From 1777e421f08ebd36873e1c3ec0a1ca1f0a2bfe55 Mon Sep 17 00:00:00 2001
From: Bernardbernoulli <48800416+Bernardbernoulli@users.noreply.github.com>
Date: Mon, 16 Sep 2024 22:45:04 +0200
Subject: [PATCH] Stuff

---
 acknowledgments.aux                        |   4 +-
 appendix.aux                               |  74 +--
 bibliography.aux                           |   6 +-
 chap01.aux                                 |  68 +--
 chap01.tex                                 |  64 ++-
 chap02.aux                                 | 227 ++++----
 chap02.tex                                 | 253 ++++-----
 chap03.aux                                 | 128 ++---
 chap04.aux                                 | 152 +++---
 chap05.aux                                 | 186 +++----
 conclusion.aux                             |   6 +-
 img/MA/NomenclatureMaskAlignerCrossSec.pdf | Bin 233678 -> 238550 bytes
 img/Plots/Background/AFMDiagram.pdf        | Bin 22255 -> 23761 bytes
 img/Plots/Background/Penumbra_diagramm.pdf | Bin 11427 -> 9949 bytes
 pdfa.xmpi                                  |   8 +-
 preface.aux                                |   2 +-
 preface.tex                                |   8 +-
 thesis.aux                                 |  19 +-
 thesis.log                                 | 596 ++++++++++++---------
 thesis.out                                 |  20 +-
 thesis.pdf                                 | Bin 284228104 -> 284234559 bytes
 thesis.synctex.gz                          | Bin 574640 -> 568416 bytes
 thesis.toc                                 | 222 ++++----
 23 files changed, 1044 insertions(+), 999 deletions(-)

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-\@writefile{lof}{\contentsline {figure}{\numberline {1.6}{\ignorespaces The beam path for an SEM (\subref  {fig:sem_setup_beam}). The $3$ detectors used in an SEM are shown near the bottom of the image. The secondary electron detector (Everhard-Thornley) and the back scattering and X-ray detector. A diagram showing electron matter interactions (\subref  {fig:sem_setup_interaction}). The green area represents the penetration depth into the sample at which the different signals can be detected. Images were taken from~\cite  {SEM_image_01} and ~\cite  {SEM_image_02}.}}{12}{figure.caption.15}\protected@file@percent }
-\newlabel{fig:sem_setup}{{1.6}{12}{The beam path for an SEM (\subref {fig:sem_setup_beam}). The $3$ detectors used in an SEM are shown near the bottom of the image. The secondary electron detector (Everhard-Thornley) and the back scattering and X-ray detector. A diagram showing electron matter interactions (\subref {fig:sem_setup_interaction}). The green area represents the penetration depth into the sample at which the different signals can be detected. Images were taken from~\cite {SEM_image_01} and ~\cite {SEM_image_02}}{figure.caption.15}{}}
+\newlabel{fig:sem_setup_beam}{{1.6a}{13}{\relax }{figure.caption.15}{}}
+\newlabel{sub@fig:sem_setup_beam}{{a}{13}{\relax }{figure.caption.15}{}}
+\newlabel{fig:sem_setup_interaction}{{1.6b}{13}{\relax }{figure.caption.15}{}}
+\newlabel{sub@fig:sem_setup_interaction}{{b}{13}{\relax }{figure.caption.15}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1.6}{\ignorespaces The beam path for an SEM (\subref  {fig:sem_setup_beam}). The $3$ detectors used in an SEM are shown near the bottom of the image. The secondary electron detector (Everhard-Thornley) and the back scattering and X-ray detector. A diagram showing electron matter interactions (\subref  {fig:sem_setup_interaction}). The green area represents the penetration depth into the sample at which the different signals can be detected. Images were taken from~\cite  {SEM_image_01} and ~\cite  {SEM_image_02}.}}{13}{figure.caption.15}\protected@file@percent }
+\newlabel{fig:sem_setup}{{1.6}{13}{The beam path for an SEM (\subref {fig:sem_setup_beam}). The $3$ detectors used in an SEM are shown near the bottom of the image. The secondary electron detector (Everhard-Thornley) and the back scattering and X-ray detector. A diagram showing electron matter interactions (\subref {fig:sem_setup_interaction}). The green area represents the penetration depth into the sample at which the different signals can be detected. Images were taken from~\cite {SEM_image_01} and ~\cite {SEM_image_02}}{figure.caption.15}{}}
 \citation{self_epitaxy}
 \@setckpt{chap01}{
-\setcounter{page}{14}
+\setcounter{page}{15}
 \setcounter{equation}{2}
 \setcounter{enumi}{0}
 \setcounter{enumii}{0}
diff --git a/chap01.tex b/chap01.tex
index 1c4424d..d19783d 100644
--- a/chap01.tex
+++ b/chap01.tex
@@ -15,7 +15,7 @@ Electron beam evaporation, also known as \textbf{E}lectron-\textbf{b}eam \textbf
 The setup of an electron beam evaporator is shown in Figure \ref{fig:e-beam_evap}. The source material is placed inside a crucible as pellets of ultrapure ($>99$ \%) material.
 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.
 
-In order to heat the source material it is hit with a high voltage electron beam ($\mathcal{O}$($1$ kV)), emitted by either an electron gun or a filament. This beam usually is focused using magnetic fields to hit the source material. The highly energetic electrons interact with the atomic nuclei and the atomic electrons of the source material and transfer energy. This energy transfer heats the hit atoms locally and eventually leads to the evaporation of atoms according to its vapor pressure.\\
+In order to heat the source material it is hit with a high voltage electron beam ($\mathcal{O}$($1$ kV)), emitted by either an electron gun or a filament. This beam usually is focused using magnetic fields to hit the source material. The highly energetic electrons interact chiefly with the atomic electrons of the source material and transfer energy. This energy transfer heats the hit atoms locally and eventually leads to the evaporation of atoms according to its vapor pressure.\\
 
 %The penetration depth of electron with ($<5$ kV) is less than 0.4 $\mu$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.\\
 
@@ -23,7 +23,7 @@ When the material's vapor pressure exceeds the surrounding environments pressure
 
 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 used.
 
-The deposition rate of the evaporator can be measured using a molecular flux monitor or a quartz balance. The deposition of a material is described by the Hertz-Knudsen equation:
+The deposition rate of the evaporator can be measured using a molecular flux monitor or a quartz balance. 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}
@@ -32,7 +32,7 @@ The deposition rate of the evaporator can be measured using a molecular flux mon
 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. 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, higher temperatures are available with e-beam evaporation. This is required, e.g. for \ce{NB}~\cite{tungsten_evaporation}.
+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}.
 
 In order to control the duration of the evaporation, a shutter is usually included. It can be closed or opened to control when the sample is exposed to the vapor beam. This is also needed for improved deposition rate accuracy, since the source material needs to initially heat up when the electron beam is started, which leads to unstable flux at the start of the evaporation. 
 
@@ -53,7 +53,7 @@ The molecular beam, the evaporator generates, is not a set of perfectly parallel
 
 The area where both beams overlap is called the "umbra" in analogy to the same phenomenon in optics (Figure \ref{fig:penumbra_explanation}, red areas). The region where only one of the cones hits the sample, but the other is blocked by the mask, is called the "penumbra" (Figure \ref{fig:penumbra_explanation}, orange areas). Hence the intended pattern on the sample is smeared out.\\
 
-The width of the penumbra $p$ is determined by the distance of the beam source to the sample $l$, as with longer length the beams will be less coherent, the size of the crucible $a$ and the distance between mask and sample $d$. Given these parameters the size of the penumbra can be estimated using Figure \ref{fig:penumbra_explanation}, since $l >> a$ the rays coming from the crucible can be assumed to be approximately parallel:\\
+The width of the penumbra $p$ is determined by the distance of the crucible to the sample $l$, the size of the crucible $a$ and the distance between mask and sample $d$. It can be estimated using Figure \ref{fig:penumbra_explanation}. For $l >> a$ the inner rays coming from the crucible are approximately parallel. This leads to the formula:\\
 
 \begin{equation}
 	\frac{a}{l} \approx \frac{p}{d} \Rightarrow p \approx\frac{da}{l}
@@ -62,16 +62,18 @@ The width of the penumbra $p$ is determined by the distance of the beam source t
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.5\linewidth]{img/Plots/Background/Penumbra_diagramm.pdf}
-    \caption{Diagram showing the geometrical reason for the creation of a penumbra in the evaporation from a non point source. The crucible is placed at distance $l$ from the mask, and beams emit from either side of the crucible to each side of the hole in the mask. The area where only beams from one side of the crucible hit the sample receives fewer particles and is called penumbra.}
+    \caption{Diagram to determine the size of the penumbra $p$. The crucible is placed at distance $l$ from the mask, and beams emit from either side of the crucible to both edges of a hole in the mask. The area where only beams from one side of the crucible hit the sample is called penumbra.}
     \label{fig:penumbra_explanation}
 \end{figure}
 
-Usually when using stencil lithography, it is desirable for the penumbra to be as small as possible. For the use case proposed for the Mask Aligner, a penumbra of $< 100$ nm is required~\cite{Bhaskar}. For this reason one tries to minimize the distance between mask and sample, as a certain size is required for the crucible to be able to evaporate lead efficiently and the distance to the beam source cannot be increased indefinitely since the amount of material that gets deposited on the sample falls off with the square of the distance to the sample. For our setup, these quantities are approximately as follows: $b=6$ mm, $l=25$ cm. For a desired penumbra of $< 100$ nm a distance between mask and sample of at most $d=4$ $\mu$m is needed.\\
+When using stencil lithography, the penumbra should be as small as possible. The target penumbra for the mask aligner used in this thesis is $< 100$ nm~\cite{Bhaskar}. A certain size is required for the crucible to be able to evaporate lead efficiently. The distance to the beam source cannot be increased indefinitely since the amount of material deposited on the sample falls off with the square of $d$. For our setup, these quantities are: $b\approx6$ mm, $l\approx25$ cm. For a desired $p < 100$ nm a distance between mask and sample of at most $d\approx4$ $\mu$m is needed.\\
 
 \subsubsection{Tilt induced penumbra}
-Formerly, the model for the penumbra assumed perfect alignment between mask and sample, but potentially large distance $d$. What can additionally happen is that the distance on one side of the mask is larger than that on the other side of the mask. 
+Formerly, the model for the penumbra assumed perfect alignment between mask and sample, but potentially large distance $d$. Additionally the distance on one side of the mask can be larger than that on the other. 
 
-The mask and the sample also have to be kept parallel as a tilt would result in a large distance on one side $d_2$ even when the other is a much closer $d_1$, which results in $2$ different penumbral lengths $p_1$ and $p_2$ along the major axis of the tilt, an illustration of this can be seen in Figure \ref{fig:penumbra_explanation_tilt_2d}. Along any other axis of the tilt other than the one where the tilt angle is largest, however, this will result in two new distances $d_1 '> d_1$ and $d_2 '< d_2$. This can be continued along a half circle until $d_1 ' = d_2 '$ where we have the situation similar to the aligned case again. Overall, this results in a penumbra, which follows a "half-moon" shape. An illustration of this can be seen in Figure \ref{fig:penumbra_explanation_tilt_sim}.\\
+This results in $2$ different penumbral lengths $p_1$ and $p_2$ along the major axis of the tilt, an illustration of this can be seen in Figure \ref{fig:penumbra_explanation_tilt_2d}. Along other 
+
+any other axis of the tilt, however, this will result in two new distances $d_1 '> d_1$ and $d_2 '< d_2$. This can be continued along a half circle until $d_1 ' = d_2 '$ where we have the situation similar to the aligned case again. This results in a penumbra, as shown in Figure \ref{fig:penumbra_explanation_tilt_sim}.\\
 
 \begin{figure}[H]
     \centering
@@ -85,11 +87,11 @@ The mask and the sample also have to be kept parallel as a tilt would result in
     \caption{}
 	\label{fig:penumbra_explanation_tilt_sim}
 	\end{subfigure}
-	\caption{A diagram of the evaporation rays for a tilted mask with only one hole (\subref{fig:penumbra_explanation_tilt_2d}) showing the 2 different penumbral widths $p_{\text{i}}$ that appear in a cross-section. (\subref{fig:penumbra_explanation_tilt_sim}) Simulated evaporation with large penumbra for a tilt angle of $45^\circ$ the penumbra, is wider on one side than on the other. The penumbra in the simulation is for a mask sample distance of $200$ $\mu$m. Program used for simulation is described in Section \ref{sec:simulation}}
+	\caption{A diagram of the evaporation rays for a tilted mask with only one hole (\subref{fig:penumbra_explanation_tilt_2d}) showing the 2 different penumbral widths $p_{\text{i}}$ that appear in a cross-section. (\subref{fig:penumbra_explanation_tilt_sim}) Simulated evaporation with large penumbra for a tilt angle of $45^\circ$ the penumbra, is wider on one side than on the other. The penumbra in the simulation is for a mask sample distance of $200$ $\mu$m and a hole diameter of $3$ $\mu$m. Program used for simulation is described in Section \ref{sec:simulation}}
     \label{fig:penumbra_explanation_tilt}
 \end{figure}
 
-Since the evaporation effectively gives a projection of a circle through an aperture, the resulting image is a conical section. If the alignment between mask and sample is perfect the projection will thus give a circle, but if alignment is off the projection will instead be an ellipse.
+Since the evaporation effectively gives a projection of a circle through an aperture, the resulting image is a conical section. If alignment is imperfect the projection will be an ellipse.
 
 \section{Measurement techniques}
 In the following, the techniques used in this thesis and their working principles will be explained.
@@ -103,36 +105,39 @@ In order to detect this bending, a laser is directed to the top of the cantileve
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.7\linewidth]{img/Plots/Background/AFMDiagram.pdf}
-    \caption{Diagram showing the configuration of an AFM. Depicted here is contact mode but the experimental setup is the same for all modes.}
+    \caption{Diagram showing the configuration of an AFM with the tip in contact with the sample. Arrows indicate movement directions.}
     \label{fig:afm_principle}
 \end{figure}
 
 \subsubsection{Modes}
-There are 3 commonly used modes for AFM operation: Contact, Tapping and non-contact. All of these operate in different regimes of the tip sample potential and thus require different ways of operation and different conditions for usage.
-\paragraph{Contact}
-The most intuitive mode of AFM measurement is contact mode.
-In contact mode the sample is directly contacted by the cantilever, this is achieved by applying a constant force to the surface with the cantilever. When passing over a higher feature of the samples surface the cantilever will bend and this deflection can be measured with the laser diode, when this occurs the z piezo is adjusted in order to preserve a constant force on the sample. By measuring the needed z adjustment, a height map image of the sample can be created. \\
-The main disadvantage of contact mode is that since the cantilever contacts the sample constantly with a constant force both the sample and the cantilever will damage relatively quickly in the process, which is why this technique is only used when this damage to cantilever and sample is non-problematic or even desired. One can for example use contact mode to scratch the sample's surface in specific locations to etch patterns into the surface. \\
-In this thesis, however, both damage to cantilever and sample should be minimized, which is why contact mode is not used.
-\paragraph{Non-Contact}
-Another possible mode for AFM usage is non-contact mode. In this mode the cantilever does not touch the sample at all and instead the attractive potential of the surface to the cantilever is used to map the topography of the sample. In order to accomplish this the cantilever is oscillated near the samples surface close to its natural resonance frequency, like in tapping mode, when the cantilever now approaches the samples surface its resonance frequency is shifted towards a lower value, which then causes the oscillation amplitude to lower with distance to the samples surface, when the tip sample distance is increased the opposite happens. Now two approaches can be taken, either one can use phase or amplitude to determine deviations from the resonance frequency of the cantilever. By either keeping the phase between driving and response at 90° or the amplitude at a set value, both are accomplished by moving the z piezo as the cantilever is moved across the sample, allowing the changes in z to give a topographical image of the sample's surface. This is called the feedback loop, as the feedback from the laser diode measurement drives the signal given to the z piezo to constantly keep the same tip sample distance.\\
-While non-contact mode does keep the tip and the sample undamaged in most cases it comes with the cost of added difficulty since the potential in the non-contact regime is relatively flat, which causes the signal given to the feedback loop to be small in scale and thus prone alterations from other sources, requiring high resolution frequency measurement from the 3d laser sensor or resulting in a low resolution image. Additionally, this technique is very sensitive to humidity as in atmospheric conditions a thin water film is on the surface of the sample and the thickness of this film can vary with conditions in the room, for this reason non-contact mode is usually reserved for UHV environments. Instead, a different, but similar technique is used for atmospheric conditions.
-\paragraph{Tapping}
-Tapping mode is a hybrid of both contact and non-contact modes. It is also sometimes called semi contact mode. Here the tip is oscillated near the resonance frequency again, but closer to the sample's surface, than in non-contact mode. This makes the oscillation see both the attractive and the repulsive part of the tip-surface potential. At the lower part of this oscillation, the tip contacts the surface, thus "tapping" it. The general idea behind the feedback loop from the non-contact mode is the same and a set point is constantly maintained, thus allowing the mapping of the surface. Due to the closer distance to the sample's surface however, both the resolution can be potentially higher and a transparency with regard to thin films on the samples surface can be achieved, at the cost of reducing the tip's lifespan, due to the tapping contacting the surface. The lifetime of the tip is however much longer, than that of contact mode and damage to the sample is, given correct operation, minimal. In this thesis, only the tapping mode of the AFM is used, as the sample was analyzed in atmospheric conditions.
+There are 3 commonly used modes for AFM operation: Contact, Tapping and non-contact. All of these operate in different regimes of the tip sample potential (Fig. \ref{fig:afm_potential}) and thus require different ways of operation and different conditions for usage.
 
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.7\linewidth]{img/Plots/AFMPotential.pdf}
-    \caption{Schematic diagram of the Lennart Jones potential governing the interaction between tip and sample in an AFM. The 3 AFM Modes are marked \textcolor{tab_green}{contact}, \textcolor{tab_blue}{tapping} and \textcolor{tab_red}{non-contact} these regions are approximate. Units on both axes are arbitrary.}
+    \caption{Schematic diagram of the Lennart Jones potential governing the interaction between tip and sample in an AFM. The 3 areas of the AFM Modes are marked \textcolor{tab_green}{contact}, \textcolor{tab_blue}{tapping} and \textcolor{tab_red}{non-contact}. These regions are approximate. Units on both axes are arbitrary.}
     \label{fig:afm_potential}
 \end{figure}
 
-There are more ways to get useful sample information from an AFM, the tip can for example be coated in a magnetic coating in order to perform Magnetic Force Microscopy, but for the purposes of this thesis other uses will be neglected.
+\paragraph{Contact}
+The most intuitive mode is contact mode.
+In contact mode the sample is directly contacted by the cantilever. This is achieved by applying a constant force to the surface with the cantilever. When passing over a higher feature of the samples surface the cantilever will bend and this deflection is measured with the laser diode. When this occurs, the z piezo is adjusted until the previous bending is restored. This restoration of bending is the feedback loop of contact mode (see Fig. \ref{fig:afm_principle}). By measuring the needed z adjustment, a height map of the sample is recorded. \\
+The main disadvantage of contact mode is that the constant force can damage the surface and the cantilever. One can even use contact mode to scratch the sample's surface in specific locations to write patterns into the surface. \\
+In this thesis, however, both damage to cantilever and sample was minimized, which is why contact mode is not used.
+\paragraph{Non-Contact}
+Another mode is non-contact mode. In this mode, the cantilever does not touch the sample at all. Instead, the attractive potential of the sample surface to the cantilever is used to map the topography. In order to accomplish this the cantilever is oscillated near the samples surface close to its natural resonance frequency. When the cantilever approaches the samples surface its resonance frequency is shifted to lower value, in each oscillation cycle. This causes the oscillation amplitude to decrease with distance to the samples surface. When the tip sample distance increases the opposite happens. \\
+Either one can use phase or amplitude to determine deviations from the resonance frequency of the cantilever. By either keeping the phase between driving and response at 90° or the amplitude of the cantilever oscillation at constant excitation. Both are accomplished by moving the z piezo as the cantilever is moved across the sample. This is the feedback loop for non-contact mode. The feedback from the laser diode measurement drives the signal given to the z piezo to constantly keep the same tip sample distance.\\
+While non-contact mode damages the tip and the sample less. It comes with the cost of added difficulty since the potential in the non-contact regime is relatively flat. Due to this feedback loop signal is small. Additionally, this technique is very sensitive to humidity as in atmospheric conditions a thin water film forms on the surface of the sample. Its thickness can vary with conditions in the room, for this reason non-contact mode is usually reserved for UHV environments. 
+
+\paragraph{Tapping}
+Tapping mode is a hybrid of both contact and non-contact modes. It is also sometimes called semi contact mode. Here the tip is oscillated near the resonance frequency, but closer than in non-contact mode. The oscillation is affected by both the attractive and the repulsive part of the tip-surface potential. At the lower part of this oscillation, the tip contacts the surface. The feedback loop is the same as in non-contact mode. Due to the closer distance to the sample's surface however, the resolution is higher and a transparency with regard to thin films on the samples surface is achieved. But the tip's lifespan is reduced, due to the tapping contacting the surface. It is however much longer, than that of contact mode and damage to the sample is minimal. In this thesis, only the tapping mode of the AFM is used. As analysis was performed under atmospheric conditions.
+
+There are more ways to get useful sample information from an AFM. The tip can, for example be alloy in a magnetic coating for Magnetic Force Microscopy. For the purposes of this thesis other uses will be neglected.
 
 AFMs provide high resolution topographical images at the nanometer scale and allow for accurate estimation of surface properties of a sample's surface. Atomic force microscopy is a commonly used tool to characterize nano-lithography samples and has been extensively used in physics, material science and biology among others~\cite{afm_physics, afm_bio}.
 
 \subsection{Scanning Electron Microscopy} 
-A \textbf{S}canning \textbf{E}lectron \textbf{M}icroscope (SEM) is a microscope in which an image of the topography of a sample is created via a focused electron beam. In order to do this, a sample is hit by a focused beam of electrons, while suspended in vacuum. When an electron hits the surface of the sample, the electron can undergo various interactions with the sample.
+A \textbf{S}canning \textbf{E}lectron \textbf{M}icroscope (SEM) provides images of the topography of a sample via a focused electron beam. The sample is hit by a focused beam of electrons, while suspended in vacuum. 
 
 \begin{figure}[H]
     \centering
@@ -150,11 +155,12 @@ A \textbf{S}canning \textbf{E}lectron \textbf{M}icroscope (SEM) is a microscope
     \label{fig:sem_setup}
 \end{figure}
 
-The electron beam of an SEM is created using an electron gun. The electron guns used are usually tungsten electrons for comparatively low cost and good reliability. Another possibility is using \textbf{F}ield \textbf{E}mission \textbf{E}lectron \textbf{G}uns (FEEG)~\cite{SEM_book}. The beam emitted from the electron gun still has too large spread to be used for SEM imaging for this reason the beam must be focused using electron lenses. Accurate focusing of the electron beam is one of the major difficulties of SEM design, and measurement uncertainty is usually dominated by optical artifacts from beam focus. In principle, electron lenses can use either electrostatic or magnetic fields, but in practice only magnetic lenses are used since they provide smaller lensing abberations. Multiple sets of lenses are used to magnetically focus the beam onto the sample~\cite{SEM_book}. The different sets of lenses used to direct the beam to the sample can be seen in Figure \ref{fig:sem_setup_beam}. Due to the use of electromagnets for lensing the parameters can be controlled relatively easily. The different lenses are used to focus the image partially manually by the user to create a sharp and stable image.
+The electron beam of an SEM is created using an electron gun. Often tungsten electron guns are used for their comparatively low cost and reliability. Another possibility is a \textbf{F}ield \textbf{E}mission \textbf{E}lectron \textbf{G}un (FEEG)~\cite{SEM_book}. The beam is focused using electron lenses. Accurate focusing of the electron beam is one of the major difficulties of SEM design, and spatial resolution is usually dominated by optical artifacts from the beam focus. In principle, electron lenses can use either electrostatic or magnetic fields. In practice only magnetic lenses are used since they provide less lensing abberations. Multiple sets of lenses are used to focus the beam onto the sample~\cite{SEM_book}. The different sets of lenses used to direct the beam to the sample can be seen in Figure \ref{fig:sem_setup_beam}. Due to the use of electromagnets for lensing the parameters can be controlled relatively easily. The control is partially automatic and partially done manually. \\
 
-The main matter interaction that is measured in an SEM is the inelastic scattering of the beam electron with a sample electron. The sample electron is ejected at a different angle from the incoming beam electron. This ejected electron is called secondary electron~\cite{SEM_book}. This as well as the other processes that can be measured in an SEM can be seen in Figure \ref{fig:sem_setup_interaction} The secondary electrons are ejected from the sample at relatively low energy of $<50$ eV and can thus be attracted with a positive bias voltage ($>10$ kV) applied to a scintillator, which then converts the attracted electrons into light photons, which are then detected via \textbf{P}hoto \textbf{M}ultiplier \textbf{T}ube (PMT). Such a detector is called \textbf{E}verhart–\textbf{T}hornley detector (ET) detector~\cite{SEM_book}. Using these detectors, it is now possible to detect the amount of secondary electrons emitted at the current beam location. This amount is based on the surface's topography, and thus by measuring the voltage given at the PMT a topographical image of the sample can be obtained. The detection of secondary electrons, back-scattered electrons and X-rays can be seen in Figure \ref{fig:sem_setup_beam}. Other types of electron are also emitted in beam sample interaction and can be detected in an SEM setup, but for this thesis only the secondary electrons are relevant.\\
+When an electron hits the surface of the sample, the electron can undergo various interactions with the sample (Fig. \ref{fig:sem_setup_interaction}).
+The main matter interaction that is measured in an SEM is the inelastic scattering of beam electrons with sample electrons. The sample electron is ejected at a different angle from the incoming beam electron. This ejected electron is called secondary electron~\cite{SEM_book}. Secondary electrons are ejected from the sample at relatively low energy of $<50$ eV and can thus be attracted with a positive bias voltage ($>10$ kV) applied to a scintillator. It converts the attracted electrons into photons, which are then detected via \textbf{P}hoto \textbf{M}ultiplier \textbf{T}ube (PMT). Such a detector is called \textbf{E}verhart–\textbf{T}hornley (ET) detector~\cite{SEM_book}. The amount of sencodary electrons detected is based on the surface's topography. Thus by measuring the voltage given at the PMT, a topographical image of the sample can be obtained. The detection of secondary electrons, back-scattered electrons and X-rays can be seen in Figure \ref{fig:sem_setup_beam}. \\
 
-SEMs give high contrast large area images with good spatial resolution and were thus used in this thesis to initially locate evaporated fields on silicon samples, but SEM imaging comes with some downsides, which is why they are not sufficient to fully characterize the samples in this thesis.
-On insulating or semiconducting samples, the electron beam of the SEM causes areas of the sample to charge up, which changes the SEM image over time and can potentially cause damage to the sample. For this reason, the electron beam has to be operated at the lower end of beam energy. In theory this limits the spatial resolution as higher energy electron have a better De-Broglie wavelength, but optical effects arising from focusing the electron beam bottleneck the resolution rather than wavelength. SEMs give good topographical images, but exact quantitative heights of features cannot be directly obtained from an SEM image without a known reference, and thus they are not sufficient for sample characterization. \\
+SEMs give high contrast large area images with good spatial resolution. They were used in this thesis to initially locate evaporated fields on silicon samples. SEM imaging comes with some downsides.
+On insulating or semiconducting samples, the electron beam of the SEM causes areas of the sample to charge up, which changes the SEM image over time and can potentially cause damage to the sample. To avoid this, the electron beam has to be operated at low beam energy. In theory this limits the spatial resolution as higher energy electron have a smaller De-Broglie wavelength $\alpha$, but optical effects arising from focusing the electron beam bottleneck the resolution. SEMs give good topographical images, but exact quantitative heights of features cannot be directly obtained from an SEM image without a known reference, and thus they are not sufficient for sample characterization. \\
 
 SEM images and in particular the related technologies of \textbf{T}ransmission \textbf{E}lectron \\ \textbf{M}icroscopy and \textbf{S}canning \textbf{Tunneling} \textbf{E}lectron \textbf{M}icroscopy have been used to characterize properties of thin films and characterize interfaces down to the single atomic scale~\cite{self_epitaxy}.\\
diff --git a/chap02.aux b/chap02.aux
index dba1803..b073f8a 100644
--- a/chap02.aux
+++ b/chap02.aux
@@ -1,124 +1,127 @@
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+\newlabel{fig:mask_old_correl}{{2.21}{38}{The 3 capacitance curves of the Mask labeled "old" scaled to be within same range, via normalization and subsequent fit of offset parameter, first to C2 and C3 fit to C1 and then C3 fit to C2. The lower plots show residuals. The residuals show the variation to be well within the error bars and overall within less than $1$ \%}{figure.caption.41}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2.22}{\ignorespaces 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.}}{39}{figure.caption.42}\protected@file@percent }
+\newlabel{fig:cross_cap_diagramm}{{2.22}{39}{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}{figure.caption.42}{}}
+\@writefile{toc}{\contentsline {paragraph}{Leakage current}{39}{section*.43}\protected@file@percent }
+\@writefile{toc}{\contentsline {paragraph}{Improved gold pin fitting}{39}{section*.44}\protected@file@percent }
+\@writefile{tdo}{\contentsline {todo}{Image of gold pins}{39}{section*.45}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.7}Stop Conditions}{40}{subsection.2.3.7}\protected@file@percent }
+\@writefile{toc}{\contentsline {paragraph}{High correlation between capacitance curves}{40}{section*.46}\protected@file@percent }
+\@writefile{toc}{\contentsline {paragraph}{Low correlation between capacitance curves}{40}{section*.47}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {2.4}Mask Aligner operation}{40}{section.2.4}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}Sample preparation}{40}{subsection.2.4.1}\protected@file@percent }
+\newlabel{sec:sample_prep}{{2.4.1}{40}{Sample preparation}{subsection.2.4.1}{}}
 \@setckpt{chap02}{
-\setcounter{page}{41}
+\setcounter{page}{42}
 \setcounter{equation}{4}
 \setcounter{enumi}{10}
 \setcounter{enumii}{0}
@@ -147,7 +150,7 @@
 \setcounter{subfigure}{0}
 \setcounter{subtable}{0}
 \setcounter{lstnumber}{1}
-\setcounter{@todonotes@numberoftodonotes}{2}
+\setcounter{@todonotes@numberoftodonotes}{5}
 \setcounter{float@type}{8}
 \setcounter{AM@survey}{0}
 \setcounter{thm}{0}
diff --git a/chap02.tex b/chap02.tex
index a9b96bd..14758a1 100644
--- a/chap02.tex
+++ b/chap02.tex
@@ -21,7 +21,7 @@ The Load Lock is equipped with a small ion getter pump, that runs on its own, al
 Another device, unrelated to this thesis, a gold evaporator, is connected to the vacuum system. It is not further discussed in this thesis, but is drawn in Figure \ref{fig:mask_aligner_chamber} since it was attached to the same system. \\
 
 \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 crucible is made from tungsten. The evaporator uses a filament placed near the crucible to bombard the crucible with highly energetic electrons. To accomplish this, a high current (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. This heat is used to degas the evaporator and to prevent contaminants from settling on the filament, when no evaporation is taking place. The heating element 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 during degassing a thermal sensor is placed on the copper cylinder. \\
+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 crucible is made from tungsten. The evaporator uses a filament placed near the crucible to bombard the crucible with highly energetic 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. This heat is used to degas the evaporator and to prevent contaminants from settling on the filament, when no evaporation is taking place. The heating element 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 during degassing a thermal sensor is placed on the copper cylinder. \\
 
 \begin{figure}[H]
     \centering
@@ -30,7 +30,7 @@ The electron beam evaporator used for the lead evaporation in the mask aligner c
     \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, controlling the amount of heating that is received by the source material. This method of temperature control is the least reliable and was not used in this thesis. The distance was previously optimized. 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 flow to the MA chamber. \\
+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. The distance was previously optimized. 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
@@ -64,8 +64,8 @@ The motor module consists of $3$ piezo motors. They move the mask along the z ax
 Often 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}
-In order to control the movement of the mask stage using the mask aligner, $3$ motors of $6$ piezo stack made of $4$ piezo crystals each are used. Piezo crystals expand/contract upon being supplied with a voltage. In order for the piezo crystals to move the stage, a sapphire prism is clamped between the $6$ piezo stacks. When one now applies a voltage to the piezo stacks, the prism is moved by the stacks. An illustration of the principle is shown in Figure \ref{fig:slip_stick_diagram}. \\
-First a slowly rising pulse is applied to the piezo moving the prism along with the piezo. This pulse is referred to as the "slow flank". Afterward, a very fast pulse ($<1$ $\mu$s) is applied, contracting the piezo back into its original position. The prism however due to its inertia remains in position. This pulse is referred to as the "fast flank". When done many times over, the prism can be moved larger distances. The direction depends on the voltage amplitude signal polarity. The simplest pulse shape allowing for this is the saw tooth wave, but other signal shapes that follow the principle can be used.
+In order to control the movement of the mask stage using the mask aligner, $3$ motors of $6$ piezo stack made of $4$ piezo crystals each are used. Piezo crystals expand/contract upon being supplied with a DC voltage. In order for the piezo crystals to move the stage, a sapphire prism is clamped between the $6$ piezo stacks. When one now applies a voltage amplitude to the piezo stacks, the prism is moved by the stacks. An illustration of the principle is shown in Figure \ref{fig:slip_stick_diagram}. \\
+First a slowly rising pulse is applied to the piezo moving the prism along with the piezo. This pulse is referred to as the "slow flank". Afterward, a very fast pulse ($<1$ $\mu$s) is applied, contracting the piezo back into its original position. The prism however due to inertia remains in position. This pulse is referred to as the "fast flank". When done many times over, the prism can be moved larger distances. The direction depends on the voltage amplitude signal polarity. The simplest pulse shape allowing for this is the saw tooth wave, but other signal shapes that follow the principle can be used.
 
 \begin{figure}[H]
     \centering
@@ -210,15 +210,15 @@ edge of the sample, and the upper side of the sample holder, cannot be observed.
 
 \begin{figure}[H]
 	\centering
-	\begin{subfigure}{0.3\textwidth}
+	\begin{subfigure}{0.32\textwidth}
     \includegraphics[width=\linewidth]{img/CameraAlignment_bad_low.pdf}
     \caption{}
 	\end{subfigure}
-	\begin{subfigure}{0.3\textwidth}
+	\begin{subfigure}{0.32\textwidth}
     \includegraphics[width=\linewidth]{img/CameraAlignment_high.png}
     \caption{}
 	\end{subfigure}
-	\begin{subfigure}{0.3\textwidth}
+	\begin{subfigure}{0.32\textwidth}
     \includegraphics[width=\linewidth]{img/CameraAlignment_good.png}
     \caption{}
 	\end{subfigure}
@@ -230,9 +230,9 @@ can see the surface of the sample holder on the upper side as well as an upwards
 shift on the side of the sample, indicating that the sample is tilted with
 respect to the camera, this is caused by a camera too high up or tilted too far
 down.}
-    
     \label{fig:camera_alignment_example}
 \end{figure}
+\todo{Fix}
 
 When the camera is aligned with the sample, the mask can now be moved close to
 the sample leaving a gap between mask and sample still. Now the
@@ -264,10 +264,8 @@ achievable optical accuracy. The progression of this can be seen in Figure \ref{
 \todo{Start here}
 \subsection{Approach curves}
 
-After optical alignment, the final step towards an aligned sample comes via
-capacitive measurement to obtain the distance to the sample surface. The 3
-capacitive sensors on the mask are aligned with the 3 motors of the Mask Aligner
-and are labeled as seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_motors}. The masks consist of a $200$ $\mu$m thick \ce{Si} body. A small $100\times100$ $\mu$m \ce{SiN} membrane, with $3$ $\mu$m holes each $10$ $\mu$m apart, is situated in the middle of the body. The \ce{SiN} actually covers the whole mask and is $1$ $\mu$m thick, but only the center part has holes and a trench below it. Around the hole membrane are $3$ gold pads, that function as the aforementioned capacitive sensors. The \ce{Au} of the gold pads is placed below an insulating $\approx 100$ nm layer of \ce{SiO2} at the bottom of a trench in the \ce{Si} body. They are at a distance of $0.7$ mm from the hole membrane and are located in an equilateral triangle around it. The dimensions of the mask and the capacitive sensors on the mask can be seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_mask}.
+After optical alignment, the mask is aligned to the sample via capacitive measurement. The 3
+capacitive sensors on the mask are for most masks setup in correspondance with the 3 motors of the Mask Aligner. They are labeled as seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_motors}. Note that this diagram is not true for all masks, since some are assembled misaligned on the mask stage. The mask consist of a $200$ $\mu$m thick \ce{Si} body. A small $100\times100$ $\mu$m \ce{SiN} membrane, with $3$ $\mu$m holes each $10$ $\mu$m apart, is situated in the center. The \ce{SiN} covers the whole mask and is $1$ $\mu$m thick. Below the center of the mask a trench is carved in the \ce{Si}. Around the hole membrane are $3$ gold pads, that function as capacitive sensors. The \ce{Au} of the gold pads is placed below an insulating $\approx 100$ nm layer of \ce{SiO2} at the bottom of a trench in the \ce{Si} body. They are at a distance of $0.7$ mm from the hole membrane and are located in an equilateral triangle around it. The dimensions of the mask and the capacitive sensors on the mask can be seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_mask}.
 
 \begin{figure}[H]
     \centering
@@ -285,7 +283,7 @@ and are labeled as seen in Figure \ref{fig:mask_aligner_nomenclature_capacitance
 	\caption{(\subref{fig:mask_aligner_nomenclature_capacitances_motors}) shows a 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 $3$ piezo motor stacks. (\subref{fig:mask_aligner_nomenclature_capacitances_mask}) shows a 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 actually used to create patterns.}
 \end{figure}
 
-The readout of the capacitance sensors is performed with a Lock-in amplifier, and the movement of the piezo motor stacks is done with the RHK piezo motor controller. Communication with both the RHK and the Lock-in amplifier is done with a Matlab script. The communication with the RHK is done via a network interface, while the Lock-in uses a serial interface. 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}.
+The readout of the capacitance sensors is performed 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. The communication with the RHK is done via a network interface, while the Lock-in uses a serial interface. 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
@@ -294,10 +292,8 @@ The readout of the capacitance sensors is performed with a Lock-in amplifier, an
     \label{fig:diagram_MA_circ}
 \end{figure}
 
-Note that this diagram is not true for all masks, since some were assembled with
-the capacitance sensors pointed in the wrong direction. 
 The capacitance of each of the $3$ sensors can be approximated using a simple
-plate capacitor model where the gold pad is one plate of the capacitor and the
+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}
@@ -307,17 +303,16 @@ the capacitor.
 where $C$ is the capacitance, $\epsilon_0$ is the vacuum permittivity, $\epsilon_r$ is the relative permittivity between the capacitor plates, $A$ is
 the area of overlap of the capacitor plates, which in this case corresponds to
 the area of the gold pad and $r$ is the distance between the gold pad and the
-\ce{Si} of the sample. \\ 
-If any of the gold pads now move a distance $r'$ closer to the sample the
-capacitance readout should increase by 
+\ce{Si} of the sample. $r$ is both the distance of $1$ $\mu$m of \ce{SiN} on the mask's surface and the mask sample distance in vacuum. \\ 
+If any of the gold pads move a distance $r'$ closer to the sample the
+capacitance increases by:
 \begin{equation}
 	C' = \epsilon_0 \epsilon_r \frac{A}{r + r'} \Rightarrow \frac{1}{C'} =
 \frac{1}{C} + \epsilon_0 \epsilon_r \frac{A}{r'}
 \end{equation}
-$r$ here has to be split into the distance of $1$ $\mu$m of \ce{SiN} on the mask's surface and the rest of the mask sample distance in vacuum. The $\epsilon_r$ value for \ce{SiN} is $6.06$ (for a thin film of $437$ nm)~\cite{SiN_dielectric} and the value for UHV can be approximated to very good accuracy as $1$, since the system is at a pressure of at least $10^{-8}$ mbar and even for atmospheric conditions $\epsilon_r \approx 1$.
+ The $\epsilon_r$ value for \ce{SiN} is $6.06$ (for a thin film of $437$ nm)~\cite{SiN_dielectric}. The value of $\epsilon_r$ in UHV is $\approx 1$, since the system is at a pressure of at least $10^{-8}$ mbar.
 The capacitance increases with a $\frac{1}{r}$ dependence. This holds true until
-the mask's surface makes contact with the sample or any contamination particles
-on the samples or the mask's surface. 
+the mask's surface makes contact with the sample. Contamination particles can also cause indirect contact of mask and sample.
 
 \begin{figure}[H]
     \centering
@@ -349,13 +344,8 @@ on the samples or the mask's surface.
     \caption{}
 	\label{fig:approach_curve_example_full}
 	\end{subfigure}
-	\caption{A capacitance (approach) curve, for one of the capacitive sensors, as
-an example (a) and the difference of each capacitance value to the last (b).
-Only one sensor is pictured. Marked are the important point where the slope of
-the $\frac{1}{r}$ curve changes. These points, where the geometry of the
-alignment process changes are marked labeled First, Second and Full contact.
-Before each of these points, the difference goes to a local maximum. These are
-marked with blue dashed lines. Below are images of the geometry between mask and
+	\caption{(a) A capacitance (approach) curve. (b) the difference of each capacitance value to the last.
+Only one sensor is pictured. 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 mark
 where the mask is touching the sample.}
     \label{fig:approach_curve_example}
@@ -363,12 +353,12 @@ where the mask is touching the sample.}
 
 The curve obtained from approaching the sample is called an approach curve. An
 example can be seen in Figure \ref{fig:approach_curve_example_cap} The same
-curve when retracting mask from sample is called a retract curve.\\
-When the alignment is not perfect, which is the expectation, the mask will upon approach start contacting the sample with one point (or potentially an edge) first. An illustration of
+curve when retracting mask from sample is called a retract curve. \\
+
+When the alignment is not perfect, the mask will start contacting the sample with one point (or potentially an edge) first. An illustration of
 this is seen in Figure \ref{fig:approach_curve_example_first} This will inhibit
-the movement of the mask on the side associated, which results in a changed
-step size. Since all motors move the mask frame and the mask is in the middle of
-it this will affect all motors step sizes, albeit in differing amounts. Due to
+the movement of the mask on associated motor. This results in a changed
+step size. Since all motors move the mask frame this will affect all motors step sizes, albeit to different degrees. Due to
 this step size change, the slope of the approach curve changes (shown in Eq.
 \ref{eq:cap_slope_change}), as seen in Figure
 \ref{fig:approach_curve_example_cap} with the label "First contact".
@@ -381,14 +371,14 @@ this step size change, the slope of the approach curve changes (shown in Eq.
 \end{equation}
 
 Where $C''$ is the final capacitance, $r$ is the distance to first contact, $r'$ is the distance since first contact and $d$ is the parameter by which the step size changes.
-When now approaching the surface further, the mask will then contact the surface
-with another point, which now puts and edge in contact with the sample (see
+When approaching the surface further, the mask will then contact the surface
+with an edge (see
 Figure \ref{fig:approach_curve_example_second}). This will have the same effect
-of changing the slope of the curve again, labeled in Figure
-\ref{fig:approach_curve_example_cap} as "Second contact". If the sample is now
+of changing the slope of the curve 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, illustrated in Figure
-\ref{fig:approach_curve_example_full}. At this point, the capacitance value no
+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}. \\
@@ -400,32 +390,25 @@ values, but instead their differences:
 \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 $C_1 < C_2 < C_3$ each $r'$ apart in distance.
-The values increase monotonically, when however the slope changes, because the
-sample is partially contacted or is in full contact, the value will suddenly
-drop. This can be seen in Figure \ref{fig:approach_curve_example_cap_diff}. When
-the peak value of this graph is known, due to prior recording of an approach
-curve one can predict the contact before it happens and stop the approach before
-the sample is contacted. This peak value of capacitance difference is called a
-"stop condition".
-
-In an ideal scenario where the mask is perfect and the only capacitance values
-to consider are the ones from the gold pads to the sample, the distance to the
-sample could be read off from the capacitance value via Eq.
+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. This can be seen in 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 of capacitance difference is called a "stop condition". The stop condition has to be determined using a calibration approach. \\
+
+When mask is perfect and the only capacitance values
+to consider are from gold pads to the sample, the distance to the
+sample can be read off from the capacitance value via Eq.
 \ref{eq:plate_capacitor}. However, with real masks the capacitance values can
-deviate drastically from the ideally expected ones, so without any point of
+deviate drastically from the expected ones. Without any point of
 reference, no statement about the absolute distance can be made.
 For this reason, the approach curve of any mask sample combination has to be
 recorded first as a calibration curve. This requires contacting the sample at
-least once. However, this calibration can still not be used to obtain absolute
-distance values for the given capacitance since upon retraction and subsequent
+least once. Absolute distance can still not be measured since upon retraction and subsequent
 approach, the capacitance values drop as seen in Figure
 \ref{fig:approach_subsequent}. This is either due to accumulation of
-misalignement due to small errors in the different Z motor step sizes and/or
-accumulation of particles on the sample/mask surface due to contacting the
-sample. \\
-In order to still get a good replicable alignment instead, the difference in
-capacitance is used, and the stop condition is used to determine good alignment
+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]
@@ -435,20 +418,19 @@ capacitance is used, and the stop condition is used to determine good alignment
     \caption{Plot of data of approach curves recorded on two different days. The
 second curve was recorded after retraction and subsequent approach. The 2 curves
 do not start at the same distance away from sample, which is why they are not
-aligned on the x-axis. A clear drop in capacitance can be observed from one
-measurement to the other regardless.}
+aligned on the x-axis. Both are driven until full contact.}
     \label{fig:approach_subsequent}
 \end{figure}
 
 \subsection{Reproducibility}
-One of the questions about the efficacy of Mask Aligner as an alignment tool is
-the reproducibility of approach curves with regard to different samples and
-other differences in conditions. In the master’s thesis of Jonas Beeker the
+Reproducibility of approach curves with regard to different samples and masks is important for the future use of the Mask Aligner. In the master’s thesis of Jonas Beeker the
 reproducibility of different masks, different locations, different approaches
-and a comparison before and after evaporation was discussed~\cite{Beeker}.
+and a comparison before and after evaporation were discussed~\cite{Beeker}.
 
 \subsubsection{Reproducibility when removing sample/mask}
 
+\todo{Here}
+
 One question concerning reproducibility is whether the approach curve is strongly affected by the exchange of mask or sample, or even just the reinsertion of mask or sample. This is important since an exchange of sample to perform a new evaporation is a common operation in the creation of patterned samples. 
 
 \begin{figure}[H]
@@ -476,54 +458,51 @@ Reinserting the sample also induced a difference in approach curves, but the dif
 
 
 \subsection{Cross capacitances} \label{subsec:cross_cap}
-The biggest problem with the for alignment with current set of masks is that the
-approach curves obtained for aligning masks with them, show heavy correlation
-between the sensors, $C_i$ see Figure \ref{fig:cross_cap_approach}~\subref{fig:cross_cap_approach_difference}-\subref{fig:cross_cap_approach_difference_2}. If
+The biggest alignment problem with current set of masks is the heavy correlation
+between mask sensors, $C_i$ see Figure \ref{fig:cross_cap_approach}~\subref{fig:cross_cap_approach_difference}-\subref{fig:cross_cap_approach_difference_2}. If
 alignment were perfect, these curves should indeed appear to be very similar
-since moving any of the motors affects all capacitance sensors due to the
-geometry of the mask stage, but each of the capacitance sensors should
-independently give a curve, which follows a $\frac{1}{r}$ behavior. From this
-follows, that if alignment is not perfect and the distances from the \ce{Si} are
-indeed different for each of the sensors the behavior of the 3 different curves
-should be much more different. A simulated approach curve for a difference of $440$ nm between $C_1$ and $C_2$ and $560$ nm between $C_1$ and $C_3$ can be seen in Figure \ref{fig:cross_cap_approach_sim}. The model assumes no capacitance between the 3 capacitance sensors and no capacitance to the environment. Additionally, the model assumes all motors drive exactly the same. This assumes the mask first makes contact with the sample at the corner that is aligned with $C_1$ such that the motor aligned with $C_1$ stops moving the stage up. After that, the same happens for $C_2$.
+since moving any of the motors affects all capacitance sensors, but each of the capacitance sensors should independently give a curve, which follows a $\frac{1}{r}$ behavior. From this
+follows, that if the distances from the \ce{Si} is different for each sensor. Their approach curves should be distinct. A simulated approach curve for a difference of $440$ nm between $C_1$ and $C_2$ and $560$ nm between $C_1$ and $C_3$ is shown in Figure \ref{fig:cross_cap_approach_sim}. The model assumes no capacitance between the 3 capacitance sensors and no capacitance to the environment. Additionally, the model assumes all motors drive exactly the same. It also assumes the mask first makes contact with the sample at the corner that is aligned with $C_1$ such that the motor aligned with $C_1$ stops moving. After that, the same happens for $C_2$.
 
 \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{The 3 capacitance curves of two example measurements of 2 different masks normalized to ensure same scale (\subref{fig:cross_cap_approach_difference}, \subref{fig:cross_cap_approach_difference_2}). (\subref{fig:cross_cap_approach_sim}) shows a simple simulation of how the approach with tilted sample would look in an ideal case.}
+	\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 same scale. (\subref{fig:cross_cap_approach_sim}) shows a simple simulation of how the approach with tilted sample would look in an ideal case.}
 	\label{fig:cross_cap_approach}
 \end{figure}
 
-The model assumes the gold plates behave as plate capacitors, with the
-difference in distance for the capacitors assumed to be $440$ nm each, so
-that the distance between C1 and C3 is $560$ nm. A distance that is well within the maximal optical accuracy of $\approx 5$ $\mu$m for maximal zoom and resolution. Even for such a small
-difference, the measured deviance between the curves, should be very visible. The
-values for the capacitances obtained should approximately follow the formula for
-a plate capacitor \ref{eq:plate_capacitor}. \\
-However, the curves measured for capacitance show a deviation in behavior from the model. Figure \ref{fig:cross_cap_approach_difference} shows this. The curves of the 3 capacitances were normalized to bring them into the same range. The different capacitances vary by $1$-$2$ order of magnitude. The largest capacitance was measured to $19.12$ pF. It starts with the capacitances with large difference and merges together for small distance. This is the opposite to the expected behavior. The general shape of the curve also is identical between all $3$, while it is expected that 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. Here again the largest capacitance was measured to be $19.78$ pF and $C_2$ and $C_3$ varied by $2$ orders of magnitude from $C_1$.
+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 $\approx 5$ $\mu$m for maximum zoom and resolution. Even for such a small difference, the deviance between the curves, is very visible. \\
+
+
+However, the curves measured for capacitance show a deviation in behavior from the model. Figure \ref{fig:cross_cap_approach_difference} shows this. The curves of the 3 capacitances were normalized to bring them into the same range. The different capacitances vary by $1$-$2$ order of magnitude. The largest capacitance was measured to $19.12$ pF. The curves start with large deviation and seem to converge. This is the opposite to the expected behavior (Fig. \ref{fig:cross_cap_approach_sim}). The general shape of the curve also is identical between all $3$, while it is expected that 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 $C_1$. 
 For the gold pads, this would give a capacitance value of $\approx 0.40$ fF at a
-distance of $50$ micron, but at a distance of $\approx 50$ micron, as measured
-optically, the capacitance values of the curve $C_1$ measured was $\approx 2.4$
-pF, which deviates by 4 order of magnitude. This corresponds more closely to the
+distance of $50$ micron, at a distance of $\approx 50$ micron, as was 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, where the expected value for a plate capacitor would be $\approx
+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, which does not take into account any stray capacitances of the system
-might have, as well as assume perfectly aligned plate capacitors. 
+of the model. It does not take into account any stray capacitances the system
+might have. \\
 
 %\begin{figure}[H]
 %    \centering
@@ -533,31 +512,20 @@ might have, as well as assume perfectly aligned plate capacitors.
 %\end{figure}
 %\todo{Plot of heavily correlated approach curves}
 
-The reason for this is most likely a leakage current from the cable connecting
-the gold pads to the Si of the Mask. This leakage current is most likely there
-due to errors in the mask preparation process, piercing the \ce{SiNi} layer
-insulating the Si. This is depicted in Figure \ref{fig:leakage_current}. These
-small tears that can happen due to small errors than cause a current path to be
-available from the Silicon of the Mask to the Si of the Sample. The order of
-magnitude from the expectation from this capacitance matches the ones measured
-more closely, suggesting this is the cause.
-
+The reason for this large deviation is most likely a leakage current from the cable connecting
+the gold pads to the Si of the Mask. This leakage current is most likely
+due to errors in the mask preparation process. These cause the \ce{SiNi} layer
+insulating the Si to tear. This is depicted in Figure \ref{fig:leakage_current}. These
+small tears that can happen due to small errors, when gluing the gold wire. This causes a path to be available from the gold wire to the \ce{Si} of the sample. The capacitance, which is now measured is 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 one possible explanation for the large correlation
-in Capacitance readings. A small Tear in the \ce{SiNi} layer removes insulation
-between the gold wire and the Si of the mask, allowing current to travel through.
-This causes the capacitance to reflect the much larger capacitance between the
-Si of the Mask and that of the sample, instead of the desired Capacitance
-between the gold pad and the Si of the sample.}
+    \caption{Diagram showing a cross section of the mask at a gold pad location. A small Tear in the \ce{SiNi} layer removes insulation between the gold wire and the Si of the mask, causing a leakage current. Parallel black lines are meant to illustrate plate capacitors. Larger plate shows larger capacitance.
+}
     \label{fig:leakage_current}
 \end{figure}
 
-Another reason for the correlation of the different capacitances could be that
-the different gold pads as well as the gold pins of the mask shuttle have
-capacitance values to each other, which can be seen as cross or parasitic
-capacitances in a circuit model. \\
+Another reason for the correlation of capacitances are cross capacitances between the gold pad sensors.  \\
 
 \begin{table}[H]
 \centering
@@ -587,9 +555,11 @@ Mask aligner and sample at $0.3$ mm distance. The distance was determined optica
 \label{tab:cross_cap}
 \end{table}
 
-In order to check for this source, measurements of the different cross
-capacitances were obtained for $3$ masks holders inside mask shuttles, as well as
-3 empty shuttles. The results are shown in Table \ref{tab:cross_cap}
+In order to check for the effect of this source, cross capacitances were measured directly between $3$ masks holders inside mask shuttles, as well as
+3 empty shuttles. This is accomplished replacing the connection from the Lock-in amplifier to the sample in Figure \ref{fig:diagram_MA_circ} with one to one of the capacitive sensors. Measurements were performed inside the Mask Aligner with 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 on their own have a 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 increases, often by an order of magnitude. This shows that cross capacitance is a large factor in the correlation. \\
 
 \begin{figure}[H]
     \centering
@@ -600,17 +570,6 @@ scale of the y-axis, and due to this the scale of the uncertainty.}
     \label{fig:mask_old_caps}
 \end{figure}
 
-The shuttles on their own have a cross capacitance values that is of the order
-of the expected capacitance from the measurement itself. When adding the mask
-the cross capacitances increase often dramatically, but when compared with the
-approach curve, the mask labeled old had the highest correlation between
-capacitances, see Figure \ref{fig:mask_old_caps}, of any measured in this thesis,
-whilst the cross capacitance values seem much lower the for example mask $3$. This
-seems to suggest, that while the cross capacitances have a strong influence on
-the correlation of the $3$ capacitance measurements, they are not the dominating
-factor for a lot of masks and that in fact leakage currents to the Si of the
-mask often determine the shape.
-
 \begin{figure}[H]
     \centering
     \includegraphics[width=0.95\linewidth]{img/Plots/Mask_Old_Correl.pdf}
@@ -621,9 +580,13 @@ and overall within less than $1$ \%.}
     \label{fig:mask_old_correl}
 \end{figure}
 
+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, but the approach curve of this mask 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 probable cause here. \\
+
 To further corroborate the similarity between the different capacitance sensors signals, the data of each was overlaid over one another. Since the capacitance ranges vary between sensors, the signals have to first be normalized to fall in the same range. Then additionally an offset has to be fitted, since they are also offset by each other. The result of this can be seen in Figure \ref{fig:mask_old_correl}. This shows even more clearly that the $3$ different capacitances give the same signal within error. 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. 
 
-The data seems to suggest multiple sources for the strong correlation between the 3 capacitance curves. Figure \ref{fig:cross_cap_diagramm} shows a circuit diagram for the known sources of capacitance correlation. In order to improve these capacitance values, a couple of this have to be done.
+This suggests, that while the cross capacitances have a strong influence on
+the correlation of the $3$ capacitance measurements, 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.
 
 \begin{figure}[H]
     \centering
@@ -641,45 +604,45 @@ of magnitude larger.}
     \label{fig:cross_cap_diagramm}
 \end{figure}
 
+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,
 for many of the current masks, to be the main source of correlation. In order to
 ensure no leakage current, a better mask preparation method has to be found that
 ensures no piercing of the \ce{SiNi} layer. This however goes beyond the scope of
-this thesis.
+this thesis. 
 
 \paragraph{Improved gold pin fitting} 
-The gold pins for the current set of masks were not precision machined by the
-workshop, but instead shaved down to the correct size by hand. This causes a
-problem with the fit between male and female side of the gold pins, which causes
-the contact between male and female gold pins to be loose. The mask holder
-should fit in the mask shuttle and then the female and male pins should snap
-together and good and stable contact should be ensured, but instead the contact
-is not stable and the cross capacitances are prone to change even with just
-wiggling the mask sometimes. 
+The gold pins for the current set of masks were cut to correct size by hand. 
+This causes a problem with the fit between male and female side of the gold pins, which causes
+the contact between male and female gold pins to be loose. This allows the mask stage inside the holder to move slightly, changing both distance to sample and giving loose contact.
+Instead, they should be machined with precision by a workshop. Additionally, a stable fit should be tested beforehand.
+
+\todo{Image of gold pins}
+
+The large cross capacitance of the mask holders should also be reduced. No proposal is made in this thesis about how to accomplish this, because the cause is undetermined. The other $2$ factors play a larger role and should be improved first.
 
 \subsection{Stop Conditions}
-When doing an approach for evaporation, first an approach on a mask has to be
-performed as a calibration. Here, two different scenarios can arise:
+When doing an approach for evaporation. As a first step an approach curve has to be
+recorded as a calibration. Here, 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 and effectively only one curve can be
-worked with. However, by performing one approach until full contact between mask
-and sample, where the curves saturate, we can align the mask to a good degree,
-at the cost of possibly damaging mask and sample. Furthermore, the values of capacitance at full contact will then be known and can upon further alignment when
-approaching for evaporation, iteratively tweak the motors until the same value is
-reached again. With this, it will not be possible to achieve perfect alignment (within step size error), but the alignment will be better than with just the optical
-alignment and subsequent approach.
-The stop condition in this case is a single peak in the derivative of the
+can be derived from the 3 different curves. Effectively only one curve can be
+worked with. The stop condition in this case is a single peak in the derivative of the
 capacitance curve. This peak in the capacitance curve happens right before first
-contact, and by stopping slightly before it, decent alignment can be achieved. 
+contact. 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 and can use this to determine how close the mask to sample distance is.
+curve. It can be used to determine how close each sensor to the sample is.
 This is the easier and safer of the two scenarios, but it requires a good mask
-holder.
+holder and mask stage. 
 
 \section{Mask Aligner operation}
 
diff --git a/chap03.aux b/chap03.aux
index 51cd79b..6703170 100644
--- a/chap03.aux
+++ b/chap03.aux
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diff --git a/chap04.aux b/chap04.aux
index c97910a..6c76f0c 100644
--- a/chap04.aux
+++ b/chap04.aux
@@ -1,85 +1,85 @@
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 \providecommand\hyper@newdestlabel[2]{}
 \citation{Olschewski}
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 \@setckpt{chap04}{
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diff --git a/chap05.aux b/chap05.aux
index e6903bc..44af917 100644
--- a/chap05.aux
+++ b/chap05.aux
@@ -1,101 +1,101 @@
 \relax 
 \providecommand\hyper@newdestlabel[2]{}
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 \citation{Bhaskar}
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+\newlabel{fig:evaporation_simulation_progression}{{5.15}{85}{Image of final simulation with parameters given in Figure \ref {fig:evaporation_simulation_first_compare} and an anharmonic oscillation with a power of $20$. The image is very grainy due to a low amount of rays cast}{figure.caption.92}{}}
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diff --git a/conclusion.aux b/conclusion.aux
index c281be2..e5e2791 100644
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diff --git a/img/MA/NomenclatureMaskAlignerCrossSec.pdf b/img/MA/NomenclatureMaskAlignerCrossSec.pdf
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diff --git a/img/Plots/Background/AFMDiagram.pdf b/img/Plots/Background/AFMDiagram.pdf
index 382e58c4a87f500e260eb804654e1f3feb9518ab..37a19e9498ad948c9b0fd8c6cf36637e82692b3b 100644
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diff --git a/img/Plots/Background/Penumbra_diagramm.pdf b/img/Plots/Background/Penumbra_diagramm.pdf
index 5c4514838704710e1633a8e5bc967ee1ddf417ab..52c7cee4e4f346d4bb0bf287445ac162d335deac 100644
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diff --git a/preface.aux b/preface.aux
index bd38dd4..f1dadcf 100644
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 \citation{Olschewski,Bhaskar}
 \@writefile{toc}{\contentsline {chapter}{Introduction}{3}{chapter*.2}\protected@file@percent }
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diff --git a/preface.tex b/preface.tex
index 644b6ff..731fa49 100644
--- a/preface.tex
+++ b/preface.tex
@@ -1,10 +1,14 @@
 \chapter*{Introduction}
 \addcontentsline{toc}{chapter}{Introduction}
 In condensed matter physics, precise fabrication of nanostructures with sharp patterns is paramount for research in various fields like electronics, photonics and quantum computing. One problem, that is highly sought after in quantum computing, is the creation of Majorana Zero Modes, as these could potentially provide a stable and controllable way to encode information. \textbf{M}ajorana \textbf{Z}ero \textbf{M}odes (MZM) are quasi particles that behave like Majorana fermions with non-Abelian statistics. MZMs are predicted to emerge at the core of vortices at superconductor/topological insulator interfaces~\cite{majorana_zero_modes}. These interfaces require pristine conditions and at the same time patterns, smaller than the coherence length ($<100$ nm) of the superconductor.\\
+
 Atmospheric conditions typically deteriorate surface properties of the required samples. Due to this \textbf{U}ltra \textbf{H}igh \textbf{V}accuum (UHV) conditions are required for the sample. This often limits the pattern creation process, as exposure to ambient conditions or other chemicals are required. \\
+
 Many methods like \textbf{E}lectron \textbf{B}eam \textbf{L}ithography or \textbf{E}xtreme \textbf{U}ltra\textbf{V}iolet \textbf{L}ithography (EUVL or EUV) give the required precision for patterning at the sub $100$ nm scale,~\cite{euv} but require resists, which typically are deposited with the help of solvents. These leave residues after the patterning process, which damage the pristine condition of the substrate. Typically, these methods can also not be performed under UHV conditions. \\
+
 Other methods of patterning superconductors on topological insulators have been proposed, but many have shortcomings that make their use impractical. There are for example scanning probe approaches,~\cite{afm_pattern} which can directly manipulate single atoms on surfaces, but require 
 long timescales and expensive equipment. Additionally, many Scanning Probe approaches still require resists, leading to the same issues as previously mentioned.\\
+
 A simple and inexpensive approach is stencil lithography employing \textbf{P}hysical \textbf{V}apor \\ \textbf{D}eposition (PVD), where a stencil (mask) is used to mask a section of the sample. When the sample is hit with a molecular vapor beam, the masked areas are protected from the impinging material and stay pristine, while the ones not protected built patterned structures. In this method, no resist is required, and the procedure can be performed at UHV conditions. Resolutions of sub-$50$ nm have been achieved~\cite{stencil_resolution}. \\
-Stencil lithography however has its downside. In order to get very high resolution, the mask and the sample have to be very close as otherwise the aperture of the mask creates a "penumbra", limiting the final resolution of the pattern on the sample. The simple and often used approach is to simply bring mask and sample into direct mechanical contact, ensuring minimal distance. This however can \\
-To avoid this a Mask Aligner operating in UHV, the subject of this work, was designed~\cite{Olschewski, Bhaskar}. It is a tool to use capacitive measurement to ensure minimal mask sample distance during PVD, while avoiding full contact with the sample, thus preserving surface condition. This work concerns the optimization, improvement and analysis of the Mask Aligner, as well as work on the creation of additional electronics and software to drive the Mask Aligners operation. 
\ No newline at end of file
+Stencil lithography however has its downsides. In order to get very high resolution, the mask and the sample have to be very close as otherwise the aperture of the mask creates a "penumbra", limiting the lateral resolution of the pattern. The simple and often used approach is to simply bring mask and sample into direct mechanical contact, ensuring minimal distance. This however can contaminate the sample or even mechanically damage it.\\
+To avoid this a Mask Aligner operating in UHV, the subject of this work, was designed~\cite{Olschewski, Bhaskar}. It uses capacitive measurement to ensure minimal mask sample distance during PVD, while avoiding full contact with the sample, thus preserving surface condition. This work concerns the optimization, improvement and analysis of the Mask Aligner, as well as work on the creation of additional electronics and software to drive the Mask Aligners operation. 
\ No newline at end of file
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 \@input{acknowledgments.aux}
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diff --git a/thesis.toc b/thesis.toc
index 08eed48..f372b1e 100644
--- a/thesis.toc
+++ b/thesis.toc
@@ -1,119 +1,119 @@
 \contentsline {chapter}{Introduction}{3}{chapter*.2}%
-\contentsline {chapter}{\numberline {1}Mask Aligner background}{4}{chapter.1}%
-\contentsline {section}{\numberline {1.1}Electron beam evaporation}{4}{section.1.1}%
-\contentsline {section}{\numberline {1.2}Stencil lithography}{6}{section.1.2}%
-\contentsline {subsubsection}{Penumbra}{6}{section*.5}%
+\contentsline {chapter}{\numberline {1}Mask Aligner background}{5}{chapter.1}%
+\contentsline {section}{\numberline {1.1}Electron beam evaporation}{5}{section.1.1}%
+\contentsline {section}{\numberline {1.2}Stencil lithography}{7}{section.1.2}%
+\contentsline {subsubsection}{Penumbra}{7}{section*.5}%
 \contentsline {subsubsection}{Tilt induced penumbra}{8}{section*.7}%
-\contentsline {section}{\numberline {1.3}Measurement techniques}{8}{section.1.3}%
+\contentsline {section}{\numberline {1.3}Measurement techniques}{9}{section.1.3}%
 \contentsline {subsection}{\numberline {1.3.1}Atomic Force Microscopy}{9}{subsection.1.3.1}%
-\contentsline {subsubsection}{Modes}{9}{section*.10}%
-\contentsline {paragraph}{Contact}{10}{section*.11}%
-\contentsline {paragraph}{Non-Contact}{10}{section*.12}%
-\contentsline {paragraph}{Tapping}{10}{section*.13}%
-\contentsline {subsection}{\numberline {1.3.2}Scanning Electron Microscopy}{11}{subsection.1.3.2}%
-\contentsline {chapter}{\numberline {2}Mask Aligner}{14}{chapter.2}%
-\contentsline {section}{\numberline {2.1}Molecular beam evaporation chamber}{14}{section.2.1}%
-\contentsline {subsection}{\numberline {2.1.1}Lead evaporator}{15}{subsection.2.1.1}%
-\contentsline {section}{\numberline {2.2}Slip stick principle}{18}{section.2.2}%
-\contentsline {section}{\numberline {2.3}Shadow mask alignment}{19}{section.2.3}%
-\contentsline {subsection}{\numberline {2.3.1}Motor screw configuration}{19}{subsection.2.3.1}%
-\contentsline {subsection}{\numberline {2.3.2}Motor calibration}{20}{subsection.2.3.2}%
-\contentsline {subsection}{\numberline {2.3.3}Optical alignment}{25}{subsection.2.3.3}%
-\contentsline {subsection}{\numberline {2.3.4}Approach curves}{27}{subsection.2.3.4}%
-\contentsline {subsection}{\numberline {2.3.5}Reproducibility}{31}{subsection.2.3.5}%
-\contentsline {subsubsection}{Reproducibility when removing sample/mask}{31}{section*.33}%
-\contentsline {subsection}{\numberline {2.3.6}Cross capacitances}{33}{subsection.2.3.6}%
-\contentsline {paragraph}{Leakage current}{38}{section*.41}%
-\contentsline {paragraph}{Improved gold pin fitting}{38}{section*.42}%
-\contentsline {subsection}{\numberline {2.3.7}Stop Conditions}{38}{subsection.2.3.7}%
-\contentsline {paragraph}{High correlation between capacitance curves}{39}{section*.43}%
-\contentsline {paragraph}{Low correlation between capacitance curves}{39}{section*.44}%
-\contentsline {section}{\numberline {2.4}Mask Aligner operation}{39}{section.2.4}%
-\contentsline {subsection}{\numberline {2.4.1}Sample preparation}{39}{subsection.2.4.1}%
-\contentsline {chapter}{\numberline {3}Electronics}{41}{chapter.3}%
-\contentsline {section}{\numberline {3.1}RHK}{41}{section.3.1}%
-\contentsline {subsection}{\numberline {3.1.1}Overview}{41}{subsection.3.1.1}%
-\contentsline {paragraph}{amplitude}{41}{section*.45}%
-\contentsline {paragraph}{sweep period}{41}{section*.46}%
-\contentsline {paragraph}{time between sweeps}{41}{section*.47}%
-\contentsline {subsection}{\numberline {3.1.2}Pulse shape}{41}{subsection.3.1.2}%
-\contentsline {section}{\numberline {3.2}KIM001}{42}{section.3.2}%
-\contentsline {subsection}{\numberline {3.2.1}Overview}{42}{subsection.3.2.1}%
-\contentsline {subsection}{\numberline {3.2.2}Pulse shape}{42}{subsection.3.2.2}%
-\contentsline {subsection}{\numberline {3.2.3}Voltage behavior}{43}{subsection.3.2.3}%
-\contentsline {section}{\numberline {3.3}Mask Aligner controller "Walker"}{44}{section.3.3}%
-\contentsline {subsection}{\numberline {3.3.1}Overview}{44}{subsection.3.3.1}%
-\contentsline {subsection}{\numberline {3.3.2}Signal generation}{45}{subsection.3.3.2}%
-\contentsline {subsection}{\numberline {3.3.3}Fast flank}{46}{subsection.3.3.3}%
-\contentsline {subsection}{\numberline {3.3.4}Amplification}{47}{subsection.3.3.4}%
-\contentsline {subsection}{\numberline {3.3.5}Parameters}{47}{subsection.3.3.5}%
-\contentsline {paragraph}{Amplitude (amp)}{47}{section*.54}%
-\contentsline {paragraph}{Voltage (volt)}{48}{section*.55}%
-\contentsline {paragraph}{Channel}{48}{section*.56}%
-\contentsline {paragraph}{Max Step}{48}{section*.57}%
-\contentsline {paragraph}{Polarity}{48}{section*.58}%
-\contentsline {subsection}{\numberline {3.3.6}Measured pulse shape}{48}{subsection.3.3.6}%
-\contentsline {subsection}{\numberline {3.3.7}Driving the Mask Aligner}{50}{subsection.3.3.7}%
-\contentsline {chapter}{\numberline {4}Mask Aligner repairs and optimizations}{52}{chapter.4}%
-\contentsline {section}{\numberline {4.1}Overview}{52}{section.4.1}%
-\contentsline {section}{\numberline {4.2}General UHV device preparation}{53}{section.4.2}%
-\contentsline {subsection}{\numberline {4.2.1}Adding components}{53}{subsection.4.2.1}%
-\contentsline {subsection}{\numberline {4.2.2}Soldering}{53}{subsection.4.2.2}%
-\contentsline {section}{\numberline {4.3}Soldering anchors}{54}{section.4.3}%
-\contentsline {section}{\numberline {4.4}Piezo re-gluing}{57}{section.4.4}%
-\contentsline {section}{\numberline {4.5}Z3 motor}{59}{section.4.5}%
-\contentsline {subsection}{\numberline {4.5.1}Front plate repair}{60}{subsection.4.5.1}%
-\contentsline {subsection}{\numberline {4.5.2}Small capacitance stack}{63}{subsection.4.5.2}%
-\contentsline {section}{\numberline {4.6}Feed through cabling optimizations}{64}{section.4.6}%
-\contentsline {section}{\numberline {4.7}Final test}{65}{section.4.7}%
-\contentsline {chapter}{\numberline {5}Evaporations and measurement}{67}{chapter.5}%
-\contentsline {section}{\numberline {5.1}Evaporation configuration}{67}{section.5.1}%
-\contentsline {section}{\numberline {5.2}Contamination}{70}{section.5.2}%
-\contentsline {section}{\numberline {5.3}Penumbra}{71}{section.5.3}%
-\contentsline {section}{\numberline {5.4}Tilt and deformation}{76}{section.5.4}%
-\contentsline {section}{\numberline {5.5}Simulation}{78}{section.5.5}%
-\contentsline {subsection}{\numberline {5.5.1}Overview and principle}{78}{subsection.5.5.1}%
-\contentsline {subsection}{\numberline {5.5.2}Results}{80}{subsection.5.5.2}%
-\contentsline {subsection}{\numberline {5.5.3}Software improvements}{84}{subsection.5.5.3}%
-\contentsline {subsection}{\numberline {5.5.4}Final Remark}{85}{subsection.5.5.4}%
-\contentsline {chapter}{Conclusions and Outlook}{86}{chapter*.90}%
-\contentsline {chapter}{Bibliography}{88}{chapter*.91}%
-\contentsline {chapter}{List of Abbreviations}{91}{chapter*.92}%
-\contentsline {chapter}{Appendix}{i}{chapter*.93}%
+\contentsline {subsubsection}{Modes}{10}{section*.10}%
+\contentsline {paragraph}{Contact}{11}{section*.12}%
+\contentsline {paragraph}{Non-Contact}{11}{section*.13}%
+\contentsline {paragraph}{Tapping}{12}{section*.14}%
+\contentsline {subsection}{\numberline {1.3.2}Scanning Electron Microscopy}{12}{subsection.1.3.2}%
+\contentsline {chapter}{\numberline {2}Mask Aligner}{15}{chapter.2}%
+\contentsline {section}{\numberline {2.1}Molecular beam evaporation chamber}{15}{section.2.1}%
+\contentsline {subsection}{\numberline {2.1.1}Lead evaporator}{16}{subsection.2.1.1}%
+\contentsline {section}{\numberline {2.2}Slip stick principle}{19}{section.2.2}%
+\contentsline {section}{\numberline {2.3}Shadow mask alignment}{20}{section.2.3}%
+\contentsline {subsection}{\numberline {2.3.1}Motor screw configuration}{20}{subsection.2.3.1}%
+\contentsline {subsection}{\numberline {2.3.2}Motor calibration}{21}{subsection.2.3.2}%
+\contentsline {subsection}{\numberline {2.3.3}Optical alignment}{26}{subsection.2.3.3}%
+\contentsline {subsection}{\numberline {2.3.4}Approach curves}{28}{subsection.2.3.4}%
+\contentsline {subsection}{\numberline {2.3.5}Reproducibility}{32}{subsection.2.3.5}%
+\contentsline {subsubsection}{Reproducibility when removing sample/mask}{32}{section*.34}%
+\contentsline {subsection}{\numberline {2.3.6}Cross capacitances}{34}{subsection.2.3.6}%
+\contentsline {paragraph}{Leakage current}{39}{section*.43}%
+\contentsline {paragraph}{Improved gold pin fitting}{39}{section*.44}%
+\contentsline {subsection}{\numberline {2.3.7}Stop Conditions}{40}{subsection.2.3.7}%
+\contentsline {paragraph}{High correlation between capacitance curves}{40}{section*.46}%
+\contentsline {paragraph}{Low correlation between capacitance curves}{40}{section*.47}%
+\contentsline {section}{\numberline {2.4}Mask Aligner operation}{40}{section.2.4}%
+\contentsline {subsection}{\numberline {2.4.1}Sample preparation}{40}{subsection.2.4.1}%
+\contentsline {chapter}{\numberline {3}Electronics}{42}{chapter.3}%
+\contentsline {section}{\numberline {3.1}RHK}{42}{section.3.1}%
+\contentsline {subsection}{\numberline {3.1.1}Overview}{42}{subsection.3.1.1}%
+\contentsline {paragraph}{amplitude}{42}{section*.48}%
+\contentsline {paragraph}{sweep period}{42}{section*.49}%
+\contentsline {paragraph}{time between sweeps}{42}{section*.50}%
+\contentsline {subsection}{\numberline {3.1.2}Pulse shape}{42}{subsection.3.1.2}%
+\contentsline {section}{\numberline {3.2}KIM001}{43}{section.3.2}%
+\contentsline {subsection}{\numberline {3.2.1}Overview}{43}{subsection.3.2.1}%
+\contentsline {subsection}{\numberline {3.2.2}Pulse shape}{43}{subsection.3.2.2}%
+\contentsline {subsection}{\numberline {3.2.3}Voltage behavior}{44}{subsection.3.2.3}%
+\contentsline {section}{\numberline {3.3}Mask Aligner controller "Walker"}{45}{section.3.3}%
+\contentsline {subsection}{\numberline {3.3.1}Overview}{45}{subsection.3.3.1}%
+\contentsline {subsection}{\numberline {3.3.2}Signal generation}{46}{subsection.3.3.2}%
+\contentsline {subsection}{\numberline {3.3.3}Fast flank}{47}{subsection.3.3.3}%
+\contentsline {subsection}{\numberline {3.3.4}Amplification}{48}{subsection.3.3.4}%
+\contentsline {subsection}{\numberline {3.3.5}Parameters}{48}{subsection.3.3.5}%
+\contentsline {paragraph}{Amplitude (amp)}{48}{section*.57}%
+\contentsline {paragraph}{Voltage (volt)}{49}{section*.58}%
+\contentsline {paragraph}{Channel}{49}{section*.59}%
+\contentsline {paragraph}{Max Step}{49}{section*.60}%
+\contentsline {paragraph}{Polarity}{49}{section*.61}%
+\contentsline {subsection}{\numberline {3.3.6}Measured pulse shape}{49}{subsection.3.3.6}%
+\contentsline {subsection}{\numberline {3.3.7}Driving the Mask Aligner}{51}{subsection.3.3.7}%
+\contentsline {chapter}{\numberline {4}Mask Aligner repairs and optimizations}{53}{chapter.4}%
+\contentsline {section}{\numberline {4.1}Overview}{53}{section.4.1}%
+\contentsline {section}{\numberline {4.2}General UHV device preparation}{54}{section.4.2}%
+\contentsline {subsection}{\numberline {4.2.1}Adding components}{54}{subsection.4.2.1}%
+\contentsline {subsection}{\numberline {4.2.2}Soldering}{54}{subsection.4.2.2}%
+\contentsline {section}{\numberline {4.3}Soldering anchors}{55}{section.4.3}%
+\contentsline {section}{\numberline {4.4}Piezo re-gluing}{58}{section.4.4}%
+\contentsline {section}{\numberline {4.5}Z3 motor}{60}{section.4.5}%
+\contentsline {subsection}{\numberline {4.5.1}Front plate repair}{61}{subsection.4.5.1}%
+\contentsline {subsection}{\numberline {4.5.2}Small capacitance stack}{64}{subsection.4.5.2}%
+\contentsline {section}{\numberline {4.6}Feed through cabling optimizations}{65}{section.4.6}%
+\contentsline {section}{\numberline {4.7}Final test}{66}{section.4.7}%
+\contentsline {chapter}{\numberline {5}Evaporations and measurement}{68}{chapter.5}%
+\contentsline {section}{\numberline {5.1}Evaporation configuration}{68}{section.5.1}%
+\contentsline {section}{\numberline {5.2}Contamination}{71}{section.5.2}%
+\contentsline {section}{\numberline {5.3}Penumbra}{72}{section.5.3}%
+\contentsline {section}{\numberline {5.4}Tilt and deformation}{77}{section.5.4}%
+\contentsline {section}{\numberline {5.5}Simulation}{79}{section.5.5}%
+\contentsline {subsection}{\numberline {5.5.1}Overview and principle}{79}{subsection.5.5.1}%
+\contentsline {subsection}{\numberline {5.5.2}Results}{81}{subsection.5.5.2}%
+\contentsline {subsection}{\numberline {5.5.3}Software improvements}{85}{subsection.5.5.3}%
+\contentsline {subsection}{\numberline {5.5.4}Final Remark}{86}{subsection.5.5.4}%
+\contentsline {chapter}{Conclusions and Outlook}{87}{chapter*.93}%
+\contentsline {chapter}{Bibliography}{89}{chapter*.94}%
+\contentsline {chapter}{List of Abbreviations}{92}{chapter*.95}%
+\contentsline {chapter}{Appendix}{i}{chapter*.96}%
 \contentsline {section}{\numberline {A}LockIn amplifier settings}{i}{section.5.1}%
 \contentsline {section}{\numberline {B}Walker principle diagram}{ii}{section.5.2}%
 \contentsline {section}{\numberline {C}Walker circuit diagrams}{ii}{section.5.3}%
 \contentsline {section}{\numberline {D}New driver electronics}{vi}{section.5.4}%
-\contentsline {paragraph}{pulse?}{vi}{section*.96}%
-\contentsline {paragraph}{pol x}{vi}{section*.97}%
-\contentsline {paragraph}{amp x}{vi}{section*.98}%
-\contentsline {paragraph}{volt x}{vi}{section*.99}%
-\contentsline {paragraph}{channel x}{vi}{section*.100}%
-\contentsline {paragraph}{maxmstep x}{vi}{section*.101}%
-\contentsline {paragraph}{step x}{vi}{section*.102}%
-\contentsline {paragraph}{mstep x}{vi}{section*.103}%
-\contentsline {paragraph}{cancel}{vii}{section*.104}%
-\contentsline {paragraph}{help}{vii}{section*.105}%
+\contentsline {paragraph}{pulse?}{vi}{section*.99}%
+\contentsline {paragraph}{pol x}{vi}{section*.100}%
+\contentsline {paragraph}{amp x}{vi}{section*.101}%
+\contentsline {paragraph}{volt x}{vi}{section*.102}%
+\contentsline {paragraph}{channel x}{vi}{section*.103}%
+\contentsline {paragraph}{maxmstep x}{vi}{section*.104}%
+\contentsline {paragraph}{step x}{vi}{section*.105}%
+\contentsline {paragraph}{mstep x}{vi}{section*.106}%
+\contentsline {paragraph}{cancel}{vii}{section*.107}%
+\contentsline {paragraph}{help}{vii}{section*.108}%
 \contentsline {section}{\numberline {E}Raycast Simulation}{vii}{section.5.5}%
-\contentsline {paragraph}{radius\_1}{vii}{section*.106}%
-\contentsline {paragraph}{angle}{vii}{section*.107}%
-\contentsline {paragraph}{radius\_mask}{vii}{section*.108}%
-\contentsline {paragraph}{distance\_circle\_mask}{vii}{section*.109}%
-\contentsline {paragraph}{distance\_sample}{vii}{section*.110}%
-\contentsline {paragraph}{rays\_per\_frame}{vii}{section*.111}%
-\contentsline {paragraph}{running\_time}{vii}{section*.112}%
-\contentsline {paragraph}{deposition\_gain}{vii}{section*.113}%
-\contentsline {paragraph}{penalize\_deposition}{vii}{section*.114}%
-\contentsline {paragraph}{first\_layer\_deposition\_prob}{vii}{section*.115}%
-\contentsline {paragraph}{oscillation\_period}{vii}{section*.116}%
-\contentsline {paragraph}{delay\_oscill\_time}{viii}{section*.117}%
-\contentsline {paragraph}{save\_in\_progress\_images}{viii}{section*.118}%
-\contentsline {paragraph}{save\_intervall}{viii}{section*.119}%
-\contentsline {paragraph}{oscillation\_dir}{viii}{section*.120}%
-\contentsline {paragraph}{oscillation\_rot\_s}{viii}{section*.121}%
-\contentsline {paragraph}{oscillation\_rot\_e}{viii}{section*.122}%
-\contentsline {paragraph}{random\_seed}{viii}{section*.123}%
-\contentsline {paragraph}{x\_min, x\_max, y\_min, y\_max}{viii}{section*.124}%
-\contentsline {paragraph}{resolution}{viii}{section*.125}%
-\contentsline {paragraph}{path}{viii}{section*.126}%
-\contentsline {chapter}{Acknowledgments}{ix}{chapter*.127}%
+\contentsline {paragraph}{radius\_1}{vii}{section*.109}%
+\contentsline {paragraph}{angle}{vii}{section*.110}%
+\contentsline {paragraph}{radius\_mask}{vii}{section*.111}%
+\contentsline {paragraph}{distance\_circle\_mask}{vii}{section*.112}%
+\contentsline {paragraph}{distance\_sample}{vii}{section*.113}%
+\contentsline {paragraph}{rays\_per\_frame}{vii}{section*.114}%
+\contentsline {paragraph}{running\_time}{vii}{section*.115}%
+\contentsline {paragraph}{deposition\_gain}{vii}{section*.116}%
+\contentsline {paragraph}{penalize\_deposition}{vii}{section*.117}%
+\contentsline {paragraph}{first\_layer\_deposition\_prob}{vii}{section*.118}%
+\contentsline {paragraph}{oscillation\_period}{vii}{section*.119}%
+\contentsline {paragraph}{delay\_oscill\_time}{viii}{section*.120}%
+\contentsline {paragraph}{save\_in\_progress\_images}{viii}{section*.121}%
+\contentsline {paragraph}{save\_intervall}{viii}{section*.122}%
+\contentsline {paragraph}{oscillation\_dir}{viii}{section*.123}%
+\contentsline {paragraph}{oscillation\_rot\_s}{viii}{section*.124}%
+\contentsline {paragraph}{oscillation\_rot\_e}{viii}{section*.125}%
+\contentsline {paragraph}{random\_seed}{viii}{section*.126}%
+\contentsline {paragraph}{x\_min, x\_max, y\_min, y\_max}{viii}{section*.127}%
+\contentsline {paragraph}{resolution}{viii}{section*.128}%
+\contentsline {paragraph}{path}{viii}{section*.129}%
+\contentsline {chapter}{Acknowledgments}{ix}{chapter*.130}%
-- 
GitLab