microscopy settings for measuring the diameter of carbon nanotubes

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Importance of atomic force

microscopy settings for measuring the diameter of carbon nanotubes

Betydelsen av atomkraftmikroskåpets inställningar för mätningar av diametern hos kolnanorör

Anton Almén

Faculty of Health, Science and Engineering Physics, nanoscience

15 ECTS

Supervisor: Krister Svensson Examiner: Thijs Jan Holleboom 2019-06-04

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Karlstad University

Faculty of Health, Science, and Technology Department of Engineering and Physics

Importance of atomic force microscopy settings for measuring the diameter of carbon nanotubes

Author: Anton Almén Supervisor: Krister Svensson Examiner: Thijs Jan Holleboom

2019-06-04

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abstract

Carbon nanotubes (CNTs) have gathered a lot of interest because of their extraordinary mechanical, electrical and thermal properties and have potential applications in a wide variety of areas such as material reinforcement and nano-electronics. The properties of nanotubes are dependent on their diameter and methods for determining this using atomic force microscopy (AFM) in tapping mode assume that the measured height of the tubes represent the real diameter. Based on early, faulty calculations, the forces in tapping mode were assumed to be much lower than in contact mode, however it was later shown that forces in tapping mode can at point of impact rival the forces present in contact mode. This means that there is a potential risk of tube deformation during tapping mode measurements, resulting in incorrectly determined diameters. This work studies CNTs deposited on a silicon-substrate to analyze the effect of three common AFM settings (tapping frequency, free oscillation amplitude and setpoint) to determine their effect on measured CNT diameters and recommendations for choosing settings are given.

Keywords: Carbon nanotubes (CNTs), Atomic force microscopy (AFM), diameter, height, tapping, frequency, phase, amplitude, setpoint

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Sammanfattning

Kolnanorör har skapat mycket intresse på grund av sina extraordinära mekaniska, elek- triska och termiska egenskaper och har lovande tillämpningar inom en mängd olika områ- den så som materialförstärkning och nanoelektronik. Kolnanorörens egenskaper påverkas kraftigt av deras diameter och de metoder som använder sig av atomkraftsmikroskopi (AFM) för att mäta diametern hos rören antar att den höjd-data man får fram är ett bra mått på den verkliga diametern hos rören. Baserat på tidiga, felaktiga beräkningar, antog man att kraften i ’tapping mode’ skulle vara mycket lägre än i ’contact mode’

vilket skulle leda till att man inte deformerar ytan man undersöker. Senare forskning visade att kraften mellan spets och prov kan vara lika stor eller rentutav större i tapping mode än i contact mode under det ögonblick då spetsen slår ner i provytan. Det medför att det finns en potentiell risk för att man deformerar kolnanorören när man mäter på dom vilket skulle resultera i att man får felaktiga värden på deras diametrar. Under det här projektet har kolnanorör som placerats på ett kisel-substrat undersökts för att analysera hur tre vanliga inställningar hos AFMet påverkar de erhållna värdena för diametern hos kolnanorören. De tre inställningarna som testats är svängnings-frekvensen, svängnings-amplituden i luft och börvärdet hos svängnings-amplituden.

Nyckelord: Kolnanorör, Atomkraftsmikroskopi (AFM), diameter, höjd, svängning, frekvens, fas, amplitud, börvärde

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Acknowledgments

I would like to thank my supervisor Krister Svensson for introducing me to the subject, teaching me the basics of operating the equipment, helping me prepare my samples and for everything he has taught me during our many discussions. I also want to thank my family and friends for their support, and for telling me to take breaks once in a while.

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1 Introduction

Carbon nanotubes (CNT) are known as the ’rock-stars’ of molecular nanotechnology because of their extraordinary mechanical strength, electrical and thermal conductivity [1]. These properties give CNTs promising applications in a wide area of fields such as reinforcing materials, replacement for silicon in next generation computer chips, highly conductive nanowires, almost frictionless nanomachine cogs and much more [2].

While CNTs have found public use, particularly in the sports industry: reinforcing tennis rackets, golf clubs and more, we seldom see CNTs in publicly available products.

The properties that CNTs have are highly dependent on the quality of the CNTs and when trying to scale up manufacturing it often affects said quality. It is also not trivial to analyze CNTs although methods for quantifying the crystalinity of CNTs have been developed [3].

Another important characteristic of CNTs is the diameter of the tubes and it is strongly affecting properties such as stiffness [4], band gap [5] and carrier mobility [6]. This can be measured using methods such as transmission electron microscopy (TEM) [7], Scanning electron microscopy (SEM) [8] or optical methods such as Rayleigh scattering [9] or resonant Raman spectroscopy [10]. Methods for using Atomic force microscopy (AFM) operated in tapping mode have been proposed [11] and assume that the real diameter can be considered to be equal to the maximum height measured when scanning over a singular tube. The early work of Q. Zhong et al [12] concluded that the forces between tip and sample are much lower in tapping mode than in contact mode. Their analysis was however faulty, calculating the force in tapping mode to be the average force in each oscillation rather than the maximum at contact. J. Spatzt et all [13] later showed that the force when the tip hits the sample in tapping mode could vary by several orders of magnitude and be equal to the force in contact mode. This is of importance when analyzing the diameter of CNTs since the tubes are hollow inside and are much weaker in the radial direction, the direction of measurement, than in the axial direction. R.

Alizadegan et al [14] showed that AFM scans of CNTs resulted in diameter values that were below the actual values of the tubes when compared to obtained values by the less invasive resonant Raman spectroscopy method.

In this study, CNTs deposited on a silicon substrate have been analyzed with AFM in tapping mode while varying three common settings of the instrument. The amplitude of oscillation in ambient air, the amplitude of oscillation when in contact to the surface in respect to the amplitude in ambient air (setpoint) and the tapping frequency of the tip relative to the self-oscillation frequency of the tip. From this study it appears that the most important setting to consider is the tapping frequency as measured tube diameters decreased when choosing tapping frequencies above the point on the resonance peak where tapping is 0^◦ out of phase during cantilever tuning. Changing the setpoint does not appear to affect tube diameter measurements. Changing tapping amplitude showed that one can obtain large variations in height measurement but no general trend was found. It was however found that too high amplitude could sometimes cause tubes to not register on topological scans and did in general cause loss of image clarity.

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This thesis shows the importance of choosing appropriate settings when using AFM.

Choosing a tapping frequency that is lower than the point discussed above and not using unnecessary large tapping amplitudes is recommended. If the sample is easily damaged, such as soft polymers, it is advisable to choose as high of a setpoint as possible and can be done by doing point spectroscopy and picking a suitable setpoint. For specifically measuring CNT diameters other methods such as TEM or SEM appear to be more reliable.

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2 Background & Theory

2.1 Graphene

Graphene is an allotrope of carbon. The structure of graphene is that of a flat monolayer of carbon atoms arranged in a hexagonal/honeycomb lattice, fig 2.1. Every atom is the same as any other in a perfect graphene-layer, with every carbon atom being sp²-hybridized. The sp²-hybrid bonds are stronger than the sp³-hybrid bonds found in diamond, and graphene have an ultimate tensile strength of 130 GPa which is greater than diamond (≈ 100 Gpa). Graphene also have extraordinary electrical properties due to the sp²-hybrid bonds. It is a zero gap semiconductor capable of conducting current via both electrons and holes with very high electrical conductivity. Carbon atoms have 4 outer shell electrons and each atom that is sp²-hybridized is bonded to 3 other atoms.

This leaves 1 electron free to move around in graphene and combined with the zero ef- fective mass of charge carriers in the structure allows electron mobilities of up to 200 000 cm²· V⁻¹· s⁻¹ [15].

Figure 2.1: Graphene structure (honeycomb lattice). [16]

Because graphene is a monolayer structure it kind of resembles a sheet of paper, and just like a sheet of paper it is possible for graphene-layers to be stacked on top of each other (Graphite), rolled into a cylinder (Carbon nanotube) or crumbled into a ball (Buck- minsterfullerene), fig 2.2.

Figure 2.2: Graphene and its related materials. [17]

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2.2 Carbon nanotubes 2.2.1 Structure

A carbon nanotube (CNT) can be imagined as a sheet of graphene rolled up into a cylinder. All atoms are sp²-hybridized and similarly to graphene, every atom in a CNT can be regarded as a surface atom. CNTs do however have a volume, in contrast to the pure 2D structure (zero volume) of graphene. This gives CNTs some altered properties, discussed more in 2.2.2.

Similar to rolling up a paper along either its short side, long side or diagonally across, one can imagine different configurations for CNTs depending on which direction a graphene-sheet is rolled up, fig 2.3.

Figure 2.3: Schematics of CNTs in the 3 different chiral configurations. [18]

The direction of rolling is categorized by two integers (m,n), also called the chiral index, representing the chirality of the tubes. A tube is said to be of the armchair variant when m = n and zigzag when n = 0. All other combinations are referred to as chiral CNTs.

The chirality of the tubes can alter some of the properties, further discussed in 2.2.2.

CNTs can also form inside each other, like Russian dolls, and are called Multi walled carbon nanotubes (MWCNT), fig 2.4. Analogously, single walled carbon nanotubes are often denoted as SWCNT.

Figure 2.4: Illustration of both single and multi walled carbon nanotubes. [19]

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2.2.2 Properties and Application

CNTs share many similar properties to graphene due to their structural similarities.

Table 2.1 display some mechanical properties of CNTs, graphene and diamond.

Table 2.1: Mechanical properties of some carbon allotropes [3][20][21].

Material Tensile strength (GPa) Young-modulus (TPa)

Graphene 130 1

SWCNT 36-140 ∼ 1

MWCNT 11-150 ∼ 0.1-0.8

Diamond 89-98 1.22

Mechanical properties of CNTs are highly dependent on their crystallinity [3] and explains the large variation in both SWCNT and MWCNT properties in table 2.1.

Thermal conductivity in SWCNTs have been observed as high as 2400-3500 W ·m⁻¹·K⁻¹ in the axial direction [22], which is comparable to diamond (2200-3320 W · m⁻¹· K⁻¹).

Thermal conductivity in the radial direction can however be as low as 1.5 W · m⁻¹· K⁻¹, essentially non-conductive [23]. The extraordinary strength and low weight of high quality CNTs have applications in reinforcing purposes in everything from sports equipment to the theoretical ’space elevator’ proposed by NASA [24].

Perhaps the most interesting properties of CNTs are the electrical ones. CNTs can be anywhere from metallic in nature to large bandgap semiconductors depending on the chirallity of the tubes. Armchair CNTs (chirality: n=m) are always metallic in nature, zigzag CNTs are large bandgap conductors while chiral CNTs (all other chiralities) can be considered small bandgap semiconductors. The bandgap is dependent on the diameter of the tubes and increases as 1/R and 1/R² for large and small bandgap tubes respectively [1]. Ultra-small SWCNTs (∼ 0.4 nm) have even been shown to exibit super conductive properties [25]. Defects in the structure such as vacancies and dopants can alter the electrical properties of CNTs drastically and could potentially be used to create nano- electronics in form of transistors, junctions and more [1]. CNTs have application in essentially all areas of electronics from fabrication of nanowires to replacing silicon in the next generation of transistors and more.

2.2.3 Manufacturing

There are multiple methods for creating CNTs but two of the most common are Arc discharge and Chemical Vapor Deposition (CVD). In arc discharge you put two electrodes (graphite rods) close together inside a chamber and run a high DC voltage between them, fig 2.5. This causes the graphite to vaporize and depending on the pressure in the chamber, the evaporated carbon atoms can form various structures such as soot, amorphous carbon, CNTs and fullerenes. Tubes made using arc discharge have been shown to have high crystallinity with few impurities [26].

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Figure 2.5: Schematics of an arc discharge setup. [27]

The CVD approach works by heating up carbon atoms in an oven such that they evaporate. The evaporated carbon atoms are then deposited onto a substrate by the use of a carrier gas such as Argon, fig 2.6. It is also possible to grow graphene using CVD but by adding catalytic particles onto the substrate it is possible to force the carbon to grow into CNTs instead. Tubes grown using CVD have lower crystallinity compared to those made using arc discharge [3]. The main advantage of the CVD approach is that this method is scalable for mass production. It also offers control over the length of the tubes since the growth-length is dependent on the growth-time and amount of material deposited.

Figure 2.6: Schematics of a Chemical vapor deposition setup. [28]

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2.3 Atomic force microscopy 2.3.1 History

The atomic force microscope (AFM) is a member of the scanning probe microscope family that started with the invention of the scanning tunneling microscope (STM) in 1981 by Gerd Binnig and Heinrich Roherer at IBM Zurich Research Laboratories [29].

STM is capable of imaging surfaces on the atomic level and earned Binning and Roherer the nobel prize in 1986 [30]. The microscope is based on the principle of quantum tunneling and operates by bringing a conductive tip very close to a conductive surface and applying a voltage difference between them. This allows electrons to tunnel between the tip and surface and by measuring the tunneling current while sweeping across the surface, information is gathered about the surface. This technique have one major flaw however, it requires the sample surface to be conductive or semiconductive, otherwise no current is possible between tip and sample.

The AFM was developed in 1985 by Binnig, Quate and Gerber to overcome this prob- lem [31]. Similarly to the STM, the AFM sweeps a very sharp tip across a sample surface while an active feedback loop is used to maintain certain parameters (setpoint) by adjusting others, giving information about the surface during the scan. The probe tip is placed at the end of a small cantilever and the microscope measures the atomic forces between the tip and sample, leading to the ability to measure on almost any type of surface, including polymers, glass, as well as conductive and semiconductive materials.

AFM is capable to measuring both the longer range attractive forces such as Van der Waals forces or electrostatic forces, and the short ranged repulsive forces due to electron orbital overlap. There are three main modes of operation for AFM used for measuring these different force interaction regimes, fig 2.7.

Figure 2.7: Typical AFM force interaction curve. Adapted from [32]

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2.3.2 Contact mode

In contact mode the tip is dragged across the sample, always in contact with the surface.

By shining a laser on top of the cantilever and using a photo-diode detector to measure the reflected beams position, fig 2.8, it is possible to calculate how the cantilever beam is deflected.

Figure 2.8: AFM schematics. Adapted from [33]

If the stiffness of the cantilever is known it is then possible to determine the force between tip and sample using Hooke’s law:

F = −kx (2.1)

where F is the force between tip and sample, k is the spring-constant of the cantilever and x is the deflection of the cantilever. Cantilevers with low stiffness are usually used for contact mode imaging because they deflect more, resulting in larger output signals.

AFMs are commonly set to try and keep a constant cantilever deflection (setpoint) during scan, rather than measuring the direct deflection. This is done by placing the sample on a piezoelectric-ceramic (z-piezo) and applying a voltage to either raise or lower the sample based on an active feedback loop. The data for how the piezo was adjusted is then used to create a topographical image of the scan.

Most samples develop a thin water layer when left exposed to air due to the ambient humidity [34]. This layer acts like a meniscus, giving rise to attractive capillary forces on

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the tip. The attraction pulls the tip towards the surface, increasing the forces between tip and sample during scan, and can for softer samples result in the tip damaging the sample surface. It is possible to eliminate the effects of a meniscus by submerging the sample in a liquid before imaging.

2.3.3 Intermittent-contact/tapping mode

Intermittent-contact is commonly referred to as tapping mode because the probe is set to oscillate such that it tap on the surface during its lowest point of oscillation. The cantilever is set to oscillate near its resonance frequency by a piezoelectric-ceramic called a shaker/driving-piezo. The AFM then tries to maintain a certain amplitude of oscillation (setpoint) by adjusting the z-piezo during scan, fig 2.9.

Figure 2.9: Illustration of how the amplitude of oscillation is affected during tapping mode. Adapted from [35]

Lateral and torsional forces are much lower in tapping mode than in contact mode because the tip only makes contact with the surface during short periods of time rather than being in constant contact, dragging along the surface. This result in a lower risk of tip degradation and damaging the surface of soft samples. This is not to say that

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imaging in tapping mode does not carry any risk of damaging the tip or sample. Q.

Zhong et al [12] demonstrated that they were able to generate reproducible images of optical fibers using tapping mode and calculated the estimated contact forces to be in the nN regime. Their calculations were based on the amplitude reduction that takes place in each oscillation cycle and is a calculation of the average force during each cycle, rather than the maximum force that occur at the moment of impact. J. Spatzt et al [13] later showed that the contact forces in tapping mode can vary by several orders of magnitude and can match those present in contact mode.

Because the tip oscillates between making contact with the surface and being further away, measurement of both long range attractive and close range repulsive forces can be done, as seen in fig 2.7. A simple model of how the tip and sample interact is to imagine the cantilever and tip as a spring interacting with another spring representing the sample, fig 2.10.

Figure 2.10: Simple spring model of the cantilever and sample system. Z_L is the equilibrium position of the cantilever and the cantilever is modelled as a spring with point mass m, spring constant k_C and quality factor Q_C. (a) describes the cantilever oscillating in free air and (b) describes the system when the tip is engaged to a sample surface. The surface is modelled as a second, stiffer spring, with spring constant k_S and quality factor Q_S. [13]

The tip can be though of as alternating between scenario (a) and (b) in figure 2.10

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during each oscillation cycle. When the tip is at its highest point of oscillation, the distance to the sample is large enough that only slightly attractive forces act on the system, equivalent to gravity pulling the point mass down towards the sample. When the tip is at its lowest point, making contact with the sample, repulsive forces dominate the system, equivalent to the stiffer spring pushing back onto the cantilever-spring. This coupling and uncoupling of a second spring has the effect of shifting the resonance frequency of the system during each oscillation, fig 2.11.

Figure 2.11: Illustration of the resonance frequency shifts that occurs when operating in tapping mode. [35]

If the cantilever is set to oscillate at its resonance frequency in free air it will oscillate with a constant amplitude. If the cantilever is then brought closer to a sample such that it starts to feel the attractive forces of the sample, the force between them will increase which will cause the resonance frequency to shift to a lower value, resulting in a drop in oscillation amplitude. Once the tip is close enough such that the repulsive forces start to dominate the system the resonance frequency will instead shift to a higher value, fig 2.11.

An ideal cantilever beam oscillating in free air would have a single bell curved resonance peak such as the one in fig 2.11 and the driving frequency would be 0^◦ out of phase at the top of the peak. Because there is a tip attached at the end of an AFM tapping probe, other modes of oscillation appears because the system is no longer a homogenous beam. These modes can be observed by sweeping through the tapping frequency of the driving-piezo and monitoring how the oscillation amplitude of the cantilever changes.

The resulting curves are known as cantilever tuning profiles and such a profile for a real tip can be seen in fig 2.12.

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Figure 2.12: Cantilever tuning profile. The red lines indicate where the tapping of the driving-piezo is 0^◦ out of phase.

A general advice when using AFM in tapping mode is to choose an operating frequency slightly below (roughly 5% below) the resonance peak [35].

The closer the equilibrium position of the cantilever oscillation is to the sample surface, the stronger the tip and sample interaction will be which causes more energy to be dissipated onto the sample. If the driving amplitude is kept constant this will then result in a reduction of the oscillation amplitude. By doing point spectroscopy, a method where the tip is placed above a user-determined point on the sample and slowly approached a set distance towards the surface and then slowly withdrawn, it is possible to analyze the energy dissipation from tip onto the sample by mapping how the phase of the driving oscillation changes, fig 2.13.

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Figure 2.13: Point spectroscopy curves from tapping on a graphene sample, illustrating elastic tapping. The dark and light blue curves indicate the tapping amplitude when the tip is approaching and withdrawing from the sample respectively. The green and yellow curves indicate the tapping phase of the driving oscillation during approach and withdrawal respectively. [23]

The sharp rise of the tapping amplitude in figure 2.13 (figure is read from right to left) is caused by the cantilever getting close enough to the sample that it starts to feel the attractive forces. This shifts the resonance frequency to lower values and if the initial operating point was below the resonance peak (as discussed above), the current operating point will be closer to the resonance peak, which results in an easier to drive cantilever and the oscillation amplitude increases. As this occurs the tapping phase drops because of the lag/delay between the drive from the shaker-piezo and the response in the cantilever oscillations. The amplitude then decreases as the cantilever is brought closer to the sample such that it starts tapping on the surface and repulsive forces begin to dominate the system, which shifts the resonance peak to higher values, making it harder to drive the cantilever oscillations.

It is possible to qualitatively determine if the tapping is elastic (figure 2.13) or not (figure 2.14) by analyzing how the tapping phase recovers when the tip is close enough to make contact with the sample surface during each oscillation.

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Figure 2.14: Point spectroscopy curves from tapping on CNTs, illustrating inelastic tapping. The dark and light blue curves indicate the tapping amplitude when the tip is approaching and withdrawing from the sample respectively. The green and yellow curves indicate the tapping phase of the driving oscillation during approach and withdrawal respectively.

If the phase drops by only a few degrees and then linearly returns back up this indicates that not much energy have been lost and the tapping is rather elastic, see fig 2.13. This is analogous to how a ball that elastically bounces on a surface will return with the same speed it came in with. If the tapping phase initially recovers more slowly, see fig 2.14, this indicates that the tapping is more inelastic. Energy is lost in the bounce/tap and the driving-piezo have to put more energy into the cantilever until the oscillation returns back. This is analogous to dropping a metal ball in sand. The ball will not bounce back up because all kinetic energy is dissipated into the sand and you have to input more energy by lifting the ball back up if you want it to return to its initial position.

The tapping phase is a convolution of multiple material properties such as adhesion,

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viscoelasticity, stiffness and energy dissipation [36]. It is therefore hard to interpret tapping phase images and determine exact values for individual properties and phase imaging is better suited for qualitative analysis [35].

The simple spring model displayed in fig 2.10 describes the interaction between an AFM probe and a sample surface consisting of one material. A more general scenario is to study particles deposited onto a substrate. This thesis for instance studies CNTs deposited on a Si-substrate. The spring model for this project becomes a 3-4 spring system depending on if the model is to include contaminants on the probe or not, fig 2.15.

Figure 2.15: Slightly more complex spring model of the cantilever and sample system. (1) describes the cantilever oscillating in free air. (2) describes the cantilever interacting with the substrate surface. (3) describes the cantilever interacting with a CNT laying on top of the substrate and (4) describes a cantilever with contaminants on the tip that is interacting with a CNT laying on top of the substrate.

Each spring in fig 2.15 have their own spring constant and quality factor and imaging becomes a convolution of multiple materials interacting with each other and studies become more qualitative rather than quantitative due to unknown parameters such as quality factors and spring constants of individual tubes.

2.3.4 Non-contact mode

In non-contact mode the AFM cantilever is set to rapidly oscillate near its resonance frequency like in tapping mode. In this mode however, the equilibrium position is set higher above the sample such that the tip never makes contact with the sample surface.

Small amplitudes (picometer to < 10 nm) are used resulting in the system only mapping out long range attractive forces such as van der Waals forces. Similarly to tapping mode, the AFM is set to maintain a constant amplitude of oscillation (setpoint) and either raise or lower the distance between tip and surface in order to achieve this, and the data for how the piezo was adjusted is translated into a topographical image. Because the

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tip never enter the repulsive/contact region of a sample, liquid layers on the surface are never penetrated and furthermore the energy dissipated from tip onto sample is much lower than all other modes of operation. This makes non-contact mode preferable when analyzing liquid and super soft samples. Similarly to tapping mode, it’s possible to image both phase and amplitude variations during scan.

2.3.5 Artifacts

AFM is not an optical form of microscopy and the images one obtain have to be inter- preted. As such there are some typical artifacts that do not portrait a correct picture that the user has to be wary of. The shape of the tip is of course a very important factor since this is what actually interact with the sample and all images are a convolution of the tip and sample. Artifacts can be categorized into 3 different types. Tip related, scanner related and other artifacts. Tip related artifacts include dull, contaminated or damaged tips as well as double/multiple tips. A dull tip will not track surface structures the same as a sharp tip, fig 2.16.

Figure 2.16: Illustration of how a dull tip gives an incorrect representation of features.

[37]

If the tip becomes very dull, or if somethings gets stuck on it such that the width of the tip becomes much larger than the structures on the surface being scanned, the resulting images will be inverted images of the tip, occurring again and again, fig 2.17

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Figure 2.17: Example of an image obtained with a contaminated tip. note how the same pattern repeat multiple times.

If parts of the tip break during scanning, one can sometimes be left with a double tip or multiple tips. Every time the tip scan over a structure, the tip sample convolution will result in a ’ghost-image’ of the structure next to the real one, fig 2.18.

Figure 2.18: Example of an image showing twinned features. [37]

Scanner related artifacts include piezo creep and bow among others. Some AFMs scan a sample by sweeping the tip across it while the sample lays still on a piezo that only adjust the height at which the sample is held. Others operate by keeping the tip

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stationary and placing the sample on a piezo that can move in all three dimensions, sweeping the sample under the tip during scan. Sometimes, especially during initial scans [38], the piezo that moves the sample can start to creep, creating stretched or compressed features, fig 2.19.

Figure 2.19: Image of a sample showing piezo-creep artifacts. [37]

.

When scanning over large areas it can happen that the piezo do not correctly adjust the position of the sample, slightly tilting it such that an arch/bow-shape appears across the entire image, resulting in images where it appears that structures at the center of the image are raised up more than those at the edges, fig2.20. These artifacts can be adjusted for by using software to do a 2D planefit of the entire image.

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Figure 2.20: Left: exaggerated illustration of how the piezoscanner would bend when moving the sample around, creating an arch which translates to decreased heights around the edges of a scan. Middle: image showing strong bow artifacts. Right: same image as middle adjusted with a 2D planefit. Adapted from [39] (Left image) and [38] (middle and right images).

Other common artifacts can occur either because of the sample or due to inappropri- ately used settings during scan. Highly reflective surfaces can sometimes reflect parts of the laser beam into the photo diode when working in contact mode, resulting in periodic patterns in the image [38]. These artifacts are more common in contact mode because the cantilever does not oscillate, so both laser beams reflected of the sample and cantilever register as DC signals in the detector. One of the most common artifacts is that of ’tails’. This occurs when the tip encounters a larger structure (very high ’mountain’

or deep ’valley’) and the feedback settings are incorrectly set. If the feedback is set to low, the AFM will not be able to react in time and the tip can crash into structures, it then attempts to correct for this and raises the tip/lower the sample. If this happens to slowly the tip will not be in contact with the surface when going down a valley or mountain. This results in images where structures can appear to have long ’tails’ where long stretches after a structure are displayed to be as high/low as the structure itself, because the tip is not in contact with the surface during these parts, fig 2.21. This can be fixed by either increasing the feedback settings or by scanning at a slower rate, giving the system more time to adjust to sudden changes in the topology of a sample.

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Figure 2.21: Tail artifacts caused by too low feeback gain.

If the feedback settings are too high, it will result in electrical noise in the image.

The system will overcompensate for deviations from the setpoint, resulting in either a too low or too high setpoint again, resulting in another overcompensation. This keeps on repeating until the gains are properly set. Images when the feedback is set too high display very noticeable noise in amplitude and phase images during scans, fig 2.22.

Figure 2.22: Noise in a phase image scan of a CD, caused by too high feedback gain.

Note the blurred lines at the center of the image.

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3 Experimental

3.1 Sample preparation

CVD grown carbon nanotubes from nanosyl (NC 3100) placed on a Silicon substrate were examined during this project. The CNTs were delivered from the manufacturer as a dry powder and was placed in a glass container filled with ethanol prior to sample preparation. The container was placed in a ultrasonic bath for 5 minutes to separate CNTs that had clumped together, fig 3.1.

Figure 3.1: Ultrasonic bath. The CNT-ethanol solution was placed inside the small glass container in the top right corner of the bath.

The container was later removed and a droplet of the solution was taken up with a precision pipette and placed onto a clean Si-slate and left to dry in ambient air until all ethanol had evaporated. The sample was kept inside the AFM the majority of the time during the project, fig 3.2, which exposed it to the ambient air and contaminants were picked up along the way. At times when other projects utilized the AFM, the sample was kept in a small plastic container.

Figure 3.2: Sample laying on top the sample holder inside the AFM.

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3.2 Instrument and setup

The sample was studied using the diInnova AFM from Veeco, fig 3.3

Figure 3.3: Left: picture of the entire workspace. The AFM can be seen in the back, standing on a vibration-suppressing table with the protective cover taken off.

Right: closeup of the AFM model name. Protective cover on.

All measurements were done in tapping mode using Tap300Al-G tips, fig 3.4. Specifics of the tip and cantilever can be found in tables 3.1 and 3.2 respectively.

Figure 3.4: Left: optical image of a tip used during the project. Right: closeup of a Tap300Al-G tip from the manufacturer. [40]

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Table 3.1: Tip data. * = typical range. [40]

Material Shape Height Setback Radius Half cone angle Silicon rotated 17 µm

(15-19 µm)*

15 µm

(10-20 µm)* <10 nm

20^◦-25^◦ along cantilever axis, 25^◦-30^◦ from side,

10^◦ at the apex

Table 3.2: Cantilever data. * = typical range. [40]

Material Silicon

Shape Beam

Force constant 40 N/m (20-75 N/m)*

Resonance frequency 300 kHz (200-400 kHz)*

Length 125 µm (115 - 135 µm)*

Width 30 µm (25 - 35 µm)*

Thickness 4 µm(3 - 5 µm)*

Coating Aluminum reflex (30 nm thick)

3.2.1 diInnova scanner specifics

The diInnova scanner AFM uses a INSC-090 piezo tube scanner capable of moving the sample in xyz-dimensions under the tip, which is placed in a static mount with a shaker piezo. There are optical sensors installed on the diInnova scanner and they analyze how the piezo have actually moved and correct for any non-linearity in the piezo that might occur during scan.

The laser beam that is reflected of the top of the cantilever is shoot from an angle such that it can reflect into a photo diode on the other side of the cantilever mount. This means that the heat generated on the cantilever from the laser beam is not uniformly distributed and this causes the cantilever to thermally drift during scans. At the start of an imaging session this results in a need to re-calibrate the laser alignment after only a few scans. The system more or less reaches an equilibrium state after approximately 4 hours of continuous laser beam exposure to the cantilever. When doing measurements it is important to take note of how much and how the laser is misaligned and try to keep this as similar as possible between scans. Taking this into account, doing things such as finding good regions with CNTs and recreating measurments from the previous day was done at the start of work sessions and proper measuring series were done later, when the cantilever either was close to, or had reached a state when re-alignment rarely had to be made.

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3.2.2 Analytic software

Images obtained during this study were analyzed using the SPIP software [41]. SPIP is a powerful tool for analyzing topological images because of its image correction and measuring toolboxes. The user can select if they want the program to do image correction such as a 2D planefit or tilt-alignment on an image based on data from the entire image, or based only on specific areas in the image. This is useful because one can exclude regions in an image that have extreme features that would heavily affect the correction.

Example of a scenario when this is useful could be an area where a lot of contaminants have build up right beside a smaller region with CNTs one wants to analyze. Excluding the region with contaminants could in this case result in a less aggressive correction of the region with CNTs while still increasing the level of detail in the region.

The program also allows the user to measure height features simply by drawing a line across them. Since individual pixels can deviate from the average height of a feature, SPIP has the feature to broaden the line and integrate the values to give more reliable data, fig 3.5.

Figure 3.5: SPIP height analyzing tool measuring the height of a CNT by integrating the lines in the box drawn across the tube. Black lines are guidelines and red lines indicate the top and bottom height values for the tube.

Gwyddion [42], another AFM image analysing program was used to double check that no anomalies in the data arose from the image analysis. Gwyddion have a similar toolbox to SPIP and can also do image corrections and integrate data over broad lines. A height measurement of the same CNT as in fig 3.5 can be seen analyzed in Gwyddion in fig 3.6.

The relative zero differ between the two images but the height of the CNT is roughly the same (2.3±0.2 nm).

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Figure 3.6: Gwyddion height analyzing tool measuring the height of a CNT by integrating the lines in the broad line drawn across the tube. Black lines are guidelines and red lines indicate the top and bottom height values for the tube.

3.2.3 Scanning electron microscopy

A Scanning electron microscope (SEM) was used to try and determine the height distri- bution of the CNTs in the sample so the data gathered using the AFM could be compared to the tubes real diameter, fig 3.7.

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Figure 3.7: SEM image of the sample showing particle buildup.

Unfortunately the buildup of particles on the surface due to stray atoms in the vacuum chamber getting hit by the SEM beam and binding to the surface (visible as squares in the middle of fig 3.7) obscured the view of the tubes. One scan was enough to cause substantial amount of buildup, making it impossible to detect any CNTs.

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4 Results & Discussion

4.1 AFM-imaging & diameter measurements

AFM images of clusters of CNTs and individual tubes obtained in this study can be seen in figure 4.1.

Figure 4.1: Various images of CNT bundles and single tubes.

Tubes in figure 4.1 appear to be short and mostly straight, uncaracteristic of CVD grown tubes that generally are longer and more curly in appearance [3]. CNTs located in different areas of the sample were found to have both positive and negative height measurements in relation to the substrate, fig 4.2.

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Figure 4.2: Image of both positive height and ’negative height’ tubes with height measurement of the tubes done in SPIP. Black lines are guidelines and red lines indicate the top and bottom height values for the tube.

CNT diameters were calculated as the absolute value of their height variation in relation to the substrate, integrating the heights over broad lines to avoid anomalies created from individual pixels with extreme values. The lowest point (highest point for ’negative height’ tubes) was measured by drawing a line between the two lowest points on either side of the tube where the substrate appear to start and then drawing a line straight from the top of the tubes, as seen in fig 4.2.

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4.2 Tapping frequency

Tapping frequency measurements were done by doing a cantilever tuning to obtain the tips frequency response and picking a point slightly below the resonance peak. The corresponding amplitude given in voltage by the program was then kept constant by adjusting drive amplitude while altering the frequency between measurements.

As discussed in 2.3.3 a general advice for choosing tapping frequency is to pick a value slightly below the resonance peak. For one of the tips used (tip 1) there was 2 peaks and the phase was not 0^◦ at the top of the larger peak,fig 4.3.

Figure 4.3: Cantilever tuning profile for tip 1.

Note the phase value in the box in the lower left corner in fig 4.3. The phase in the program goes from 0 − 360^◦ so the chosen operating point (red triangle) is less than 0.7^◦ out of phase and should be slightly more to the left to be perfectly in phase. If one follows the general advice given (5% below the resonance peak) the tapping frequency chosen in fig 4.3 would be too low. The point where tapping is 0^◦ out of phase was however found

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to be an important point when measuring the dependence on tapping frequency. Data for the CNT heights as a function of the tapping frequency are shown in fig 4.4.

Figure 4.4: Measured CNT height versus frequency of oscillation relative to the point where the tapping is 0^◦ out of phase (= null aligned phase).

We see from fig 4.4 that operating on the higher frequency side of the ’null-aligned resonance point’ (positive x-values) give drastically lower values compared to operating on the lower frequency side (negative x-values).

4.3 Free oscillation amplitude

If the tapping frequency is maintained at a constant value one can think of the free oscillation amplitude as a measurement of the total kinetic energy contained in the cantilever during tapping. Measurements of CNT diameters were done by picking and maintain- ing a tapping frequency in the cantilever tuning and keeping the setpoint at the same percentage of the free oscillation amplitude while increasing the driving amplitude. This ensures that the only parameter that is changed is the voltage driving the shaker-piezo resulting in an increased tapping amplitude (the setpoint amplitude also increases since it is set as a percentage of the free oscillation amplitude and it is the percentage that is kept constant). Measured height values for CNTs as a function of the free oscillation amplitude are shown in fig 4.5.

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Figure 4.5: measured CNT height versus free oscillation amplitude of the cantilever.

The CNT heights measured with tip 1 all appear to increase up to a certain point as the amplitude is increased and then fall back down when the amplitude gets too large.

These findings were not reproducible when using another tip (2). Unfortunately the area where the initial measurements (tip 1) were done had degraded to a point were it was not possible to do measurements on the same tubes with tip 2. This makes it hard to draw any exact conclusions from the data as either the findings from tip 1 or 2 could be deviating from a more general trend such as the one seen for the tapping frequency, fig 4.4. The only conclusion that can be drawn from fig 4.5 is that measured heights of individual tubes can vary greatly depending on the chosen free oscillation amplitude.

Using amplitudes larger than those in fig 4.5 resulted in blurry images such that no height data could be obtained from them. This suggests that too high oscillation amplitudes negatively affect the image clarity of CNTs.

There was an interesting finding made during the measurements of the CNT bundle (orange data-series in fig 4.5). The bundles that appeared to have negative height in the low amplitude topological scans completely disappeared in the topological scan when operating at large amplitudes, fig 4.6.

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Figure 4.6: Top left: phase image at low amplitude. Top right: topological image at low amplitude. Bottom left: phase image at high amplitude. Bottom right:

topological image at high amplitude.

There are two things to note from fig 4.6. First of all the phase image changes consid- erably between the low and high amplitude scans. In the large amplitude scan it becomes possible to see that these are not individual tubes but rather bundles of tubes aligned in stripes/bands and the tubes change from representing a negative phase shift (dark color) to representing a positive phase shift (light color) in comparison to the substrate. The second thing to note is that the position of the CNT bundles are clearly visible in the topological image for the low amplitude scan, but they appear to blend into the substrate and disappear for the high amplitude scan.

4.4 Setpoint

The setpoint parameter in tapping mode is a measurement of how much lower the tapping amplitude is when the tip is engaged to the surface compared to the amplitude when the tip is oscillating freely above the sample. Another way of viewing this is as a measurement of how much energy the cantilever transfer to the sample compared to the total energy stored in the cantilever. A smaller setpoint allows the system to decrease the amplitude more, resulting in more of the energy being transferred between tip and sample.

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The height profile for a few CNTs was measured while varying the setpoint between roughly 20-95 % of the free oscillation amplitude. These measurements were done for both a frequency far below the resonance and for a frequency at the resonance peak on some of the tubes. The resulting heights as a function of the setpoint are shown in fig 4.7.

Figure 4.7: Measured CNT height plotted against the chosen setpoint (%) with linear regression fits for each data series.

The setpoint does not appear to have any noticeable effect on the measured heights of the CNTs, even if the tip is allowed to transfer most of its energy onto the tubes. Some of the linear regression fits (y = kx + m) have positive k values while others have negative k values and the linear regression fit with the largest deviation from no-dependence was k = 0.0048 obtained for CNT 4 measured with tip 2 and a low tapping frequency. The trend of smaller measured heights for higher operating frequencies was observed here as well and appears to not be related to the chosen setpoint.

A point spectroscopy curve on both the CNTs and the Si-substrate studied in this project can be seen in figure 4.8.

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Figure 4.8: MATLAB reconstruction of the point spectroscopy data from engaging the tip on both a CNT and the Si-substrate, overlaid on each other. The chosen tapping amplitude setpoint was 5.5 V indicated by the black line intersecting the amplitude curves at Z_position= 0.

The tapping appears to be similar on both the CNT and Si-substrate and the tapping appears to be inelastic, indicated by a phase shift of almost 90^◦ (= completely out of phase) followed by an initially slow recovery of the tapping phase (nonlinear recovery), as discussed in section 2.3.3. As we can see in figure 4.8 the sudden phase drop around Z_position = −0.003 µm happens slightly earlier when the tip is engaging on the CNT compared to when engaging the Si-substrate but they are otherwise very similar. This indicates that the energy-dissipation from cantilever and tip onto the sample is similar regardless if there are tubes present or not and explains why measured CNT heights remain consistent for different setpoints.

The sudden phase shift matches up with the sudden amplitude shift between the CNT and Si-substrate curves. This indicates that while the CNT and Si-substrate affect the oscillation of the cantilever similarly, there is a slight difference, and the cantilever starts to feel the forces slightly earlier when engaging the CNT compared to when engaging the Si-substrate. As explained in section 2.3.3 this first results in the resonance peak shifting

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to lower frequencies when the attractive forces are felt which causes the amplitude to increase and later when the repulsive forces are felt the amplitude decreases. The slightly higher maximum of the tapping amplitude on the Si-substrate compared to the CNT could either be caused by a slight difference in the magnitude of the attractive forces from the Si compared to the CNT acting on the tip, or it could be due to noise in the data. Zooming in on the tapping amplitude curves at Z_position = 0 reveals that there is a small amount of noise in the data, fig 4.9.

Figure 4.9: Zoom in on the tapping amplitude curves from figure 4.8 at Z_position = 0.

We can see that there is a slight variation in the tapping amplitude on the CNT and Si- substrate at Z_position = 0. This point should always align with the setpoint amplitude and thus, independent on what material the tip is being engaged on, the tapping amplitude curve should always go through the setpoint amplitude at Z_position = 0. The fact that neither curve is exactly at the setpoint amplitude (5.5 V) at Z_position = 0 tells us that there is noise in the data. The curves are however very close to the setpoint (±0.05 V) and the tapping amplitude can vary between 0 − 10 V in the AFM software so a variation of ±0.05 V can be considered an acceptable amount of noise (<5%).

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5 Conclusion

This thesis show that it is important to choose appropriate settings when using AFM to analyze CNTs. Diameter variations close to double in size were obtained by adjusting the settings and even tubes that appeared to have ’negative’ height were observed.

Tapping frequency appears to be the most impactful setting and can give resulting CNT diameters that appear almost twice as large depending on which tapping frequency is chosen. One should consider the shape of the cantilever tuning curves when deciding on a tapping frequency and chose a frequency lower than the point where tapping is 0^◦ out of phase. Operating at frequencies lower than this point all give similar results (larger diameters with low variation) so it is advisable to chose an operating frequency that is clearly below this point such that there is a low risk of entering the dangerous zone due to the resonance frequency shift that occurs during tapping.

Tubes appeared to be smaller when using very low oscillation amplitudes (<10 nm) and appeared larger when increasing the amplitude to 20-40 nm to finally decrease in size for amplitudes <70 nm. This result was not reproducible when doing similar measurements with another tip and the only thing that can be said is that improper free oscillation amplitudes can cause large variation in measured CNT diameters but no single trend was found. There was however an interesting finding that for large amplitudes (<50) it was possible to make bundles of CNTs almost completely blend in with the substrate in topological scans while they were clearly visible in the phase scans. The advice given is to go for as small amplitudes as possible that still give detailed images. This is to reduce risk of damage to both tip and sample since a higher amplitude have more stored energy in each oscillation.

Changing the setpoint does not appear to affect the measured diameter of the CNTs which is explained largely by looking at the phase and amplitude curves during point spectroscopy measurements on both CNT and the Si-substrate and noting that the energy dissipation appears to be similar on both CNT and Si-substrate. It is recommended to do point spectroscopy on both the particles one wish to analyze and the substrate they are placed on to ensure that the tip interacts similarly on both. If this is not the case it is hard to say if one can assume that setpoint still have little to no impact on the resulting measurements.

Because there are such large variations in the measured CNT diameters for both tapping amplitude and frequency it becomes impossible to determine the real CNT diameters for certain. If one wish to do this, other methods such as TEM or SEM are recommended alternatives until a better method is developed for AFM.

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6 Outlook

More work is needed to accurately determine how the free oscillation amplitude affects the measurements in AFM tapping mode. Another possible study would be to reproduce this kind of study with different particles and/or substrates. Finding samples where the particles behave drastically different than the substrate and especially see if the no-dependence of the setpoint parameter remains the same. Analysing CNTs that are partially laying on a substrate and partially suspended in the air could further make for an interesting variation of this study. This exact study could be reproduced in addition to determine the real CNT diameters by some other method and would shine even more light on how AFM settings affects the obtained data.

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microscopy settings for measuring the diameter of carbon nanotubes

Importance of atomic force