.528 0.170

Au 2.28(center) 2.73 -0.060 0.028

2.27(B2) 2.71 -0.048 0.009

Au (5,5)

CO 0.77(B1) 2.10 0.441 -0.050

O 5.13(center) 2.05 -0.507 0.139

Au 2.69(center) 2.74 -0.006 0.045

58


Figure 4.3: Adsorption geometries for CO adsorption on Au (5,3) at top (a), B1

(b), and Au (5,5) at B1 (c) sites, oxygen adsorption on Au (5,3) at center (d), B1

(e), and Au (5,5) at center (f) sites, respectively. The C, O, and Au atoms are

depicted in grey, red, and yellow, respectively.

interaction between the CO molecule and Au tube. For the B1 site adsorption

(Fig. 4.3b), the distortion of the tube is much weaker although the adsorption

energy in this case is almost the same as the top site adsorption. For the case

of Au (5,5) tube, the lowest energy state occurs when the CO molecule binds to

the B1 site (Fig. 4.3c). The binding energy, 0.77 eV, is higher than the case of

Au (5,3) by about 0.2 eV. In all cases, electron transfers from the CO molecule

to the adjacent Au atom, leading to slightly positively charged CO molecule and

negatively charged Au atom (Table. 4.1).

Compared to CO, the binding of O atom on Au tubes is much stronger (Table. 4.1).

For the case of Au (5,3), similarly, there are two nearly degenerate adsorption

configurations, the center (Fig. 4.3d) and the B1 site (Fig. 4.3e) adsorption, with

the adsorption energy of 4.66 and 4.65 eV respectively. For Au (5,5), the center site

59


adsorption (Fig. 4.3f) is the most stable configuration with the adsorption energy

of 5.13 eV. When binded on B1 site of Au (5,3), a significant distortion of the Au

tube occurs. Moreover, a relatively larger electronegativity of O atom enables a net

partial charge transfer from Au to the adsorbate and makes gold atoms positively

charged (Table. 4.1).

Adsorption of one extra Au atom on Au tubes is also considered. For both Au

tubes, the adsorption energy of the lowest energy configuration is larger than 2.2

eV (Table. 4.1), suggesting that in the procedure of fabrication, it is very possible

to have Au adatoms on Au tubes. Later, we will show how the Au adatom affects

electronic and transport properties of Au tubes.

4.1.3 Electronic structures of CO and O adsorbed gold

nanotubes

In this part, we describe the electronic structures of CO and O absorbed Au (5,3)

and Au (5,5) tubes. First, to understand the interaction between CO molecule

and Au tubes, we plot in Fig. 4.4 LDOS projected on the CO molecule and the

binded Au atom. Similar to the case of CO binding to Au nano clusters,[134]

the HOMO and LUMO of CO have the biggest contribution to the chemisorption

since the energy levels of these two states change significantly upon adsorption

due to the hybridization with Au states. For the top site adsorption on Au (5,3)

(Fig. 4.4a), the CO HOMO orbital 5σ is pushed below the 1π orbital whose energy

level doesn’t change much, and the LUMO orbital 2π∗ is pushed below Fermi

energy and overlaps with the whole continuous d band of Au, leading to the partial

60


population of this orbital (the backdonation process [135, 136]). The amount of

electrons backdonated to the 2π∗ orbital can be roughly estimated by integrating

the LDOS of CO within the energy range of the Au d band. In this case, about

0.9 electron is transferred from Au d bands to the CO anti-binding orbital 2π∗. In

the figure, we also plot the wave functions of several molecular orbitals of CO after

adsorption, from which we can see that indeed the 5σ orbital strongly hybridizes

with Au states, and 4σ as well as two degenerate 1π orbital (1π − 1 and 1π − 2)

only weakly interact with the Au tube. When CO adsorbs on B1 site of Au (5,3)

(Fig. 4.4b), differently from top site adsorption, 1π orbital also contributes to the

chemisorption by significantly hybridizing with Au states, and as a result, the

degeneracy between 1π− 1 and 1π− 2 is lifted. Amount of electrons backdonated

to 2π∗ orbital in this case (1.57 electrons) is estimated to be much larger than that

of the top site adsorption.

The significantly different backdonation strength between the top site and B1 site

adsorption implies a way to distinguish these two almost degenerate adsorption

configurations of CO on Au (5,3) in experiment. The more the CO anti-binding

2π∗ orbital is backdonated, the weaker the CO bond will be. The strength of the

CO bond can be seen from the bond length and also the vibrational frequency

of the stretching mode of the molecule, the latter of which can be measured in

experiment. Indeed, the CO bond length of the B1 adsorption, 1.165 A, is larger

than that of the top adsorption, 1.151 A due to the stronger backdonation. Note

that the bond length of free CO molecule is 1.128 A (Our calculated value of 1.146

A). The vibrational frequency of the CO stretching mode is calculated to be 2094

cm−1 for top adsorption and 1919 cm−1 for B1 adsorption. The difference between

61


Figure 4.4: LDOS and orbitals of CO adsorbed on Au (5,3) at top (a), B1 (b) sites

and Au (5,5) at B1 (c) site. The LDOS projected on the CO molecule is shown

in black and that projected on the gold atom with the shortest distance from the

C atom is colored yellow. The populations of CO orbitals are calculated through

integrating over the relevant peaks. Included also are the vibrational frequencies of

stretching mode for different adsorption configurations. Notice that the frequency

of free CO molecule is calculated as 2128 cm−1

62


Figure 4.5: Comparison of Au states after O atomic adhesion with those of the pris-

tine (5,3) (a) and (5,5) (b) Au tubes. For the adsorbed tubes, LDOS is projected

onto Au atom with the shortest distance from the O atom.

these two vibrational frequencies should be able to be seen in experiment. As a

test of the method of calculating vibrational spectra, for the same mode of the free

CO molecule, our calculations give the frequency of 2128 cm−1, which is in good

agreement with the experimental value of 2140 cm−1.[137]

The backdonation of 2π∗ orbital, and the splitting of 1π − 1 and 1π − 2, are also

observed for the lowest energy adsorption of CO on Au (5,5), the B1 adsorption

(Fig. 4.4c). Here, the nearly 1 eV of the splitting of two 1π orbitals is much larger

than that of the B1 adsorption of Au (5,3) (about 0.5 eV). The CO bond length in

this case is calculated to be 1.172 A, and the corresponding vibrational frequency of

the CO stretching mode is 1922 cm−1, about the same as that of the B1 adsorption

on Au (5,3).

In Fig. 4.5, we show the LDOS of the Au atom binded with O before and after

O adsorption. Again, for Au (5,3), there are two nearly degenerate adsorption

configurations, the center and the B1 adsorption, and for Au (5,5), the most stable

63


Figure 4.6: Quantum conductance spectrum for CO adsorbed Au (5,3)(a) and Au

(5,5) (b). The conductance spectra of pristine tubes (dashed lines) are also given

for comparison

configuration occurs when the O atom binds to the center position. For all cases,

the O adsorption causes great changes of LDOS of the binded Au atom, indicating

the strong interaction between the O and the Au tube.

4.1.4 Conductance of CO and O absorbed Au tubes

In this section we present the conductance variations of the Au (5,3) and Au (5,5)

due to the adsorption of CO and atomic O. It has been reported that for an Au

monoatom chain that has one unit of conductance, the adsorption of a single CO

molecule can make it non-conductive where the conductance of Au monochain

reduces from 1 G0 to 0 (transition from metal to insulator) after adsorption at top

site.[13] It would be interesting to see how the adsorption of CO or O modifies the

conductance of Au (5,3) or (5,5) tubes that essentially are the aggregation of five

strands of Au atoms.

64


Figure 4.7: Quantum conductance spectrum for oxygen adsorbed Au (5,3) (a) and

Au (5,5) (b). The conductance spectra of pristine tubes (dashed lines) are also

given for comparison

The calculated conductance spectra of the pristine and CO adsorbed Au (5,3) and

Au (5,5) are shown in Fig. 4.6. The conductance of both pristine tubes at Fermi

energy is 5 G0, in agreement with previous studies.[133] For Au (5,3), the CO

adsorption decreases the conductance at Fermi energy of the tube by 0.9 G0 for both

top and B1 adsorptions, suggesting that Au (5,3) may be used as a chemical sensor

for CO molecules. For Au (5,5), the lowest-energy configuration of CO adsorption

decreases the conductance at Fermi energy of the tube by 0.5 G0. Compared to CO,

effects of O atom on transport properties are much more pronounced. (Fig. 4.7).

The reasons are twofold: stronger potential-well scattering and distortion of Au

tubes due to stronger O adsorption compared with CO adsorption. For both tubes,

the O adsorption causes the drop of the conductance at Fermi energy by around 2

G0.

65


Figure 4.8: Conductance as a function of energy for defective Au (5,3) tube with

defects arising from Au adhesion (a) and monovacancy (b) on the tube. The relaxed

defective structures are given as the insets, where the atoms around the defective

site are highlighted by violet balls. It can be seen that the Au adatom distorts the

tube differently at different adsorption sites.

4.1.5 Defect effects on conductance of Au tubes: Au ad-

sorbate and vacancy

Finally, we discuss the effects of two types of defects, the Au monovacancy and

the defect arising from the adhesion of one extra Au atom, on conductance of

Au tubes. In Table. 4.1, we give the adsorption energies of a single Au atom on

Au (5,3) (2.28eV@center and 2.27 eV@B2) and Au (5,5) (2.69eV@center). The

formation energies of a monovacancy are calculated to be 3.32 and 3.52 eV for

Au (5,3) and Au (5,5) respectively. The high adsorption energies of one Au atom

and relatively low formation energies of monovancy suggest that these two types

of defects are likely to occur in the fabrication of Au tubes.

The conductance spectra and optimized structures of defective Au (5,3) are given

66


Figure 4.9: Conductance as a function of energy for defective Au (5,5) tube with

defects arising from Au adhesion (blue line) and monovacancy (red line) on the

tube. The relaxed defective structures are given as the insets, where the atoms

around the defective site are highlighted by violet balls.

in Fig. 4.8. For the cases of an extra Au atom adsorbed on the tube (B2 and center

sites), after relaxation, pyramid-like structures are formed as shown in Fig. 4.8a.

The conductance spectra of both adsorption configurations show very similar be-

haviors, and at Fermi energy, the conductance decreases by about 0.8 G0. For Au

monovacancy, the defect decreases the conductance of the tube at Fermi energy

about 1.2 G0 (Fig. 4.8b). Similarly, the Au monovacancy on Au (5,5) causes a

0.9 G0 of drop of the conductance at Fermi energy (Fig. 4.9). The Au adatom on

Au (5,5) only leads to a decrease of 0.3 G0 of the conductance as we can see from

Fig. 4.9. In all cases, the drop of conductance can be due to the distortion of the

atomic chains formed in the tube or break of the conducting channel due to the

defects. In addition, scattering around these defective sites where new localized

states may be formed can be enhanced and thus reducing the conductance.

67


4.2 Mechanically and chemically tuning of the

work function of CNT

4.2.1 Work function of CNT

Several recent studies have shown that work functions of CNTs may be critically

important in functioning of some CNT-based devices [138–142]. For example,

Schottky barrier formed at metal-CNT junction that is closely related to work

functions of two materials has been demonstrated to be crucial for performance

of CNT-based FETs and diodes.[138, 139] It has also been shown experimentally

that the efficiency of CNT-based field emitting devices sensitively depends on work

functions of CNTs.[143] Therefore, a practical and effective method that can be

used to modify, tune and control work functions of CNTs is highly desired.

One important factor which can exert tremendous effects on properties of CNTs

is mechanical deformation, and the understanding of strain effect also forms the

basis for CNT constructed as nano-electromechanical devices.[144] As a practical

issue, strain in CNTs is important since mechanical deformations are inevitable

in the process of fabricating CNT-based devices. It has been pointed out that

structure deformation in a CNT often drastically changes its intrinsic properties.

Some experimental and theoretical studies showed that conductance of a metallic

CNT could decrease by orders of magnitude when under a small strain around

5%.[145, 146] Some other studies suggested that a metallic CNT may undergo

a metal-semiconductor transition when strained, and the bandgap of the CNT

68


sensitively depends on the strain.[147, 148] Despite the importance of strain on

electronic properties of CNTs, detailed studies of strain effects on work functions

of CNTs fell short. On the other hand, doping of potassium has been found to

be an effective way to realize n-type CNT-based devices.[25] However, the exact

effect associated with potassium doping in CNTs has less been studied. In this

section, we present our theoretical investigations under the framework of DFT on

correlations between uniaxial strain and work functions of pristine and potassium-

decorated CNT (5,5) and CNT (9,0). CNT (5,5) and CNT (9,0) are chosen in this

study since they are two typical CNTs for aGNR and zGNR, respectively.

4.2.2 Computational details

Our calculations are conducted within the framework of DFT using plane wave

basis with cutoff energy of 400 eV and ultrasoft pseudopotentials[149] in VASP

package.[150] In all calculations, the GGA in PW91 format [151] and 1×1×5

Monkhorst-Pack k sampling[152] were used. Supercells for both CNTs employed

in calculations are shown in Fig. 4.10. Uniaxial tensile (positive) or compres-

sive (negative) strain is applied to CNTs by elongating (positive) or shortening

(negative) CNTs along the tube axis followed by a full relaxation of all atoms

except for two outermost layers (as shown in Fig. 4.10) whose atomic configu-

rations are fixed to those without strain. Structural deformation caused by this

kind of strain is nonuniform along the tube axis, and mimics that in real CNT-

based devices which often employ a metal-CNT-metal configuration and contain

nonuniform structure deformation due to the stretching or compressing by two

69


Figure 4.10: Supercells of CNT (9,0) (upper) and CNT (5,5) (bottom) employed

in calculations. Strains are applied by elongating or shortening the length of tubes

along the tube axis (z axis) with two outermost layers (shadowed area) fixed to

their bulk structures without strain. In all calculations, the periodically replicated

CNTs (in both x and y directions) are separated by a vacumm region of 10 A.

metal contacts. The reported experimental values of the breaking strain are quite

diverse, and range from 13 % - 17 % due to the variability of the samples and

measurement conditions.[153, 154] In this study, we consider strain changes from

-10 % to +10 %.

70


Figure 4.11: Relation between work function (W) and potentials of CNT (5,5)

under -1% compressive strain

4.2.3 Strain effects on work function of pristine CNT

Work function is defined as the energy needed to remove one electron from the

system, thus can be calculated by subtracting the Fermi energy from the electro-

static potential in the middle of the vacuum (Fig. 4.11). Work functions of CNT

(5,5) and CNT (9,0) without strain are estimated by our calculations to be 4.38

eV and 4.40 eV respectively, which are consistent with previous studies.[140, 143]

We found that strain has great effects on work functions of both CNTs, and when

strained, the work function of CNT (5,5) behaves very differently from that of

CNT (9,0) as shown in Fig. 4.12. When strain changes from -10 % to +10 %, the

work function of the CNT (5,5) increases monotonically from 3.95 eV to 4.57 eV,

whereas the work function of the CNT (9,0) varies between 4.27 eV and 5.24 eV

in a complicated manner. Within this range of strain, the amount of changes of

work function, 0.62 eV for CNT (5,5) and 0.97 eV for CNT (9,0), are quite sig-

nificant, which shows strong effects of strain and suggests that tuning strain may

71


-0.10 -0.05 0.00 0.05 0.10

4.00

4.25

4.50

4.75

5.00

5.25

Wor

k Fu

nctio

n(eV

)

Strain

CNT(5,5)

CNT(9,0)

Figure 4.12: Work functions of CNT (5,5) and CNT (9,0) Vs. strain. Tensile strain

is positive and compressive strain is negative. For CNT (5,5), the work function

changes monotonically when strain changes from -10 % to +10 %. For CNT (9,0),

when strain changes from -2% and 4%, the work function behaves similar to that

of CNT (5,5).

be an effective method to control the Schottky barrier at metal-CNT junction.

Since previous studies have shown that the Schottky barrier at metal-CNT junc-

tion is critical for chemical bonding at contacts,[155] and crucial for performance of

CNT-based devices,[138, 139] we believe that understanding strain effects on work

functions of CNTs is important for future design and control of nanoscale CNT-

based devices. The complicated behavior of the work function of CNT (9,0) under

strain is quite interesting. Within the range of strain from -2% to 4%, the work

function of CNT (9,0) behaves quite similar to that of CNT (5,5). When the strain

is less than -2% or bigger than 4%, the work function starts to significantly deviate

from the monotonic behavior of CNT (5,5). Here, the strain of -2% and 4% are two

turning points. To understand this, we plotted the DOS of electrons for CNT (9,0)

72


at compressive strain in Fig. 4.13(a), and tensile strain in Fig. 4.13 (b). Since our

calculations showed that the variations of electrostatic potential in the middle of

the vacuum are very small when strain changes, in the figure, we set the reference

energy (0.0 eV) to the electrostatic potential of vacuum. Several interesting things

can be seen from this figure. First, when under strain, CNT (9,0) undergoes a

metal-semiconductor transition as predicted in literature.[147]. Second, variations

of work function under strain as shown in Fig. 4.12 can be completely understood

by the changes of Fermi energy at different strains as depicted in Fig. 4.13. For

example, for compressive strain, the Fermi energy increases from strain 0.0 to -2%,

and decreases from strain -2% to 4%, which leads to the decrease of work function

from strain 0.0 to -2%, and the increase of work function from strain -2% to 4%

as shown in Fig. 4.12. The sudden decrease of Fermi energy from tensile strain

4% to 5% corresponds to the sudden increase of work function at the same tensile

strain as shown in Fig. 4.12. It is worthy mentioning here that the Fermi energy

is calculated from the charge neutrality which is actually determined by the tail of

DOS of HOMO-like states. Therefore, underlying the change of Fermi energy is the

change of HOMO states due to strain which in turn determines the change of work

function. We also calculated DOS for CNT (5,5) under different strains (not shown

here). For CNT (5,5), there is no metal-semiconductor transition that agrees with

literature,[156, 157] and DOS changes continuously with strain for all cases. The

electronic structures of CNT (9,0) and CNT (5,5) are intrinsically different: (9,0)

is a semi-metal which will undergo a metal-semiconductor transition under a small

strain, while (5,5) is truly metallic, and this is the reason why their work functions

respond completely differently to strain. We believe that our calculations shown

here for CNT (5,5) and (9,0) are helpful for understanding strain effects on work

73


Figure 4.13: Electron DOS as a function of energy for CNT (9,0) at different

compressive (a), and tensile (b) strains. Dashed lines denote Fermi energies. Note:

The electrostatic potential in the middle of vaccum is set to be 0.0 eV.

functions of other CNTs.

4.2.4 Work function of potassium-adsorbed CNT

It has been well-known that coating of alkali metals can greatly reduce the work

function of CNTs, which may significantly improve the efficiency of CNT-based

field-emitting devices[158] and tuning the polarity of the carriers to realize a n-

type CNT-based FET. It is naturally interesting to see if we can gain further

control of the work functions of CNTs by combining alkali metal coating and

tuning strain. First, we test the effects of potassium coating on CNT (9,0) and

(5,5) without strain. For this purpose, we calculated the adsorption energies of a

single K atom on different adsorbing sites of CNT (9,0) and CNT (5,5) (as shown

in Fig. 4.14), and found that for both CNTs, the most stable adsorption site is

74


the hollow site with the adsorption energy of 1.73 eV for CNT (9,0) and 1.04 eV

for CNT (5,5), agreeing well with literature [159]. We then gradually increased

the number of K atoms adsorbed per supercell on CNTs, and then calculated the

change of work functions after the structure optimization. As shown in Fig. 4.15,

for both CNTs, when the coating density increases, the work function first rapidly

decreases by more than 2.0 eV, and then slowly goes up. For CNT (9,0), the

work function reaches its minimum value of 2.2 eV at the coating density of 5.56%

(denoted as A in Fig. 4.15 (a)), and the minimum work function of CNT (5,5)

is 1.98 eV occurring at the coating density of 6.25% (B in Fig. 4.15 (a)). The

atomic structures of K-coated CNT (9,0) and (5,5) with minimum work functions

are shown in Fig. 4.15 (b) ( A: upper, and B: lower). Our calculations are in good

agreement with observations of previous studies that a great reduction of work

functions of CNTs can be achieved by alkali metal coating.[158, 160]

4.2.5 Strain effect on work function of potassium-decorated

CNT

The uniaxial strain as described above is then applied to K-coated CNT (5,5) and

CNT (9,0). Before discussing the change of work functions, we first take a look

at effects of strain on adsorption energies of a single K atom on both CNTs. As

shown in Fig. 4.16 (a), the strain has much stronger effects on adsorption energy of

K on CNT (5,5) than that of CNT (9,0) especially for tensile strain. When strain

changes from 0.0 to 10%, the adsorption energy of K on CNT (5,5) increased by as

much as 0.87 eV. The significant change of adsorption energy under strain implies

75


Figure 4.14: A schematic description of different adsorbing sites (purple circles) of

K atom on CNT (9,0) (left) and CNT (5,5) (right): Bridge sites B1, B2 ; Hollow

site H, and top site T. Binding energies for different sites are calculated to be B1 :

1.58 eV, B2 : 1.62 eV, H : 1.73 eV, T : 1.59 eV for CNT (9,0), and B1 : 0.95 eV,

B2 : 0.92 eV, H : 1.04 eV, T : 0.92 eV for CNT (5,5),repectively.

potential applications of modifying chemical properties of CNT-based systems via

tuning strain. The variations of work function with strain were calculated for

two K-coated CNTs (as shown in Fig. 4.16 (b)) which have lowest work functions

upon K coating. Interestingly, when under strain, work functions of K-coated

CNTs show drastically different behaviors comparing with those of pristine cases.

First, the strain dependence becomes much weaker, and second, work functions

decrease when strain increases except for the case of K-coated CNT (5,5) in the

small range of strain from 6% to 10%. When strain changes from -10% to +10%,

the work function of K-coated CNT (9,0) varies between 2.27 eV and 2.08 eV, and

the work function of K-coated CNT (5,5) changes between 2.05 eV and 1.95 eV

for all strains. These drastic changes of strain-dependence of work functions upon

K coating strongly suggest that the combination of the chemical decoration and

76


Figure 4.15: Work function of potassium deposited CNT (9,0) and CNT (5,5)

Vs. deposition density (x in KxC). For CNT (9,0), the work function reaches its

minimum value of 2.2 eV at the coating density of 5.56% (denoted as A in (a)),

and the minimum work function of CNT (5,5) is 1.98 eV occurring at the coating

density of 6.25% (B in (a)). The atomic structures of K-coated CNT (9,0) and

(5,5) with minimum work functions are shown in Fig. 5 (b) ( A: upper, and B:

lower).

77


Figure 4.16: Strain effects on adsorption energies of K@CNTs, and work functions

of K adsorbed CNTs: (a) Adsorption energy of a single K atom on CNT (9,0) and

(5,5) as a function of strain; (b) Strain dependence of work functions of K coated

CNT (9,0) as shown in Fig. 5 (b) (upper), and K coated CNT (5,5) (lower one in

Fig. 5 (b)).

tuning of strain is a powerful method in controlling work functions of CNT-based

systems.

Charge transfer between K atoms and two CNTs as function of strain was calcu-

lated via Bader charge analysis[161] in order to understand the decrease of work

functions of K-coated CNTs. In Fig. 4.17 (a), we plot the calculated charge trans-

fer per K atom for the K-coated tubes under strain ranging from -10% to +10%.

For the case of zero strain, the amount of charge transfer per K atom was found to

be 0.63 and 0.75 electrons for CNT (5,5) and CNT (9,0) respectively. In Fig. 4.17

(b), we show the isosurface of the differential charge density between isolated CNT

(5,5), K atoms, and K-coated CNT (5,5). The plum (green) color denotes the

accumulation (diminishing) of electrons. For both tubes, the amount of charge

78


Figure 4.17: (a) Calculated average charge transfer per K atom to CNT (5,5) and

CNT (9,0) at different strains. When strain changes from -10% to 10%, the charge

transfer for two tubes monotonically increases. (b) Isosurface of the differential

charge density between isolated CNT (5,5), K atoms, and K-coated CNT (5,5).

transferred from K atoms to CNTs monotonically increases with strain. There-

fore, it can be expected that the dipole moment normal to tube surfaces caused

by the charge transfer increases with strain, which will likely lead to the decrease

of work function according to previous studies.[162]

4.3 Summary

First principles calculations have been performed to study the effects of adsorbates

(CO molecule and O atom) and defects on electronic structures and transport

properties of Au nanotubes (Au (5,3) and Au (5,5)). For CO adsorption, various

adsorption sites of CO on the Au tubes were considered. Vibrational frequency of

the CO molecule was found to be very different for two nearly degenerate stable

79


adsorption configurations of Au (5,3), implying the possibility of distinguishing

these two configurations via measuring the vibrational frequency of CO in experi-

ment. After CO adsorption, the conductance of Au (5,3) decreases by 0.9 G0, and

the conductance of Au (5,5) decreases by approximately 0.5 G0. For O adsorbed

Au tubes, O atoms strongly interact with Au tubes, leading to around 2 G0 of

drop of conductance for both Au tubes. These results may have implications for

Au-tube based chemical sensing. When a monovacancy defect is present, we found

that for both tubes, the conductance decreases by around 1 G0. Another type of

defect arising from the adhesion of one Au atom is also considered. For this case,

for Au (5,3) tube, it is found that the defect decreases the conductance by nearly

1 G0, whereas the decrease of the conductance is only 0.3 G0 for Au (5,5) tube due

to the adsorption of the extra Au atom.

For the study of work function of CNT, variations of work functions with strain

for both pristine and potassium coated CNT (5,5) and CNT (9,0) are calculated

via first principles methods under the framework of DFT. For pristine cases, the

strain shows strong effects on work functions of both CNTs, and the work function

of CNT (5,5) behaves quite differently with strain from that of CNT (9,0). The

different strain dependence of work functions of two CNTs is caused by intrinsic

difference between metallic CNT (5,5) and semi-metallic CNT (9,0). We also found

that the strain has great influence on chemical adsorption of K atoms on CNTs. In

the case of CNT (5,5), the adsorption energy of a single K atom increases by 0.87

eV when strain changes from 0.0 to 10%. At last, work functions of K-coated CNTs

show drastically different strain dependence from that of pristine case. Our findings

strongly suggest that tuning of strain may be a powerful method in controlling work

80


functions of CNT-based systems, and our calculations on CNT (5,5) and CNT (9,0)

are helpful for understanding work functions of other CNTs under strain. Alkali

metal doping is more effective than strain especially at low dopant rate. The results

present in this chapter will be helpful for the understanding and control of work

function of CNT for electronic and field emission applications.

81

Chapter 5

Strain effect on the spin injection

and electronic tunneling of

Co2CrAl/NaNbO3/Co2CrAl

In this Chapter, first-principles calculations are carried out to study effects of strain

on transport properties of Co2CrAl/NaNbO3/Co2CrAl MTJ. Sodium niobate is

chosen for the spacer layer due to its wide ferroelectric and piezoelectric applica-

tions, while Co2CrAl is an important electrode in the family of Co2Cr1−xFexAl,

and Co2CrAl has recently received much attention for its remarkable magnetore-

sistive properties and the ability of preserving half-metallic behavior even at the

surface and interface. Both spin polarization and tunnel magnetoresistance of the

MTJ were found to respond to positive (tensile) and negative (compressive) strains

asymmetrically. While a compressive strain up to 4% only causes slight increases

82

Chapter 5. Strain effect on the spin injection and electronic tunneling ofCo2CrAl/NaNbO3/Co2CrAl

in the spin polarization and small fluctuations in tunnel magnetoresistance, a pos-

itive strain of a few percent significantly reduces the tunnel magnetoresistance.

This study provides a theoretical understanding on relationship between transport

properties through a MTJ and interface atomic structural changes induced by an

external strain.

5.1 Computational details

The CCA(001)/NNO(001) heterostructure is created by directly stacking CCA(001)

on NNO(001) without any rotation, as shown in Fig. 5.1.The in-plane lattice con-

stants of cubic CCA are slightly reduced to match those of NNO which stabilizes in

the orthorhombic perovskite structure (space group: Pbcm) with lattice constants

a = 5.570 A, b = 5.631 A, and c = 15.701 A. A small lattice mismatch of 2.4%

occurs between the distorted CCA (c/a = 1.05) and NNO. The lattice parameter

of the supercell in the direction normal to the interfaces is adjusted until the total

energy of the system reaches a minimum. Odd numbers of CCA (19) and NNO (9)

atomic planes are used in the model to prevent formation of artificial electrostatic

fields across the interfaces.

Our calculations are based on spin-polarized density functional theory using the

projector augmented wave method with Perdew-Burke-Ernzerhof general gradient

approximation (PAW-PBE) in VASP package. A cutoff energy of 400 eV and

a 6×6×1 Monkhorst-Pack k sampling [152] were chosen to achieve convergence

83


Figure 5.1: Atomic structure of the CCA/NNO/CCA MTJ. The models are built

by stacking CCA directly on NNO along the [001] crystaline direction.

of energy and forces. Structural relaxations are performed until the Hellmann-

Feynman forces on the atoms become less than 0.02 eV/A. In the conductance

calculations, the transport properties were calculated by ATK code within the

NEGF formalism.[110, 129, 130] Single-ζ polarized basis and a cutoff energy of

150 Ry for the grid integration were adopted in transport calculations. GGA-

PBE approximation [108] and a 6 × 6 × 100 Monkhorst-Pack grid for accurately

k-point sampling were used in the coherent conductance calculation. The zero-bias

conductance was evaluated by integrating the electron transmission for states at

the Fermi level over the 2D Brillouin zone using a uniform 200×200 k|| mesh which

aims to accurately treat any transmissions associated with interface states.

5.2 Energetics and electronic structure analysis

Since CCA consists of alternate Co and CrAl planes in the [001] direction and simi-

larly NNO is composed of alternate NbO2 and NaO planes, a CCA(001)/NNO(001)

interface can be built with Co- or CrAl-terminated CCA and NbO2- or NaO-

terminated NNO. In addition to the four interface models (models 1-4 in Table. 5.1)

84


built with various combinations of CCA(001) and NNO(001) terminations, we con-

sider another model (model 5) which is also formed by CrAl-terminated CCA and

NaO-terminated NNO, but the CCA is shifted related to NNO in the interface

plane so that Cr forms bond with O and Al is bonded to Na, instead of the Al-O

and Cr-Na bonds in the interface built by directly stacking CCA on NNO (model

4). To evaluate the relative stability of the various interface structures, we calcu-

late the interfacial cohesive energy (Eint) which is defined as Wice=(ECCA+ENNO-

ECCA/NNO/CCA)/2A, where ECCA/NNO/CCA is the total energy of the supercell, ECCA

(ENNO) is the energy of CCA (NNO), calculated using the same supercell but with

the NNO (CCA) part removed. 2A is the total surface area of the 2 interfaces in

the supercell. The calculated interface cohesive energies and the lengths of atomic

bonds formed at the interfaces are listed in Table. 5.1. The large values of inter-

face cohesive energies indicate that all five interfaces are stable which is consistent

with the fact that the junction of Heusler alloys can usually stabilize with distinct

interfacial structures. It is interesting to note that both CrAl-NaO interfaces are

surprisingly more stable than the CrAl-NbO2 interface which has double the num-

ber of interfacial oxygen bonds. However, the strongest cohesion between CCA or

NNO is exhibited by the Co-NbO2 interface with O atoms lying on top of Co atoms

as shown in Fig. 5.1. The large cohesive energy of this interface, with Eint = 2.46

J/m2, is accompanied by the strong Co-O bond. The Co-O bond length (1.938

A) is close to that in bulk CoO. Since the binding energy of this interface is 20%

larger than that of the next most stable interface, this model is used in subsequent

calculations of electronic structure, SP and spin injection.

The spin-polarized local density of states (LDOS) of the CCA/NNO/CCA MTJ is

85


Table 5.1: Calculated cohesive energies and interface bond lengths for various

CCA/NNO interfaces.

Model Interface Cohesive energy (J/m2) Interface bond (Bond length (A))

1 Co-NbO2 2.46 Co-O (1.938), Co-Nb (2.712)

2 Co-NaO 1.72 Co-O (1.852), Co-Na (2.683)

3 CrAl-NbO2 1.64 Al-O (1.985), Cr-O (1.965)

4 CrAl-NaO 2.01 Al-O (1.830), Cr-Na (2.814)

5 CrAl-NaO 1.93 Cr-O (1.886), Al-Na (2.914)

shown in Fig. 5.2. The constraint of the lateral lattice constants of CCA to match

those of NNO induces minor changes to the magnetic property of CCA compared to

bulk cubic CCA. Result of our calculations shows that the local magnetic moment

of Co is 0.73 µB and that of Cr is 1.61 µB in the orthorhombic phase, which are

very close to those in cubic CCA (0.77 µB for Co and 1.54 µB for Cr).

The most important feature of the LDOS shown in Fig. 5.2 is that the half metallic

character of CCA is preserved at the interface, despite of substantial modifications

of the electronic properties of the interfacial atoms compared to those in the bulk.

For instance, the spin moments of the interfacial Co (0.39 µB) and Cr (1.11 µB)

become smaller than the corresponding values in bulk CCA. The minority band

gap is reduced from ∼0.5 eV (GGA value) for Co atom in bulk CCA to ∼0.2 eV

for interfacial Co atom due to orbital mixing between the Co 3d and O 2p orbitals.

This strong hybridization pushes down the bonding state of the interfacial O atoms

by nearly 1 eV (Fig. 5.2d). In addition to these bonding states between O and

Co atoms in the low energy part of the 3d states of the interfacial Co atoms, the

86


Figure 5.2: LDOS for the majority (top panels) and minority (bottom panels) spin

electrons projeted to the O, Co and Nb atoms at the Co-NbO2 interface and in

bulk region, respectively. The vertical dashed line indicates the position of the

Fermi level.

87


oxygen LDOS displays a broad band of antibonding states, ranging from −3 eV

to 3 eV, which are absent in bulk NNO. Similar metal induced gap states (MIGS)

appear more prominently for the interfacial Nb atoms as shown in Fig. 5.2f. Since

the length of the Nb-Co bond is 2.71 A and the Wigner radii of Nb and Co atoms

are 1.27 and 1.30 A respectively, direct bonding between the interfacial Nb and Co

atoms seems unlikely, and these MIGS on Nb atoms must arise from an indirect

coupling between Nb and Co mediated by the O atom. This indirect coupling leads

to a substantial exchange-splitting of these states in the 2 eV interval below the

Fermi energy (Fig. 5.2f) and a magnetic moment of 0.05 µB on the interfacial Nb

atom which is aligned antiparallel to those of the Co atoms. This situation is quite

similar to the case of Co/SrTiO3 junction where the interfacial Ti atom is found

to possess a small magnetic moment which is antiferromagnetically coupled with

that of the interfacial Co atom.[163]

5.3 Strain effects on the spin injection and tun-

nel magnetoresistance

Next we discuss the strain effects on the SP and electronic tunneling of the MTJ.

A uniaxial strain along the normal direction of the interface is considered and is

realized in our model through changing the length of the supercell while fixing the

atomic positions in the extreme left and extreme right unit cells of CCA in Fig. 5.1.

The system is then relaxed under the constraint of fixed supercell parameter c. The

SP of each atom is defined as (ρ↑− ρ↓)/(ρ↑+ ρ↓), where ρ↑ and ρ↓ are the majority

88


Figure 5.3: Variation of the planar averaged SP along the interface normal direction

of the CCA/NNO/CCA MTJ, at various values of applied strain. The position of

the Co-NbO2 interface plane is indicated by the vertical dashed line. The horizontal

dashed line corresponds to 100% SP in each case.

89


and minority LDOS, respectively, at the Fermi level projected on the atom. The

calculated in-plane averaged SP is shown in Fig. 5.2 for various strain values.

Since the structure and SP are symmetric with respect to the middle of the MTJ

structure, only the SP for half of the MTJ is shown in the figure. A 100% SP can be

observed for atoms at the CCA side corresponding to the half-metallic character of

CCA. At zero strain, an extremely high SP (nearly 100%) is seen at the Co-NbO2

interface and extends to the NNO part. When a compressive strain is applied, a

steady increase of SP in the NNO part can be clearly observed. This can be due to

stronger coupling at the interface between interfacial atoms under the compressive

strains. On the other hand, considering the fact that the minority band gap of

CCA originates from the eu-t1u splitting due to interaction between the nearest

Co atoms,[79] the splitting can be enhanced under a compressive strain due to

increased hybridization. Under a moderate positive strain, SP in the NNO part

drops slightly while the polarization at CCA side remains high (>90%). However,

when the strain approaches 4%, the SP decreases dramatically. This cannot be

attributed to structural instabilities since no significant structural changes occur

in the heterostructure at this strain and the Co-O bond length increases only

slightly, from 1.938 A at zero strain to 1.947 A at 4% strain.

90


5.4 Strain effects on the tunnel magnetoresis-

tance

According to Julliere,[164] SP is a key quantity in determining TMR of a MTJ. The

asymmetrical response of SP to positive and negative strains applied to the MTJ

prompted us to calculate the electron tunneling and TMR across the junction. The

TMR ratio is defined as (G↑↑−G↑↓)/G↑↓, where G↑↑ and G↑↓ are conductances of the

MTJ when the magnetizations of the two electrodes are parallel and antiparallel,

respectively. The calculated k�-resolved transmission in the parallel magnetization

configuration is shown in Fig. 5.4. The majority spin states around the Γ point

show no transmission, which was also found in the CCA/MgO system.[165] The

features of the transmission function are related to the shape of the Fermi surface

folded into the Brillouin zone of the deformed orthorhombic CCA supercell. For

the minority-spin states, the transmission shows spiky structures, but of much

smaller magnitudes, which can be attributed to the resonant tunneling of weak

interface states. The strong transmission of the majority states and much smaller

and spiky transmission peaks for the minority states suggest that a high TMR

ratio can be expected. The calculated TMR ratio shown in Fig. 5.4c confirms this

prediction. Furthermore, the TMR ratio fluctuates with compressive strain, but

decreases rapidly with the tensile strain. At 4% of tensile strain, the TMR ratio

drops by two orders of magnitude compared to the strain free value. This result is

in good agreement with recent experimental observations[166] with Co2MnSi-based

MTJ in which it was found that the TMR fluctuates slightly, without any abrupt

changes, in the process of applying a hydrostatic pressure on the system. However,

91


Figure 5.4: In-plane wave vector k� = (kx, ky) dependence of majority-spin (a) and

minority-spin (b) transmissions at the Fermi level of the CCA/NNO/CCA MTJ

in the parallel magnetization configuration without strain. (c) TMR ratio as a

function of strain.

to the best of our knowledge, no experiment has been conducted to investigate the

effect of a positive strain on such a system.

The difference between the k�-resolved majority transmissions of the strained MTJ

and the strain free MTJ in the parallel magnetic configuration is shown in Fig. 5.5a

for −4% strain and in Fig. 5.5c for 4% strain, respectively. At the strain of −4%,

large changes are seen at the highly conducting k-points compared to transmission

at zero strain which is shown in Fig. 5.5b. These k-dependent changes can be

qualitatively understood by tunneling probability of electrons at the Fermi sur-

face. In contrast, at 4% strain, new transmission channels, which are absent in the

transmission spectrum of the strain free MTJ, are found in the central region of

the Brillouin zone where a hole appears in the Fermi surface (Fig. 5.5d and 5.5e).

92


Figure 5.5: The differences between majority-spin transmissions at the Fermi

level in the parallel magnetization configuration in strained and strain free

CCA/NNO/CCA MTJ: (a) G↑↑(−4%)−G↑↑(0), (c) G↑↑(4%)−G↑↑(0). The trans-

mission at zero strain is given in (b). The Fermi surfaces corresponding to the two

folded bands in the Brillouin zone of the orthorhombic Co2CrAl are shown in (d)

and (e), respectively.

93


These additional conducting channels can be related to the interface states result-

ing from hybridization between atomic orbitals of interface atoms due to the strain

induced interface structural changes. These interface states also greatly enhance

the conductance of the minority electrons and destroy the half-metallic character

of CCA at the interface. Since the conductance in the antiparallel magnetic con-

figuration of the electrodes G↑↓(k�) can be approximated by the geometrical mean

of the majority and minority conductances obtained for the parallel configuration,

i.e., G↑↓(k�) =√

G↑↑(k�)G↓↓(k�), one can expect G↑↓(k�) to increase dramatically

for states around Γ and a substantial reduction in the TMR at 4% strain, as shown

in Fig. 5.4c.

5.5 Summary

In conclusion, results of our first-principles calculation show that both the SP and

TMR of the CCA/NNO/CCA MTJ present asymmetrical responses to positive

and negative strains. While a high SP is maintained at the interface and the TMR

ratio fluctuates slightly under compressive strain, a positive strain of 4% leads

to a drop of TMR by ∼2 orders of magnitude due to electron tunneling through

the interface states. Our study shows that a strain applied to the MTJ results in

significant changes in transport properties of the Heulser/semiconductor junction.

94

Chapter 6

Conclusions and perspectives

In the preceding pages, first principles calculations have been carried out to study

the physical properties of nanomaterials for their potential applications in nano-

electronics and spintronics. Firstly, coherent electron transport through a single

light sensitive diarylethene molecule sandwiched between two GNRs was simu-

lated based on DFT and NEGF techniques. The “open” and “closed” isomers of

the diarylethene molecule that can be converted between each other upon photo-

excitation were found to have drastically different I-V characteristics, suggesting

that the GNR-diarylethene-GNR junction can be used as a high-performance light

controllable molecular switch with a current ratio of ON/OFF states above 103.

We also reported a strong rectification behavior of 6-zGNR-diarylethene-x -aGNR

junctions with average rectification ratios of 1635, 34 and 11 for the cases of x=10,

12, and 14 respectively. The rectification mainly arises from the bias-dependent

variation of the energy level of the diarylethene molecule’s LUMO orbital relative

95

Chapter 6. Conclusions and perspectives

to the band gap of the semiconducting GNR. Therefore, the appropriate choice of

the band gap of the semiconducting electrode and the alignment of the molecule’s

frontier orbitals with the semiconducting gap are important for achieving the high

rectification ratio. Moreover, the interface states localized in molecule-GNR con-

tacts were found to play important roles in electron tunneling. The reported recti-

fication mechanism provides a new way to achieve high rectification ratio (>>100)

in single-molecule based devices, and the asymmetric G-D-G junctions may form

the basis for a new class of high-performance molecular rectifiers.

For gold nanotube and CNTs, chemical modification and mechanical loading are

found to be two effective ways of tuning the properties of these nanotube systems.

For gold nanotubes, the influence of adsorbates (CO molecule and O atom) on the

electronic and transport properties of Au (5,3) and Au (5,5) nanotubes was inves-

tigated. For CO adsorption, the calculation predicts that the drop of conductance

of Au(5,5) (0.5 G0) is about a half of that of Au(5,3) (0.9 G0). The backdonation

mechanism exists for both tubes which is manifested in the variations of the C-O

bond length and stretching frequency of CO molecule on the tubes with differ-

ent amounts of the occupancy of the antibonding 2π∗ orbital. Our conductance

calculations show that the adsorption of O atom strongly distorts the Au tubes,

which blocks two channels for transmission for both tubes. In addition, the metal-

lic bonding nature of Au-Au bond and high mobility of Au atoms suggest that

these systems are prone to be defective. Effect of defects either arising from the

Au adsorption or Au vacancy, which are unavoidable during the production, on

conductance and transport has been calculated. The result shows that Au adatoms

can be deposited on the tubes with relatively large adsorption energies. For both

96

Chapter 6. Conclusions and perspectives

tubes the vacancy leads to about 20% decrease of conductance. For CNTs, vari-

ations of work functions with strain for both pristine and potassium coated CNT

(5,5) and CNT (9,0) are calculated. For pristine cases, the strain shows strong ef-

fects on work functions of both CNTs, and the work function of CNT (5,5) behaves

quite differently with strain from that of CNT (9,0). We also found that the strain

has great influence on K-coated CNTs. Work functions of K-coated CNTs show

drastically different strain dependence from that of pristine cases. Our findings

strongly suggest that tuning of strain may be a powerful method in controlling

work functions of CNT-based systems.

The last part of this thesis is devoted to the spin polarization and spin injection of

Co2CrAl/NaNbO3/Co2CrAl MTJ. The electronic structure and variations of spin

polarization and TMR ratio with strain for Co2CrAl/NaNbO3/Co2CrAl MTJ are

investigated. Both the SP and TMR present asymmetrical responses to positive

and negative strains. It is well accepted that chemical defect such as vacancy

and antisite which can destroy the half-metallic character of Heusler alloy, how-

ever, our study shows that strain can lead to huge modifications of properties of

Heulser/semiconductor junctions. Future work may be carried out to study the

effect of coexistence of strain and chemical defects at the interface on TMR prop-

erties.

97

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First-principles Simulations of Nanomaterials for

Nanoelectronics and Spintronics

CAI YONGQING

NATIONAL UNIVERSITY OF SINGAPORE

2011

Documents

First-principles Simulations of Nanomaterials for ... · Abstract Rapid developments of nanoelectronics and spintronics call for the design of new materials for building blocks of