National University of Singapore Department of Physics · 2020. 8. 17. · the sample, I truly appreciate ... PDMS nanopillars. (inset) Drawing of adherent cell-cell junctions. (d)

National University of Singapore

Faculty of Science

Department of Physics

AY2016/17 PC4199 Honours Project in Physics (Physics in Technology)

Study of optomechanical properties of 2D TMDS assembled on pillars array

Wong Zi Heng

A0097283U

Supervisor: Professor Sow Chorng Haur

This thesis is submitted in partial fulfilment of the requirements for the Degree of

Bachelor of Science (Honours) in Physics (Specialisation in Physics in Technology)

2

Acknowledgement

I would like to sincerely thank my supervisor Professor Sow Chorng Haur for giving me the

opportunity to work under him and I have learnt a lot about nanoscience from him. He has

always been supportive towards me and believes in my abilities despite my circumstances.

I would also like to thank my mentor Mr Lim Kim Yong for his patience and kind

understanding during this period of time. Though we did not managed to successfully assemble

the sample, I truly appreciate him for taking his time off to help me with the experimental

portion and also meeting me from time to time. I would like to extend my thanks to my UROPS

mentor Dr Zheng Minrui for teaching me how to use COMSOL Multiphysics during my third

year, without which I would not have been able to work on this project. Even though he is no

longer in the lab, he does not hesitate to help me when I seek him for assistance and continues

to encourage me.

I would like to express my appreciation to my buddy Mr Poon Jun Xian, Cyrus for always

looking out for me and ensuring that everything is fine. I’m really blessed to have such a great

friend like him and I’m sincerely grateful about it.

I would like to thank everyone in our lab for helping me out in one way or another and always

being so kind and friendly. The warm culture of our lab is something that I am and will always

be proud of.

Special mention to my suitemates in CAPT, Mr Koh Eng Tiong Jonathan, Mr Lee Hwee Xiong

Julian, Mr Hong Li Wee and also Mr Poon Jun Xian Cyrus for helping me day in day out over

the year. Things would not have been possible without them I am thankful for all that they have

done for me and all the times that we’ve shared.

Last but not least, I would like to express my deepest gratitude to my parents for being

supportive to me all my life and always trusting me in everything I do. Things have been

challenging for my family after my injury in August 2013 that resulted in my paralysis and I

hope I can do them proud despite my circumstances.

Everything would not have been possible without the help from everyone around me and I’m

thankful for everyone for continuing in believing in me.

3

Table of Contents

Abstract ………………………………………………………………………………………. 5

1. Introduction and Motivation ………………………………………………………….. 6

2. Methodology ………………………………………………………………………... 10

2.1. Study of the relationship between applied force and resultant strain in thin film

(Fixed edges) ……………………………………………………………………. 11

2.2. Study of the relationship between applied force and resultant strain in thin film

(Fixed pillars) …………………………………………………………………… 13

2.3. Study of the relationship between applied force and resultant displacement in

nanopillar ……………………………………………………………………….. 14

3. Results and Discussion ……………………………………………………………... 17

3.1. Analysis of the relationship between applied force and resultant strain in thin

film. (Fixed edges) ……………………………………………………………… 17

3.1.1. Analysis of the effects of magnitude of applied force on the resultant

strain in thin film for different number of layers ……………………………. 17

3.1.2. Analysis of the effects of angle of applied force on the resultant strain in

thin film for different number of layers ……………………………………... 22

3.1.2.1. Short discussion on error message ………………………….. 25

3.1.3. Analysis of the effects of radius of nanopillars on the resultant strain in

thin film for different number of layers ……………………………………... 30

3.2. Analysis of the relationship between applied force and resultant strain in thin

film. (Fixed pillars) ……………………………………………………………... 34

3.2.1. Analysis of the effects of magnitude of applied force on the resultant

strain in thin film at centre and nearest nanopillars for different number of

layers ………………………………………………………………………... 34

3.2.2. Analysis of the effects of angle of applied force on the resultant strain in

thin film at centre and nearest nanopillars for different number of

layers ……………………………………....................................................... 39

4

3.2.3. Analysis of the effects of separation between nanopillars on the resultant


layers ……………………………………....................................................... 42

3.3. Analysis of the relationship between applied force and resultant displacement

in nanopillar …………………………………………………………………….. 45

3.3.1. Analysis of the effects of magnitude of applied force and angle of applied

force on the resultant displacement in nanopillar …………………………… 45

3.3.2. Analysis of the effects of radius of nanopillars and magnitude of applied


3.3.3. Analysis of the effects of height of nanopillars and magnitude of applied


4. Conclusion and Future Work ………………………………………………………... 52

4.1. Conclusion …………………………………………………………………. 52

4.2. Future Work ………………………………………………………………... 53

List of Tables ………………………………………………………………………………... 55

List of Figures ………………………………………………………………………………. 56

References …………………………………………………………………………………... 61

Appendices ………………………………………………………………………………….. 63

5

Abstract

Leveraging on the change in electrical properties of some nanomaterials when subjected to

forces, microelectromechanical systems (MEMS) has been developed for these materials to be

a microforce sensor. In this project, we investigated the optomechanical properties of

molybdenum disulfide (MoS2) thin film assembled on poly(methyl methacrylate) (PMMA)

nanopillars array with the help of COMSOL Multiphysics 5.2 computational simulation

software. We managed to establish some relationships between variables such as the strain

experienced by thin film being inversely proportional to the number of layers of thin films and

the radius of nanopillars, and the resultant displacement in nanopillar being directly

proportional to the height of the nanopillar and inversely proportional to the radius of the

nanopillar. This allows us to gain basic understanding and idea to some of the different

correlations and discover the order of the variables we are working with. With this, we can

better estimate the dimensions and parameters that is suitable for us to experimentally prepare

a sample and set up experiments for gathering meaningful data.

6

1. Introduction and Motivation

Sensors are systems that are designed to detect changes in surroundings by responding with a

measurable response that correlates with the input. There are many different types of sensors

that reacts to different changes, such as force, sound, light, motion, temperature, and generate

a corresponding quantifiable output. One such example is a weighing machine. The force acting

on a spring causes the spring to compress, and through prior scaling to correlate the force and

the change in the length of the spring, we can know the weight of an object by measuring the

response observed in the spring.

With the advancement in science into the micro and nano scale, traditional mechanical systems

as such are unable to measure these extremely small forces as they are insufficiently sensitive.

New methods have been developed in recent decades to create micro force sensors that are able

to detect such small forces.

Figure 1.1. (a) Structural model of ZnO nanorods in pressure sensor. [1] (b) Averaged voltage

versus pressure plots for different ZnO sensor designs. [1] (c) Design of SiNWs force sensor.

[2] (d) Normalised voltage versus force plot for SiNWs sensor. [2]

7

Materials such as zinc oxide (ZnO) nanorods [1] and silicon nanowires (SiNWs) [2] has been

discovered to alter their electrical properties such as electric potential when subjected to forces

and has thus been used in the creation of microelectromechanical systems (MEMS) to measure

small forces as shown in Figure 1.1. Other properties that are not electrical can also be exploited

in the same way as long as correlation is observed when subjected to forces.

Figure 1.2. (a) Scanning Electron Microscope (SEM) image of PDMS nanopillars array. (b)

SEM image of biological cell on PDMS nanopillars array. (c) Image of deflection mapping of

PDMS nanopillars. (inset) Drawing of adherent cell-cell junctions. (d) Image of force mapping

of PDMS nanopillars. [3]

Other than being able to measure small forces, it is also of value to be able to measure these

small forces locally as the force can vary greatly across small distances since the system is at a

very small scale. Mapping of local forces has been done with poly(dimethylsiloxane) (PDMS)

nanopillars array [3] as shown in Figure 1.2. Deflection of the individual PDMS nanopillars

caused by biological cells are correlated to the magnitude and direction of the force and local

forces can be mapped in this way.

8

Figure 1.3. (a) Evolution of the Raman spectra of the monolayer MoS2 under uniaxial strain.

[4] (b) Raman shift versus strain plot for E’+ and E’- modes of the monolayer MoS2 under

uniaxial strain. [4] (c) Evolution of the Raman spectra of the monolayer MoS2 under uniaxial

strain. [5] (d) Schematic illustration of atomic displacements of monolayer MoS2 for A1g and

E2g’ modes. [5] (e) Raman shift frequency versus strain plot for A1g, E2g’+ and E2g’

- modes of

the monolayer MoS2 under uniaxial strain. [5] (f) Evolution of the Raman spectra of the

monolayer WS2 under uniaxial strain. [6] (g) Schematic illustration of atomic displacements of

monolayer WS2 for A1’ and E’ modes. [6] (h) Raman shift frequency versus strain plot for A1’,

E’+ and E’- modes of the monolayer WS2 under uniaxial strain. [6]

In this project, we attempt to study the optomechanical properties of two dimensional (2D)

transition metal disulfides (TMDS) assembled on pillars array. Recent studies have shown a

correlation between Raman peak shifts and the strain experienced in TMDS thin films such as

molybdenum disulfide (MoS2) [4] [5] and tungsten disulfide (WS2) [6] as shown in Figure 1.3.

A uniaxial strain of about 1% results in a redshift in Raman peak for E’- mode by about 4cm-1

for monolayer MoS2 [4] [5] and about 2cm-1 for monolayer WS2 [6]. By understanding

(i) the relationship between the force required to produce the strain in the thin film and

(ii) the relationship between the force required to produce a displacement in the

nanopillar,

we hope to eventually correlate the Raman peak shifts in the thin film to the displacement in

the nanopillar that causes the strain. Through this, we hope to lay the foundation to the

comprehension of such systems as a potential micro force sensor.

9

This is done with the help of COMSOL Multiphysics 5.2 computational simulation software

where finite element analysis is performed on computer aided design (CAD) drawings. For

most problems, it is not possible to generate an analytical solution to solve the partial

differential equations. [7] Finite element analysis works by dividing the structure into smaller

parts called finite elements that are simpler to solve. The solutions to these finite elements are

combined with calculus of variations to approximate a numerical solution.

The computational simulation results will allow us to predict the correlation and analyse the

possible factors that affects the correlation. With this understanding, we can better estimate the

dimensions and parameters that is suitable for us to experimentally prepare a sample and set

up experiments for gathering meaningful data.

10

2. Methodology

Figure 2.1. CAD drawings created in COMSOL Multiphysics of 2D TMDS thin film

assembled on PMMA nanopillars array structure.

Figure 2.1 shows a small portion of the simulated structure of 2D TMDS thin film assembled

on poly(methyl methacrylate) (PMMA) nanopillars array. For easy reference in the rest of the

report, the top surface of the 2D TMDS thin film shall be denoted to be surface α while the

surface that is in contact with the PMMA nanopillars array shall be denoted to be surface β.

The advantage of using PMMA as our nanopillars array is that it can be prepared with good

control of the structure such as the pillar height, radius and separation and has been used for

development of biosensors and biomechanical devices. [8] This is similar to PDMS nanopillars

array being used by researchers in France when they performed force mapping for a biological

cell. [3] Figure 2.2 shows SEM images of different pillar height and radius of PMMA

nanopillars samples. We use MoS2 as our thin film of study as it is one of the most common

TMDS around.

The simulations are split into two main components to study two relationships:

(i) the relationship between the force required to produce the strain in the thin film and

(ii) the relationship between the force required to produce a displacement in the

nanopillar.

11

Figure 2.2. SEM images of PMMA nanopillars array of different pillar diameters and height.

Source from Dr. Yu Miao from Professor Yan Jie’s Group from Mechanobiology Institute

(MBI).

2.1.Study of the relationship between applied force and resultant strain in thin film.

(Fixed edges)

Figure 2.3. COMSOL Multiphysics images of (a) 2D TMDS thin film of 1μm by 1μm with

varying thickness. Cylindrical PMMA of 50nm radius and 0.6nm thickness at the centre on top

of the thin film. (b) Fixed constraint applied to edges of thin film as highlighted in blue. (c)

Force applied over PMMA as highlighted in blue.

12

Figure 2.3 shows the simulation drawings in the first series of study. A small portion of the 2D

TMDS thin film is simulated with an area of 1μm by 1μm as we follow from the samples shown

in Figure 2.2 where the distance between nanopillars is 500nm. The thickness of the thin film

will be varied in the simulations to study its influence. The thickness of monolayer MoS2 is

simulated at 0.6nm according to published literature [9] and is varied from 1 to 5 layers. A thin

cylindrical layer of PMMA is added to the simulation where the force will be applied. The

radius is set to be 50nm following from the D100 nanopillars array from Figure 2.2.

After the geometry and parameters are drawn, materials are assigned to the respective

components. Solid mechanics module is selected for the simulation as we are interested in the

study of forces, displacement and strain. The relevant material properties in this case are

density, Young’s modulus and Poisson’s ratio. Data provided in COMSOL Multiphysics are

verified where missing information are entered and nano and bulk values are compared with

known literature. [8] [10]

A fixed constraint is applied to the edges of the thin film and the force is applied over the thin

PMMA as seen in Figure 2.3 (b) and 2.3 (c) respectively to set the conditions for simulation.

Meshing is done for the structure before the results are computed. As the structure is rather

small, element size of ‘finer’ is selected for the tetrahedral meshing process, where ‘finer’ is

the 3rd finest element size out of 9 predefined sizes ranging from ‘extremely fine’ to ‘extremely

coarse’. The completed mesh contains an order of 105 domain elements, 105 boundary elements

and 103 edge elements.

To study the effects of the magnitude of the applied force on the strain experienced by the thin

film, simulations are ran by varying the force from 10nN to 1000nN in the x-direction which

is parallel to the thin film since displacement of the nanopillar is mainly along the direction.

Considering that the displacement of the nanopillar will include some in the z-direction which

is perpendicular to the thin film, simulations are also ran by varying the angle for a 10nN force

to see its influence on the strain experienced by the thin film.

13

As the nanopillars can be made to be of different radius as seen in Figure 2.2, it is useful to

understand how the difference in nanopillar radius can affect the strain experienced in the thin

film. This can give us insight on the selection of a suitable dimensions when preparing the

sample. Thus, simulations are ran for nanopillar radius varying from 40nm to 80nm, following

from Figure 2.2, for a 10nN applied force in the x-direction which is parallel to the thin film.

2.2.Study of the relationship between applied force and resultant strain in thin film.

(Fixed pillars)


varying thickness. 3 by 3 cylindrical PMMA of 50nm radius and 0.6nm thickness on top of the

thin film spaced 500nm apart from each other. (b) Fixed constraint applied to surrounding thin

PMMA as highlighted in blue. (c) Force applied over centre PMMA as highlighted in blue.

Figure 2.4 shows the simulation drawings in the second series of study. Instead of applying the

fixed constraint to the edges of the thin film, the simulation is enlarged to add in surrounding

PMMA and fixed constraint is applied to these surrounding PMMA as seen in Figure 2.4 (b).

We can then compare the differences in results obtained for the two series of simulations. The

area of the thin film simulated in the second series of study is expanded to be 2μm by 2μm,

maintaining the same nanopillars separation of 500nm. The thickness of the thin film will be

varied from 1 to 5 layers of MoS2 like in the first series of simulations to study the effect of

varying thickness. Following from the nanopillars array samples as seen in Figure 2.2, a square

lattice arrangement of nanopillars is drawn in this series of simulations.

14

After the geometry and parameters are drawn, the rest of the inputs are made similar to the first

series of simulations for the materials and the meshing. The completed mesh contains more

elements as the structure is larger but the order of the number of elements remains the same.

The force is still applied over then thin PMMA in the centre as seen in Figure 2.4 (c).

Once again, we vary the force from 10nN to 1000nN in the x-direction to study the effects of

the magnitude of the applied force on the strain experienced by the thin film. In this second

series of simulations, other than just studying the strain experienced around the centre

nanopillar where the force is being applied, we can also look at the strain experienced around

the surrounding nanopillars.

Other than varying the angle of the force along the xz-direction, we also vary the angle of a

10nN force along the xy-direction where the force is parallel to and along the plane of the thin

film. This allow us to look at the strain experienced around the surrounding nanopillars when

the angle of the force along the thin film is varied.

As the nanopillars array can be made to be of different nanopillar separation distance, it is

useful to understand how the difference in nanopillar separation can affect the strain

experienced in the thin film at the centre and surrounding nanopillars. This can give us insight

on the selection of a suitable dimensions when preparing the sample. Thus, simulations are ran

for nanopillar separation varying from 250nm to 1000nm, for a 10nN applied force in the x-

direction which is parallel to the thin film.

2.3.Study of the relationship between applied force and resultant displacement in

nanopillar.

Figure 2.5 shows the simulation drawing for the study of the relationship between the applied

force and resultant displacement in PMMA nanopillar. A small portion of the nanopillars array

is simulated following the dimensions of D100_SHORT as seen in Figure 2.2 where the pillar

height is 1.1μm and pillar radius is 50nm. With a pillar separation of 500nm, the 3 by 3

15

nanopillars array simulated has an area of 2μm by 2μm. A thin base layer of 2μm thick is

simulated.

Figure 2.5. COMSOL Multiphysics image of 3 by 3 nanopillars array with 1.1μm pillar height,

50nm pillar radius and 500nm pillar separation. 2μm thick of base layer is simulated as well.

Force applied over top of centre nanopillar as indicated by the arrow.

After the geometry and parameters are drawn, PMMA material data is assigned to the structure.

Similar to previous simulations, solid mechanics module is selected as our study interest

remains the same. Density, Young’s modulus and Poisson’s ratio of PMMA are verified with

known literature. [8] A fixed constraint is applied to the bottom of the base layer and the force

is applied over the top of the centre PMMA nanopillar. Meshing is done for the structure before

the results are computed. Once again, the element size is selected as ‘finer’ and the completed

mesh contains an order of 105 domain elements, 104 boundary elements and 103 edge elements.

To study the effects of the magnitude of the applied force on the resultant displacement in the

nanopillar, simulations are ran by varying the force from 6nN to 12nN in the x-direction which

is perpendicular to the nanopillar since displacement of the nanopillar is mainly along the

direction. Considering that the displacement of the nanopillar will include some in the z-

direction which is parallel to the nanopillar, simulations are also ran by varying the angle for

the applied force to see its influence on the resultant displacement in the nanopillar.

16

As the nanopillars can be made to be of different radius as seen in Figure 2.2, it is useful to

understand how the difference in nanopillar radius can affect the resultant displacement in the

nanopillar. This can give us insight on the selection of a suitable dimensions when preparing

the sample. Thus, simulations are ran for nanopillar radius varying from 40nm to 80nm,

following from Figure 2.2, for a range of magnitude of applied force in the x-direction which

is perpendicular to the to the nanopillar.

Other than varying the radius of the nanopillar, we can also vary the height of the nanopillar as

seen in Figure 2.2. Thus, it is useful for us to understand how the difference in nanopillar height

can affect the resultant displacement in the nanopillar. This can also give us insight on the

selection of a suitable dimensions when preparing the sample. Simulations are ran for

nanopillar height varying from 0.5μm to 2.0μm, following from Figure 2.2, for a range of

magnitude of applied force in the x-direction which is perpendicular to the to the nanopillar.

17

3. Results and Discussion

3.1.Analysis of the relationship between applied force and resultant strain in thin film.

(Fixed edges)

3.1.1. Analysis of the effects of magnitude of applied force on the resultant strain in

thin film for different number of layers.

Figure 3.1. Strain plot of surface α for 10nN force applied in the x-direction for (a) 1 layer (b)

2 layers (c) 3 layers (d) 4 layers (e) 5 layers of thin film.



18

Figure 3.3. Strain plot of surface α for 100nN force applied in the x-direction for (a) 1 layer

(b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers of thin film.



19



The strain plots can be interpreted in the following manner: red corresponds to area of larger

strain while blue corresponds to area of smaller strain. Figures 3.1 to 3.5 show the strain plots

of surface α for a range of 1 to 5 layers of MoS2 thin film for a range of forces from 10nN to

1000nN. Note that strain plot shows surface α which is the surface not in contact with the

nanopillars. The compiled data values are shown in appendix A. Comparing the strain plots

across the different number of layers of thin film, we can see that the strain is observed over a

larger area when the number of layers increases. However, the same trend is not observed when

the magnitude of the applied force changes, the area seems to remain the same. The strain

experienced by the thin film also increases when the number of layer decreases. Importantly,

the strain experienced by the thin film increases when the magnitude of the applied force

increases.

20

Figure 3.6. Graph plots of (a) strain versus force (b) strain versus force [log plot] (c) strain

versus number of layers for different magnitudes of forces applied in the x-direction for

different number of layers of thin film.

y = 0.0079x + 2E-06

y = 0.0024x + 1E-06

y = 0.0012x - 1E-06

y = 0.0008x + 1E-06y = 0.0005x + 1E-060.00000

1.00000

2.00000

3.00000

4.00000

5.00000

6.00000

7.00000

8.00000

9.00000

0 200 400 600 800 1000 1200

Stra

in (

%)

Force (nN)

Strain versus Force

1 layer

2 layers

3 layers

4 layers

5 layers

Linear (1 layer)

Linear (2 layers)

Linear (3 layers)

Linear (4 layers)

Linear (5 layers)

y = 0.0079x + 2E-06

y = 0.0024x + 1E-06y = 0.0012x - 1E-06

y = 0.0008x + 1E-06

y = 0.0005x + 1E-06

0.00100

0.01000

0.10000

1.00000

10.00000

1 10 100 1000

Stra

in (

%)

Force (nN)

Strain versus Force

1 layer

2 layers

3 layers

4 layers

5 layers

Linear (1 layer)

Linear (2 layers)

Linear (3 layers)

Linear (4 layers)

Linear (5 layers)

(a)

(b)

21




To better study the relationships between the strain experienced by the thin film, the magnitude

of the applied force and the number of layers of thin film, we plot the data collected into graphs

as shown in Figure 3.6.

Fitting the data between the strain experienced by the thin film and the magnitude of the applied

force gives a linear relationship. As we increase the magnitude of the applied force over a few

orders, a logarithmic plot shown in Figure 3.6 (b) gives a clearer view of this relationship. From

Figure 3.6 (a), we can see that the gradient of the plot becomes steeper for lesser number of

layers. This suggest that the thin film is more sensitive to forces when there is lesser number

of layers. The linearity between these two variables is particularly useful as we can predict the

strain results for a force acting in the same direction in the same sample by just factoring it

accordingly.

Fitting the data between the strain experienced by the thin film and the number of layers of the

thin film gives a power relationship. For an applied force in the same direction, in this case x-

y = 0.0774x-1.661

y = 0.3871x-1.661

y = 0.7743x-1.661

y = 3.8714x-1.661

y = 7.7428x-1.661

0.00000

1.00000

2.00000

3.00000

4.00000

5.00000

6.00000

7.00000

8.00000

9.00000

0 1 2 3 4 5 6

Stra

in (

%)

Number of layers

Strain versus Number of layers

10nN

50nN

100nN

500nN

1000nN

Power (10nN)

Power (50nN)

Power (100nN)

Power (500nN)

Power (1000nN)

(c)

22

direction, the number of layers of the thin film is inversely proportional to the strain

experienced by the thin film by a power of 1.661. This power is the same regardless of the

magnitude of the applied force to the thin film. The sensitivity of the strain experienced by the

thin film to the magnitude of the applied force can be seen in Figure 3.6 (c) as the coefficient

is larger for a larger magnitude of applied force.

With these data, we can approximate and propose the following analytical relationship for the

strain experienced by the thin film to be

𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑑 𝑏𝑦 𝑡ℎ𝑖𝑛 𝑓𝑖𝑙𝑚 ∝ 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒

(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟𝑠 𝑜𝑓 𝑡ℎ𝑖𝑛 𝑓𝑖𝑙𝑚53)

3.1.2. Analysis of the effects of angle of applied force on the resultant strain in thin

film for different number of layers.

Figure 3.7. Definition of angle of applied force based on axes of (a) COMSOL Multiphysics

image of 2D TMDS thin film of 1μm by 1μm with varying thickness. Cylindrical PMMA of

50nm radius and 0.6nm thickness at the centre on top of the thin film. (b) Axes for structure

shown in (a). (c) Angle measured from x-direction towards z-direction.

Figure 3.7 shows the definition of the angle of applied force where a force purely in the x-

direction parallel to the thin film is considered to be 0o and the angle is measured towards the

z-direction since the bending of nanopillar will go towards the z-direction. Note that Figure 3.7

shows surface β, which is the surface where the nanopillars are in contact with the thin film.

23

Figure 3.8. Strain plot of surface α for 10nN force applied at 15o for (a) 1 layer failed to find

solution due to error. Space left there for easier and more intuitive viewing across figures. (b)





24




Table 3.1. Compiled results for strain values on surface α for different angles of a 10nN force

applied for different number of layers of thin film. Failed to find solution for 1 layer due to

error from 15o onwards.

Figures 3.1, 3.8 to 3.10 show the strain plots of surface α for a range of 2 to 5 layers of MoS2

thin film for an applied 10nN force over a range of angles 0o to 45o. The compiled data values

are shown in Table 3.1. Similar to previous discussions, the strain experienced by the thin film

increases when the number of layer decreases. Importantly, the strain experienced by the thin

film increases when the angle of the applied force increases. From Table 3.1, we can see that

the increase in the strain experienced by the thin film is large as the angle of the applied force

increases. This suggests that the contribution to the strain experienced by the thin film due to

25

forces perpendicular to the thin film is very significant. However, realistically, the main

component of the force experienced in the real system would be parallel to the thin film with

only little contributions from the perpendicular component.

3.1.2.1 Short discussion on error message.

It was also noted that simulations for 1 layer of thin film failed to find a solution from 15o

onwards. The generated error message is as follows: “Failed to find a solution. The relative

error is greater than the relative tolerance. Returned solution is not converged.” As the number

of layers decreases, the structure gets thinner and the relative error begins to become

increasingly significant as well. This seems to cause the solution to be unable to converge

resulting in the inability to generate a solution. This is also seen in subsequent studies made.

Table 3.2. Compiled strain values for different magnitudes of forces applied in the x-direction

obtained through simulation and fitting.

26

Figure 3.11. (a) Graph plot of strain versus number of layers for different magnitudes of forces

applied in the x-direction [same figure as Figure 3.6 (c)] (b) Same graph plotted leaving out

data points for 1 layer.

Since the same error message is seen in many cases, here we do a short discussion of

extrapolation of results using data generated from the previous section for strain experienced

by thin film for different magnitude of applied force. As shown in Figure 3.11 (b), we plotted

a graph by leaving out the data points for 1 layer thin film and performed a fitting. We can see

that the magnitude of the power fitted is slightly smaller by 2.53%.

y = 0.0774x-1.661

y = 0.3871x-1.661

y = 0.7743x-1.661

y = 3.8714x-1.661

y = 7.7428x-1.661

0.00000

1.00000

2.00000

3.00000

4.00000

5.00000

6.00000

7.00000

8.00000

9.00000

0 1 2 3 4 5 6

Stra

in (

%)

Number of layers


10nN

50nN

100nN

500nN

1000nN

Power (10nN)

Power (50nN)

Power (100nN)

Power (500nN)

Power (1000nN)

y = 0.0733x-1.619

y = 0.3666x-1.619

y = 0.7332x-1.619

y = 3.666x-1.619

y = 7.3319x-1.619

0.00000

0.50000

1.00000

1.50000

2.00000

2.50000

3.00000

0 1 2 3 4 5 6

Stra

in (

%)

Number of layers


10nN

50nN

100nN

500nN

1000nN

Power (10nN)

Power (50nN)

Power (100nN)

Power (500nN)

Power (1000nN)

(a)

(b)

27

We then compare the strain values obtained from simulation with strain values obtained from

the power fit shown in Figure 3.11 (a) and 3.11 (b) and compiled in Table 3.2. When the fit is

done with the inclusion of the strain values for 1 layer, the strain values obtained through this

fit differs from the simulated strain values by a small average of 1.65%. When the fit is done

without the strain values for one layer, the strain values obtained through this fit differs from

the previous fit by an average of 5.30%. Comparing the strain values obtained through the fit

done omitting the strain values with 1 layer against the simulated strain values, the overall

difference is calculated to be an average of 6.86%. This difference should be kept in mind when

extrapolating for values.

Figure 3.12. Graph plots of (a) strain versus angle [quadratic fit] (b) strain versus angle [cubic

fit] (c) strain versus number of layers for different angles of a 10nN applied force for different

number of layers of thin film.

y = -1E-05x2 + 0.0102x + 0.0223

y = -3E-06x2 + 0.0045x + 0.0114

y = -1E-06x2 + 0.0025x + 0.0072

y = -2E-07x2 + 0.0016x + 0.00510

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 10 20 30 40 50

Stra

in (

%)

Angle (o)

Strain versus Angle

1 layer

2 layers

3 layers

4 layers

5 layers

Poly. (2 layers)

Poly. (3 layers)

Poly. (4 layers)

Poly. (5 layers)

(a)

28




To better study the relationships between the strain experienced by the thin film, the angle of

the applied force and the number of layers of thin film, we plot the data collected into graphs

as shown in Figure 3.12.

y = -2E-06x3 + 0.0001x2 + 0.0084x + 0.024

y = -8E-07x3 + 5E-05x2 + 0.0036x + 0.0123

y = -5E-07x3 + 3E-05x2 + 0.002x + 0.0078

y = -3E-07x3 + 2E-05x2 + 0.0012x + 0.00550

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 10 20 30 40 50

Stra

in (

%)

Angle (o)

Strain versus Angle

1 layer

2 layers

3 layers

4 layers

5 layers

Poly. (2 layers)

Poly. (3 layers)

Poly. (4 layers)

Poly. (5 layers)

y = 0.0774x-1.661

y = 0.6555x-1.968

y = 1.266x-1.969

y = 1.7902x-1.97

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6

Stra

in (

%)

Number of layers


0

15

30

45

Power (0)

Power (15)

Power (30)

Power (45)

(c)

(b)

29

Fitting the data between the strain experienced by the thin film and the angle of the applied

force gives a polynomial regression. As we increase the order of the polynomial function fitted,

the coefficient of determination, also known as the R2 value goes to 1. However, the coefficient

of higher order terms decreases, indicating a reduced contribution by the higher order terms.

We can observe that as the number of layers of thin film decreases, the coefficient of the higher

order terms also increases, resulting in the plot being more curved for lesser number of layers.

This means that as the number of layers of thin film decreases, the effect of increasing the angle

of the force on the strain experienced by the thin film becomes more significant.


thin film gives a power relationship. For an applied force in the same direction, the number of

layers of the thin film is inversely proportional to the strain experienced by the thin film by a

power. Comparing across the different angles, we can see that the magnitude of the power

increases with increasing angle where perpendicular contribution from the applied force

increases. We can see that the magnitude of the power approaches 1.97 quickly when there is

perpendicular contribution from the applied force. This means that forces in the perpendicular

direction to the thin film will cause the relationship between strain experienced by the thin film

and the number of layers of thin film to deviate away from what is seen in the previous section,

suggesting that this perpendicular contribution is a factor that affects the power.

30

3.1.3. Analysis of the effects of radius of nanopillars on the resultant strain in thin

film for different number of layers.

Figure 3.13. Strain plot of surface α for 10nN force applied in the x-direction over a nanopillar

radius of 40nm for (a) 1 layer (b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers of thin film.



31






thin film for an applied 10nN force over nanopillar with radius varying from 40nm to 80nm.

The compiled data values are shown in appendix B. Similar to previous discussions, the strain

experienced by the thin film increases when the number of layer decreases. The strain is also

32

observed over a larger area when the number of layers of thin film increases. Comparing the

strain plots across the different nanopillar radii, we can observe that the strain is observed over

a larger area when the nanopillar radius increases. Importantly, the strain experienced by the

thin film increases when the nanopillar radius decreases.

Figure 3.17. Graph plots of (a) strain versus nanopillar radius [power fit] (b) strain versus

nanopillar radius [quartic fit] (c) strain versus number of layers for 10nN force applied in the

x-direction over different nanopillar radii for different number of layers of thin film.

y = 2.8451x-0.918

y = 1.4947x-1.056

y = 0.7721x-1.06

y = 0.5015x-1.066

y = 0.3411x-1.057

0

0.02

0.04

0.06

0.08

0.1

0.12

0 10 20 30 40 50 60 70 80 90

Stra

in (

%)

Nanopillar radius (nm)

Strain versus Nanopillar radius

1 layer

2 layers

3 layers

4 layers

5 layers

Power (1 layer)

Power (2 layers)

Power (3 layers)

Power (4 layers)

Power (5 layers)

y = -2E-08x4 + 4E-06x3 - 0.0003x2 + 0.0087x + 0.0473

y = 3E-09x4 - 8E-07x3 + 8E-05x2 - 0.0046x + 0.1201

y = 3E-10x4 - 1E-07x3 + 2E-05x2 - 0.0014x + 0.0476

y = 4E-10x4 - 1E-07x3 + 2E-05x2 - 0.0011x + 0.0338

y = 1E-09x4 - 3E-07x3 + 3E-05x2 - 0.0014x + 0.0327

0

0.02

0.04

0.06

0.08

0.1

0.12

10 20 30 40 50 60 70 80 90

Stra

in (

%)


Strain versus Nanopillar radius

1 layer

2 layers

3 layers

4 layers

5 layers

Poly. (1 layer)

Poly. (2 layers)

Poly. (3 layers)

Poly. (4 layers)

Poly. (5 layers)

(a)

(b)

33




To better study the relationships between the strain experienced by the thin film, the radius of

the nanopillar and the number of layers of thin film, we plot the data collected into graphs as

shown in Figure 3.17.

Fitting the data between the strain experienced by the thin film and the radius of nanopillar can

be performed for both power and polynomial fit as seen in Figure 3.17 (a) and 3.17 (b)

respectively. A more convenient relationship to note is that the power fit seems to suggest that

the strain experienced by the thin film and the radius of the nanopillar is roughly inversely

proportional. The sensitivity of the strain experienced by the thin film to the number of layers

of thin film can be seen in Figure 3.17 (a) as the coefficient is larger for a lesser number of

layers of thin film.


thin film gives a power relationship. For an applied force in the same direction, the number of

layers of thin film is inversely proportional to the strain experienced by the thin film by a power

y = 0.0948x-1.637

y = 0.0774x-1.661

y = 0.065x-1.673

y = 0.0568x-1.696

y = 0.0487x-1.692

0

0.02

0.04

0.06

0.08

0.1

0.12

0 1 2 3 4 5 6

Stra

in (

%)

Number of layers


40nm

50nm

60nm

70nm

80nm

Power (40nm)

Power (50nm)

Power (60nm)

Power (70nm)

Power (80nm)

(c)

34

of roughly -1.67 on average. This power is similar to what is being observed in section 3.1.1,

suggesting that varying the area in which the force is applied over has little influence on its

power. Varying the radius of nanopillar only causes the coefficient to decrease as the radius of

nanopillar increases.


strain experienced by the thin film to be

𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑑 𝑏𝑦 𝑡ℎ𝑖𝑛 𝑓𝑖𝑙𝑚

∝ 1

(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟𝑠 𝑜𝑓 𝑡ℎ𝑖𝑛 𝑓𝑖𝑙𝑚53)(𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟)

3.2. Analysis of the relationship between applied force and resultant strain in thin film.

(Fixed pillars)

3.2.1. Analysis of the effects of magnitude of applied force on the resultant strain in

thin film at centre and nearest nanopillars for different number of layers.


failed to find solution due to error. Space left there for easier and more intuitive viewing across

figures. (b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers of thin film.

35







36







Figures 3.18 to 3.22 show the strain plots of surface α for a range of 2 to 5 layers of MoS2 thin

film for a range of forces from 10nN to 1000nN. Comparing the strain plots across the different

37

number of layers of thin film, we can see that the strain is observed over a larger area when the

number of layers increases. However, the same trend is not observed when the magnitude of

the applied force changes, the area seems to remain the same. The strain experienced by the

thin film also increases when the number of layer decreases. A simple comparison of the strain

values across the range of forces shows that the strain experienced by the thin film increases

when the magnitude of the applied force increases and a same linear trend is being observed.

All these trends and observations are similar to what is discussed in section 3.1.1. and thus

verifies the results between the two series of simulations. The strain values computed in this

section are slightly smaller than in section 3.1.1 due to the difference in the applied fixed

constraint.

It was also noted that simulations for 1 layer of thin film failed to find a solution and the

generated error message is the same as follows: “Failed to find a solution. The relative error

is greater than the relative tolerance. Returned solution is not converged.” As the number of

layers decreases, the structure gets thinner and the relative error begins to become increasingly

significant as well. This seems to again cause the solution to be unable to converge resulting in

the inability to generate a solution. However, it was discussed in section 3.1.2.1 that

extrapolation could be performed but with a slight difference in results due to differences that

arose from fitting.

38

Figure 3.23. Graph plot of strain versus number of layers for centre and nearest nanopillar for

10nN force applied in the x-direction for different number of layers of thin film.

To better study the relationships between the strain experienced by the thin film at the centre

and nearest nanopillar, and the number of layers of thin film, we plot the data collected for

10nN force into a graph as shown in Figure 3.23. Since the strain experienced by the thin film

and the magnitude of the applied force varies linearly, it is reasonable to perform the analysis

for just one of the magnitude of applied force, in this case 10nN, since the trend will still apply

but just vary by a proportional factor.

Comparing the strain experienced by the thin film at the centre nanopillar and the nearest

nanopillar, we can see that as the number of layers of thin film increases, the strain experienced

by the thin film at the nearest nanopillar tend towards the strain experienced by the thin film at

the centre nanopillar. At 5 layers of thin film, the strain experienced by the thin film at the

nearest nanopillar becomes greater than the strain experienced by the thin film at the centre

nanopillar. This seems to suggest that as the number of layers of thin film increases, the strain

can be better coupled to the nearest nanopillar. Thus, we can infer that lesser number of layers

of thin film will be more useful if we want to do a more accurate local force mapping.

y = 0.0564x-1.476

y = 0.0334x-1.128

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5 6

Stra

in (

%)

Number of layers


Strain at centre nanopillar

Strain at nearest nanopillar

Power (Strain at centrenanopillar)

Power (Strain at nearestnanopillar)

39

3.2.2. Analysis of the effects of angle of applied force on the resultant strain in thin

film at centre and nearest nanopillars for different number of layers.

Figure 3.24. COMSOL Multiphysics image of 2D TMDS thin film of 2μm by 2μm with

varying thickness. Cylindrical PMMA of 50nm radius and 0.6nm thickness in a square lattice

on top of the thin film. (a) Definition of angle of applied force measured from x-direction

towards y-direction. (b) Definition of surrounding nearest nanopillars labelled A, B and C.

Figure 3.24 (a) shows the definition of the angle of applied force where a force purely in the x-

direction parallel to the thin film is considered to be 0o and the angle is measured towards the

y-direction. For easy reference in the rest of the section, the surrounding nearest nanopillars

shall be defined to be A, B and C as shown in Figure 3.24 (b).

40







41





thin film for an applied 10nN force over a range of angles 0o to 45o. Similar to previous

discussions, the strain experienced by the thin film increases when the number of layer

decreases. The strain experienced by the thin film is also observed over a larger area when the

number of layers of thin film increases. Comparing the strain plots across the different applied

force angles, we can see that the strain experienced by the thin film is observed over a larger

area when the angle of the applied force increases.

It was also noted that simulations for 1 layer of thin film failed to find a solution again due to

the same reason where the relative error is greater than relative tolerance, resulting in the

inability for the solution to converge and generate a solution. We have discussed in section

3.1.2.1 that extrapolation could be performed but with a slight difference in results due to

differences that arose from fitting.

Comparing the strain experienced by the thin film at the centre nanopillar and the surrounding

nanopillars, we can once again see that as the number of layers of thin film increases, the strain

42

experienced by the thin film at the surrounding nanopillars tend towards the strain experienced

by the thin film at the centre nanopillar. This agrees with the observation made in the previous

section.

We can also observe the redistribution of strain experienced by the thin film at the surrounding

nanopillars occurring as the angle of the applied force increases. As the angle of the applied

force increases, strain experienced by the thin film observed at A decreases and redistributes,

causing the strain experienced by the thin film observed at B and C to increase. Strain

experienced by the thin film observed at C is larger than strain experienced by the thin film

observed in B and this could be due to C being closer to the centre nanopillar than B. This may

mean that the strain coupling effect between the centre and surrounding nanopillar increases

when the distance between the nanopillar decreases. As the applied force reaches 45o, the strain

experienced by the thin film is redistributed such that the strain experienced by the thin film at

A and C becomes approximately equal.

3.2.3. Analysis of the effects of separation between nanopillars on the resultant


layers.

Figure 3.28. Strain plot of surface α for 10nN force applied in the x-direction for nanopillars

separation of 250nm for (a) 1 layer (b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers of thin film.

43


separation of 750nm for (a) 1 layer failed to find solution due to error. Space left there for

easier and more intuitive viewing across figures. (b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers

of thin film.


separation of 1000nm for (a-c) 1-3 layers failed to find solution due to error. Space left there

for easier and more intuitive viewing across figures. (d) 4 layers (e) 5 layers of thin film.

44


thin film for an applied 10nN force over a range of nanopillar separation from 250nm to

1000nm. Similar to previous discussions, the strain experienced by the thin film increases when

the number of layer decreases. The strain experienced by the thin film is also observed over a

larger area when the number of layers of thin film increases. Comparing the strain plots across

the different nanopillar separation distances, we can see that the strain experienced by the thin

film is observed over a larger area when the distance between nearest nanopillars increases.

It was also noted that some of the simulations failed to find a solution again due to the same

reason where the relative error is greater than relative tolerance, resulting in the inability for

the solution to converge and generate a solution. We have discussed in section 3.1.2.1 that

extrapolation could be performed but with a slight difference in results due to differences that

arose from fitting.

Comparing the strain experienced by the thin film at the centre nanopillar and the nearest

nanopillars, we can once again see that as the number of layers of thin film increases, the strain

experienced by the thin film at the nearest nanopillar tend towards the strain experienced by

the thin film at the centre nanopillar. This agrees with the observation made in the previous

two sections.

This trend of strain experienced by the thin film at the surrounding nanopillars tending towards

the strain experienced by the thin film at the centre nanopillar becomes even more significant

as the nanopillar separation becomes smaller. This confirms the prediction made at the end of

the previous section where we see a smaller strain experienced by the thin film at the

surrounding nanopillar further away from the centre nanopillar. This also means that the

redistribution of strain experienced by the thin film discussed at the end of the previous section

becomes less significant as the nanopillar separation increases.

At a nanopillar separation of 250nm, the strain experienced by the thin film at the nearest

nanopillar becomes greater than the strain experienced by the thin film at the centre nanopillar,

45

similar to what is being observed when the nanopillar separation is at 500nm for 5 layers of

thin film as seen in Figure 3.18 (e). We can hence deduce that increasing the number of layers

of thin film has the same effect as reducing the nanopillar separation in improving the strain

coupling between the two nanopillars. This implies that to minimise the strain coupling effects

between nanopillars array, the number of layers of thin film should be kept minimal and the

nanopillar separation should be large.

3.3.Analysis of the relationship between applied force and resultant displacement in

nanopillar.

3.3.1. Analysis of the effects of magnitude of applied force and angle of applied

force on the resultant displacement in nanopillar.



Definition of angle of applied force measured from x-direction towards negative z-direction.

Figure 3.31 shows the definition of the angle of applied force where a force purely in the x-

direction perpendicular to the nanopillar is considered to be 0o and the angle is measured

towards the negative z-direction since the bending of the nanopillar will go towards the

negative z-direction

The displacement plots for a range of applied force from 6nN to 12nN over a range of angles

0o to 45o are shown in appendix C. The compiled data values are shown in appendix D.

46

Figure 3.32. Graph plots of (a) displacement versus force (b) displacement versus angle for

different magnitudes of forces applied for different angles.

To better study the relationships between the resultant displacement in the nanopillar, the

magnitude of the applied force and the angle of the applied force, we plot the data collected

into graphs as shown in Figure 3.32. From Figure 3.32 (a), we can see that the resultant

displacement in the nanopillar increases as the magnitude of the applied force increases. Figure

y = 0.032x - 3E-06

y = 0.0309x + 0.0003y = 0.0277x + 0.0003

y = 0.0227x - 0.0002

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 2 4 6 8 10 12 14

Dis

pla

cem

ent

(μm

)

Force (nN)

Displacement versus Force

0

15

30

45

Linear (0)

Linear (15)

Linear (30)

Linear (45)

y = 6E-08x3 - 3E-05x2 + 3E-05x + 0.1922

y = 9E-08x3 - 4E-05x2 + 3E-05x + 0.2563

y = 1E-07x3 - 5E-05x2 + 3E-05x + 0.3203

y = 1E-07x3 - 6E-05x2 + 3E-05x + 0.3844

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 5 10 15 20 25 30 35 40 45 50

Dis

pla

cem

ent

(μm

)

Angle (o)

Displacement versus Angle

6

8

10

12

Poly. (6)

Poly. (8)

Poly. (10)

Poly. (12)

(a)

(b)

47

3.32 (b) shows that the resultant displacement in the nanopillar decreases as the angle of the

applied force increases.

Fitting the data between the resultant displacement in the nanopillar and the magnitude of the

applied force gives a linear relationship. From Figure 3.32 (a), we can see that the gradient of

the plot becomes less steep as the angle of the applied force increases. This suggest that the

angle of the applied force is a factor that affects the gradient of the linear relationship. The

linearity between these two variables is particularly useful as we can predict the resultant

displacement for a force acting in the same direction in the same sample by just factoring it

accordingly.

Fitting the data between the resultant displacement in the nanopillar and the angle of the applied

force gives a polynomial regression. As we increase the order of the polynomial function fitted,

the coefficient of determination, also known as the R2 value goes to 1. However, the coefficient

of higher order terms decreases, indicating a reduced contribution by the higher order terms.

We can observe that as the magnitude of the applied force increases, the coefficient of the

higher order terms also increases, resulting in the plot being more curved for higher magnitude

of forces. This means that as the magnitude of the applied force increases, the effect of

increasing the angle of the force on the resultant displacement of the nanopillar becomes more

significant. This is also the reason for the change in gradient as discussed above. However,

realistically, the main component of the force experienced in the real system would be

perpendicular to the nanopillar with only little contributions from the parallel component.

3.3.2. Analysis of the effects of radius of nanopillars and magnitude of applied force

on the resultant displacement in nanopillar.

The displacement plots for a range of applied force from 6nN to 12nN over a range of

nanopillar radii 40nm to 80nm are shown in appendix E. The compiled data values are shown

in appendix F.

48

Figure 3.33. Graphs plots of (a) displacement versus nanopillar radius (b) displacement versus

force for different magnitudes of forces applied for different nanopillar radii.

To better study the relationships between the resultant displacement in the nanopillar, the radius

of nanopillar and the magnitude of the applied force, we plot the data collected into graphs as

shown in Figure 3.33. From Figure 3.33 (a), we can see that the resultant displacement in the

nanopillar decreases as the radius of the nanopillar increases. Figure 3.33 (b) shows that the

resultant displacement in the nanopillar increases as the magnitude of the applied force

increases.

y = 883344x-3.921

y = 1E+06x-3.921

y = 1E+06x-3.921

y = 2E+06x-3.921

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90

Dis

pla

cem

ent

(μm

)


Displacement versus Nanopillar radius

6

8

10

12

Power (6)

Power (8)

Power (10)

Power (12)

y = 0.0771x + 1E-05

y = 0.032x - 3E-06

y = 0.0156x - 4E-06y = 0.0086x - 4E-06y = 0.0051x - 1E-050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14

Dis

pla

cem

ent

(μm

)

Force (nN)


40

50

60

70

80

Linear (40)

Linear (50)

Linear (60)

Linear (70)

Linear (80)

(a)

(b)

49

Fitting the data between the resultant displacement in the nanopillar and the radius of the

nanopillar gives a power relationship. For an applied force in the same direction, in this case

x-direction, the radius of the nanopillar is inversely proportional to the resultant displacement

of the nanopillar by a power of 3.921. This power is the same regardless of the magnitude of

the applied force to the nanopillar. The sensitivity of the resultant displacement to the

magnitude of the applied force can be seen in Figure 3.33 (a) as the coefficient is larger for a

larger magnitude of applied force.


applied force gives a linear relationship, agreeing with the previous section. From Figure 3.33

(b), we can see that the gradient of the plot becomes less steep as the radius of the nanopillar

increases. This suggest that the radius of the nanopillar is a factor that affects the gradient of

the linear relationship.


resultant displacement of nanopillar to be

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟 ∝ 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒

𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟4

3.3.3. Analysis of the effects of the height of nanopillars and the magnitude of applied

force on the resultant displacement in nanopillar.

The displacement plots for a range of applied force from 6nN to 12nN over a range of

nanopillar height 0.5μm to 2.0μm are shown in appendix G. The compiled data values are

shown in appendix H.

50

Figure 3.34. Graphs plots of (a) displacement versus nanopillar height (b) displacement versus

force for different magnitudes of forces applied for different nanopillar heights.

To better study the relationships between the resultant displacement in the nanopillar, the

height of nanopillar and the magnitude of the applied force, we plot the data collected into

graphs as shown in Figure 3.34. From Figure 3.34 (a), we can see that the resultant

displacement in the nanopillar increases as the height of the nanopillar increases. Figure 3.34

(b) shows that the resultant displacement in the nanopillar increases as the magnitude of the

applied force increases.

y = 0.1469x2.918

y = 0.1962x2.9138

y = 0.2449x2.918

y = 0.2939x2.918

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

Dis

pla

cem

ent

(μm

)

Nanopillar height (μm)

Displacement versus Nanopillar height

6

8

10

12

Power (6)

Power (8)

Power (10)

Power (12)

y = 0.0033x + 0.0001y = 0.0126x + 7E-06

y = 0.032x - 3E-06y = 0.0651x - 7E-06y = 0.1155x - 7E-06

y = 0.187x - 7E-06

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14

Dis

pla

cem

ent

(μm

)

Force (nN)


0.5

0.8

1.1

1.4

1.7

2

Linear (0.5)

Linear (0.8)

Linear (1.1)

Linear (1.4)

(a)

(b)

51

Fitting the data between the resultant displacement in the nanopillar and the height of the

nanopillar gives a power relationship. For an applied force in the same direction, in this case

x-direction, the height of the nanopillar is directly proportional to the resultant displacement of

the nanopillar by a power of 2.918. This power is the same regardless of the magnitude of the

applied force to the nanopillar. The sensitivity of the resultant displacement to the magnitude

of the applied force can be seen in Figure 3.34 (a) as the coefficient is larger for a larger

magnitude of applied force.


applied force gives a linear relationship, agreeing with the previous two sections. From Figure

3.34 (b), we can see that the gradient of the plot becomes steeper as the height of the nanopillar

increases. This suggest that the height of the nanopillar is a factor that affects the gradient of

the linear relationship.


resultant displacement of nanopillar to be

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟

∝ (𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒)(𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟3)

52

4. Conclusion and Future Work

4.1.Conclusion

We recognise that there is no limit to the number of variables we can work on for the

simulations and that the simulations cannot fully replicate all the conditions, but this study with

the help of COMSOL Multiphysics 5.2 allow us to gain basic understanding and idea to some

of the different correlations and discover the order of the variables we are working with. With

this, we can better estimate the dimensions and parameters that is suitable for us to

experimentally prepare a sample and set up experiments for gathering meaningful data.

Based on the results we obtained from the simulations done for MoS2 thin film, we can

approximate and propose the following analytical relationship for the strain experienced by the

thin film to be

𝑆𝑡𝑟𝑎𝑖𝑛 𝑒𝑥𝑝𝑒𝑟𝑖𝑒𝑛𝑐𝑒𝑑 𝑏𝑦 𝑡ℎ𝑖𝑛 𝑓𝑖𝑙𝑚

∝ 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒

(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟𝑠 𝑜𝑓 𝑡ℎ𝑖𝑛 𝑓𝑖𝑙𝑚53)(𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟)

We also found out that larger number of layers of thin film will result in stronger strain coupling

with surrounding nanopillars. This relationship of stronger strain coupling is also observed

when the distance between nanopillars are smaller.

We also discovered that the area of the strain experienced by the thin film is larger when the

number of layers of thin film is increased. This effect of larger area of strain experienced by

the thin film can also be observed if the nanopillars array has a larger nanopillar radius or a

smaller nanopillar separation.

Similarly, based on the results we obtained from the simulations done for PMMA nanopillars,

we can approximate and propose the following analytical relationship for the resultant

displacement of nanopillar to be

53

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟

∝ (𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒)(𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟3)

𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑛𝑎𝑛𝑜𝑝𝑖𝑙𝑙𝑎𝑟4

This analytical relationship derived for PMMA nanopillar is verified with theory where in the

linear regime of small deformations, the deflection of the pillars is directly proportional to the

force. The linear elastic theory of a cylinder bent by the application of a lateral force F gives

the following relation:

𝐹 = (3

4𝜋𝐸

𝑟4

𝐿3)∆𝑥

where F is the force, E is the Young’s modulus, r is the radius of pillar, L is the length of pillar

and Δx is the deflection of pillar. [11]

It is important for us to note that since the displacement of nanopillar is linearly proportional

to the force, and the force is linearly proportional to the strain experienced by the film, and the

strain experienced by the film is linearly proportional to the Raman shift as seen in Figure 1.3

(b) [4] and Figure 1.3 (e) [5], we can directly and simply correlate the Raman shift to the

displacement of nanopillar.

4.2.Future Work

With the understanding of the relationships with the different variables and the order of

magnitude, we can estimate suitable parameters to build and construct our sample. To produce

a strain of order about 1% in a monolayer of MoS2, the order of magnitude of force required is

roughly 100nN. The PMMA nanopillar radius needs to be large despite the fact that it causes

the strain to be experienced by the thin film to be smaller. This is because for a reasonable

displacement in the nanopillar without fracture, a larger nanopillar radius is required to

correspond to a force of the order of 100nN. This nanopillar radius will preferably be at the

order of about 100nm and the nanopillar height at the order of about 1μm. As the spot size for

Raman spectroscopy is at the order of 1μm [12], a nanopillar separation of the same order of

1μm will prevent two spots being counted at one. Moreover, a larger nanopillar separation also

54

help to reduce strain coupling between nanopillars. We can then conduct experiments on our

sample and perform correlation between the Raman shifts and the displacement of the

nanopillar.

55

List of Tables

Table 3.1. Compiled results for strain values on surface α for different angles of a 10nN force

applied for different number of layers of thin film. Failed to find solution for 1 layer due to

error from 15o onwards.

Table 3.2. Compiled strain values for different magnitudes of forces applied in the x-direction

obtained through simulation and fitting.

56

List of Figures

Figure 1.1. (a) Structural model of ZnO nanorods in pressure sensor. [1] (b) Averaged voltage

versus pressure plots for different ZnO sensor designs. [1] (c) Design of SiNWs force sensor.

[2] (d) Normalised voltage versus force plot for SiNWs sensor. [2]

Figure 1.2. (a) Scanning Electron Microscope (SEM) image of PDMS nanopillars array. (b)

SEM image of biological cell on PDMS nanopillars array. (c) Image of deflection mapping of

PDMS nanopillars. (inset) Drawing of adherent cell-cell junctions. (d) Image of force mapping

of PDMS nanopillars. [3]

Figure 1.3. (a) Evolution of the Raman spectra of the monolayer MoS2 under uniaxial strain.

[4] (b) Raman shift versus strain plot for E’+ and E’- modes of the monolayer MoS2 under

uniaxial strain. [4] (c) Evolution of the Raman spectra of the monolayer MoS2 under uniaxial

strain. [5] (d) Schematic illustration of atomic displacements of monolayer MoS2 for A1g and

E2g’ modes. [5] (e) Raman shift frequency versus strain plot for A1g, E2g’+ and E2g’

- modes of

the monolayer MoS2 under uniaxial strain. [5] (f) Evolution of the Raman spectra of the

monolayer WS2 under uniaxial strain. [6] (g) Schematic illustration of atomic displacements of

monolayer WS2 for A1’ and E’ modes. [6] (h) Raman shift frequency versus strain plot for A1’,

E’+ and E’- modes of the monolayer WS2 under uniaxial strain. [6]

Figure 2.1. CAD drawings created in COMSOL Multiphysics of 2D TMDS thin film

assembled on PMMA nanopillars array structure.

Figure 2.2. SEM images of PMMA nanopillars array of different pillar diameters and height.

Source from Dr. Yu Miao from Professor Yan Jie’s Group from Mechanobiology Institute

(MBI).


varying thickness. Cylindrical PMMA of 50nm radius and 0.6nm thickness at the centre on top

of the thin film. (b) Fixed constraint applied to edges of thin film as highlighted in blue. (c)

Force applied over PMMA as highlighted in blue.


varying thickness. 3 by 3 cylindrical PMMA of 50nm radius and 0.6nm thickness on top of the

thin film spaced 500nm apart from each other. (b) Fixed constraint applied to surrounding thin

PMMA as highlighted in blue. (c) Force applied over centre PMMA as highlighted in blue.

57



Force applied over top of centre nanopillar as indicated by the arrow.














Figure 3.7. Definition of angle of applied force based on axes of (a) COMSOL Multiphysics

image of 2D TMDS thin film of 1μm by 1μm with varying thickness. Cylindrical PMMA of

50nm radius and 0.6nm thickness at the centre on top of the thin film. (b) Axes for structure

shown in (a). (c) Angle measured from x-direction towards z-direction.










58

Figure 3.11. (a) Graph plot of strain versus number of layers for different magnitudes of forces

applied in the x-direction [same figure as Figure 3.6 (c)] (b) Same graph plotted leaving out

data points for 1 layer.



























59




Figure 3.23. Graph plot of strain versus number of layers for centre and nearest nanopillar for

10nN force applied in the x-direction for different number of layers of thin film.

Figure 3.24. COMSOL Multiphysics image of 2D TMDS thin film of 2μm by 2μm with

varying thickness. Cylindrical PMMA of 50nm radius and 0.6nm thickness in a square lattice

on top of the thin film. (a) Definition of angle of applied force measured from x-direction

towards y-direction. (b) Definition of surrounding nearest nanopillars labelled A, B and C.











separation of 250nm for (a) 1 layer (b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers of thin film.


separation of 750nm for (a) 1 layer failed to find solution due to error. Space left there for

easier and more intuitive viewing across figures. (b) 2 layers (c) 3 layers (d) 4 layers (e) 5 layers

of thin film.


separation of 1000nm for (a-c) 1-3 layers failed to find solution due to error. Space left there

for easier and more intuitive viewing across figures. (d) 4 layers (e) 5 layers of thin film.



Definition of angle of applied force measured from x-direction towards negative z-direction.

60

Figure 3.32. Graph plots of (a) displacement versus force (b) displacement versus angle for

different magnitudes of forces applied for different angles.

Figure 3.33. Graphs plots of (a) displacement versus nanopillar radius (b) displacement versus

force for different magnitudes of forces applied for different nanopillar radii.

Figure 3.34. Graphs plots of (a) displacement versus nanopillar height (b) displacement versus

force for different magnitudes of forces applied for different nanopillar heights.

61

References

[1] Nabar, B. P., Celik-Butler, Z., & Butler, D. P. (2015). Self-powered tactile pressure

sensors using ordered crystalline ZnO nanorods on flexible substrates toward robotic

skin and garments. IEEE Sensors Journal, 15(1), 63-70.

doi:10.1109/JSEN.2014.2337115

[2] Tan, E. L., Lin, A. T., Lim, R., Hamidullah, M., Cheng, M., He, C.. . Tan, K. K. (2013).

Silicon nanowires (SiNWs) based force sensor for membrane contact measurement.

Paper presented at the 46.

[3] Roure, O. d., Saez, A., Buguin, A., Austin, R. H., Chavrier, P., Siberzan, P., . . . Gennes,

P. d. (2005). Force mapping in epithelial cell migration. Proceedings of the National

Academy of Sciences of the United States of America, 102(7), 2390-2395.

doi:10.1073/pnas.0408482102

[4] Conley, H. J., Wang, B., Ziegler, J. I., Haglund, J., Richard F, Pantelides, S. T., &

Bolotin, K. I. (2013). Bandgap engineering of strained monolayer and bilayer

MoS2. Nano Letters, 13(8), 3626.

[5] Wang, Y., Cong, C., Qiu, C., & Yu, T. (2013). Raman spectroscopy study of lattice

vibration and crystallographic orientation of monolayer mos2 under uniaxial strain.

[6] Yanlong Wang Chunxiao Cong Weihuang Yang Jingzhi Shang Namphung Peimyoo

Yu Chen Junyong Kang Jianpu Wang Wei Huang Ting Yu. (2015). Strain-induced

direct-indirect bandgap transition and phonon modulation in monolayer WS2. 纳米研

究：英文版, 8(8), 2562-2572. doi:10.1007/s12274-015-0762-6

[7] COMSOL Inc. Multiphysics Cyclopedia. The Finite Element Method (FEM). Retrieved

from https://www.comsol.com/multiphysics/finite-element-method.

[8] Wei, G., Bhushan, B., Ferrell, N., & Hansford, D. (2005). Microfabrication and

nanomechanical characterization of polymer microelectromechanical system for

biological applications. Journal of Vacuum Science & Technology A: Vacuum,

Surfaces, and Films, 23(4), 811-819. doi:10.1116/1.1861937

[9] Tan, L. K., Liu, B., Teng, J. H., Guo, S., Low, H. Y., Tan, H. R.. . Loh, K. P. (2014).

Atomic layer deposition of a MoS₂ film. Nanoscale, 6(18), 10584.

62

[10] Castellanos-Gomez, A., Poot, M., Steele, G. A., van der Zant, Herre S J, Agraït, N., &

Rubio-Bollinger, G. (2012). Elastic properties of freely suspended MoS2 nanosheets.

Advanced Materials (Deerfield Beach, Fla.), 24(6), 772.

[11] Landau, L. & Lifschitz, E. (1990) in Theorie de l’Élasticite´ (M.I.R., Moscow) 2nd Ed.,

pp. 107–126.

[12] HORIBA Ltd. Scientific. What analysis spot size is used for a Raman microscope?

Retrieved from http://www.horiba.com/scientific/products/raman-

spectroscopy/raman-academy/raman-faqs/what-analysis-spot-or-laser-spot-size-is-

used-for-a-raman-microscope/

63

Appendices

A. Compiled results for strain values on surface α for different magnitudes of forces

applied in the x-direction for different number of layers of thin film.

B. Compiled results for strain values on surface α for 10nN force applied in the x-direction

over different nanopillar radii for different number of layers of thin film.

64

C. Displacement plots for a range of applied force from 6nN to 12nN over a range of

angles 0o to 45o.

D. Compiled results for displacement values for different magnitudes of forces applied for

different angles.

65

E. Displacement plots for a range of applied force from 6nN to 12nN over a range of

nanopillar radii 40nm to 80nm.

F. Compiled results for displacement values for different magnitudes of applied force for

different nanopillar radii.

66

G. Displacement plots for a range of applied force from 6nN to 12nN over a range of

nanopillar height 0.5μm to 2.0μm.

H. Compiled results for displacement values for different magnitudes of applied force for

different nanopillar height.

Documents

National University of Singapore Department of Physics · 2020. 8. 17. · the sample, I truly appreciate ... PDMS nanopillars. (inset) Drawing of adherent cell-cell junctions. (d)