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\title[2D Nanoparticle sample Atomic Force Microscopy measurements]{2D
Nanoparticle sample Atomic Force Microscopy measurements}

% author setup
\author[1]{\fnm{Camille} \sur{Beard}}\author[1]{\fnm{Adam} \sur{Bowen}}\author[1]{\fnm{Jose} \sur{Chavez}}
% affil setup
\affil[1]{\orgdiv{Physics and Astronomy}, \orgname{California State
University Long Beach}}

% abstract 


% keywords

\begin{document}
\maketitle


\subsection{Abstract}\label{abstract}

\indent The Park Systems atomic force microscope was used to obtain
images of Au particles, as well as a platinum Ditelluride (\(PtTe_{2}\))
flake. A height-height correlation function was implemented to analyze
the topography of Au particles. The image of the \(PtTe_{2}\) flake was
further analyzed in order to obtain any well-defined angles of the
two-dimensional material flake. It has been determined from the
height-height correlation function that the roughness (\(\sigma\)) or
the average effective grain size to be 52.11 nm with an uncertainty of
1.235 nm. The coherence length, \(\xi\), was found to be 835.3 nm with
an error of 0.37 nm. The Hurst(H) value is 0.9204. Starting from the top
and going clockwise, the angles of the \(PeTe_{2}\) flake we could
determine were 123, 96, 244, 159, and 124 degrees.

\subsection{Introduction}\label{introduction}

\indent Atomic Force Microscopy (AFM) is a third wave surface scanning
method used to measure properties such as friction, electrical forces,
capacitance, magnetic forces, conductivity, viscoelasticity, surface
potential, and resistance ({``Atomic {Force} {Microscopy} {\textbar}
{Nanoscience} {Instruments}''} n.d.) at nanometer scale. It uses the Van
der Waals force to analyze material properties of nanomaterials. One of
the advantages the AFM has over Scanning Electron Microscopy (SEM) is
that it can measure non-conductive thin films. This gives us the ability
to measure biological and soft matter materials. SEM utilizes a beam of
electrons to detect the electromagnetic interactions of the sample. The
information from these interactions is used to create an image of the
sample. However, since there is no direct contact between the device and
the sample, the resolution can be limited. In an AFM, we have a
cantilever that can directly touch the sample when measuring materials
in static mode. Although direct contact is not necessary and we can set
the measurements to be done in dynamic mode where the cantilever is near
but not touching the sample(Garcı́a and Pérez 2002). Due to the proximity
between the cantilever and sample, all kinds of interatomic and
intermolecular forces can be detected. Some of these include magnetic
forces, electrostatic forces, mechanical contact forces, and Van der
Waals forces. The Lennard Jones potential is used to model weak Van der
Waals bonds ({``Van {Der} {Waals} {Force} - an Overview {\textbar}
{ScienceDirect} {Topics}''} n.d.) in a material:

\$\$V(r) = 4\textbackslash epsilon{[}(
\textbackslash frac\{\textbackslash sigma\}\{r\})\^{}\{12\} -(
\textbackslash frac\{\textbackslash sigma\}\{r\})\^{}\{6\} {]}\$\$

We observe that this potential is a suitable model for short range
interactions. This is a significant aspect of the system that AFM takes
into account.

There are two different modes that the AFM can operate on. They are
static mode and dynamic mode. In static mode, the cantilever comes into
contact with the sample, whereas in dynamic mode, the cantilever is
allowed to oscillate in order to obtain the attractive and repulsive
forces. For the purposes of this lab, the static mode was employed in
order to obtain images for our samples.

The samples analyzed in this lab were gold (Au) particles and platinum
ditelluride \(PtTe_{2}\) flakes. In general, using AFM is a good way to
determine the properties of materials. Using AFM imaging for Au
particles allows us to obtain clear topographical characteristics of the
material. This can shed light on the properties of these materials on
the microscale. After AFM imaging is applied on the \(PtTe_{2}\) flake,
we can determine the angles of two-dimensional material. Knowing
properties about both of these materials can come in handy in the
development of new technologies.

\subsection{Experiment}\label{experiment}

\indent The first part of any experiment is to read the necessary
manuals for all equipment that will be used. In the case of the Park
AFM, we read sections of the Park AFM and the SmartScan software
manuals. The first part is to turn on the computer, the control
elements, and the activation table. With the instruments all on, the
software was then turned on and given roughly 10 to 15 seconds for the
program to reset. We ran a frequency sweep to ensure that all equipment
was working within the acceptable range. After our scan we saw the Q
factor at 9497 and the resolution frequency at 333.2kHz. We then logged
that information as well as our names into the Park AFM logbook to leave
a trail that all equipment is in working shape. We were now ready to
work with the physical equipment. We need to make sure that the
cantilever is both attached and intact. We unlocked the focal optics
wheel by pushing a small lever back, turned the wheel until the
cantilever was visible (noting it was visibly undamaged), then pulled
the lever back gently until there was a slight resistance indicating the
wheel was locked and can be let go of. The data is recorded by a
quadrant photodiode (QPD) that receives the information via an infrared
laser that is shone at an angle onto the cantilever and reflected back
into the position sensing QPD. On the Smartscan software there is a
position section that once clicked, has the values of the lateral,
horizontal, and intensity values displaced. By moving the knobs on the
XY stage, the beam was positioned on the cantilever, and the horizontal
and lateral values were minimized with a vertical value of -0.3V and
horizontal value of +0.14V. The intensity would rise and fall as the
beam moved, but with minimal displacement, the intensity sum was a value
of 2.97V which was close enough to the desired 3V value we were working
towards. The next step is a visual quadrantrant check. The beam is shown
in a square area depicted by a disk. If the beam is at the optimal spot,
the disk is green, but if the beam needs more adjusting, the disk will
appear as red.

Once the beam is centered and green and the intensity close to 3V, we
began to prep the sample. To keep a sanitary loading station, gloves
were put on, placed a kimwipe on the table and pulled a pair of tweezers
to handle the sample. To load the sample on the sample mount, we snipped
a small piece of double sided tape,placed it on the mount, revealed the
other side of the adhesive and lightly touched the adhesive a few times.
This was to remove some adhesive to make the sample removal easier so no
risk of damaging the adhesive. The sample was placed on the tape making
sure that a corner is off the adhesive for a removal ledge. The stage
and the mount are both magnetized, so when placing the mount on the
stage, it was important to load the mounted sample by bringing it slowly
from the side then raising it just enough to place on the magnet. This
caution was exercised so the sample mounted stage didn't hit the stage
and damage the sample. Our first experiment was to examine a flake of
gold. The specific sample used was T020200122Si16. As an optional step,
we chose to readjust the focal optics so the camera could see the sample
in focus rather than the cantilever, and saved the image.

\begin{figure}

\centering{

\includegraphics{Cantilever.png}

}

\caption{\label{fig-AuFocus}Image of the gold (Au) sample
T020200122Si16. The image is focused on the sample of gold, with the
slightly out of focus cantilever in the field of view as well. The
purple light seen on the arm of the cantilever is from the ultraviolet
laser that is shining onto the cantilever, reflecting back, and hitting
the quadrant photodiode (QPD) positioning sensor. While normally
invisible, the wavelength of the UV light used is bordering the visible
and therefore, some light is able to be seen. At the top left corner,
there is a small window showing the quadrant photodiode sensor reading
with an intensity readout below. The QPD reading is 2.96V which is very
close to our target voltage of 3.00V, but within a reasonable
deviation.}

\end{figure}%

With the sample loaded, we ran the image function on the Park AFM, and
we had our first scan. We set the scan window to be 50μm by 50μm, the
resolution to be 256 pixels and ran the Image function. We saved a
snapshot of the topology the scan yielded of the sample under the file
name 2024913\_PHYS545\_JCCBAB\_AFM\_T020200122Si16. The folder made to
hold the data was named 2024913\_PHYS545\_JCCBAB\_Au depicting the date,
the class, the initials of the lab members, and the sample name for the
file as well as element for the folder. The scan took place and the
cantilever was automatically moved down to the surface of the sample.
The scan revealed the surface as well as any debris. If any debris was
detected, the best course of action would be to move the scan parameters
to avoid this, which is exactly what we did as there was a small piece
of debris detected under our initial sweep. We ran a few scans to
optimize the parameters and saved all data.

With all the data collected, saved, properly named, and stored, we began
the clean up procedure. The first part is to unlock the focal optics and
turn the wheel to move the optic to the top, then relock. As with all
types of AFM's, taking care to not break the cantilever tip is
paramount. There is an automatic lift button on the software we clicked
and let the cantilever lift. Then the end button was clicked which
lifted the cantilever up a substantial amount. Unfortunately, the end
button does not always lift the cantilever up all the way, so the end
button must be clicked up to 4 or 5 times to have the tip a safe
distance raised. With the tip raised to a safe distance, the sample
loaded mount was able to be carefully pulled to the side and down to
remove just as carefully as it was initially placed. The sample loaded
mount is to be placed on a clean Kimwipe, and the sample is to be
removed from the mount using tweezers and placed back in its storage
box. The double sided adhesive can be thrown away, and the mount placed
back in the Park AFM toolbox. The software is then shut down, taking
roughly 10 seconds or so. When the software is fully closed, the AFM
controller, computer, and activation time are turned off. The sample is
returned to where it belongs and the toolbox was placed back under the
table on top of the computer. With everything shut down and put away,
the last step of the clean up procedure is to sign the logbook with the
state of the cantilever being intact.

Our next experiment was with a sample of Platinum Ditelluride. We turned
on the computer, the activation table, and the AFM controller. The
software was turned on and the frequency sweep was done. We chose one of
four available options of Platinum Ditelluride samples to work with and
prepped gathered the materials for mounting.

\begin{figure}

\centering{

\includegraphics{SampleChoicePt2Te2.jpg}

}

\caption{\label{fig-samp_choice}Platinum Ditelluride (\(PtTe_2\))
samples (SL20240916) offered by Dr Gredig for our second example. The
sample used was the one in the lower left hand corner as pointed out by
the pair of tweezers pointing to the one used.}

\end{figure}%

The values were logged into the log book with our names and the new
date. The new sample we were using was put down as well. The sample was
mounted with the double sided adhesive and carefully placed on the
stage. The focal optics were moved into place to see the cantilever
intact and the sample was prepped. We made a new folder
20240920\_PHYS545\_JCCBAB\_SL20240916 for the new data from the day. We
took a snapshot of the sample as seen by the camera and named the file
20240920\_PHYS545\_JCCBAB\_SL20240916\_Sample\_Position. We ran the
position function in the SmartScan software to position the cantilever
on the sample, then ran the Image function. The scan of the first image
was taken at 5μm by 5μm and was saved under the file name
20240920\_PHYS545\_JCCBAB\_SL20240916\_5um. Unfortunately there was no
flake detected at this spot, and another scan was run at 20μm by 20μm
with a lower resolution of 128 pixels to speed up scan time. With a
flake detected, the scan parameters were adjusted back down to 5μm by
5μm around the flake and another scan was taken named
20240920\_PHYS545\_JCCBAB\_SL20240916\_5um\_128x. Happier with these
results, the resolution was increased back to 256 pixels and the data
was saved under 20240920\_PHYS545\_JCCBAB\_SL20240916\_5um\_256px.

\begin{figure}

\centering{

\includegraphics[width=4.80208in,height=\textheight]{Pt.png}

}

\caption{\label{fig-Pt_colored}Image of Platinum Ditelluride sample
SL20240916 with file name
20240920\_PHYS545\_JCCBAB\_SL20240916\_5um\_256px. Image is taken with
the parameters: pixel resolution of 256, screen width \(5\mu m\) by
\(5\mu m\)}

\end{figure}%

With all data saved, the clean up procedure was begun. The focal optics
were raised to the top, the cantilever was lifted 50μm at a time by
pressing the lift button followed by the end button several times, and
the sample was removed. The sample was carefully removed off of the
sample mount and placed back into its proper storage container, the
adhesive was thrown away, and the sample mount was put back in the AFM
toolbox with the tweezers used to remove the sample. The software is
shut down next, followed by turning off the activation table, AFM
controller and the computer. With everything shut down, turned off, and
put away, the log book is signed out with the status of the cantilever
and the experiment is done.

\subsection{Results and Analysis}\label{results-and-analysis}

We used the nanoAFM and ggplot2 packages on R to collect and plot the
Park AFM data. The nanoAFM package to open the Park AFM data. Using a
height-height correlation function we found the average effective grain
size of Au particles and a single \(PtTe_2\) flake. The correlation
function finds values of roughness (\(\sigma\)), coherence length
(\(\xi\)), and the Hurst value (H) which is used to measure the
persistance of an effective grain. We also measured the angles of
defined edges of a \(PtTe_{2}\) projection using a protractor. The HHCF
is defined as:

\(g(r) = \langle \left[ h(\vec{x}) - h(\vec{x} - \vec{r}) \right]^2\rangle\)

When r is the displacement vector. The height correlation fit we used in
the data analysis was:

\(g(r) = 2 \sigma^2[ 1 - e^{-( \frac{r}{\xi})^{2/H}}]\)

\(\sigma\) is roughness, \(\xi\) is coherence length, and H is the Hursh
value.

\begin{figure}

\centering{

\includegraphics{Au_top.png}

}

\caption{\label{fig-top_au}Topological Image and line profile of Au
sample
20240913\_PHYS545\_JCCBAB\_AFM\_TD20200122Si16\_20240913\_5.0x5.0+Topography\_Backward\_004
measuring the particle height in nm in the x (5 um) and y (5 um) plane.
The profile has a peak greater that 30 nm. The HHCF fit is in red.}

\end{figure}%

Using the nanoAfm package in R we found the height of the gold particles
using the profile function. We saw that the gold particles have a
roughly uniform shape and are not compact. The gold particle heights
hovered around 20 to 30 nm. The difference in heights could be a result
of deformation of gold particles after being transferred to the
substrate or deformations of the Silicon substrate.

\begin{figure}

\centering{

\includegraphics{graph1.png}

}

\caption{\label{fig-g}Height-height correlation function (HHCF) of Au
Sample
20240913\_PHYS545\_JCCBAB\_AFM\_TD20200122Si16\_20240913\_5.0x5.0+Topography\_Backward\_004
measuring the average effective grain size of Au particles.}

\end{figure}%

Using the nanoAFM package the HHCF found the roughness (\(\sigma\)) of
the effective grain size to be 7.294 nm with an uncertainty of 0.009 nm
which is on the order of pm. The coherence length, \(\xi\), to be 89.45
nm with an error of 1.93 nm. The H value is 1.123. These values could be
because the surface isn't homogeneous so H isn't an accurate value for
gauging roughness.

\begin{figure}

\centering{

\includegraphics{graph2.png}

}

\caption{\label{fig-gr1}Height-height correlation function of
\(PtTe_{2}\) sample
20240920\_PHYS\_JCCBAB\_SL20240916\_5um\_256px\_20240920\_5.0x5.0+Topography\_Forward\_005.
The HHCF fit is in red.}

\end{figure}%

The HHCF found the roughness (\(\sigma\)) of the average effective grain
to be 52.11 nm with an uncertainty of 1.235 nm. The \(\xi\) to be 835.3
nm with an error of 0.37 nm. The H value is 0.9204. This could be
because the surface isn't even because we are looking at one flake next
to a flat surface so we can determine that the roughness value isn't an
accurate fit.

\begin{figure}

\begin{minipage}{0.50\linewidth}

\includegraphics[width=9.26042in,height=\textheight]{Pt_top.png}

\subcaption{\label{}a) \(PtTe_2\) image saved through SmartScan}
\end{minipage}%
%
\begin{minipage}{0.50\linewidth}

\includegraphics[width=2.4375in,height=\textheight]{angles.jpg}

\subcaption{\label{}b) \(PtTe_2\) image projected into a whiteboard with
angles drawn and labeled}
\end{minipage}%

\caption{\label{fig-pt}We determined the angles of the \(PtTe_2\) flake
using a protractor on the image projected onto a whiteboard. Not all the
corners of the flake are clearly defined, so we measured the ones we
deemed appropriate for measurement. The angles of the flake we could
determine were 123, 96, 244, 159, and 124 degrees going clockwise
starting at the top. These results are what we would expect from a
two-dimensional material. Whereas with dirt particles, we would expect
there to be no well-defined angles or shape. These angles are
highlighted in image b.}

\end{figure}%

Rather than using software, the image was projected and a protractor was
utilized to determine the well-defined angles of the two-dimensional
flake. In our case, our uncertainty is about 1 degree, as that is what
the smallest increment in the projector we used was. This is about what
we'd expect from a two-dimensional material. Though not all of the sides
of the flake have well-defined angles, we do expect at least some
because platinum ditelluride is considered a two-dimensional molecule,
thus when cutting up the lattice, these well-defined angles are expected
to emerge.

\subsection{Conclusion}\label{conclusion}

\indent AFM is a useful way to determine the properties of different
materials on the microscale. This form of imaging has many advantages
over other forms of microscopy, such as SEM because it has the ability
to image samples that are non-conductive. The physical contact between
the cantilever and the sample is very advantageous because it allows us
to accurately reconstruct images from forces other than the
electromagnetic forces. In this experiment, we were able to analyze the
topography of the particles using the height-height correlation and the
shape of the two-dimensional \(PtTe_{2}\) flake by measuring the angles.
Obtaining accurate topographical representations of such materials at
such a small scale provides insights for how it may be implemented among
other materials. Knowledge about the properties of these materials can
help us explore different possibilities for the fabrication of new
technologies.

\subsection{Acknowledgments}\label{acknowledgments}

\indent This project was assisted in part by Dr.~Thomas Gredig and
Filipe with their assistance safely using the PARK AFM. I would also
like to thank the people who took the time to make the samples provided
by Dr.~Gredig that were used in our experiments.

\phantomsection\label{refs}
\begin{CSLReferences}{1}{0}
\bibitem[\citeproctext]{ref-noauthor_atomic_nodate}
{``Atomic {Force} {Microscopy} {\textbar} {Nanoscience}
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\url{https://www.nanoscience.com/techniques/atomic-force-microscopy/}.

\bibitem[\citeproctext]{ref-garcia_dynamic_2002}
Garcı́a, Ricardo, and Rubén Pérez. 2002. {``Dynamic Atomic Force
Microscopy Methods.''} \emph{Surface Science Reports} 47 (6): 197--301.
\url{https://doi.org/10.1016/S0167-5729(02)00077-8}.

\bibitem[\citeproctext]{ref-noauthor_van_nodate}
{``Van {Der} {Waals} {Force} - an Overview {\textbar} {ScienceDirect}
{Topics}.''} n.d. Accessed October 4, 2024.
\url{https://www.sciencedirect.com/topics/pharmacology-toxicology-and-pharmaceutical-science/van-der-waals-force}.

\end{CSLReferences}




\end{document}
