Study of Defect and Doping on Electrical and Tribological Behaviors of

Graphene and Graphene Like Materials

Fariba Nazari

Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan

Natrue, 2016, 539,502

Contents

Short Introduction to Tribology

Potential Energy Surface and Artificial Neural Network

Registry Index

Electronic Properties of Doped and Defected Typical 2D Structures

Tribological Properties of Doped and Defected Typical 2D Structures

The term derives from the Greek root

Tribology

“ Tribo ” “Logia”And

That means to rub, grind, or wear away "study of”And

Tribology is defined as the science and technology of

Interacting surfaces in relative motion, which involves friction,

wear, and lubrication

Phys.Chem.Chem.Phys., 2015, 17, 12908

Because of its enormous practical and technological importance, the friction

problem has stimulated progress over the centuries

Frictional motion plays a central role in diverse systems and phenomena that span

vast ranges of scales from

The nanometer contacts inherent in micromachines and nanomachines

Biological molecular motors

The geophysical scales characteristic of earthquakes

Springer International Publishing Switzerland 2015

E. Gnecco and E. Meyer (eds.), Fundamentals of Friction and Wear on the Nanoscale,

NanoScience and Technology, DOI 10.1007/978-3-319-10560-4_10

Historical figures from Leonardo da Vinci onward have brought friction into the

field of physics, with the formulation of time-honored phenomenological

frictional laws, which have been referred to as the Coulomb-Amontons laws

These statements can be briefly summarized as follows

(iii) kinetic friction does not depend on the sliding velocity and is smaller than

static friction

(i) Frictional force is independent of the apparent area of contact

(ii) Frictional force is proportional to the normal load

In the light of a mass of empirical data, serious

Attempts were made in the first half of the 20th century

toward a microscopic understanding of these laws

Rev. Mod. Phys. , 2013, 85 , 529-552

David Tabor

1913

-2005

Peter Jost1921-2

016

Frank Philip Bowden and David Tabor (1950) showed that, at

a microscopic level, the actual area of contact between surfaces is a

very small fraction of the apparent area. This actual area of contact,

caused by "asperities" (roughness) increases with pressure

Physics today, 2006,72

http://www.telegraph.co.uk/obituaries/2016/06/15/peter-jost-mechanical-engineer--obituary/

First, progress in the general area of complexity

Third, The developments in nanotechnology

Second, computer simulations

Springer International Publishing Switzerland 2015

E. Gnecco and E. Meyer (eds.), Fundamentals of Friction and Wear on the Nanoscale,

NanoScience and Technology, DOI 10.1007/978-3-319-10560-4_10

The development of new tools allowing nanometer-scale measurements.

STM AFM SNOM

One area that has greatly benefited from the efforts mentioned above is tribology

Experimental observations (for instance, velocity and temperature

dependencies of friction) have been rationalized within simplified models

including empirical parameters

Despite the practical and fundamental importance of friction and the growing

efforts in the field, many key aspects of the dynamics of friction are not yet

well understood

Even for the most studied nanoscale systems, such as AFM sliding on graphite or

NaCl surfaces, a microscopic mechanism of friction is still lacking

Nature Materials, 2010, 9, 8-10

New areas of tribology

Since the 1990s, new areas of tribology have emerged

Biotribology

Green tribology

(Human joint prosthetics, Dental materials)

(Tribology of clean energy sources, Green lubricants, Biomimetic tribology)

Nanotribology

( MEMS/NEMS)

Nanotribology is a branch of tribology and was coined by Krim,

Solina and Chiarello

Nano-electromechanical systems (NEMS)

Micro-electromechanical systems (MEMS)

PLOS ONE , 2013 , 8 (12) , e81094

Owing to larger surface area in MEMS or NEMS

Surface forces such as adhesion, friction, and meniscus

and viscous drag forces become large

There is a need to develop

lubricants and identify lubrication methods that are

suitable for MEMS/NEMS

Researchers anticipated that once the principal

mechanisms had been identified in these nanometer-

size systems, they could be “scaled up” for better

understanding of friction in technologically relevant,

macroscopic systems

12

Intrinsic complexity of highly nonlinear and non-equilibrium

processes going on in any tribological contact

Which include detachment and reattachment of multiple

microscopic junctions

Springer International Publishing Switzerland 2015

E. Gnecco and E. Meyer (eds.), Fundamentals of Friction and Wear on the Nanoscale,

NanoScience and Technology, DOI 10.1007/978-3-319-10560-4_10

13

Potential Energy Surface

Fix positions of nuclei, {R1…RN}, solve DFT equations self-consistently.

22

2

( ') '[ ( )] ( ) ( )

| | | ' |

( ) | ( ) |

Rxc i i i

R

i i

i

Z e r drV r r r

r R r r

r f r

14

15

16

Moiré pattern

17

The form of the potential is chosen based on physical

considerations

The form of the potential is chosen based on mathematical

considerations

If the systems are too large for the application of electronic

structure methods

They are particularly useful

If long MD trajectories or extended Monte Carlo simulations are

required

If many MD trajectories are needed to obtain statistically

converged results

International Journal of Quantum Chemistry 2015, 115, 1032–1050

18

Ideal Potential

Requirements

Transferable

International Journal of Quantum Chemistry 2015, 115, 1032–1050

19

Artificial neural networks (NNs) constitute class of flexible

functions

Inputs

Outp

ut

D. Kriesel, A Brief Introduction to: Neural Networks. Germany: Dr. Peter Kemp, Notary (ret.), Bonn, 2005.

20

Firing neuron stimulating its neighbors

21International Journal of Quantum Chemistry 2015, 115, 1032–1050

22

The values of the nodes in the first hidden layer are then

calculated in two steps

A), For each node m in the hidden layer a weighted sum 𝑥𝑚𝑙 of

the input coordinates {Gi} is calculated, and the bias weight is

added the bias weight is added

B) Then, a non-linear function 𝑓𝑚𝑙 is applied to 𝑥𝑚

𝑙 , which provides the capability

to fit arbitrary functions. This finally yields the numerical value 𝑦𝑚𝑙 of the node

International Journal of Quantum Chemistry 2015, 115, 1032–1050

23International Journal of Quantum Chemistry 2015, 115, 1032–1050

24

Artificial Neural Network

25

50×24 Grid

26

27

Unit cell of bilayer Graphene consist 4 C atom

28

29Phys. Chem. Lett., 14, 2013, 2376.

The Registry Index: A Quantitative Measure of

Materials’ Interfacial Commensurability

30

RI is based on simple geometrical parameter

𝑅𝐼 ∝ 𝑆𝑖𝑗

31Phys. Chem. Lett., 14, 2013, 2376.

32

ri=?

O. Hod, Phys. Chem. Lett., 14, 2013, 2376.

En

erg

y (

Ry)

33Phys. Chem. Lett., 14, 2013, 2376.

ri=0.5LCC

G@G

34

Different electronegativities of B and N atoms

Eg=0 eVEg=4.65 (5.97) eV

Isoelectronic counterpart of graphene

35

Obviously, synthesized samples always contain defects of different types.

36F. Banhart et al., ASC Nano, 5, 2011, 26

585-Extended Line Defect

or “Self-doping”, in which extended defects are introduced into the

graphene lattice

Topological Defect

37J. Lahiri et al., Nat. Nanotech., 5, 2010, 326

38

Graphene or

h-BN

585 ELD 5775 ELD

Zigzag edge

Arm

chair

edge

Eg=2.75 eV

G as a metallic wire h-BN as a semicond. wire

39

VBES CBES

585 extended defect in

40

Eg=3.21 eV

G-585-ELD G

increase the charge transport of

41

h-BN h-BN-585-ELD

42

Coexistence of defect and doping

43

Coexistence of defect and doping

44

Doping

45

Direct band gap

Indirect band gap

46

Movable Elements

Schemes of graphene-based NEMS. A: nanorelay(position 'on'), B: nanorelay (position 'off'),

Physica E: Low-dimensional Systems and Nanostructures, 44, 949, 2012

Bilayer graphene

47

o No movemento No heato No friction

Pushing the object against the other causes ”Sliding Friction”

o Larges surface contacto Extreme high heato Tremendous energy needed to move object

48M. Dienwiebel et al., Phys. Rev. Lett., 92, 2004, 126101.

Frictional force microscopy

49

Moiré pattern

50M. Dienwiebel et al., Phys. Rev. Lett., 92, 2004, 126101.

Narrow peaks with high friction

Moiré pattern

Sufficiently large heterogeneous

layered interfaces act as promising

candidates for dry lubrication purposes

51

52

Effect of doping on tribological properties of 2D materials

BNC2

53

G h-BN BNC2

BNC2@G BNC2@h-BN BNC2@BNC2

54

BNC2@G

55

BNC2@BN

56

BNC2@BNC2

Unit cell of bilayer Graphene consist 4 C atom

57

58

RIh−BNC2/G=

SCC−SCCAB + SCN−SCN

AB +(SCB−SCBAB)

SCCAA−SCC

AB + SCNAA−SCN

AB +(SCBAA−SCB

AB)

rC = 0.7155 Å, rN = 0.69 Å, rB = 0.1 Å

59

𝑅𝐈 Τℎ−𝐵𝑁𝐶2 ℎ−𝐵𝑁 =𝑆𝐶𝑁 − 𝑆𝐶𝑁

𝐴𝐵 + 𝑆𝐶𝐵 − 𝑆𝐶𝐵𝐴𝐵 + 𝑆𝑁𝑁 − 𝑆𝑁𝑁

𝐴𝐵 + 𝑆𝐵𝐵 − 𝑆𝐵𝐵𝐴𝐵 − 𝑆𝑁𝐵 − 𝑆𝑁𝐵

𝐴𝐵

ሻ𝑆𝐶𝑁𝐴𝐴 − 𝑆𝐶𝑁

𝐴𝐵 + 𝑆𝐶𝐵𝐴𝐴 − 𝑆𝐶𝐵

𝐴𝐵 + 𝑆𝑁𝑁𝐴𝐴 − 𝑆𝑁𝑁

𝐴𝐵 + 𝑆𝐵𝐵𝐴𝐴 − 𝑆𝐵𝐵

𝐴𝐵 − (𝑆𝑁𝐵𝐴𝐴 − 𝑆𝑁𝐵

𝐴𝐵

rC=0.7155Å, rN=0.6276Å, rB=0.2868Å

60

𝑅𝐈 Τℎ−𝐵𝑁𝐶2 ℎ−𝐵𝑁𝐶2 =𝑆𝐶𝑁 − 𝑆𝐶𝑁

𝐴𝐵 + 𝑆𝐶𝐵 − 𝑆𝐶𝐵𝐴𝐵 + 𝑆𝐶𝐶 − 𝑆𝐶𝐶

𝐴𝐴 + 𝑆𝑁𝑁 − 𝑆𝑁𝑁𝐴𝐴 + 𝑆𝐵𝐵 − 𝑆𝐵𝐵

𝐴𝐴 + 𝑆𝑁𝐵 − 𝑆𝑁𝐵𝐴𝐴

ሻ𝑆𝐶𝑁𝐴𝐴 − 𝑆𝐶𝑁

𝐴𝐵 + 𝑆𝐶𝐵𝐴𝐴 − 𝑆𝐶𝐵

𝐴𝐵 + 𝑆𝐶𝐶𝐴𝐴 − 𝑆𝐶𝐶

𝐴𝐵 + 𝑆𝑁𝑁𝐴𝐴 − 𝑆𝑁𝑁

𝐴𝐵 + 𝑆𝐵𝐵𝐴𝐴 − 𝑆𝐵𝐵

𝐴𝐵 + (𝑆𝑁𝐵𝐴𝐴 − 𝑆𝑁𝐵

𝐴𝐵

rC=0.7155Å, rN=0.6494Å, rB=0.2625Å

61

BNC2@G

Robust superlubricity

Effect of flake size and misfit angle on the corrugation of the sliding RI surface of the heterogeneous h-BNC2/graphene interface. (a) Schematic

representation of a square 72 × 42 h-BNC2 flake on top of an graphene layer with a misfit angle of 0°; (b) Maximal variations of the RI calculated alonglinear paths in the sliding direction as a function of interlayer misfit angle. The inset shows maximal RI corrugation as a function of flake size (number of

atoms in the flake). The different diagrams presented in panel (b) are normalized as to the size of the relevant h-BNC2 flake such that a maximal RI

corrugation of 1 is obtained for a strained h-BNC2 flake consisting of the same number of atoms and geometry having no lattice mismatch with the

underlying graphene layer.

62

BNC2@h-BN

Effect of flake size and misfit angle on the corrugation of the sliding RI surface of the heterogeneous h-BNC2/h-BN interface. (a) Schematic representation

of a square 72 × 42 h-BNC2 flake on top of an graphene layer with a misfit angle of 45°. (b) Maximal variations of the RI calculated along linear paths inthe sliding direction as a function of interlayer misfit angle. (Inset) Maximal RI corrugation as a function of flake size (number of atoms in the flake).

Robust superlubricity

63

BNC2@BNC2

Effect of flake size and misfit angle on the corrugation of the sliding RI surface of the heterogeneous h-BNC2/h-BNC2 interface. (a) Schematic

representation of a square 72 × 42 h-BNC2 flake on top of an graphene layer with a misfit angle of -20°. (b) Maximal variations of the RI calculated alonglinear paths in the sliding direction as a function of interlayer misfit angle. (Inset) Maximal RI corrugation as a function of flake size (number of atoms in

the flake).

Superlubricity

64

Effect of topological defect on tribological properties of 2D materials

Defected nano-flake

65

66

1- Calculation of PES

2- Fitting process for finding the circles radii

3- Calculation of RI

4- Analysis of RI corrugation

67

𝑅𝐼 =σ𝑖≠𝑗𝑁𝐴 𝑆𝑖𝑗 − σ𝑖≠𝑗

𝑁𝐴 𝑆𝑖𝑗𝑋

σ𝑖≠𝑗𝑁𝐴 𝑆𝑖𝑗

𝑌 − σ𝑖≠𝑗𝑁𝐴 𝑆𝑖𝑗

𝑋

68

GD@G

BND@BN

69

GD@BN

BND@G

70

71

0.0

0.5

1.0

-20 0 20 40 60 80

RI

corr

ug

ati

on

Misfit angle Φ (degree)

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

A=32, B=68,C=204, D=520, E=700 and F=1908

A=32C=204F=1908

0.0

0.5

1.0

-20 0 20 40 60 80

RI

corr

ug

ati

on

Misfit angle Φ (degree)

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

A B C D E F

Narrowing with increasing flake size

of the RI corrugation maximal peak is found but without

decreasing the intensity of the peaks

72

0.0

0.5

1.0

-20 0 20 40 60 80

RI

corr

ug

ati

on

Misfit angle Φ (degree)

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.0

0.2

0.4

0.6

0.8

1.0

A B C D E FMa

x R

Ico

rru

ga

tion

Defect in the sliding flake

results in a state with robust superlubricity.

73

GD@G

GD@BN

BND@G

BND@BN

74

75

Conclusion

GrapheneZero band gap

h-BNinsulator

DefectedGraphene

5 5

8

87

7

5 55 5

5 5 5 5

7

585 ELD

Metallic wire

5775 ELD

Metallic sheet

n

n

Defectedh-BN

Semi. Con. wire Semi. Con. wire

o The presence of individual defects

increases the charge transport

character.

o The coexistence of dopants and defects

causes the direct–indirect band gap

change.

o The electrical properties of systems strongly depend on the

orientation of grain boundaries and whether these are

parallel or perpendicular to the extended line defects.

76

Conclusion

Incommensurability Between layers

Monolayer anisotropy

77

Conclusion

BNC2@Graphene

Robust superlubricity

BNC2@BNC2

Superlubricity

BNC2@h-NBLargest incommensurability

Most monolayer anisotropy

78

Conclusion

GD@G and BND@BN

homo-junctions

Symmetry breaking of the

sliding flake

Robust superlubricity

GD@BN and BND@G hetero-junctions

The 585 extended line defect (585-ELD)

Largest incommensurability

and monolayer anisotropy

79

One can suggest that coexistence of dopantsand defects in layered systems will provideappropriate electrical and mechanicalproperties that make them extremely wellsuited for use in nanoelectromechanicalsystems.

Conclusion