chap02.tex

% !TeX spellcheck = <en-US>
%\chapter{Mask Aligner}

\section{Electron beam evaporation}
Electron beam evaporation, also known as \textbf{E}lectron-\textbf{b}eam \textbf{P}hysical \textbf{V}apor \textbf{D}eposition (EBPVD) is a \textbf{P}hysical \textbf{V}apor \textbf{D}eposition (PVD) technique that in \textbf{U}ltra \textbf{H}igh \textbf{V}acuum (UHV) deposits material onto a substrates surface.

\begin{figure}[H]
	\centering
	\includegraphics[width=0.5\linewidth]{img/EBeamDep.pdf}
	\caption{Schematic of a general electron beam evaporation chamber. The B-field is used to focus the beam onto the source. The shutter can interrupt the beam directed to the sample. The funnel is used to focus the vapor beam. }
	\label{fig:e-beam_evap}
\end{figure}

The setup of an electron beam evaporator is shown in Figure \ref{fig:e-beam_evap}. The source material is placed inside a tungsten crucible as pellets of ultrapure ($>99$ \%) material.
To heat the source material, it is bombarded with a high-voltage electron beam ($\mathcal{O}$($1$~kV)), which is emitted by either an electron gun or a filament. This beam usually is focused using magnetic fields to hit the source material. Energy transfer heats the hit atoms and eventually leads to the evaporation according to its vapor pressure.\\

%The crucible is also heated during the evaporation process, in order to prevent it from being damaged, a material with a high melting point is chosen. Tungsten with a melting point of 3695 K ~\cite{Tungsten_melt} is usually chosen. 
%Additionally, the crucible usually has to be water cooled to avoid outgassing during the evaporation process.
%The penetration depth of electron with ($<5$ kV) is less than 0.4 {\textmu}m (estimated using CASINO Monte Carlo software)~\cite{CASINO} so the heating occurs only very near to the source material's surface. This allows for less energy loss and more controlled evaporation as the crucible and the rest of the system is not heated by the electron beam directly, but only by the radiant heat emitted by the source material.\\

When the material's vapor pressure exceeds the surrounding environments pressure, a vapor forms. The sample is kept at a temperature much colder than the source material's temperature, due to this the material beam will condense on the substrate's surface forming a thin film. To regulate the deposition process, a shutter is employed, allowing for controlled release of the material. \\

In order to ensure the material beam reaches the sample in a direct path, the mean free path (MFP) of a traveling particle has to be larger than the distance to the sample's surface. For this reason, high vacuum (HV) (MFP of $10$ cm to $1$ km) or ultra-high vacuum conditions (UHV) (MFP of $1$ km to $10^5$ km) are needed.

The deposition rate of the evaporator can be measured using a molecular flux monitor. The deposition rate of a material is described by the Hertz-Knudsen equation:

\begin{equation}
	\frac{dN}{A dt} = \frac{\alpha (p_\text{e} - p)}{\sqrt{2 \pi m k_\text{B} T}}
	\label{eq:hertz_knudsen}
\end{equation}

Where $N$ is the number of gas molecules deposited, $A$ is the surface area, $t$ is time, $\alpha$ is the sticking coefficient, $p$ is the gas pressure of the impinging gas, $m$ is the mass of a single particle, $k_\text{B}$ is the Boltzmann constant, $p_\text{e}$ is the vapor pressure of the material at the sample temperature and $T$ is the temperature~\cite{knudsen}. The sticking parameter of a material can be looked up in literature. With this, the total deposition rate can then be estimated. In practice since the pressure of the impinging gas is difficult to determine this is difficult to estimate, since it requires precise knowledge on the temperature of the source, that is typically not measured. Instead, usually calibration evaporations are performed for different heating powers and different times to determine the deposition rate for a given setup.

Comparing e-beam evaporation with so-called sputtering of material onto a surface, it offers more controlled deposition~\cite{Vapor_depo_princ}. In sputtering, high energy particles are produced hitting the sample, which can lead to local roughening~\cite{sputter_damage}.
In contrast to thermal evaporation, where the source is typically heated by Joule heating from a resistive current, higher temperatures are available with e-beam evaporation. This is required, e.g.\ for \ce{Nb}~\cite{tungsten_evaporation}.

\section{Molecular beam evaporation chamber}
\begin{figure}[H]
    \centering
    \includegraphics[width=0.9\linewidth]{img/MaskAlignerChamber.pdf}
    \caption{Circuit diagram of the mask aligner and its associated vacuum
system. It consists of the mask aligner (MA) chamber, the main chamber, the
Pb evaporator and the \ce{Au} evaporator. The \ce{Au} evaporator is attached to the same vacuum system, but is unrelated to the Mask Aligner. The configuration depicted is used for
evaporation. The \textcolor{tab_green}{green} line shows the sample/mask extraction
and insertion path with the wobble stick. The black arrow shows the molecular beam
path from the \ce{Pb} evaporator. BA stands for Bayard-Alpert pressure gauge. This diagram is accurate for the setup on 01.08.24.}
    \label{fig:mask_aligner_chamber}
\end{figure}

The Mask Aligner vacuum system (Figure \ref{fig:mask_aligner_chamber}) consists of two areas that can be separated with vacuum gate valves~\cite{Mask_Aligner}. The \textbf{M}ain \textbf{C}hamber (MC) with the Mask Aligner (MA) chamber, and the \ce{Pb} evaporator. The second one is the \textbf{L}oad \textbf{L}ock (LL), a vacuum suitcase that is used to insert new samples and masks into the system. The system is pumped to UHV pressures by a turbomolecular pump and a prepump (rotary vane). 
Between prepump and turbo molecular pump is a pressure sensor to determine if the prepump is providing suitable backing pressure. A valve to a nitrogen bottle allows the system to be vented with an inert gas to avoid contamination.\\
The main chamber is equipped with an Ion Getter Pump, such that the Load Lock can be separated from the turbomolecular pump, without loss of UHV conditions. The pumping system is separated via $2$ \textbf{A}ll \textbf{M}etal \textbf{C}orner \textbf{V}alves (AMCV) (Fig. \ref{fig:mask_aligner_chamber}). Additionally, the Load Lock and the main chamber are separated by a Gate Valve. In order to detect leaks or contaminants in the vacuum system, a mass spectrometer is attached to the main chamber. \\
The Load Lock is equipped with a small ion getter pump, that runs on its own, allowing it to keep UHV conditions, even while separated from the main pump loop. A garage with spaces for up to $14$ samples ($10$: $12\times12$ cm$^2$, $4$: Omicron size) is part of the Load lock. Masks occupy $2$ sample slots due to additional height. For insertion and removal of masks and sample into the Mask Aligner, a wobble stick is attached to the Load lock chamber. The path of the wobble stick to the Mask Aligner is marked \textcolor{tab_green}{green} in Figure \ref{fig:mask_aligner_chamber}. \\
Another device, unrelated to this thesis, a gold evaporator, is connected to the vacuum system. It is not further discussed in this thesis. \\

\subsection{Lead evaporator}
The electron beam evaporator used for the lead evaporation in the mask aligner chamber was built by Florian Forster in $2009$~\cite{florian_forster}. It is shown schematically in Figure \ref{fig:ma_evap}. The evaporator uses a filament placed near the crucible to bombard the crucible with electrons. To accomplish this, a high voltage (up to $1$ kV) is applied between filament and crucible to accelerate electrons to the crucible. In addition, the system is heated by radiative heat from the filament current. The resulting heating power is linearly dependent on the voltage applied and quadratic in the current. This heat is used to degas the evaporator and to prevent contaminants from settling on the filament, when no evaporation is taking place. The filament and crucible are surrounded by a copper cylinder, that functions as a heat sink. The heat sink is water cooled to prevent outgassing of the surrounding due to heating by the filament or crucible. To control the temperature of the \ce{Cu} cylinder a thermal sensor is placed on the copper cylinder. \\

\begin{figure}[H]
    \centering
    \includegraphics[width=0.8\linewidth]{img/MA/Evaporator.pdf}
    \caption{Solidworks diagram of the evaporator used on the Mask Aligner.}
    \label{fig:ma_evap}
\end{figure}

In order to control the molecular flux, one can change the current applied to the filament or the voltage accelerating the electrons. Additionally, the crucible can be shifted on the z-axis closer to or further away from the filament. This method of temperature control is the least reliable and was not used in this thesis. In order to determine the flux current of $\text{Pb}^+$ ions leaving the crucible, it is measured by a flux monitor positioned at the top of the evaporator. Above the flux monitor is a shutter which can be used to open the molecular flux to the MA chamber. \\

\begin{figure}[H]
    \centering
	\begin{subfigure}{0.42\textwidth}
    \includegraphics[width=\linewidth]{img/MA/NomenclatureMaskAlignerFront.pdf}
    \caption{}
	\label{fig:mask_aligner_nomenclature_motors}
	\end{subfigure}
	\begin{subfigure}{0.42\textwidth}
   
\includegraphics[width=\linewidth]{img/MA/NomenclatureMaskAlignerCrossSec.pdf}
    \caption{}
	\label{fig:mask_aligner_nomenclature_components}
	\end{subfigure}
	\caption{(\subref{fig:mask_aligner_nomenclature_motors}) the nomenclature for the motors of Mask Aligner. (\subref{fig:mask_aligner_nomenclature_components}) the components of the Mask Aligner  \textbf{A} carrying frame \textbf{B} piezo stack, \textbf{C} stoppers, \textbf{D} sliding rail for x-movement, \textbf{E} sample stage, \textbf{F} sample \textbf{G}
sample holder, \textbf{H} mask frame, \textbf{I} mask stage, \textbf{J} mask, \textbf{K} mask shuttle,
\textbf{L} neodymium magnet, \textbf{M} \ce{Al2O3} plate, \textbf{N} \ce{CuBe}
spring, \textbf{O} piezo motor front plate, \textbf{P} sapphire prism,
\textbf{Q} lower body. In \textcolor{tab_red}{red} the molecular
beam path to the mask is displayed.}
    \label{fig:mask_aligner_nomenclature}
\end{figure}

The Mask Aligner can be separated into 3 sections:
The upper sample module (Fig. \ref{fig:mask_aligner_nomenclature_components}, A-G), the central mask module (Fig. \ref{fig:mask_aligner_nomenclature_components}, I-K) and the lower motor module (Fig. \ref{fig:mask_aligner_nomenclature_components}, L-Q). \\
The sample module carries the sample and moves of the sample along the x direction. It contains a sliding rail (Fig. \ref{fig:mask_aligner_nomenclature_components} D) along which the sample stage (Fig. \ref{fig:mask_aligner_nomenclature_components}, E) can be moved. The sample holder is fixed with spring tension inside the sample stage (Fig. \ref{fig:mask_aligner_nomenclature_components}, G). It can be exchanged in-situ.  \\

The mask module consists of the mask frame (Fig. \ref{fig:mask_aligner_nomenclature_components}, H), which holds the mask shuttle (Fig. \ref{fig:mask_aligner_nomenclature_components}, K). It also contacts the capacitance sensors on the mask using \ce{CuBe} leaf springs. The contacts are connected to shielded coaxial cables running to the vacuum feedthroughs. The shielding is ground to the Mask Aligner body (Fig. \ref{fig:mask_aligner_nomenclature_components}, Q). \\

The motor module consists of three piezo motors. They move the mask along the z axis via three different pivot points. They are labeled Z1, Z2 and Z3 (Figure \ref{fig:mask_aligner_nomenclature_motors}). Each motor consists of a sapphire prism (Fig. \ref{fig:mask_aligner_nomenclature_components}, P) that is clamped by $6$ piezo stacks made up of $4$ piezo plates ($\approx 0.4$ nF) each. Four of the stacks are glued directly to the Mask Aligner body. The last two are attached to a metal plate (Fig. \ref{fig:mask_aligner_nomenclature_components}, O). It is pressed against the sapphire prism via a \ce{CuBe} leaf spring (Fig. \ref{fig:mask_aligner_nomenclature_components}, N). The tension of the \ce{CuBe} spring can be adjusted with a screw mounted on it. This adjustment is critical for the reliable operation of the piezo motor. On top of the sapphire prism, an \ce{Al2O3} plate (Fig. \ref{fig:mask_aligner_nomenclature_components}, M) is attached. It has a small groove in the center, where a neodymium magnet (Fig. \ref{fig:mask_aligner_nomenclature_components}, L) is located. It connects the motor to the mask frame, where a similar \ce{Al2O3} plate is placed. The three pivot points created by the magnets build an equilateral triangle, with the mask in the center. When only one motor moves up, the mask frame is tilted on the axis defined by the other two motors pivot points and the side of the mask moves closer to the sample. With the three motors arranged in a triangle arbitrary angles can be realized. Since the motor step size is $\approx 70$ nm the angular precision is approximately $\tan^{-1}(\frac{70 \text{ nm}}{23 \text{ mm}}) \approx 1.74 \times 10^{-4}$ degrees. \\
The direction is specified by mathematical sign, where $-$ specifies the approach direction, while $+$ specifies retract (Fig. \ref{fig:mask_aligner_nomenclature_motors}).\\

\section{Slip stick principle}
The movement of the mask stage is controlled by the mask aligner, which utilizes a system consisting of three motors, each comprising six piezo stacks. Each piezo stack is made up of four piezo crystals that expand or contract when a DC voltage is applied. To facilitate the movement of the stage, a sapphire prism is clamped between the six piezo stacks. When a voltage amplitude is applied to the piezo stacks, the prism is displaced by the stacks, enabling precise movement of the stage. The operating principle of this mechanism is illustrated in Figure \ref{fig:slip_stick_diagram}. \\
The movement of the prism is achieved through a two-stage process. Initially, a slowly increasing pulse, known as the "slow flank," is applied to the piezo, causing it to move the prism. This is followed by a rapid pulse, lasting less than $1$ {\textmu}s, which contracts the piezo back to its original position. However, due to inertia, the prism remains in its new position. This rapid pulse is referred to as the "fast flank." By repeating this sequence, the prism can be moved in a controlled manner. The direction of movement is determined by the polarity of the voltage amplitude signal. The simplest waveform that can achieve this movement is a sawtooth wave, although other signal shapes that adhere to this principle can also be used.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.9\linewidth]{img/SlipStickGrafix.pdf}
    \caption{Image showing the slip-stick principle. On the right an example signal is shown.}
    \label{fig:slip_stick_diagram}
\end{figure}

\section{Shadow mask alignment}
\subsection{Motor screw configuration}

To ensure that the three motors produce similar step sizes, the friction between the prism and the piezo stacks is adjusted. This is achieved through the use of three screws, one located on each motor's leaf spring (as shown in Figure \ref{fig:screw_firmness_screw_image}). By adjusting these screws, the force applied by the front plate to the prism can be controlled, thereby influencing the friction between the prism and the piezo stacks. To determine the optimal screw firmness for achieving similar step sizes among the three motors, the relationship between screw firmness and step size must be established. This is done by measuring the time it takes for a motor to travel a known distance. This method provides a fast and precise way to determine a suitable number of rotations. An example of how screw firmness affects step size is illustrated in Figure \ref{fig:screw_firmness_plot}.
%
%In order to make sure the motors can all give similar step sizes, there are 3
%screws (see Figure \ref{fig:screw_firmness_screw_image}). One is located on each motor's leaf spring. They can control the amount of force the front plate applies to the prism and thus the friction between the prism and piezo stacks. In order to achieve similar step size for the three motors. The step size in dependence of the screw firmness has to be determined. This is done by measuring
%the time it takes for a motor to travel a known distance. For example the
%distance of one solder anchor can be used as it is known
%to be $2$ mm. This gives a measurement fast and precise enough to determine a suitable number of rotations.
%An example for how the screw firmness affects the step size can be seen in Figure \ref{fig:screw_firmness_plot}.

\begin{figure}[H]
    \centering
	\begin{subfigure}{0.375\textwidth}
	\centering
    \includegraphics[width=\linewidth]{img/MA/Calibration_screw_image.pdf}
	\caption{}
	\label{fig:screw_firmness_screw_image}
	\end{subfigure}
	\begin{subfigure}{0.55\textwidth}
    \includegraphics[width=\linewidth]{img/Plots/ScrewRot_SwappedPlate.pdf}
	\caption{}
	\label{fig:screw_firmness_plot}
	\end{subfigure}
    \caption{(\subref{fig:screw_firmness_screw_image}) frontal view of the motor Z2 marked in red is the screw used for calibration of the motors on the Mask Aligner. (\subref{fig:screw_firmness_plot}) example curves of how the screws of Z2 and Z3 affect the given motor's step size. The $0.0$ screw rotation is arbitrary. $+$ means retraction and $-$ means approach (Fig. \ref{fig:mask_aligner_nomenclature_motors}). The jumps in signal result from the \ce{CuBe} plate slipping across the winding of the screw. }
    \label{fig:screw_firmness}
\end{figure}

\subsection{Motor calibration}
For the Mask Aligner, the step sizes, of the different motors have to be measured. In the best case they all have the same step size such that the mask is approached without being tilted. The step size calibration is used to determine the distance of mask and sample, when the distance is too small to be optically determined.\\

In order to achieve this, a Bresser MicroCam II camera with a resolution of $20$ megapixel is
mounted on a frame in front of the window of the mask aligner chamber. The
frame can be positioned via 3 micrometer screws in x, y and z
direction. Additionally, the camera can be rotated around $2$ axes allowing full
control of the camera angle. \\

The step size calibration procedure involves the following steps:
\begin{itemize}
	\item Drive the motor for 2000, 4000, 6000, 8000, and 10000 steps.
	\item After each set of steps, measure the distance the prism has traveled in the camera image using the Bresser MicroCam II software.
	To do this, draw a line at the initial position of the motor, referencing a distinct point on the motor (as shown in Figure \ref{fig:calibration_uhv_points_of_interest}).
	\item After driving the motor, draw another line at the end position.
	\item Measure the distance between the two lines using the software.
\end{itemize}
An example of this process for motors Z1 and Z2 is shown in Figure \ref{fig:calibration_uhv_example_driving} for a $1000$-step measurement. \\

%The procedure for step size calibration is: $2000$, $4000$,
%$6000$, $8000$ and $10000$ steps are driven. After each set of steps the distance
%the prism has traveled in the image of the camera is measured. This is done with the Bresser MicroCam II software. In the software a line is drawn at the initial position, from a remarkable point on the motor (Fig. \ref{fig:calibration_uhv_points_of_interest}). After driving another line is drawn at the end position. The distance between these is measured using the software. An example for motor Z1 and Z2 is shown in Figure \ref{fig:calibration_uhv_example_driving} for a $1000$ step measurement. If changes to the motors have been performed a calibration has to be performed outside of UHV before reinsertion into UHV. Afterwards the motors have to be calibrated in UHV. \\

\begin{figure}[H]
	\centering
	\begin{subfigure}{0.42\textwidth}
		\includegraphics[width=\linewidth]{img/CalibrationUHV_Z1.pdf}
		\caption{}
		\label{fig:calibration_uhv_points_of_interest_z1}
	\end{subfigure}
	\begin{subfigure}{0.42\textwidth}
		\includegraphics[width=\linewidth]{img/CalibrationUHV_Z2_Z3.pdf}
		\caption{}
		\label{fig:calibration_uhv_points_of_interest_z2z3}
	\end{subfigure}
	\caption{Points of interest for the calibration of the step size of the three piezo motors in
		UHV. (a) motor Z1, \textcolor{tab_red}{red:} top of sapphire prism, \textcolor{tab_green}{green:} end of top plate used for step size determination (b)
		motors Z2/Z3, \textcolor{tab_red}{red:} screws on the motor plate that are close to motor Z2 and Z3 respectively, \textcolor{tab_green}{green:} lines used for step size determination.}
	\label{fig:calibration_uhv_points_of_interest}
\end{figure}

\begin{figure}[H]
    \centering
	\begin{subfigure}{0.495\textwidth}
		\centering
	    \includegraphics[width=\linewidth]{img/MA/CalibrationZ1.pdf}
	    \caption{}
		\label{fig:calibration_uhv_example_driving_z1}
	\end{subfigure}
	\begin{subfigure}{0.495\textwidth}
		\centering
	    \includegraphics[width=\linewidth]{img/MA/CalibrationZ2.pdf}
	    \caption{}
		\label{fig:calibration_uhv_example_driving_z2}
	\end{subfigure}
	\caption{Comparison of photographs recorded prior and after $1000$ steps were driven. (\subref{fig:calibration_uhv_example_driving_z1}) top of motor Z1, inset shows a zoom in of the top plate. The image after driving $1000$ approach steps superimposed. \textcolor{tab_red}{Red} lines show the top edge difference and resulting travel length. (\subref{fig:calibration_uhv_example_driving_z2}) same as (\subref{fig:calibration_uhv_example_driving_z1}) for the screw used to determine step size for motor Z2. Inset shows both approach and retract for $1000$ steps.}
    \label{fig:calibration_uhv_example_driving}
\end{figure}

%Outside UHV the best points are small scratches on the prisms
%\ce{Al2O3} plate, since these are already in a focal plane with the motors.
The camera-based distance measurement is calibrated using an object of known size in the focal plane. One suitable example is the Nd magnets, which have a diameter of $5$ mm. \\

However, motors Z2 and Z3 are not directly visible in the Mask Aligner chamber. Instead, the two screws located near these motors (as shown in Figure \ref{fig:calibration_uhv_points_of_interest} \subref{fig:calibration_uhv_points_of_interest_z2z3}) are observed. For calibration purposes, the diameter of these screws is used, which is known to be $3$ mm.
Since the screws are slightly closer to the camera than the motors themselves, a simple trigonometric model (illustrated in Figure \ref{fig:calibration_screw_diff_explain}) is used to account for this difference. This model reveals that for every unit of distance the motor moves, the screws move by a factor of $h' = \frac{17.8}{23.74} \approx 0.75$. \\

The screws are a little closer to the camera than the motors themselves, this is accounted for by using a simple trigonometric model seen in Figure \ref{fig:calibration_screw_diff_explain}. 
With this one gets that for each unit of distance the motor moves, the screws move by $h' = \frac{17.8}{23.74} \approx 0.75$. \\

\begin{figure}[H]
    \centering
    \includegraphics[width=0.6\linewidth]{img/Plots/Calibrations/screw_diff_explain.pdf}
    \caption{Top view of the Mask Aligner with the motors Z1-Z3 and the screws on the mask frame displayed. The triangle and line construction shows the derivation for the motor movement from screw movement.}
    \label{fig:calibration_screw_diff_explain}
\end{figure}

\begin{figure}[H]
	\centering
	\includegraphics[width=0.8\linewidth]{img/Plots/Calibrations/80V.pdf}
	\caption{Upper curves: Measured distance of motors traveled as a function of steps driven with linear fit and marked results step size. $+$ is retract $-$ is approach (see Fig. \ref{fig:mask_aligner_nomenclature_motors}). Lower curves: deviation of the data points from fit.}
	\label{fig:calibration_example}
\end{figure}

A linear fit is performed for the given data. The slope gives the step size. Results are shown in Figure \ref{fig:calibration_example}. After each set of steps it has to be ensured, that the mask frame is not tilted. Excessive tilt will affect the step size. After each set of steps, it is essential to verify that the mask frame is not tilted, as excessive tilt can influence the step size. Additionally, care must be taken to avoid exceeding the movement range of the piezos, detaching the Nd magnets from the frame, or causing the sapphire prism to fall out of the motor. The measurement has to be done for both driving directions separately, since the step sizes will be different. Indeed, in Fig. \ref{fig:calibration_example} shows that the positive retract direction has consistently larger step sizes. Furthermore, the Z3 motor displays a larger difference in step size between approach and retract compared to the other two motors. \\

To account for the varying step sizes between the three motors, different voltage pulses can be applied to each motor. A calibration is necessary to determine the relationship between step size and voltage, which is illustrated in Figure \ref{fig:calibration_voltage}. \\

\begin{figure}[H]
    \centering
   
\includegraphics[width=0.9\linewidth]{img/Plots/Calibrations/VoltageBehaviour.pdf}
    \caption{Step size as a function of voltage (DC peak) with linear fit and resulting slopes marked.}
    \label{fig:calibration_voltage}
\end{figure}

The behavior is linear in the voltage, but the slope is slightly different for
each motor. An optimum, where all motors drive similarly is at $80$ V. Also noticeable is a strong difference in slope for
Z3. Z3 is much more influenced by voltage than the other motors, where the
step size/V is larger by $\approx 0.3$. This calibration is used to compensate motor step size variations to avoid tilting. For this different voltage pulses need to be applied to the difference motor channels. The electronics required for this are discussed further in Chapter \ref{sec:walker}.\\

The motor behavior exhibits a linear relationship with voltage, but the slope of this relationship varies between motors. An optimal point, where all motors respond similarly, is found at $80$ V. Notably, the Z3 motor exhibits a significantly different slope, with a step size per Volt that is approximately $0.3$ larger than the other motors. This calibration is used to compensate for variations in motor step size, which helps to prevent tilting. To achieve this, different voltage pulses need to be applied to the various motor channels. The electronics required for this purpose are discussed in more detail in Chapter \ref{sec:walker}.\\

\subsection{Optical alignment}
The capacitance sensors cannot be used for alignement when the mask sample distance is very large, since the signal is noise dominated at that point. Therefore, one starts by aligning optically, down to the optical limit ($25$ {\textmu}m) of this setup. \\
To do that the sample has to be aligned so that its surface normal
is perpendicular to the camera's view direction. No sample surface can be
seen in camera view. No upwards tilt can be observed when viewing the side
edge of the sample, and the upper side of the sample holder, cannot be observed. \\

In Fig. \ref{fig:camera_alignment_example_low}, the surface of the sample can be seen, which means the camera is not in line
with the sample, but rather positioned too far up or tilted upward. In Fig. \ref{fig:camera_alignment_example_high}, one
can see the surface of the sample holder. Additionally, the side of the sample is tilted upwards in the image. The camera is positioned too high up or tilted downward. An example of good camera alignment is shown in Figure \ref{fig:camera_alignment_example_good}
\\

\begin{figure}[H]
	\centering
	\begin{subfigure}{0.32\textwidth}
    \includegraphics[width=\linewidth]{img/CameraAlignment_bad_low.pdf}
    \caption{}
	\label{fig:camera_alignment_example_low}
	\end{subfigure}
	\begin{subfigure}{0.32\textwidth}
    \includegraphics[width=\linewidth]{img/CameraAlignment_high.png}
    \caption{}
	\label{fig:camera_alignment_example_high}
	\end{subfigure}
	\begin{subfigure}{0.32\textwidth}
    \includegraphics[width=\linewidth]{img/CameraAlignment_good.png}
    \caption{}
	\label{fig:camera_alignment_example_good}
	\end{subfigure}
	\caption{Examples of camera views for different alignment situations. (a) camera
placed or angled too low, (b) too high and (c) placed in good alignment. }
    \label{fig:camera_alignment_example}
\end{figure}

To measure length scales the Bresser MikroCamLab software is used. To calibrate the length scale of the software the sample ($5940 \pm 20 $ {\textmu}m) is chosen.

After the camera alignment the mask is moved close to the sample until a small gap remains. Then any mask sample tilt is corrected iteratively (Fig. \ref{fig:optical_approach_a}). Then the mask is moved toward the sample until only a five pixel gap remains (Fig. \ref{fig:optical_approach}\subref{fig:optical_approach_b}, \subref{fig:optical_approach_c}).  Direct contact of the sample has to be avoided at this stage. In camera view direction, the mask and sample should now be aligned within
achievable optical accuracy.
 
\begin{figure}[H]
    \centering
	\begin{subfigure}{0.32\textwidth}
    \includegraphics[width=\linewidth]{img/OpticalAlign01.png}
    \caption{}
	\label{fig:optical_approach_a}
	\end{subfigure}
	\begin{subfigure}{0.32\textwidth}
    \includegraphics[width=\linewidth]{img/OpticalAlign02.png}
    \caption{}
	\label{fig:optical_approach_b}
	\end{subfigure}
	\begin{subfigure}{0.32\textwidth}
    \includegraphics[width=\linewidth]{img/OpticalAlign03.png}
    \caption{}
	\label{fig:optical_approach_c}
	\end{subfigure}
	\caption{The progression of optical alignment up from $65 \pm 5$ {\textmu}m (a) to $25 \pm 5$ {\textmu}m (c) mask sample distance. Measurement was obtained optically using measurement software and the sample's edge as a reference length.}
    \label{fig:optical_approach}
\end{figure}


\newpage
\subsection{Capacitive distance measurements}

The mask is aligned with the sample using capacitive measurements. The three capacitive sensors on the mask are configured to correspond with the three motors, as shown in Figure \ref{fig:mask_aligner_nomenclature_capacitances_motors}. The sensors are labeled accordingly, although it is worth noting that not all masks are assembled correctly. \\
The masks used in this setup were manufactured by Norcada in Canada. Each mask consists of a $200$ {\textmu}m thick \ce{Si} body. At the center of the mask, a $100\times100$ {\textmu}m silicon nitride (\ce{SiN}) membrane is situated, featuring circular holes with a diameter of $3$ {\textmu}m, spaced $10$ {\textmu}m apart. The SiN layer covers the entire mask and is 1 {\textmu}m thick. A trench is carved into the Si body below the center of the mask. \\
Three gold pads, functioning as capacitive sensors, are located around the hole membrane. These pads are positioned below an insulating layer of approximately $100$ nm thick silicon dioxide (\ce{SiO2}), which is situated at the bottom of a trench in the \ce{Si} body. The gold pads are $0.7$ mm away from the hole membrane and are arranged in an equilateral triangle around it. The dimensions of the mask and the capacitive sensors are illustrated in Figure \ref{fig:mask_aligner_nomenclature_capacitances_mask}.

\begin{figure}[H]
    \centering
	\begin{subfigure}{0.495\textwidth}
		\includegraphics[width=\linewidth]{img/MA/NomeclatureMotorsAndCapacitance.pdf}
		\caption{}
		\label{fig:mask_aligner_nomenclature_capacitances_motors}
	\end{subfigure}
	\begin{subfigure}{0.38\textwidth}
		\includegraphics[width=0.9\linewidth]{img/MA/Mask.pdf}
		\caption{}
		\label{fig:mask_aligner_nomenclature_capacitances_mask}
	\end{subfigure}
	\label{fig:mask_aligner_nomenclature_capacitances}
	\caption{(\subref{fig:mask_aligner_nomenclature_capacitances_motors}) cross-section of the Mask Aligner showing the labeling and rough positioning of the capacitance sensors on the mask (inner \textcolor{tab_red}{red} triangle) in relation to the three piezo motor stacks. (\subref{fig:mask_aligner_nomenclature_capacitances_mask}) diagram of the mask's dimensions as well as labeling of the mask's sensors. The inset shows the dimensions of the holey part of the mask, which is used to create patterns. Below is a cross section of the materials used.}
\end{figure}

The readout of the capacitance sensors is carried out with a Lock-in amplifier. The piezo motors are controlled with pulses from the RHK piezo motor controller. Communication with both the RHK and the Lock-in amplifier is done with a Matlab script. Figure \ref{fig:diagram_MA_circ} shows a diagram of the communication circuit. Settings of the Lock-in amplifier are available in Appendix \ref{app:lock_in}.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.75\linewidth]{img/MA/SchaltDiagramRHK.pdf}
    \caption{Diagram showing how communication with the RHK and the Lock-in amplifier is done and how they interact with elements in vacuum. Red lines are input, black lines are output lines. The capacitance relay is used to measure $C_i$ one after another. The RHK relay controls, which motor is currently driven.}
    \label{fig:diagram_MA_circ}
\end{figure}

The capacitance of each of the three sensors can be approximated using a parallel
plate capacitor model. The gold pad is one plate of the capacitor and the
overlap of its bounds with the \ce{Si} sample can be seen as the other plate of
the capacitor:
\begin{equation}
	C = \epsilon_0 (\frac{A}{r} + \epsilon_{r, \text{\ce{SiN}}} \frac{A}{r_{\text{\ce{SiN}}}} + \epsilon_{r, \text{\ce{SiO2}}} \frac{A}{r_{\text{\ce{SiO2}}}})
	\label{eq:plate_capacitor}
\end{equation}
where $C$ is the capacitance, $\epsilon_0$ is the vacuum permittivity, $\epsilon_r$ is the relative permittivity of the corresponding material, $A$ is
the area of the gold pad and $r$ is the distance between the mask surface and the sample. $r_{\text{\ce{SiN}}}$ and $r_{\text{\ce{SiO2}}}$ $ $
are the thickness of the \ce{SiN} and \ce{SiO2} layers above the gold pad. This holds true until
the mask's surface gets in contact with the sample. Contamination particles can also cause indirect contact of mask and sample.
The distance to the sample can in theory be read off from the capacitance value via Eq.
\ref{eq:plate_capacitor}. In practice, the capacitance values obtained with real masks can significantly deviate from the theoretical model. Without a reference point, it is impossible to determine the absolute distance between the mask and the sample. To address this, a measurement of the capacitance is taken while the mask is brought into contact with the sample and then retracted, providing a reference calibration.


\begin{figure}[H]
    \centering
	\begin{subfigure}{0.45\textwidth}
    \includegraphics[width=\linewidth]{img/Diagram/ApproachExplanation.pdf}
    \caption{}
	\label{fig:approach_curve_example_cap}
	\end{subfigure}
	\begin{subfigure}{0.45\textwidth}
    \includegraphics[width=\linewidth]{img/Diagram/ApproachExplanation_diff.pdf}
    \caption{}
	\label{fig:approach_curve_example_cap_diff}
	\end{subfigure}
	\begin{subfigure}{0.3\textwidth}
   
\includegraphics[width=\linewidth]{img/Diagram/ApproachCurve_FirstContact.png}
    \caption{}
	\label{fig:approach_curve_example_first}
	\end{subfigure}
	\begin{subfigure}{0.3\textwidth}
   
\includegraphics[width=\linewidth]{img/Diagram/ApproachCurve_SecondContact.png}
    \caption{}
	\label{fig:approach_curve_example_second}
	\end{subfigure}
	\begin{subfigure}{0.3\textwidth}
   
\includegraphics[width=\linewidth]{img/Diagram/ApproachCurve_FullContact.png}
    \caption{}
	\label{fig:approach_curve_example_full}
	\end{subfigure}
	\caption{(a) capacitance (approach) curve. (b) difference of each capacitance value.
Only one sensor is shown. Marked with blue dashed lines are the important points where the slope of the $\frac{1}{r}$ curve changes. Below are images of the geometry between mask and
sample at First (c), Second (d) and Full contact (e). Red lines or points indicate
where the mask is touching the sample.}
    \label{fig:approach_curve_example}
\end{figure}

A typical approach curve, from a measured distance of $25 \pm 5$ {\textmu}m to full contact is shown in Figure \ref{fig:approach_curve_example_cap}. The corresponding $dC$ curve \\

Typically, the mask initially contacts the sample at a single point or edge, as illustrated in Figure \ref{fig:approach_curve_example_first}. This initial contact restricts the movement of the mask on the corresponding motor, resulting in a change in the step size. Consequently, the slope of the approach curve changes. \\
If the mask subsequently contacts the sample at another point (Figure \ref{fig:approach_curve_example_second}), the step size decreases again, which is labeled as "Second contact" in Figure \ref{fig:approach_curve_example_cap}. \\
As the sample is approached further, the mask's movement becomes limited to the axis that aligns the mask with the sample perfectly (Figure \ref{fig:approach_curve_example_full}). At this point, the capacitance value remains constant, as the distance between the mask and sample can no longer be reduced. This point is marked as "Full contact" in Figure \ref{fig:approach_curve_example_cap}. \\

%Usually the mask will start contacting the sample with one point (or potentially an edge) first. An illustration of
%this is shown in Figure \ref{fig:approach_curve_example_first}. The first contact inhibits
%the movement of the mask on the associated motor, resulting in a changed
%step size. Due to this step size change, the slope of the approach curve changes. 
%If the mask contacts the sample with another point (Figure \ref{fig:approach_curve_example_second}) the step size decreases again. This is labeled in Figure
%\ref{fig:approach_curve_example_cap} as "Second contact". If the sample is
%approached further, the only axis of movement left for the mask is the one
%aligning the mask to the sample perfectly (Figure
%\ref{fig:approach_curve_example_full}). At this point, the capacitance value no
%longer changes since the distance between mask and sample can no longer be
%decreased. This point is labeled "Full contact" in Figure
%\ref{fig:approach_curve_example_cap}. \\

The difference in capacitance increases monotonically. Upon any contact the step size changes and the $dC$ curve (example Fig. \ref{fig:approach_curve_example_cap_diff}) gives a local maximum. This can be used to define a stop condition. A value $5-10$ steps before the peak~\cite{Beeker} is determined in a calibration measurement to full contact. When this value is reached in any subsequent approach the approach is stopped. 
%How close the value can be chosen to the peak depends on the noise of the signal. \\
%Another way of looking at this is to consider the differences between $2$ capacitance values:
%\begin{equation}
%	C_2 - C_1 = \epsilon_0 \epsilon_r \frac{A}{r + r'} - \epsilon_0 \epsilon_r
%\frac{A}{r} < C_3 - C_2 = \epsilon_0 \epsilon_r \frac{A}{r + 2r'} - \epsilon_0
%\epsilon_r \frac{A}{r + r'}
%\end{equation}
%Where $C_1$, $C_2$ and $C_3$ are $3$ different capacitance values where $C_1 < C_2 < C_3$. They are $r'$ apart in distance.
%The values increase monotonically, when however the slope changes, the difference will suddenly drop (Figure \ref{fig:approach_curve_example_cap_diff}). When
%the peak value of this graph is known one can predict the contact before it happens and stop the approach before the sample is contacted. This peak value can be used to define a "stop condition". The stop condition has to be determined using a calibration approach. In practice the stop condition has to be chosen a few steps before the peak due to noise. \\

%Absolute distance can still not be measured since upon retraction and subsequent
%approach, the capacitance values drop. This is either due to accumulation of
%misalignement from tilting and/or
%accumulation of particles on the sample/mask surface.
%In order to still get replicable alignment, the difference of
%capacitance is used. 
%%The stop condition is used to determine good alignment~\cite{Beeker}. 

%\begin{figure}[H]
%	\centering
%	\includegraphics[width=0.95\linewidth]{img/MA/SubsequentApproachDeviation.pdf}
%	\caption{Approach curves recorded on two subsequent days. The
%		second curve was recorded after retraction and subsequent approach. The 2 curves
%		do not start at the same distance away from sample, therefore they are not
%		aligned on the x-axis. Both are driven until full contact. Capacitance 3 shows noisy signal for unknown reasons.}
%	\label{fig:approach_subsequent}
%\end{figure}

\subsection{Reproducibility}
Reproducibility of approach curves with regard to different samples and masks is important for the future use of the Mask Aligner. In the master thesis of Jonas Beeker the
reproducibility of different masks, different locations, different approaches
and a comparison before and after evaporation were discussed~\cite{Beeker}.

\subsubsection{Reproducibility when removing sample/mask}

One concern regarding reproducibility is whether the approach curve is significantly influenced by swapping or reinserting the mask or sample. This issue can be addressed by creating a calibration approach curve with one sample and then exchanging it for another. This method potentially enables evaporation measurements on samples that have never been in contact with a mask. A first step is to determine this for reinsertion of the same sample.

\begin{figure}[H]
    \centering
	\begin{subfigure}{0.495\textwidth}
    \includegraphics[width=\linewidth]{img/MA/InsertionReproducibility.pdf}
    \caption{}
	\label{fig:approach_replicability_cap}
	\end{subfigure}
	\begin{subfigure}{0.495\textwidth}
    \includegraphics[width=\linewidth]{img/MA/InsertionReproducibility_diff.pdf}
    \caption{}
	\label{fig:approach_replicability_cap_diff}
	\end{subfigure}
	\caption{(\subref{fig:approach_replicability_cap}) 3 subsequent approach curves.  (\subref{fig:approach_replicability_cap_diff}) corresponding differences in capacitance. \textcolor{tab_green}{Green} is the initial curve. The \textcolor{tab_blue}{blue} curve is after sample has been carefully removed and reinserted. For the \textcolor{tab_red}{red} curve the mask was removed and reinserted. Larger fluctuations in the signal visible on the \textcolor{tab_blue}{Blue} curve are due to an accidental change in time constant of the LockIn Amplifier.}
    \label{fig:approach_replicability}
\end{figure} 

Reinsertion of the mask resulted in a substantial change in the approach curve, which can likely be attributed to newly induced tilt on the mask. This shift is evident in the difference between the green and red curves shown in Figure \ref{fig:approach_replicability}.\\
Alternatively, minor movement of the mask frame on the \ce{Nd} magnets, causing the mask to tilt, could also be a contributing factor. This issue is inherent to the current design of the Mask Aligner and cannot be resolved without a fundamental redesign. \\

Reinsertion of the sample also resulted in a difference in approach curves of $\approx 0.5 \pm 0.2$ pF, as shown in Figure \ref{fig:approach_replicability} (blue and green curves). The overall trend of the curve remains consistent, but the absolute values exhibit a change. However, the peak in $dC$ underwent a significant shift. A stop condition determined based on the green curve (e.g., $0.04$ pF) would exceed the point of first contact on the blue curve. This implies that after switching samples, a conservative stop condition must be selected to avoid overshooting. \\

%
%\subsection{Capacitance correlations} \label{subsec:cross_cap}
%
%%\begin{figure}[H]
%%    \centering
%%	\begin{subfigure}{0.32\textwidth}
%%		\centering
%%		\includegraphics[width=\linewidth]{img/Diagram/cross_example_1.pdf}
%%	    \caption{}
%%	    \label{fig:cross_cap_approach_difference}
%%	\end{subfigure}
%%	\begin{subfigure}{0.32\textwidth}
%%		\centering
%%		\includegraphics[width=\linewidth]{img/Diagram/cross_example_2.pdf}
%%	    \caption{}
%%	    \label{fig:cross_cap_approach_difference_2}
%%	\end{subfigure}
%%	\begin{subfigure}{0.32\textwidth}
%%		\centering
%%		\includegraphics[width=\linewidth]{img/Diagram/ExplanationCurveDifference.pdf}
%%	    \caption{}
%%	    \label{fig:cross_cap_approach_sim}
%%	\end{subfigure}
%%	\caption{(\subref{fig:cross_cap_approach_difference}, \subref{fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure the same scale. (\subref{fig:cross_cap_approach_sim}) shows a simple simulation of the approach with tilted sample.}
%%	\label{fig:cross_cap_approach}
%%\end{figure}
%
%%For the gold pads, this would result in a capacitance of $\approx 0.40$ fF, at a distance of $\approx 50$ micron (measured optically). The capacitance values of the curve $C_1$ was $\approx 2.4$
%%pF, which deviates by $4$ orders of magnitude. This corresponds more closely to the
%%value expected for capacitance from the \ce{Si} of the mask to the \ce{Si} of
%%the sample. The expected value for a plate capacitor would be $\approx
%%1.44$ pF. The deviation in this case can be explained by the oversimplification
%%of the model. It does not take into account any stray capacitances the system
%%might have. \\
%%
%%The model in Figure \ref{fig:cross_cap_approach_sim} assumes a distance between the sensors on the z-axis of $440$ nm for C1-C2 and $220$ nm for C2-C3. A distance that is well within the optical accuracy of $\approx 5$ {\textmu}m for maximum zoom and resolution. Even for such a small difference, the deviation between the curves, is easily visible. \\
%%
%%However, measured capacitances show a deviation in behavior from the model (Fig. \ref{fig:cross_cap_approach_difference}). The different capacitances vary by $1$-$2$ order of magnitude. The largest capacitance was measured to $19.12$ pF. The curves (Fig. \ref{fig:cross_cap_approach_difference}) start with large deviation and converge near full contact. This is the opposite to the expected behavior (Fig. \ref{fig:cross_cap_approach_sim}). The general shape of the curves is identical for all $3$, while it is expected that the first contact affects the $3$ capacitances differently. \\
%%
%%Another mask (Figure \ref{fig:cross_cap_approach_difference_2}) shows behavior more close to the expected, with a difference for the $3$ capacitances at first contact. However, $C_2$ and $C_3$ behave identically again. The largest capacitance was measured to be $19.78$ pF and $C_2$ and $C_3$ varied by $2$ orders of magnitude from $C_1$. \\
%
%%\begin{figure}[H]
%%    \centering
%%    \includegraphics[width=0.9\linewidth]{img/SimilarityApproach.pdf}
%%    \caption{}
%%    \label{fig:cross_cap_approach_sim}
%%\end{figure}
%%\todo{Plot of heavily correlated approach curves}
%
%The masks used for approach and subsequent evaporation are in theory supposed to have $3$ independent capacitance sensors that together give a measurement of the distance and tilt of the mask. However, the masks show strong correlation between the $3$ sensors(Fig. \ref{fig:example_correlation_capacitances}). This prohibits precise control of the alignment. \\
%In his master thesis Jonas Beeker looked at the possibility of capacitances between the $3$ sensors as a possible reason for this strong correlation. It was determined that for a cross capacitance of more than $150$ fF the capacitance curves cannot be distinguished anymore\cite{Beeker}. 
%
%\begin{figure}[H]
%	\centering
%	\includegraphics[width=0.9\linewidth]{img/MA/CorrelationExample.pdf}
%	\caption{3 capacitance curves of a mask scaled to be
%		within the same range. The lower plots show deviations from comparison curve.}
%	\label{fig:example_correlation_capacitances}
%\end{figure}
%
%
%
%\begin{table}[H]
%	\centering
%	\begin{tabular}{|l|l|l|l|}
%		\hline         & C C1-C2 (pF) & C C1-C3 (pF) & C C2-C3 (pF)  \\
%		\hline \hline
%		Mask 1           & $7.11 \pm 0.02$      & $3.20 \pm 0.12$       & $0.19 \pm
%		0.06$        \\ \hline
%		Mask 2           & $0.64 \pm 0.06$      & $0.64 \pm 0.06$       & $0.85 \pm
%		0.02$        \\ \hline
%		Mask 3           & $3.33 \pm 0.04$       & $3.94 \pm 0.07$      & $0.86 \pm
%		0.02$        \\ \hline
%		Mask old         & $0.50 \pm 0.02$        & $0.29 \pm 0.09$        & $0.35 \pm
%		0.14$        \\ \hline \hline
%		Mask shuttle 1   & $0.24 \pm 0.02$      & $0.25 \pm 0.02$     & $0.041 \pm
%		0.004$       \\ \hline
%		Mask shuttle 2   & $0.30 \pm 0.04$     & $0.29 \pm 0.03$     & $0.041 \pm 0.004$
%		\\ \hline
%		Mask shuttle 3   & $0.23 \pm 0.02$      & $0.25 \pm 0.02$      & $0.049 \pm
%		0.004$      \\ \hline \hline
%		Shuttles average & $0.26 \pm 0.03$     & $0.26 \pm 0.02$     & $0.043 \pm 0.004$
%		\\ \hline
%	\end{tabular}
%	\caption{Table of cross capacitance measurement results. }
%	\label{tab:cross_cap}
%\end{table}
%
%The reason for this large deviation is a leakage current from the cable connecting
%the gold pads to the Si of the Mask. This most likely happens
%due to accidental piercing of the insulating \ce{SiO2} layer during assembly of the gold cable. This is depicted in Figure \ref{fig:leakage_current}. The capacitance measured is in this case dominated by the leakage capacitance from \ce{Si$_\text{Sample}$} to \ce{Si$_\text{Mask}$} (Figure \ref{fig:leakage_current}).
%
%
%\begin{figure}[H]
%    \centering
%    \includegraphics[width=0.5\linewidth]{img/LeakageCurrent.pdf}
%    \caption{Diagram showing a cross section of the mask at a gold pad location. A small tear in the \ce{SiO2} layer removes insulation between the gold wire and the Si of the mask. Parallel black lines depict plate capacitors illustratively. Larger plate shows larger capacitance.
%}
%    \label{fig:leakage_current}
%\end{figure}
%
%\begin{figure}[H]
%	\centering
%	\includegraphics[width=0.75\linewidth]{img/CrossCapacitances.pdf}
%	\caption{Circuit diagram of the measurement setup with the cross
%		capacitances and parasitic capacitances for the mask shuttle. The $C_i$ refer to
%		the main capacitances that are used for mask alignment. $C_{ij}$ refers to a
%		cross capacitance between capacitance sensor $i$ and sensor $j$.
%		$C_{mask-sample}$ refers to the capacitance between the Si of the Mask and the
%		Si of the Sample, usually this should not be measured since the Si of the Mask
%		is separated from the gold pads with a SiN layer, but should that layer be
%		pierced or otherwise allow a leakage current (if the resistances $R_{i, Leak}$
%		are small enough) this will be measured instead of $C_i$, since it is an order
%		of magnitude larger.}
%	\label{fig:cross_cap_diagramm}
%\end{figure}
%
%
%\newpage
%
%Another reason for the correlation of capacitances are cross capacitances between the gold pad sensors. \\
%
%%In order to quantify the effect of this source, cross capacitances were measured directly between $3$ masks holders inside mask shuttles, as well as
%%3 empty shuttles. For the measurement Input and output of the Lock-in were connected to two of the capacitance sensors of the mask. Measurements were performed inside the Mask Aligner with a sample inserted. Additionally, mask shuttles without any mask inserted were tested for cross capacitance. The results are shown in Table \ref{tab:cross_cap} \\
%%
%%The shuttles themselves have large cross capacitance values. It is of the same order of magnitude as the capacitance expected from gold pad to sample. When adding the mask
%%the cross capacitances increase, often by an order of magnitude. \\
%%
%%To check if this is also the dominant cause of correlation, the mask labeled "old" is looked at more closely. The cross capacitance values for this mask were small compared with the other masks (Table \ref{tab:cross_cap}). The approach curve of this mask however, shows the heaviest correlation of all masks tested. This indicates that in this case a leakage current from gold to mask \ce{Si} is the main cause. \\
%%
%%To confirm the similarity between the different capacitance sensors signals, the data of each was overlaid over one another. The data was normalized to allow for comparison. Then an offset was fitted. The result of this can be seen in Figure \ref{fig:mask_old_correl}. The $3$ different capacitance sensors give the same signal. Systematic deviations in the residuals are only visible near the jump in capacitance signal, which is of unknown cause. The deviations are within $0.1$~\%, which is on the same order as the expected measurement error for the given LockIn parameters. 
%
%\begin{figure}[H]
%    \centering
%    \includegraphics[width=0.9\linewidth]{img/Plots/Mask_Old_Caps.pdf}
%    \caption{The 3 capacitance curves of the Mask labeled "old". Of note is the difference in scale of the capacitance signal.}
%    \label{fig:mask_old_caps}
%\end{figure}
%
%\begin{figure}[H]
%    \centering
%    \includegraphics[width=0.95\linewidth]{img/Plots/Mask_Old_Correl.pdf}
%    \caption{3 capacitance curves of the Mask labeled "old" scaled to be
%within the same range. The lower plots show deviations from comparison curve. }
%    \label{fig:mask_old_correl}
%\end{figure}
%
%
%This leads to the conclusion that while the cross capacitances have a strong influence on
%the correlation, they are not the dominating
%factor. Both leakage currents and cross capacitances have to be considered and their sources minimized. \\
%
%Figure \ref{fig:cross_cap_diagramm} shows a circuit diagram for the known sources of capacitance correlation.
%
%In order to decrease the correlation between the sensors the following methods are proposed:
%
%\paragraph{Leakage current}
%The leakage current between the Si of the Mask and the Si of the sample seems to be the main source of correlation. A better mask preparation method has to be found that ensures no piercing of the \ce{SiNi} layer. This will be investigated in the near future in a Bachelor thesis.
%
%\paragraph{Improved gold pin fitting} 
%The gold pins for the current set of masks were cut to size by hand. 
%%This causes a problem with the fit between male and female side of the gold pins.
%%The mask stage can move inside the holder slightly. This changes both distance to sample and gives a loose contact.
%Instead, they should be machined with precision by a workshop. The stability of the fit should be tested after assembly.

%\subsection{Stop Conditions}
%During recording of a calibration approach curve two different scenarios can arise:
%
%\paragraph{High correlation between capacitance curves}
%When all 3 capacitance curves are heavily correlated, no alignment information
%can be derived from the 3 different curves. Effectively only one curve is measured. The stop condition in this case is a single peak in the derivative of that one
%capacitance curve. By picking a condition close to the peak good alignment can be achieved. 
%
%By performing one approach until full contact between mask and sample the mask can be aligned
%at the cost of possibly damaging mask and sample. This has to be done on the first curve. 
%Furthermore, the values of capacitance at full contact will afterward be known. They can upon further alignment be used to iteratively tweak the motors until a similar same value is reached again. With this method small tilting can be compensated. \\
%
%\paragraph{Low correlation between capacitance curves}
%When all 3 capacitance curves are mostly uncorrelated, information of the mask sample can be gathered directly from the value of each
%curve. In this case the absolute value of the $3$ capacitance curves can be used to determine when to stop the approach. Optimal values can be iteratively reached, by moving the $3$ motors separately. \\
%This is the easier and safer of the two scenarios, but it requires a good mask
%holder and mask stage. 

\section{Mask Aligner operation}

\subsection{Sample preparation} \label{sec:sample_prep}
The evaporation of a superconductor onto any material requires a clean sample surface. To clean a \ce{Si}(111) sample, the following steps have to be taken:

\begin{enumerate}
	\item Select chips from a \ce{Si} wafer and place them into a petri dish. Clean the chip
using acetone and then IPA in an ultrasonic bath.
	\item Using a soft-tip tweezer, carefully grasp a silicon chip and maintain a stable grip. Then, gently blow pressurized nitrogen across the surface of the chip to remove any coarse particles. Be careful not to direct the nitrogen stream at the surface, as this may dislodge the chip from the tweezer. Instead, blow the nitrogen across the surface to effectively clean it. Repeat this process for each chip.
	\item Submerge the silicon chips in a beaker filled with pure acetone and then place the beaker in an ultrasonic bath. Run the ultrasonic bath for 10 minutes at $55^\circ$C.
	\item Take the chips out of the acetone with a soft tip tweezer and rinse them with IPA. Then submerge them in a beaker filled with IPA and clean them again in the ultrasonic bath for 10 minutes.
	\item Take the chip out again and repeat the last step with demineralized water. While waiting, combine the hardener and resin of the 2 part epoxy EPO-TEK E4110-LV to ensure it is ready for a later step.
	\item Take the chip out and blow it dry with pressurized nitrogen, following the same procedure as step 2.
	\item Place 4 dots of mixed epoxy EPO-TEK E4110-LV into the grooves of the sample holder at the edges. Carefully grab the chip and place it from the top as straight as possible onto the sample holder.
 	\item Carefully place the sample holder in an oven heated to $150^\circ$ C and let the resin cure for $15$ minutes. 
	\item Document the sample's surface cleanliness using an optical microscope image and an AFM image
	\item Place the sample as quickly as possible in the Mask Aligner Load Lock and pump the system down to avoid further contamination.
\end{enumerate}
%If the sample is intended to be analyzed in an STM, the sample preparation should happen in an UHV environment to ensure further cleanliness and the sample should be transported directly via the Load Lock UHV suitcase attached to the Mask Aligner Chamber.