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index a530a4a2636f054af7e5bd220aed1073c438fde4..40604e705701ddea3efc7c0f018fc42f5826c318 100644
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 \bibcite{Tungsten_evap}{{10}{}{{}}{{}}}
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 \bibcite{sputter_damage}{{13}{}{{}}{{}}}
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diff --git a/chap01.aux b/chap01.aux
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+\newlabel{fig:sem_setup}{{1.7}{16}{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}
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diff --git a/chap01.tex b/chap01.tex
index d7b9399b65483f7456df5c7a48cbfd93aab69d39..87a072a80228d26d2a081559872f65bc461fbd7b 100644
--- a/chap01.tex
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@@ -13,11 +13,11 @@ Electron beam evaporation, also known as \textbf{E}lectron-\textbf{b}eam \textbf
 \end{figure}
  
 The general setup of an electron beam evaporator is seen 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 the crucible itself from being damaged a material with high melting point has to be 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 prevent damaging the system.
+The crucible is also heated during the evaporation process, in order to prevent the crucible itself from being damaged a material with high melting point has to be 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 prevent damaging the system.
 
 In order to heat the source material locally beyond its boiling point it is hit with a high current electron beam ($\mathcal{O}$($1$ kV)), emitted by either an electron gun or a filament, this beam usually has to be 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 causes the system to reach its melting and then its boiling point, if enough current is applied to give the required heating power. \\
 
-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.\\
+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.\\
 
 When the material reaches its boiling point, it forms a vapor, which is directed through a funnel to the sample's surface. The sample is kept at a temperature much colder than the source material's boiling temperature, due to this the material beam will deposit and condense on the substrate's surface forming a thin film. \\
 
@@ -29,17 +29,17 @@ The deposition rate of the evaporator can be measured using a molecular flux mon
 	\label{eq:hertz_knudsen}
 \end{equation}
 
-where $N$ is the number of gas molecules deposited, $A$ is the surface area, $t$ is time, $\alpha$ is the sticking parameter, $p$ is the gas pressure of the impinging gas, $m$ is the mass of a single particle, $k_B$ is the Boltzmann constant and $T$ is the temperature.\cite{knudsen} When the sticking parameter of the material substrate is known the vapor pressure can be obtained from the particle flux measured per area. With this, the total deposition rate can then be estimated. In practice, this is however difficult to estimate, since the pressure of the evaporant gas is difficult to determine. Instead, usually a calibration evaporations are performed for different particle fluxes and different times to determine the deposition rate for a given setup. Since the Hertz-Knudsen equation is linear in gas pressure, this should give a linear dependence.
+where $N$ is the number of gas molecules deposited, $A$ is the surface area, $t$ is time, $\alpha$ is the sticking parameter, $p$ is the gas pressure of the impinging gas, $m$ is the mass of a single particle, $k_B$ is the Boltzmann constant and $T$ is the temperature~\cite{knudsen}. When the sticking parameter of the material substrate is known the vapor pressure can be obtained from the particle flux measured per area. With this, the total deposition rate can then be estimated. In practice, this is however difficult to estimate, since the pressure of the evaporant gas is difficult to determine. Instead, usually a calibration evaporations are performed for different particle fluxes and different times to determine the deposition rate for a given setup. Since the Hertz-Knudsen equation is linear in gas pressure, this should give a linear dependence.
 
-Some of the advantages that e-beam evaporation has over other techniques such as thermal evaporation or sputtering are that due to the high energy localized heating, materials, which require high temperature to reach their boiling point, like tungsten ($5828$ K)\cite{Tungsten_evap} or niobium ($5017$ K)\cite{Tungsten_evap} can be evaporated using e-beam evaporation.\cite{tungsten_evaporation} The deposition rate can also be controlled with high precision using the current applied to create the electron beam. \cite{Vapor_depo_princ} \\
-The high energy electron beam is directed directly at the source material and is unlikely to interact with the samples surface, in contrast to for example sputtering, where the high energy particles depositing the material can interact and either implant unwanted material or dislodge substrate material damaging the substrate surface. \cite{sputter_damage}
+Some of the advantages that e-beam evaporation has over other techniques such as thermal evaporation or sputtering are that due to the high energy localized heating, materials, which require high temperature to reach their boiling point, like tungsten ($5828$ K)~\cite{Tungsten_evap} or niobium ($5017$ K)~\cite{Tungsten_evap} can be evaporated using e-beam evaporation~\cite{tungsten_evaporation}. The deposition rate can also be controlled with high precision using the current applied to create the electron beam~\cite{Vapor_depo_princ}. \\
+The high energy electron beam is directed directly at the source material and is unlikely to interact with the samples surface, in contrast to for example sputtering, where the high energy particles depositing the material can interact and either implant unwanted material or dislodge substrate material damaging the substrate surface~\cite{sputter_damage}.
 
-E-beam evaporation offers more control over deposition rate than thermal evaporation, and it is easier to evaporate material which require high evaporation temperatures with e-beam evaporation. \cite{Vapor_depo_princ}
+E-beam evaporation offers more control over deposition rate than thermal evaporation, and it is easier to evaporate material which require high evaporation temperatures with e-beam evaporation~\cite{Vapor_depo_princ}.
 
 In order to control the duration of the evaporation precisely, a shutter is usually included in the evaporation chamber which 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. By closing the shutter, this can be avoided.
 
 \subsection{Mask Aligner 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} The crucible of this evaporator is made from tungsten. The evaporator uses a filament placed near the crucible to bombard the material placed inside the crucible with highly energetic electrons. To accomplish this, a high current (up to $1$ kV) is applied between filament and crucible to emit electrons from the filament to the crucible. In addition, the system can be heated with radiative heat from the filament. This is also 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 for the system. The heat sink needs to be water cooled to prevent damage to the evaporator. In order to prevent cooling failure, a thermal sensor measures the temperature of 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}. The crucible of this evaporator is made from tungsten. The evaporator uses a filament placed near the crucible to bombard the material placed inside the crucible with highly energetic electrons. To accomplish this, a high current (up to $1$ kV) is applied between filament and crucible to emit electrons from the filament to the crucible. In addition, the system can be heated with radiative heat from the filament. This is also 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 for the system. The heat sink needs to be water cooled to prevent damage to the evaporator. In order to prevent cooling failure, a thermal sensor measures the temperature of the copper cylinder. \\
 
 
 \begin{figure}[H]
@@ -79,7 +79,7 @@ The width of the penumbra $p$ is determined by the distance of the beam source t
     \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.\\
+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.\\
 
 \subsubsection{Tilt induced penumbra}
 Formerly, the model for the penumbra assumed perfect alignment between mask and sample, but potentially large distance $d$, but 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. 
@@ -144,7 +144,7 @@ Tapping mode is a hybrid of both contact and non-contact modes. It is also somet
 
 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.
 
-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}
+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.
@@ -161,15 +161,15 @@ A \textbf{S}canning \textbf{E}lectron \textbf{M}icroscope (SEM) is a microscope
 	\caption{}
 	\label{fig:sem_setup_interaction}
 	\end{subfigure}
-    \caption{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}.}
+    \caption{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}.}
     \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. 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 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.\\
+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.\\
 
 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. \\
 
-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}\\
+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 c615cebee3ac7f0afdd8a862c5a7873a00c79be7..448f81f965cdcc8f1942bc2d438c420367f808c5 100644
--- a/chap02.aux
+++ b/chap02.aux
@@ -15,8 +15,12 @@
 \newlabel{fig:mask_aligner_chamber}{{2.2}{20}{Circuit diagram of the mask aligner and its associated vacuum system. The system consists of the mask aligner chamber, the main chamber, the Pb evaporator and the AU evaporator. The AU evaporator is attached to the same vacuum system, but is unrelated to the Mask Aligner. The configuration depicted is used for evaporation. The section labeled load lock is a vacuum suitcase and can be detached. The \textcolor {tab_green}{green} path shows the sample/mask extraction and insertion path with the wobble stick. The black arrow shows the molecular beam path from the \ce {Pb} evaporator}{figure.caption.17}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {2.2}Shadow mask alignment}{21}{section.2.2}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Motor calibration}{21}{subsection.2.2.1}\protected@file@percent }
-\@writefile{lof}{\contentsline {figure}{\numberline {2.3}{\ignorespaces Example curves showing how rotations of the screws of Z2 and Z3 affect the given motor's step size. A point where the 3 motors are in agreement has to be found iteratively. The jumps in signal after certain rotations result from the \ce {CuBe} plate slipping across the winding of the screw at certain spots.}}{22}{figure.caption.18}\protected@file@percent }
-\newlabel{fig:screw_firmness}{{2.3}{22}{Example curves showing how rotations of the screws of Z2 and Z3 affect the given motor's step size. A point where the 3 motors are in agreement has to be found iteratively. The jumps in signal after certain rotations result from the \ce {CuBe} plate slipping across the winding of the screw at certain spots}{figure.caption.18}{}}
+\newlabel{fig:screw_firmness_screw_image}{{2.3a}{22}{\relax }{figure.caption.18}{}}
+\newlabel{sub@fig:screw_firmness_screw_image}{{a}{22}{\relax }{figure.caption.18}{}}
+\newlabel{fig:screw_firmness_plot}{{2.3b}{22}{\relax }{figure.caption.18}{}}
+\newlabel{sub@fig:screw_firmness_plot}{{b}{22}{\relax }{figure.caption.18}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2.3}{\ignorespaces \subref  {fig:screw_firmness_screw_image} shows a frontal view of the motor Z2 marked in red is the screw used for calibration of the motors on the Mask Aligner. \subref  {fig:screw_firmness_plot} shows example curves of how the screws of Z2 and Z3 affect the given motor's step size. A point where the 3 motors are in agreement has to be found iteratively. The jumps in signal after certain rotations result from the \ce {CuBe} plate slipping across the winding of the screw at certain spots. }}{22}{figure.caption.18}\protected@file@percent }
+\newlabel{fig:screw_firmness}{{2.3}{22}{\subref {fig:screw_firmness_screw_image} shows a frontal view of the motor Z2 marked in red is the screw used for calibration of the motors on the Mask Aligner. \subref {fig:screw_firmness_plot} shows example curves of how the screws of Z2 and Z3 affect the given motor's step size. A point where the 3 motors are in agreement has to be found iteratively. The jumps in signal after certain rotations result from the \ce {CuBe} plate slipping across the winding of the screw at certain spots}{figure.caption.18}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {2.4}{\ignorespaces Diagram explaining how to derive the deviation of measured step size on the screws near the Z2 and Z3 motors from the actual step size of the motors.}}{23}{figure.caption.19}\protected@file@percent }
 \newlabel{fig:calibration_screw_diff_explain}{{2.4}{23}{Diagram explaining how to derive the deviation of measured step size on the screws near the Z2 and Z3 motors from the actual step size of the motors}{figure.caption.19}{}}
 \newlabel{fig:calibration_uhv_points_of_interest_z1}{{2.5a}{24}{\relax }{figure.caption.20}{}}
@@ -45,7 +49,7 @@
 \newlabel{sub@fig:mask_aligner_nomenclature_capacitances_motors}{{a}{29}{\relax }{figure.caption.26}{}}
 \newlabel{fig:mask_aligner_nomenclature_capacitances_mask}{{2.11b}{29}{\relax }{figure.caption.26}{}}
 \newlabel{sub@fig:mask_aligner_nomenclature_capacitances_mask}{{b}{29}{\relax }{figure.caption.26}{}}
-\newlabel{fig:mask_aligner_nomenclature_capacitances}{{\caption@xref {fig:mask_aligner_nomenclature_capacitances}{ on input line 305}}{29}{Approach curves}{figure.caption.26}{}}
+\newlabel{fig:mask_aligner_nomenclature_capacitances}{{\caption@xref {fig:mask_aligner_nomenclature_capacitances}{ on input line 312}}{29}{Approach curves}{figure.caption.26}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {2.11}{\ignorespaces (\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.}}{29}{figure.caption.26}\protected@file@percent }
 \citation{SiN_dielectric}
 \@writefile{lof}{\contentsline {figure}{\numberline {2.12}{\ignorespaces Diagram showing how communication with the RHK and the Lock-in amplifier is done and how they interact with elements in vacuum. Red lines are input, black lines are output lines. The capacitance relay is used to measure $C_i$ in order. The RHK relay controls, which motor is currently driven.}}{30}{figure.caption.27}\protected@file@percent }
@@ -86,8 +90,8 @@
 \newlabel{sub@fig:cross_cap_approach_sim}{{c}{35}{\relax }{figure.caption.32}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {2.16}{\ignorespaces 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.}}{35}{figure.caption.32}\protected@file@percent }
 \newlabel{fig:cross_cap_approach}{{2.16}{35}{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}{figure.caption.32}{}}
-\@writefile{lof}{\contentsline {figure}{\numberline {2.17}{\ignorespaces 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.}}{36}{figure.caption.33}\protected@file@percent }
-\newlabel{fig:leakage_current}{{2.17}{36}{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}{figure.caption.33}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2.17}{\ignorespaces 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.}}{36}{figure.caption.33}\protected@file@percent }
+\newlabel{fig:leakage_current}{{2.17}{36}{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}{figure.caption.33}{}}
 \@writefile{lot}{\contentsline {table}{\numberline {2.1}{\ignorespaces Table of cross capacitance measurement to determine possible causes for large values in approach curves. All measurements were done with Mask shuttle in Mask aligner and sample at $0.3$ mm distance. The distance was determined optically with Bresser MicroCam II and MikroCamLabII.}}{37}{table.caption.34}\protected@file@percent }
 \newlabel{tab:cross_cap}{{2.1}{37}{Table of cross capacitance measurement to determine possible causes for large values in approach curves. All measurements were done with Mask shuttle in Mask aligner and sample at $0.3$ mm distance. The distance was determined optically with Bresser MicroCam II and MikroCamLabII}{table.caption.34}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {2.18}{\ignorespaces The 3 capacitance curves of the Mask labeled "old", the plots look the same, sharing all features and general shape. The main difference is the scale of the y-axis, and due to this the scale of the uncertainty.}}{38}{figure.caption.35}\protected@file@percent }
diff --git a/chap02.tex b/chap02.tex
index f8becf7ca4e5be4182a50e4bdce7a1b2f14e264d..f589c3eeacd53ae0fde10e893c79c7f69214b9b9 100644
--- a/chap02.tex
+++ b/chap02.tex
@@ -53,7 +53,7 @@ path from the \ce{Pb} evaporator.}
     \label{fig:mask_aligner_chamber}
 \end{figure}
 
-The Mask Aligner vacuum system consists of three distinct vacuum chambers that can be separated with vacuum gate valves.\cite{Mask_Aligner} The first part is the \textbf{M}ain \textbf{C}hamber (MC), in which the Mask Aligner is located, and the evaporator chamber used to create a molecular beam into the main chamber, secondly the \textbf{L}oad \textbf{L}ock (LL), which is a vacuum suitcase that is used to insert new samples and masks into the system and thirdly a Turbomolecular pump loop used to pump the system down to UHV vacuum pressures. The main chamber is equipped with an Ion Getter Pump, due to this the system can be separated from the main pumping loop of the Turbo molecular pump, without loss of vacuum pressure. The system is separated via $2$ \textbf{A}ll \textbf{M}etal \textbf{C}orner \textbf{V}alves (AMCV), one located directly on the main chamber and one separating the evaporator from the Turbomolecular pump loop. Additionally, the Load Lock and the main chamber are separated using a Gate Valve. In order to detect leaks in the vacuum system, a mass spectrometer is also attached to the main chamber. \\
+The Mask Aligner vacuum system consists of three distinct vacuum chambers that can be separated with vacuum gate valves~\cite{Mask_Aligner}. The first part is the \textbf{M}ain \textbf{C}hamber (MC), in which the Mask Aligner is located, and the evaporator chamber used to create a molecular beam into the main chamber, secondly the \textbf{L}oad \textbf{L}ock (LL), which is a vacuum suitcase that is used to insert new samples and masks into the system and thirdly a Turbomolecular pump loop used to pump the system down to UHV vacuum pressures. The main chamber is equipped with an Ion Getter Pump, due to this the system can be separated from the main pumping loop of the Turbo molecular pump, without loss of vacuum pressure. The system is separated via $2$ \textbf{A}ll \textbf{M}etal \textbf{C}orner \textbf{V}alves (AMCV), one located directly on the main chamber and one separating the evaporator from the Turbomolecular pump loop. Additionally, the Load Lock and the main chamber are separated using a Gate Valve. In order to detect leaks in the vacuum system, a mass spectrometer is also attached to the main chamber. \\
 The Load Lock is equipped with a small ion getter pump, that runs on its own, allowing it to keep UHV pressures for extended periods of time, even while separated from the main pump loop. A garage with spaces for up to $10$ samples and $4$ additional spaces for Omicron samples is part of the Load Lock. This allows insertion of multiple samples and masks, that can then be later inserted into the main chamber. For insertion and removal of masks and sample, a wobble stick is attached to the Load Lock chamber. The sample/mask insertion path of the wobble stick can be seen in \textcolor{tab_green}{green} in Figure \ref{fig:mask_aligner_chamber}. The Load Lock is designed to be a detachable vacuum suitcase, allowing samples to be stored in the garage and then transported with the suitcase to another vacuum system without intermediate exposure to ambient conditions.\\
 The main pump loop consists of a rotary vane prepump and a turbomolecular pump. Between prepump and turbo molecular pump is a pressure sensor to determine if the prepump is providing suitable backing pressure and a valve, which can be opened to a Nitrogen bottle to allow the system to be vented to atmospheric pressure with an inert gas. \\
 The 3 parts are seen as distinct, as the 3 components can be decoupled safely once the entire system is pumped to UHV without risk of losing vacuum pressure since no part of the system is not pumped. \\ 
@@ -66,18 +66,25 @@ motor moves when one pulse is applied, has to be measured. This should be done i
 order to make sure all motors run with similar step sizes and inside UHV to
 determine the final step size for approach curves, since in UHV the contribution to the step sizer from friction is increased. The calibration is used to determine a value for the distance of mask and sample, when the distance is small enough that it can no longer be optically determined.\\
 In order to make sure the motors can all give similar step sizes, there are 3
-screws, one on each motor's front plate, that can control the amount of force
+screws (see Figure  \ref{fig:screw_firmness_screw_image}), one on each motor's front plate, that can control the amount of force
 the front plate applies to the prism and thus the amount of friction the piezo
 stacks each apply to the prism. An example curve for how the screw firmness
-affects the step size can be seen in Figure \ref{fig:screw_firmness}.
+affects the step size can be seen in Figure \ref{fig:screw_firmness_plot}.
 
 \begin{figure}[H]
     \centering
-    \includegraphics[width=0.6\linewidth]{img/Plots/ScrewRot_SwappedPlate.pdf}
-    \caption{Example curves showing how rotations of the screws of Z2 and Z3
-affect the given motor's step size. A point where the 3 motors are in agreement
-has to be found iteratively. The jumps in signal after certain rotations result
-from the \ce{CuBe} plate slipping across the winding of the screw at certain spots.}
+	\begin{subfigure}{0.375\textwidth}
+	\centering
+    \includegraphics[width=\linewidth]{img/MA/Calibration_screw_image.png}
+	\caption{}
+	\label{fig:screw_firmness_screw_image}
+	\end{subfigure}
+	\begin{subfigure}{0.55\textwidth}
+    \includegraphics[width=\linewidth]{img/Plots/ScrewRot_SwappedPlate.pdf}
+	\caption{}
+	\label{fig:screw_firmness_plot}
+	\end{subfigure}
+    \caption{\subref{fig:screw_firmness_screw_image} shows a frontal view of the motor Z2 marked in red is the screw used for calibration of the motors on the Mask Aligner. \subref{fig:screw_firmness_plot} shows example curves of how the screws of Z2 and Z3 affect the given motor's step size. A point where the 3 motors are in agreement has to be found iteratively. The jumps in signal after certain rotations result from the \ce{CuBe} plate slipping across the winding of the screw at certain spots. }
     \label{fig:screw_firmness}
 \end{figure}
 
@@ -335,7 +342,7 @@ capacitance readout should increase by
 	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 $\epsilon_r \approx 1$.
+$r$ 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 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. 
@@ -447,7 +454,7 @@ 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
-\cite{Beeker}. 
+~\cite{Beeker}. 
 
 \begin{figure}[H]
     \centering
@@ -466,7 +473,7 @@ 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 different masks, different locations, different approaches
-and a comparison before and after evaporation was discussed.\cite{Beeker}
+and a comparison before and after evaporation was discussed~\cite{Beeker}.
 
 \subsubsection{Reproducibility when removing sample/mask}
 
@@ -565,10 +572,10 @@ more closely, suggesting this is the cause.
 
 \begin{figure}[H]
     \centering
-    \includegraphics[width=0.65\linewidth]{img/LeakageCurrent.pdf}
+    \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.
+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.}
diff --git a/chap03.tex b/chap03.tex
index 5065e300dad016640fc7874544f5c37ddce6c64b..7f4a61b89a65156ad0fac8467c8c2fe451d20db8 100644
--- a/chap03.tex
+++ b/chap03.tex
@@ -98,7 +98,7 @@ Due to the aforementioned behaviors of the KIM001 device, the device was found t
 In order to find a suitable replacement for the RHK Piezo Motor controller, a new device to drive control pulses to the piezo stacks in the mask aligner was built. The PCB is heavily based around the piezo Walker electronics designed to control the piezo Walker used for SEM control. Due to this, the device is often referred to as the "Mask Aligner Walker", even though it is not a walker or stepper motor controller. Adaptations were made to adjust it to the desired slip-stick behavior needed for application in the mask aligner. The Controller takes a serial input command and then drives sinusoidal steps with a sharp fast flank in the middle of them. Controllable are the amplitude of the signal and the number of steps. A simplified overview of the entire signal generation process is shown in Appendix \ref{app:walker_diagram}. The following section will look at each part of the process depicted in detail.
 
 \subsection{Signal generation}
-The core of the Mask aligner controller is an Arduino DUE.~\cite{arduino_datasheet} The  \textbf{C}entral to \textbf{P}rocessing \textbf{U}nit CPU of the Arduino DUE the "Atmel SAM3X8E ARM Cortex-M3 CPU" is a $32$-Bit ARM-Core microcontroller. Intgrated into the CPU is a $12$-Bit \textbf{D}igital to \textbf{A}nalog \textbf{C}onverter (DAC).~\cite{arduino_cpu_datasheet} The DAC comes with two output channels that can be controlled to output a signal simultaneously. The Arduino CPU is responsible for the generation of the original signal shape in software. The Arduino generates a signal internally with a sampling rate of $404$ kHz with the shape given by:
+The core of the Mask aligner controller is an Arduino DUE~\cite{arduino_datasheet}. The  \textbf{C}entral to \textbf{P}rocessing \textbf{U}nit CPU of the Arduino DUE the "Atmel SAM3X8E ARM Cortex-M3 CPU" is a $32$-Bit ARM-Core microcontroller. Intgrated into the CPU is a $12$-Bit \textbf{D}igital to \textbf{A}nalog \textbf{C}onverter (DAC)~\cite{arduino_cpu_datasheet}. The DAC comes with two output channels that can be controlled to output a signal simultaneously. The Arduino CPU is responsible for the generation of the original signal shape in software. The Arduino generates a signal internally with a sampling rate of $404$ kHz with the shape given by:
 \begin{equation}
      S = 4095 * \frac{A}{2 \pi} * \sin(2 \pi * t/P) + t/P
 \end{equation}
@@ -124,7 +124,7 @@ The Signal given by the Arduino contains aliasing artifacts from the digital to
 
 \subsection{Fast flank}
 
-After this step the signal is bimodal and of the correct shape, but for the desired slip-stick behavior this only gives the slow flank. The fast flank is achieved by taking the signal given here and feeding it into a hardware inverter, whilst retaining both the original (normal) and the inverted signal. The retained signals can be seen in Figure \ref{fig:signal_switch_entry} When the signal is at its plateau, a hardware switch is used to change from the normal to the inverted signal. Examples of the signal are shown in Figure \ref{fig:signal_switch_switched}. The switching is achieved via a ADG1436 switch that has a transition time of $<200$ ns \cite{switch_datasheet}, this puts it well within the $<1$ $\mu$s time span required for the slip behavior of the signal's fast flank. Circuits diagrams for this can be found in Appendix \ref{app:circuit_electronics}.
+After this step the signal is bimodal and of the correct shape, but for the desired slip-stick behavior this only gives the slow flank. The fast flank is achieved by taking the signal given here and feeding it into a hardware inverter, whilst retaining both the original (normal) and the inverted signal. The retained signals can be seen in Figure \ref{fig:signal_switch_entry} When the signal is at its plateau, a hardware switch is used to change from the normal to the inverted signal. Examples of the signal are shown in Figure \ref{fig:signal_switch_switched}. The switching is achieved via a ADG1436 switch that has a transition time of $<200$ ns~\cite{switch_datasheet}, this puts it well within the $<1$ $\mu$s time span required for the slip behavior of the signal's fast flank. Circuits diagrams for this can be found in Appendix \ref{app:circuit_electronics}.
 
 \begin{figure}[H]
     \centering
diff --git a/chap04.aux b/chap04.aux
index 02459176e4a9cb20788c2a13e816630642cdb907..21e082d0af145ac4e96863d11c1cc82cdc7f865a 100644
--- a/chap04.aux
+++ b/chap04.aux
@@ -36,7 +36,7 @@
 \newlabel{sub@fig:solder_anchors_examples_shear_02}{{d}{59}{\relax }{figure.caption.62}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {4.3}{\ignorespaces Examples of the different approaches taken to solve the issues with the solder anchor points. (\subref  {fig:solder_anchors_examples_glue_bottom}) shows attaching a solder anchor to the bottom of a previously used solder ceramic. (\subref  {fig:solder_anchors_examples_AlO}) shows the replacement of a solder ceramic with a thinner \ce {Al2O3} plate. (\subref  {fig:solder_anchors_examples_shear_01}) and shows the initial state of a solder ceramic interfering with the prism and then (\subref  {fig:solder_anchors_examples_shear_02}) shows the solder ceramic after some of the solder was carefully taken off, allowing the prism to now move freely.}}{59}{figure.caption.62}\protected@file@percent }
 \newlabel{fig:solder_anchors_examples}{{4.3}{59}{Examples of the different approaches taken to solve the issues with the solder anchor points. (\subref {fig:solder_anchors_examples_glue_bottom}) shows attaching a solder anchor to the bottom of a previously used solder ceramic. (\subref {fig:solder_anchors_examples_AlO}) shows the replacement of a solder ceramic with a thinner \ce {Al2O3} plate. (\subref {fig:solder_anchors_examples_shear_01}) and shows the initial state of a solder ceramic interfering with the prism and then (\subref {fig:solder_anchors_examples_shear_02}) shows the solder ceramic after some of the solder was carefully taken off, allowing the prism to now move freely}{figure.caption.62}{}}
-\citation{olschewski}
+\citation{Olschewski}
 \@writefile{toc}{\contentsline {section}{\numberline {4.4}Piezo re-gluing}{60}{section.4.4}\protected@file@percent }
 \newlabel{sec:piezo_reglue}{{4.4}{60}{Piezo re-gluing}{section.4.4}{}}
 \newlabel{fig:Z3_reglue_process_off}{{4.4a}{61}{\relax }{figure.caption.63}{}}
diff --git a/chap04.tex b/chap04.tex
index ff0b059b5707c191551b601454c597d249497d4a..0d0689428b411be5175a48542cb6ec168ffb5e28 100644
--- a/chap04.tex
+++ b/chap04.tex
@@ -2,7 +2,7 @@
 \chapter{Mask Aligner repairs and optimizations}
 \section{Overview}
 
-The Mask Aligner was built in 2015.\cite{Olschewski} Since then some problems had developed with the function of the Mask Aligner and its performance was limited. In order to alleviate and prevent further problems, repairs had to be performed on several of the piezo motor stacks. In order to possibly prevent further problems from occurring, various measures were taken as preemptive measures. The following chapter will detail the repairs and optimizations that were performed on the Mask Aligner. 
+The Mask Aligner was built in 2015~\cite{Olschewski}. Since then some problems had developed with the function of the Mask Aligner and its performance was limited. In order to alleviate and prevent further problems, repairs had to be performed on several of the piezo motor stacks. In order to possibly prevent further problems from occurring, various measures were taken as preemptive measures. The following chapter will detail the repairs and optimizations that were performed on the Mask Aligner. 
 
 \begin{figure}[H]
     \centering
@@ -121,7 +121,7 @@ All motors were checked for soldering anchor points that could potentially inter
 After this step, the prism would no longer get stuck when driving and could cleanly drive the whole range of possible motion. \\
 
 \section{Piezo re-gluing} \label{sec:piezo_reglue}
-The piezo motors of the 3 motor stacks in the Mask Aligner were glued in 2015 with the non-conductive EPO-TEK H70E glue.\cite{olschewski} This glue has over time lost some of its sticking ability, even though the Mask Aligner is usually in UHV. For this reason, 2 of the piezo stacks, one on motor Z1 and one on Motor Z3, had by the time previous repairs were performed completely detached. These stacks needed to be re-glued to the surface of the Mask Aligner Body, in order to provide proper support for the driving of the prisms. \\
+The piezo motors of the 3 motor stacks in the Mask Aligner were glued in 2015 with the non-conductive EPO-TEK H70E glue~\cite{Olschewski}. This glue has over time lost some of its sticking ability, even though the Mask Aligner is usually in UHV. For this reason, 2 of the piezo stacks, one on motor Z1 and one on Motor Z3, had by the time previous repairs were performed completely detached. These stacks needed to be re-glued to the surface of the Mask Aligner Body, in order to provide proper support for the driving of the prisms. \\
 
 \begin{figure}[H]
     \centering
diff --git a/chap05.aux b/chap05.aux
index aa2a192728297b8c6dbe461abfe3df52827213d4..681557e8938f6d6e4501d8a702e34a47c3996b8c 100644
--- a/chap05.aux
+++ b/chap05.aux
@@ -14,24 +14,24 @@
 \newlabel{sub@fig:Evaporation_diagramm_sample_img}{{a}{72}{\relax }{figure.caption.75}{}}
 \newlabel{fig:Evaporation_diagramm_mask_img}{{5.3b}{72}{\relax }{figure.caption.75}{}}
 \newlabel{sub@fig:Evaporation_diagramm_mask_img}{{b}{72}{\relax }{figure.caption.75}{}}
-\@writefile{lof}{\contentsline {figure}{\numberline {5.3}{\ignorespaces Diagram showing the Evaporation performed on the sample (\subref  {fig:Evaporation_diagramm_sample_img}). Red squares represent the evaporation fields. The number shows the order of evaporations. Distances are measured using an optical microscope. Fields are at a $10^\circ $ angle with respect to the sample holder. (\subref  {fig:Evaporation_diagramm_mask_img}) shows a microscope image of the mask taken before evaporation. The mask holder is placed straight in the microscope. The mask itself is angled on the mask holder.}}{72}{figure.caption.75}\protected@file@percent }
-\newlabel{fig:Evaporation_diagramm}{{5.3}{72}{Diagram showing the Evaporation performed on the sample (\subref {fig:Evaporation_diagramm_sample_img}). Red squares represent the evaporation fields. The number shows the order of evaporations. Distances are measured using an optical microscope. Fields are at a $10^\circ $ angle with respect to the sample holder. (\subref {fig:Evaporation_diagramm_mask_img}) shows a microscope image of the mask taken before evaporation. The mask holder is placed straight in the microscope. The mask itself is angled on the mask holder}{figure.caption.75}{}}
-\@writefile{toc}{\contentsline {section}{\numberline {5.2}Contamination}{72}{section.5.2}\protected@file@percent }
+\@writefile{lof}{\contentsline {figure}{\numberline {5.3}{\ignorespaces Diagram showing the Evaporation performed on the sample (\subref  {fig:Evaporation_diagramm_sample_img}). Red squares represent the positions of the evaporated fields. The number shows the order of evaporations. Distances are measured using an optical microscope. Fields are at a $10^\circ $ angle with respect to the sample holder. (\subref  {fig:Evaporation_diagramm_mask_img}) shows a microscope image of the mask taken before evaporation. The mask holder is placed straight in the microscope. The mask itself is angled on the mask holder.}}{72}{figure.caption.75}\protected@file@percent }
+\newlabel{fig:Evaporation_diagramm}{{5.3}{72}{Diagram showing the Evaporation performed on the sample (\subref {fig:Evaporation_diagramm_sample_img}). Red squares represent the positions of the evaporated fields. The number shows the order of evaporations. Distances are measured using an optical microscope. Fields are at a $10^\circ $ angle with respect to the sample holder. (\subref {fig:Evaporation_diagramm_mask_img}) shows a microscope image of the mask taken before evaporation. The mask holder is placed straight in the microscope. The mask itself is angled on the mask holder}{figure.caption.75}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {5.2}Contamination}{73}{section.5.2}\protected@file@percent }
 \newlabel{fig:evaporation_contamination_img}{{5.4a}{73}{\relax }{figure.caption.76}{}}
 \newlabel{sub@fig:evaporation_contamination_img}{{a}{73}{\relax }{figure.caption.76}{}}
 \newlabel{fig:evaporation_contamination_anal}{{5.4b}{73}{\relax }{figure.caption.76}{}}
 \newlabel{sub@fig:evaporation_contamination_anal}{{b}{73}{\relax }{figure.caption.76}{}}
-\@writefile{lof}{\contentsline {figure}{\numberline {5.4}{\ignorespaces (\subref  {fig:evaporation_contamination_img}) shows an AFM image of field $3$ without any grain removal applied. Data was obtained on multiple different spots on the sample. \textcolor {tab_red}{Red} and \textcolor {tab_green}{green} lines show the average height and width of the contamination particles obtained from peak fits. (\subref  {fig:evaporation_contamination_anal}) shows line cuts obtained from contamination particles.}}{73}{figure.caption.76}\protected@file@percent }
-\newlabel{fig:evaporation_contamination}{{5.4}{73}{(\subref {fig:evaporation_contamination_img}) shows an AFM image of field $3$ without any grain removal applied. Data was obtained on multiple different spots on the sample. \textcolor {tab_red}{Red} and \textcolor {tab_green}{green} lines show the average height and width of the contamination particles obtained from peak fits. (\subref {fig:evaporation_contamination_anal}) shows line cuts obtained from contamination particles}{figure.caption.76}{}}
-\@writefile{toc}{\contentsline {section}{\numberline {5.3}Penumbra}{73}{section.5.3}\protected@file@percent }
+\@writefile{lof}{\contentsline {figure}{\numberline {5.4}{\ignorespaces (\subref  {fig:evaporation_contamination_img}) shows an AFM image of field $3$ without any grain removal applied. Data was obtained on multiple different spots on the sample. (\subref  {fig:evaporation_contamination_anal}) shows line cuts obtained from contamination particles. \textcolor {tab_red}{Red} and \textcolor {tab_green}{green} lines show the average height and width of the contamination particles obtained from peak fits.}}{73}{figure.caption.76}\protected@file@percent }
+\newlabel{fig:evaporation_contamination}{{5.4}{73}{(\subref {fig:evaporation_contamination_img}) shows an AFM image of field $3$ without any grain removal applied. Data was obtained on multiple different spots on the sample. (\subref {fig:evaporation_contamination_anal}) shows line cuts obtained from contamination particles. \textcolor {tab_red}{Red} and \textcolor {tab_green}{green} lines show the average height and width of the contamination particles obtained from peak fits}{figure.caption.76}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {5.3}Penumbra}{74}{section.5.3}\protected@file@percent }
 \newlabel{fig:penumbra_tilt_sigmas}{{5.5a}{74}{\relax }{figure.caption.77}{}}
 \newlabel{sub@fig:penumbra_tilt_sigmas}{{a}{74}{\relax }{figure.caption.77}{}}
 \newlabel{fig:Evaporation_diagramm_field}{{5.5b}{74}{\relax }{figure.caption.77}{}}
 \newlabel{sub@fig:Evaporation_diagramm_field}{{b}{74}{\relax }{figure.caption.77}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {5.5}{\ignorespaces AFM image of evaporated \ce {Pb} dot (\subref  {fig:penumbra_tilt_sigmas}) illustrating the penumbral widths used for evaporation analysis $\sigma _s$ and $\sigma _l$, depicted in \textcolor {tab_red}{red}, and the major axis of the tilt \textcolor {tab_green}{(green)}. $\sigma _s$ is drawn larger than actually measured, since the measured value would be hardly visible. The \textcolor {tab_blue}{blue} lines are the major $a$ and minor $b$ axis of the ellipse formed on the evaporated dot. Inset shows the same image in the phase data. The data stems from Evaporation 5 In Chapter 5. (\subref  {fig:Evaporation_diagramm_field}) shows an AFM image of the top right part of the evaporated field labeled $3$. Grains were reduced using post-processing. Black circles show the dots chosen for further examination on this particular field.}}{74}{figure.caption.77}\protected@file@percent }
 \newlabel{fig:penumbra_tilt_sigmas_and_field_show}{{5.5}{74}{AFM image of evaporated \ce {Pb} dot (\subref {fig:penumbra_tilt_sigmas}) illustrating the penumbral widths used for evaporation analysis $\sigma _s$ and $\sigma _l$, depicted in \textcolor {tab_red}{red}, and the major axis of the tilt \textcolor {tab_green}{(green)}. $\sigma _s$ is drawn larger than actually measured, since the measured value would be hardly visible. The \textcolor {tab_blue}{blue} lines are the major $a$ and minor $b$ axis of the ellipse formed on the evaporated dot. Inset shows the same image in the phase data. The data stems from Evaporation 5 In Chapter 5. (\subref {fig:Evaporation_diagramm_field}) shows an AFM image of the top right part of the evaporated field labeled $3$. Grains were reduced using post-processing. Black circles show the dots chosen for further examination on this particular field}{figure.caption.77}{}}
-\@writefile{lof}{\contentsline {figure}{\numberline {5.6}{\ignorespaces Example of the analysis performed on each of the recorded dots for a single line cut. (a) shows the raw AFM data before cleaning with a large amount of very bright contaminant particles. (b) shows the cleaned image, as well as the line cut \textcolor {tab_green}{(green)} from which the line cut data (c) was obtained. The black lines show how multiple line cuts were obtained on a single image to obtain values for $\sigma _s$ and $\sigma _l$. The fit shows the two different penumbra widths induced by the tilt $\sigma _s$ and $\sigma _l$ for a single line cut.}}{76}{figure.caption.78}\protected@file@percent }
-\newlabel{fig:evaporation_analysis}{{5.6}{76}{Example of the analysis performed on each of the recorded dots for a single line cut. (a) shows the raw AFM data before cleaning with a large amount of very bright contaminant particles. (b) shows the cleaned image, as well as the line cut \textcolor {tab_green}{(green)} from which the line cut data (c) was obtained. The black lines show how multiple line cuts were obtained on a single image to obtain values for $\sigma _s$ and $\sigma _l$. The fit shows the two different penumbra widths induced by the tilt $\sigma _s$ and $\sigma _l$ for a single line cut}{figure.caption.78}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5.6}{\ignorespaces Example of the analysis performed on each of the recorded dots for a single line cut. (a) shows the raw AFM data before cleaning with a large amount of very bright contaminant particles. (b) shows the cleaned image, as well as the line cut \textcolor {tab_green}{(green)} from which the line cut data (c) was obtained. The black lines in (b) show how multiple line cuts were obtained on a single image to obtain values for $\sigma _s$ and $\sigma _l$. The fit parameters are the two different penumbra widths induced by the tilt $\sigma _s$ and $\sigma _l$ for a single line cut.}}{76}{figure.caption.78}\protected@file@percent }
+\newlabel{fig:evaporation_analysis}{{5.6}{76}{Example of the analysis performed on each of the recorded dots for a single line cut. (a) shows the raw AFM data before cleaning with a large amount of very bright contaminant particles. (b) shows the cleaned image, as well as the line cut \textcolor {tab_green}{(green)} from which the line cut data (c) was obtained. The black lines in (b) show how multiple line cuts were obtained on a single image to obtain values for $\sigma _s$ and $\sigma _l$. The fit parameters are the two different penumbra widths induced by the tilt $\sigma _s$ and $\sigma _l$ for a single line cut}{figure.caption.78}{}}
 \newlabel{fig:evaporation_measured_penumbra_sigs}{{5.7a}{77}{\relax }{figure.caption.79}{}}
 \newlabel{sub@fig:evaporation_measured_penumbra_sigs}{{a}{77}{\relax }{figure.caption.79}{}}
 \newlabel{fig:evaporation_measured_penumbra_sigl}{{5.7b}{77}{\relax }{figure.caption.79}{}}
@@ -63,6 +63,8 @@
 \newlabel{fig:evaporation_SEM_analysis}{{5.10}{81}{An example of the clogging noticed on $4$ of the mask holes (\subref {fig:evaporation_SEM_analysis_clog}) and the tilt direction from \ref {fig:evaporation_tilts} overlayed over the SEM image of the mask after it was rotated to match the fields}{figure.caption.82}{}}
 \@writefile{toc}{\contentsline {section}{\numberline {5.5}Simulation}{81}{section.5.5}\protected@file@percent }
 \newlabel{sec:simulation}{{5.5}{81}{Simulation}{section.5.5}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.5.1}Overview and principle}{81}{subsection.5.5.1}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.5.2}Results}{83}{subsection.5.5.2}\protected@file@percent }
 \newlabel{fig:evaporation_simulation_first_compare_AFM}{{5.11a}{83}{\relax }{figure.caption.83}{}}
 \newlabel{sub@fig:evaporation_simulation_first_compare_AFM}{{a}{83}{\relax }{figure.caption.83}{}}
 \newlabel{fig:evaporation_simulation_first_compare_SIM}{{5.11b}{83}{\relax }{figure.caption.83}{}}
@@ -86,12 +88,12 @@
 \newlabel{sub@fig:evaporation_simulation_rejection_after}{{b}{86}{\relax }{figure.caption.86}{}}
 \newlabel{fig:evaporation_simulation_rejection_comparison}{{5.14c}{86}{\relax }{figure.caption.86}{}}
 \newlabel{sub@fig:evaporation_simulation_rejection_comparison}{{c}{86}{\relax }{figure.caption.86}{}}
-\@writefile{lof}{\contentsline {figure}{\numberline {5.14}{\ignorespaces Simulated evaporation dots without (\subref  {fig:evaporation_simulation_rejection_prev}) and with (\subref  {fig:evaporation_simulation_rejection_after}) $90$ \% probability to reject a deposition, when no previous deposition happened on the target pixel. (\subref  {fig:evaporation_simulation_rejection_comparison}) shows the AFM image parameters for simulation were obtained from for comparison. The parameters of the ellipse are the same as in Figure \ref {fig:evaporation_simulation_first_compare}.}}{86}{figure.caption.86}\protected@file@percent }
-\newlabel{fig:evaporation_simulation_rejection}{{5.14}{86}{Simulated evaporation dots without (\subref {fig:evaporation_simulation_rejection_prev}) and with (\subref {fig:evaporation_simulation_rejection_after}) $90$ \% probability to reject a deposition, when no previous deposition happened on the target pixel. (\subref {fig:evaporation_simulation_rejection_comparison}) shows the AFM image parameters for simulation were obtained from for comparison. The parameters of the ellipse are the same as in Figure \ref {fig:evaporation_simulation_first_compare}}{figure.caption.86}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {5.14}{\ignorespaces Simulated evaporation dots without (\subref  {fig:evaporation_simulation_rejection_prev}) and with (\subref  {fig:evaporation_simulation_rejection_after}) $90$ \% probability to reject a deposition, when no previous deposition happened on the target pixel. (\subref  {fig:evaporation_simulation_rejection_comparison}) shows the AFM image from which the parameters for the simulation were obtained. The parameters of the ellipse are the same as in Figure \ref {fig:evaporation_simulation_first_compare}.}}{86}{figure.caption.86}\protected@file@percent }
+\newlabel{fig:evaporation_simulation_rejection}{{5.14}{86}{Simulated evaporation dots without (\subref {fig:evaporation_simulation_rejection_prev}) and with (\subref {fig:evaporation_simulation_rejection_after}) $90$ \% probability to reject a deposition, when no previous deposition happened on the target pixel. (\subref {fig:evaporation_simulation_rejection_comparison}) shows the AFM image from which the parameters for the simulation were obtained. The parameters of the ellipse are the same as in Figure \ref {fig:evaporation_simulation_first_compare}}{figure.caption.86}{}}
 \@writefile{lof}{\contentsline {figure}{\numberline {5.15}{\ignorespaces 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.}}{87}{figure.caption.87}\protected@file@percent }
 \newlabel{fig:evaporation_simulation_progression}{{5.15}{87}{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.87}{}}
-\@writefile{toc}{\contentsline {paragraph}{Software improvements}{87}{section*.88}\protected@file@percent }
-\@writefile{toc}{\contentsline {paragraph}{Conclusion}{88}{section*.89}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.5.3}Software improvements}{87}{subsection.5.5.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {subsection}{\numberline {5.5.4}Final Remark}{88}{subsection.5.5.4}\protected@file@percent }
 \@setckpt{chap05}{
 \setcounter{page}{89}
 \setcounter{equation}{1}
@@ -104,16 +106,16 @@
 \setcounter{part}{0}
 \setcounter{chapter}{5}
 \setcounter{section}{5}
-\setcounter{subsection}{0}
+\setcounter{subsection}{4}
 \setcounter{subsubsection}{0}
 \setcounter{paragraph}{0}
 \setcounter{subparagraph}{0}
 \setcounter{figure}{15}
 \setcounter{table}{1}
-\setcounter{section@level}{4}
+\setcounter{section@level}{2}
 \setcounter{Item}{18}
 \setcounter{Hfootnote}{0}
-\setcounter{bookmark@seq@number}{54}
+\setcounter{bookmark@seq@number}{58}
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diff --git a/chap05.tex b/chap05.tex
index 128f4ef4362a0839d0567cb2e747332119700489..809d1c464d7d4df2b5dd4588ca97bf7bf02b89be 100644
--- a/chap05.tex
+++ b/chap05.tex
@@ -2,7 +2,7 @@
 \chapter{Evaporations and measurement}
 \section{Evaporation configuration}
 
-As a test for positioning and top optimize the growth of \ce{Pb} islands on a \ce{Si} sample, while minimizing the shadow obtained from mask sample alignment, evaporations were performed on a \ce{Si} sample. The \ce{Si}(111) sample was prepared and cleaned using the process described in Section \ref{sec:sample_prep}. Cleanliness of the sample and mask were confirmed optically before insertion into the Load Lock.
+As a test for positioning and to optimize the growth of \ce{Pb} islands on a \ce{Si} sample, while minimizing the shadow obtained from mask sample alignment, evaporations were performed on a \ce{Si} sample. The \ce{Si}(111) sample was prepared and cleaned using the process described in Section \ref{sec:sample_prep}. Cleanliness of the sample and mask were confirmed optically before insertion into the Load Lock.
 
 \begin{figure}[H]
     \centering
@@ -11,7 +11,7 @@ As a test for positioning and top optimize the growth of \ce{Pb} islands on a \c
     \label{fig:evaporation_approach_curve}
 \end{figure}
 
-Five subsequent evaporations were performed at different lateral positions on the sample. Each field was evaporated at different mask sample distances, as described by the approach curve. The approach curve to full contact of this particular sample is shown in Figure \ref{fig:evaporation_approach_curve} \\  
+Five subsequent evaporations were performed at different lateral positions on the sample. Each evaporation consists of a field of $9 \times 9$ $3$ $\mu$m \ce{Pb} circles, as seen previously in Figure \ref{fig:mask_aligner_nomenclature_capacitances_mask}. Each field was evaporated at different mask sample distances, as described by the approach curve. The approach curve to full contact of this particular sample is shown in Figure \ref{fig:evaporation_approach_curve} \\  
 
 \begin{itemize}
 	\item Field 1: Full contact
@@ -63,14 +63,14 @@ The pressure of the main chamber before each of the evaporations was $4.5 \times
 		\label{fig:Evaporation_diagramm_mask_img}
 	\end{subfigure}
     
-    \caption{Diagram showing the Evaporation performed on the sample (\subref{fig:Evaporation_diagramm_sample_img}). Red squares represent the evaporation fields. The number shows the order of evaporations. Distances are measured using an optical microscope. Fields are at a $10^\circ$ angle with respect to the sample holder. (\subref{fig:Evaporation_diagramm_mask_img}) shows a microscope image of the mask taken before evaporation. The mask holder is placed straight in the microscope. The mask itself is angled on the mask holder.}
+    \caption{Diagram showing the Evaporation performed on the sample (\subref{fig:Evaporation_diagramm_sample_img}). Red squares represent the positions of the evaporated fields. The number shows the order of evaporations. Distances are measured using an optical microscope. Fields are at a $10^\circ$ angle with respect to the sample holder. (\subref{fig:Evaporation_diagramm_mask_img}) shows a microscope image of the mask taken before evaporation. The mask holder is placed straight in the microscope. The mask itself is angled on the mask holder.}
     \label{fig:Evaporation_diagramm}
 \end{figure}
 
-Figure \ref{fig:Evaporation_diagramm_sample_img} shows the positions of the evaporated fields in regard to the sample edges and each other. 
+Figure \ref{fig:Evaporation_diagramm_sample_img} shows the positions of the evaporated fields in regard to the sample edges and each other. The fields angle was measured to be about $10^\circ$ with regard to the sample edge. This comes from a slight misalignment of the mask on the mask holder, as seen in Figure \ref{fig:Evaporation_diagramm_mask_img}.
 
 \section{Contamination}
-The entire sample's surface is contaminated with small particles, which are about $\approx 50$ nm in height and of a size on the order of $ 10$ nm. The contaminants are not visible in an optical microscope. After cleaning, the sample was only checked optically, which is why it is unknown if they were present after cleaning or were deposited after. 
+The entire sample's surface is contaminated with small particles, which are about $\approx 50$ nm in height and of a diameter on the order of $ 10$ nm. The contaminants are not visible in an optical microscope. After cleaning, the sample was only checked optically, which is why it is unknown if they were present after cleaning or were deposited afterwards. 
 
 \begin{figure}[H]
     \centering
@@ -86,18 +86,18 @@ The entire sample's surface is contaminated with small particles, which are abou
 		\caption{}
 		\label{fig:evaporation_contamination_anal}
 	\end{subfigure}
-    \caption{(\subref{fig:evaporation_contamination_img}) shows an AFM image of field $3$ without any grain removal applied. Data was obtained on multiple different spots on the sample. \textcolor{tab_red}{Red} and \textcolor{tab_green}{green} lines show the average height and width of the contamination particles obtained from peak fits. (\subref{fig:evaporation_contamination_anal}) shows line cuts obtained from contamination particles.}
+    \caption{(\subref{fig:evaporation_contamination_img}) shows an AFM image of field $3$ without any grain removal applied. Data was obtained on multiple different spots on the sample. (\subref{fig:evaporation_contamination_anal}) shows line cuts obtained from contamination particles. \textcolor{tab_red}{Red} and \textcolor{tab_green}{green} lines show the average height and width of the contamination particles obtained from peak fits.}
     \label{fig:evaporation_contamination}
 \end{figure}
 
-The data in Figure \ref{fig:evaporation_contamination} shows that the particles are up to $\approx 40$ nm in height and with an average height of $20 \pm 10$ nm. The particles are on average $40 \pm 10$ in width. Height and width were obtained by fitting flattened Gaussian functions to the particles line cuts and extracting $2\sigma$ as well as the height of the peak. The distribution of particles across the sample surface appears approximately isotropic across the surface.
+The data in Figure \ref{fig:evaporation_contamination} shows that the particles are up to $\approx 40$ nm in height and with an average height of $20 \pm 10$ nm. The particle's average width is $40 \pm 10$. Height and width were obtained by fitting flattened Gaussian functions to the particles line cuts and extracting $2\sigma$ as well as the height of the peak. The distribution of particles across the sample surface appears approximately isotropic.
 
-In addition, the sample was contaminated with larger particles possibly from long exposure at atmospheric conditions as well as being inside the Mask Aligner Chamber during vacuum bakeout, where the system is heated to $>100$°C on $2$ separate occasions. The size of these larger particles was approximately determined to be in the order of $\mathcal{O}(100 \text{nm})$ using SEM and on the order of $\mathit{O}(10)$ $\mu$m in diameter. \\
-Since the sample was checked only optically before insertion into UHV the small particle contamination might have been overlooked. It is suggested that in future before the sample is inserted into UHV eventual contamination should be quantified in an AFM measurement. 
+In addition, the sample was contaminated with larger particles possibly from long exposure at atmospheric conditions as well as being inside the Mask Aligner Chamber during vacuum bakeout, where the system is heated to $>100$°C on $2$ separate occasions. The size of these larger particles was determined to be in the order of $\mathcal{O}(100 \text{nm})$ using SEM and on the order of $\mathit{O}(10)$ $\mu$m in diameter. \\
+Since the sample was checked only optically before insertion into UHV the small particle contamination might have been overlooked. It is suggested that in future before the sample is inserted into UHV possible contamination should be quantified in an AFM measurement and if necessary more cleaning steps performed.
 
 \section{Penumbra}
 
-To analyze the penumbra, for a circular in this case since there are many different penumbral widths (see Figure \ref{fig:penumbra_explanation_tilt}) for each angle in a circle, the chosen relevant lengths discussed will be the $2$ lengths along the axis of tilt $\sigma_s$ and $\sigma_l$. Additionally, the angle of tilt and the semi major and semi minor axis of the ellipse were measured. An example of how this would look can be seen in Figure \ref{fig:penumbra_tilt_sigmas} \\
+To analyze the penumbra, different penumbras are analyzed, since the evaporated \ce{Pb} dots are not entirely circular (see Figure \ref{fig:penumbra_explanation_tilt}). Due to the elliptical abberation visible on the dots two different penumbra widths are analyzed. These are labeled $\sigma_s$ and $\sigma_l$. Both are defined along the major axis of the elliptical abberation. Additionally, the angle of tilt and the semi major and semi minor axis of the ellipse were measured. An example of how this would look can be seen in Figure \ref{fig:penumbra_tilt_sigmas} \\
 
 \begin{figure}[H]
     \centering
@@ -116,12 +116,12 @@ To analyze the penumbra, for a circular in this case since there are many differ
     \label{fig:penumbra_tilt_sigmas_and_field_show}
 \end{figure}
 
-In order to obtain the width of the penumbra, as well as other characteristics of the performed evaporation, AFM measurements were taken. For all fields, at least one measurement was taken of the $4$ cardinal direction by first measuring a low resolution image of the top right of the field and selecting $3$ dots to take higher resolution images of. One on the top, one on the right and one in the center. An example of this is shown in Figure \ref{fig:Evaporation_diagramm_field}. The same process is repeated for the lower left of the field. The center dot is not recorded again in the lower left image. With this high resolution, images of dots in all 4 cardinal directions as well as the center are obtained. These are not necessarily the ones in the middle of the $4$ cardinal directions, and can be different dots across the 5 different fields. Dots were not picked for direct correspondence to the cardinal direction, but for low amount of artifacts in the AFM image.\\
+In order to obtain the width of the penumbra, as well as other characteristics of the performed evaporation, AFM measurements were taken. For all fields, at least one measurement was taken of the $4$ cardinal direction by first measuring a low resolution image of the top right of the field and selecting $3$ dots to take higher resolution images of. One on the top, one on the right and one near the center. An example of this is shown in Figure \ref{fig:Evaporation_diagramm_field}. The dot visualized on the left of the image is near the center of the whole field, as the image shows only a partial field. The same process is repeated for the lower left of the field. The center dot is not recorded again in the lower left image. With this high resolution, images of dots in all 4 cardinal directions as well as the center are obtained. These are not necessarily the ones in the middle of the $4$ cardinal directions, and can be different dots across the 5 different fields. Dots were not picked for direct correspondence to the cardinal direction, but for low amount of artifacts in the AFM image.\\
 First, the data is cleaned by masking the contamination of the \ce{Si} sample. This works very well since the evaporated dots are of a height of $\approx 3$ nm, while the contamination particles are of the much greater height $\approx 50$ nm. The area under the mask is now interpolated in order to erase most of the particles. \\
 The width of the penumbra was then obtained by getting line cuts close to the line along which the tilt of the dots points and by fitting a Gaussian fall of to the slopes of the resulting line cut. The fit function is:
 
 \begin{equation}
- f(x, a, b, h, \mu, \sigma_s, \sigma_l, r) = \begin{cases} 
+ f(x, b, h, \mu, \sigma_s, \sigma_l, r) = \begin{cases} 
       b + h * \exp(\frac{(x - (\mu - r))^2}{2\sigma_s^2}) & x\leq \mu - r\\
       b + h & \mu - r\leq x\leq \mu + r \\
       b + h * \exp(\frac{(x - (\mu + r))^2}{2\sigma_l^2}) & \mu + r \leq x 
@@ -150,11 +150,11 @@ Also obtained by this method are the height and the diameter of each dot.
     	\includegraphics[width=0.95\linewidth]{img/Evaporation/TopField5Fit.pdf}
     	\caption{}
 	\end{subfigure}
-	\caption{Example of the analysis performed on each of the recorded dots for a single line cut. (a) shows the raw AFM data before cleaning with a large amount of very bright contaminant particles. (b) shows the cleaned image, as well as the line cut \textcolor{tab_green}{(green)} from which the line cut data (c) was obtained. The black lines show how multiple line cuts were obtained on a single image to obtain values for $\sigma_s$ and $\sigma_l$. The fit shows the two different penumbra widths induced by the tilt $\sigma_s$ and $\sigma_l$ for a single line cut.}
+	\caption{Example of the analysis performed on each of the recorded dots for a single line cut. (a) shows the raw AFM data before cleaning with a large amount of very bright contaminant particles. (b) shows the cleaned image, as well as the line cut \textcolor{tab_green}{(green)} from which the line cut data (c) was obtained. The black lines in (b) show how multiple line cuts were obtained on a single image to obtain values for $\sigma_s$ and $\sigma_l$. The fit parameters are the two different penumbra widths induced by the tilt $\sigma_s$ and $\sigma_l$ for a single line cut.}
     \label{fig:evaporation_analysis}
 \end{figure}
 
-This process was performed for every recorded dot and with multiple line cuts near the line in which the tilt is pointing, as well as for both trace and retrace images. This gives multiple data points for each image for both $\sigma_s$ and $\sigma_l$. The final values for each dot were then obtained by taking the mean and standard deviation for all the line cuts. When drawing line cuts, contamination grains were avoided if possible as these might affect fit accuracy.
+This process was performed for every recorded dot and with multiple line cuts near the line in which the tilt is pointing, as well as for both trace and retrace images. This gives multiple data points for each image for both $\sigma_s$ and $\sigma_l$. The final values for each dot were then obtained by taking the mean and standard deviation for all the line cuts. When drawing line cuts, contamination grains were avoided whenever possible as these might affect fit accuracy.
 
 \begin{figure}[H]
     \centering
@@ -181,15 +181,15 @@ This process was performed for every recorded dot and with multiple line cuts ne
 	\caption{Data obtained from the previously described method for each of the 5 evaporations, from evaporated dot each from the center of the field, the left, the right, the bottom and the top. The dot chosen depended on measurement condition such as contamination and phase characteristics of the dot. The data shows the smaller penumbra $\sigma_s$ (\subref{fig:evaporation_measured_penumbra_sigs}) the larger penumbra $\sigma_l$ (\subref{fig:evaporation_measured_penumbra_sigl}), the height of the dot (\subref{fig:evaporation_measured_penumbra_height}) and the diameter of the circle (\subref{fig:evaporation_measured_penumbra_circle_r}).}
     \label{fig:evaporation_measured_penumbra}
 \end{figure}
-Figure \ref{fig:evaporation_measured_penumbra} shows the values obtained from analysis of exemplary \ce{Pb} dots of each field. For each field a dot on the top of the field, one on the bottom, one near the center and on each on the left and the right were chosen to analyze. The dots were chosen based on how contaminated the data looked in an AFM image of the top right and bottom left of the field, and if the phase showed line artifacts. \\
-The data in Figure \ref{fig:evaporation_measured_penumbra_sigs} shows that for the smaller penumbra values of well below the threshold of $100$ nm can be found, with most of the fields lying near $50$ nm. Showing that the evaporation gave very sharp interfaces. From the evaporation conditions it would be expected, that field $1$ and field $5$ should be very similar and both should show smaller penumbra than the other fields, but this does not appear to be the case. While field $5$ shows some of the smallest penumbras, its behavior seems to be more akin to field $3$ than $1$. Field $4$ also has the largest penumbras, which is unexpected since it was evaporated at the point of second contact and should thus perform better than both field $3$ and field $2$. Both field $2$ and $4$ have the largest uncertainties, due to more noisy data, which could explain this discrepancy. The difference between top, bottom, right, left and center seems to be within measurement uncertainty and thus no conclusive statements can be made about it.\\
+Figure \ref{fig:evaporation_measured_penumbra} shows the values obtained from analysis of exemplary \ce{Pb} dots of each field. For each field one dot on the top of the field, one on the bottom, one near the center and on each on the left and the right were chosen to analyze. The dots were chosen based on how contaminated the data looked in an AFM image of the top right and bottom left of the field, and if the phase showed line artifacts. \\
+The data in Figure \ref{fig:evaporation_measured_penumbra_sigs} shows that for the smaller penumbra values of well below the threshold of $100$ nm can be found, with most of the fields lying near $50$ nm. Showing that the evaporation gave very sharp interfaces. From the evaporation conditions it would be expected, that field $1$ and field $5$ should be very similar and both should show smaller penumbra than the other fields, but this does not appear to be the case. While field $5$ shows some of the smallest penumbras, its behavior seems to be more akin to field $3$ than $1$. Field $4$ also has the largest penumbras, which is unexpected since it was evaporated at the point of second contact and should thus perform better than both field $3$ and field $2$. Both field $2$ and $4$ have the largest uncertainties, due to more noisy data, which could explain this discrepancy. The differences between top, bottom, right, left and center are within measurement uncertainty and thus no conclusive statements can be made about it.\\
 
 
 The height of the dots (Figure \ref{fig:evaporation_measured_penumbra_height}) is spread around a mean value of $2.6 \pm 0.3$ nm and shows strong deviation from the expected $5$ nm, obtained from calibration measurements for the particle flux that was used in the evaporation. This seems to suggest a large amount of \ce{Pb} particles never reaches the mask, even though they are expected to by the setup conditions. \\
 
-The diameter of the \ce{Pb} dots would be expected to decrease with subsequent evaporation due to clogging of the mask. This trend is mirrored in the data as the average diameter of evaporation decreases from $3.02 \pm 0.04$ for field $1$ to $2.947 \pm 0.008$ for field $4$ with a linear fit to the average values giving a decrease in diameter of $0.017 \pm 0.004$ $\mu$m per evaporation. The eccentricity of the dot's outer shape was determined by measuring the diameter of multiple line cuts on the circle via fit and comparing measurements of perpendicular line cuts. The resulting eccentricity was as in the weighted mean $0.2 \pm 0.1$, which suggest that the dots are circular within measurement accuracy. This means the outer dot shape does not seem to be affected by the tilting effects.\\
+The diameter of the \ce{Pb} dots would be expected to decrease with subsequent evaporation due to clogging of the mask. This trend is mirrored in the data as the average diameter of evaporation decreases from $3.02 \pm 0.04$ $\mu$m for field $1$ to $2.947 \pm 0.008$ $\mu$m for field $4$ with a linear fit to the average values giving a decrease in diameter of $0.017 \pm 0.004$ $\mu$m per evaporation. The eccentricity of the dot's outer shape was determined by measuring the diameter of multiple line cuts on the circle via fit and comparing measurements of perpendicular line cuts. The resulting eccentricity was as in the weighted mean $0.2 \pm 0.1$, which suggest that the dots are circular within measurement accuracy. This means the outer dot shape is not affected by the tilting effects.\\
 
-The larger penumbra data (Figure \ref{fig:evaporation_measured_penumbra_sigl}) indicates no pattern for each field and only possibly a reduction in penumbra for the bottom and center dots. This might be due to different dots being chosen for each analysis, some of which are not completely at the top or bottom (or left and right), but one row below or above. In the following, the penumbra and direction of tilt will be treated in a more thorough manner. \\
+The larger penumbra data (Figure \ref{fig:evaporation_measured_penumbra_sigl}) indicates no pattern within each field and only possibly a reduction in penumbra for the bottom and center dots. This might be due to different dots being chosen for each analysis, some of which are not completely at the top or bottom (or left and right), but one row below or above. In the following, the penumbra and direction of tilt will be treated more thoroughly. \\
 
 \section{Tilt and deformation}
 
@@ -211,7 +211,7 @@ The larger penumbra data (Figure \ref{fig:evaporation_measured_penumbra_sigl}) i
 
 All evaporated dots, even when the capacitance signal was within the full contact regime, showed signs of a tilt between mask hole and sample in the form of a half moon shaped second penumbra. If this was due to a misalignment between the entire mask and the sample, one would expect the direction of the tilt to be the same for the entire evaporated field and the size of the second penumbra to diminish along the direction of the tilt. But as seen in Figure \ref{fig:evaporation_tilts} the direction of the tilt is not uniform and instead seems to point outwards for the dots on the edge. This suggests the mask itself is slightly bent towards the edges, resulting in an alignment error. \\
 
-The smallest minor that was found in the AFM data was $2.15 \pm 0.08$ $\mu$m against the $3.01\pm 0.05$ $\mu$m of the evaporated circle. This would imply a tilt from one side of the dot on the mask to the other of $44 \pm 9 ^\circ$, which implies a difference in mask sample distance from one side of the hole in the mask to the other side of it of $2.08 \pm 0.31$ $\mu$m. Even with a mask sample distance on average of $1$ $\mu$m this is still possible since one side can be retracted from the mask by $2.08 \pm 0.31$ $\mu$m rather than the other being closer, but this still implies a massive deformation of the mask membrane.
+The smallest minor that was found in the AFM data was $2.15 \pm 0.08$ $\mu$m against the $3.01\pm 0.05$ $\mu$m of the evaporated circle. This would imply a tilt from one side of the dot on the mask to the other of $44 \pm 9 ^\circ$, which implies a difference in mask sample distance from one side of the hole in the mask to the other side of $2.08 \pm 0.31$ $\mu$m. Even with a mask sample distance average of $1$ $\mu$m this is still possible since one side can be retracted from the mask by $2.08 \pm 0.31$ $\mu$m rather than the other being closer, but this still implies a significant deformation of the mask membrane.
 
 The different angles the tilt takes can be seen in Figure \ref{fig:evaporation_tilts}. All the lead dots show a tilt and displacement as defined in Figure \ref{fig:penumbra_tilt_sigmas}, but noticeably the inner dots show lower tilt and displacement, than the ones on the outside of the field. The lead dots on the outer edge of the field point outwards from the field center, which could suggest an upwards bending of the mask towards the center of the field. \\
 
@@ -233,7 +233,7 @@ The different angles the tilt takes can be seen in Figure \ref{fig:evaporation_t
     \label{fig:evaporation_SEM}
 \end{figure}
 
-To confirm the Mask was undamaged during the evaporation, SEM images were taken of the mask as well as the sample. The resulting images can be seen in Figure \ref{fig:evaporation_SEM}. The evaporation of field $2$ shown in Figure \ref{fig:evaporation_SEM_sample} shows the elliptical tilt also visible in the AFM images. The elliptical part of the evaporation shows different color in the SEM image, which is an indicator, that the conductivity is different from the part of the dot. \\
+To confirm the Mask was undamaged during the evaporation, SEM images were taken of the mask as well as the sample. The resulting images can be seen in Figure \ref{fig:evaporation_SEM}. The evaporation of field $2$ shown in Figure \ref{fig:evaporation_SEM_sample} shows the elliptical tilt also visible in the AFM images. The elliptical part of the evaporation shows different value in the SEM image, which is an indicator, that the conductivity is different from the part of the dot. \\
 The image of the mask (Figure \ref{fig:evaporation_SEM_mask}) shows no damage to the mask. The white areas are charging artifacts and were not stable in multiple images. The mask looks to be bending, but this is most likely due to charging artifacts and an inherent fish-eye effect of SEM images at high magnifications. Furthermore, some clogging from the underside of the mask is visible in the SEM images in Figure \ref{fig:evaporation_SEM_mask}.
 
 \begin{figure}[H]
@@ -255,10 +255,11 @@ The image of the mask (Figure \ref{fig:evaporation_SEM_mask}) shows no damage to
 \end{figure}
 
 An example of this clogging in the SEM image is shown in Figure \ref{fig:evaporation_SEM_analysis_clog}
-To further check if the clogging artifacts correspond to the directions of tilt shown in Figure \ref{fig:evaporation_tilts} the directions are overlayed in Figure \ref{fig:evaporation_SEM_analysis_clog_overlay}. The directions correspond to the direction shown in the SEM image, except for some outliers. It also mostly points outwards. For a lot of points the clogging is not clearly visible in the image however, so no strong conclusion can be made from the SEM image alone.
+To further check if the clogging artifacts correspond to the directions of tilt shown in Figure \ref{fig:evaporation_tilts} the directions are overlayed in Figure \ref{fig:evaporation_SEM_analysis_clog_overlay}. The directions correspond to the direction shown in the SEM image, except for some outliers. It also mostly points outwards. For a lot of points the clogging is not clearly visible in the image however, so that no strong conclusion can be drawn from the SEM image alone.
 
 \section{Simulation} \label{sec:simulation}
-In order to gain more information about the different hypothesis for the tilted evaporation dots, a simple evaporation simulation was written. The simulation is based on ray tracing and is written in the open source Godot game engine, since game engines support checking of rays against collision natively and thus a ray tracing simulation could be implemented quickly. \\
+\subsection{Overview and principle}
+In order to gain more information about the different hypotheses for the tilted evaporation dots, a simple evaporation simulation program was written. The simulation is based on ray tracing and is written in the open source Godot game engine, since game engines support checking of rays against collision natively and thus a ray tracing simulation could be implemented quickly. \\
 
 The simulation works as follows:
 At a time $0$ at a distance $L$ from the sample a random point inside the circle is generated, and from it a ray is cast to a point behind the sample. The point behind the mask is chosen such that the ray casts in a cone with opening angle $\phi$. The ray is then checked against collision with a mask hole, which is represented by a cylinder collider with very small height. When collision with the mask "hole" is determined, the ray is cast again and the position at which the sample would be hit is determined. This position is then recorded as a hit in an array, that is structured like an image, spanning a user defined area around the middle of the sample and with user specified resolution. For each element in the array, the amount of hits the "pixel" has received is stored. This step is repeated many times in a single time step.\\
@@ -270,12 +271,14 @@ At a time $0$ at a distance $L$ from the sample a random point inside the circle
 %    \label{fig:evaporation_simulation_godotcoords}
 %\end{figure}
 
-Objects in the Godot game engine are moved, rotated and scaled with a $3 \times 4$ matrix called a transform matrix. This matrix performs rotations via their quaternion representation, which is a way to represent $3$-dimensional rotations as a $4$ component complex number. Modifying the transform matrix directly is possible, but would be very unintuitive and cumbersome, so the engine allows modification of the component's displacement and scale via $3$D vectors. The components of the displacement vector will be called x, y and z. The rotation can be modified via Euler angles. Internally the Euler angles are called, based on the axis they rotate around,  x, y and z as well. To avoid confusion the angles will be called $\alpha$, $\beta$ and $\gamma$, where $\alpha$ rotates around the x-axis, $\beta$ around the y-axis and $\gamma$ around the z-axis.
+Objects in the Godot game engine are moved, rotated and scaled with a $3 \times 4$ matrix called a "transform" matrix. This matrix performs rotations via their quaternion representation, which is a way to represent $3$-dimensional rotations as a $4$ component complex number. Modifying the transform matrix directly is possible, but would be very unintuitive and cumbersome, so the engine allows modification of the component's displacement and scale via $3$D vectors. The components of the displacement vector will be called x, y and z. The rotation can be modified via Euler angles. Internally the Euler angles are called x, y and z as well, based on the axis they rotate around. To avoid confusion the angles will be called $\alpha$, $\beta$ and $\gamma$, where $\alpha$ rotates around the x-axis, $\beta$ around the y-axis and $\gamma$ around the z-axis.
 
-In order to simulate vibration effects, the cylinder collider for the mask can be moved and rotated in a periodic manner. The rotation, position and oscillation period are user parameters. And after each time step the collider is moved and in the next iteration the new collider position and rotation is checked against. The position of the current time step is obtained by linear interpolation between the start position and rotation and the end position and rotation. The interpolation parameter is determined with the function $|\sin(\frac{t}{T})|$, where $T$ is the period of the oscillation in time steps and $t$ is the current time step. This allows the simulation of $3$D vibrations in the resulting image. It does not take into account possible bending of the mask, since the colliders are stiff rigid bodies, but using rotation, bending can be locally approximated. \\
+In order to simulate vibration effects, the cylinder collider for the mask can be moved and rotated in a periodic manner. The rotation, position and oscillation period are parameters defined by the user. And after each time step the collider is moved and in the next iteration the new collider position and rotation is checked against. The position of the current time step is obtained by linear interpolation between the start position and rotation and the end position and rotation. The interpolation parameter is determined with the function $|\sin(\frac{t}{T})|$, where $T$ is the period of the oscillation in time steps and $t$ is the current time step. This allows the simulation of $3$D vibrations in the resulting image. It does not take into account possible bending of the mask, since the colliders are stiff rigid bodies, but using rotation, bending can be locally approximated. \\
 
 After a user specified time has passed, the amount of hits on each pixel is saved into a file and the image can then be displayed using a python script. For a more detailed look at the different parameters the script provides, see the Appendix \ref{sec:appendix_raycast}.\\
 
+\subsection{Results}
+
 \begin{figure}[H]
     \centering
 	\begin{subfigure}{0.45\linewidth}
@@ -303,7 +306,7 @@ The mask being deformed by nearly $45^\circ$ at a single hole site locally would
     \label{fig:evaporation_simulation_overlap}
 \end{figure}
 
-The amplitude of displacement in the case in Figure \ref{fig:evaporation_simulation_first_compare_SIM} is $\approx 0.4$ $\mu$m, this is in line with the peak to peak amplitude of an active turbomolecular pump given by $1$ $\mu$m, obtained in the PhD thesis of Priyamvada Bhaskar.~\cite{Bhaskar} Some features of the AFM measurement are mirrored in the simulation, however it does not match the simulated image in a decent number of characteristics. The "half moon" shaped penumbra (\textcolor{tab_red}{red} in Figure \ref{fig:evaporation_simulation_first_compare_AFM}) in the AFM image is very rough, but on average of equal height, while in the simulation the penumbra gradually lowers from the highest part. The lower edge of the elliptical shape visible in the AFM dot below the circle (\textcolor{tab_cyan}{cyan} in Figure \ref{fig:evaporation_simulation_first_compare_AFM}) is so faint as to be invisible in the AFM image, while it is very pronounced in the simulated image and the lower edge is sharp in the AFM image $61 \pm 9$ nm while it is smeared out in the simulated image. \\
+The amplitude of displacement in the example in Figure \ref{fig:evaporation_simulation_first_compare_SIM} is $\approx 0.4$ $\mu$m, this is in line with the peak to peak amplitude of an active turbomolecular pump given by $1$ $\mu$m, obtained in the PhD thesis of Priyamvada Bhaskar~\cite{Bhaskar}. Some features of the AFM measurement are mirrored in the simulation, however it does not match the simulated image in a number of characteristics. The "half moon" shaped penumbra (\textcolor{tab_red}{red} in Figure \ref{fig:evaporation_simulation_first_compare_AFM}) in the AFM image is very rough, but on average of equal height, while in the simulation the penumbra gradually lowers from the highest part. The lower edge of the elliptical shape visible in the AFM dot below the circle (\textcolor{tab_cyan}{cyan} in Figure \ref{fig:evaporation_simulation_first_compare_AFM}) is so faint as to be invisible in the AFM image, while it is very pronounced in the simulated image and the lower edge is sharp in the AFM image $61 \pm 9$ nm while it is smeared out in the simulated image. \\
 
 The different roughness from circle and ellipse might suggest different possible reasons. First it could be a chronological effect where the circle is deposited first, and the ellipse is deposited second. Another possibility is that the vibration cause the displacement and bending of the mask in a pattern that is anharmonic, which causes the extreme points of the oscillation to be preferred. In order to investigate possible sources of this effect, the simulation was amended. \\
 
@@ -328,7 +331,7 @@ The different roughness from circle and ellipse might suggest different possible
     \label{fig:evaporation_simulation_sharpness}
 \end{figure}
 
-The effect of this can be seen in Figure \ref{fig:evaporation_simulation_sharpness_stick_initial} compared with the simpler model Figure \ref{fig:evaporation_simulation_sharpness_stick_simple}) this gives an image more simple to the AFM measurement. Another possibility is an oscillation, which is not harmonic. For this instead of choosing the oscillation as $\sin(\frac{t}{T} + \phi)$ with $t$ being current time, $T$ the oscillation period and $\phi$ being a phase shift, the oscillation is instead parametrized as $\sin(\frac{t}{T} + \phi)^p$ with $p$ being the oscillation power. The resulting image can be seen in Figure \ref{fig:evaporation_simulation_sharpness_stick_power}. The effect of this is very similar to the initial circular shape. The vibrations causing the deformation and tilt are unlikely to be very anharmonic, but due to growth of thin films happening near grains, the actual growth of \ce{Pb} on the \ce{Si} is concentrated at the extreme positions of the oscillation.
+The effect of this can be seen in Figure \ref{fig:evaporation_simulation_sharpness_stick_initial} compared with the simpler model (Figure \ref{fig:evaporation_simulation_sharpness_stick_simple}) this gives an image more similar to the AFM measurement. Another possibility is an oscillation, which is not harmonic. For this instead of choosing the oscillation as $\sin(\frac{t}{T} + \phi)$ with $t$ being current time, $T$ the oscillation period and $\phi$ being a phase shift, the oscillation is instead parametrized as $\sin(\frac{t}{T} + \phi)^p$ with $p$ being the oscillation power. The resulting image can be seen in Figure \ref{fig:evaporation_simulation_sharpness_stick_power}. The effect of this is very similar to the initial circular shape. The vibrations causing the deformation and tilt are unlikely to be very anharmonic, but due to growth of thin films happening near grains, the actual growth of \ce{Pb} on the \ce{Si} is concentrated at the extreme positions of the oscillation.
 
 When looking at the measured AFM image, it is very noticeable, that the surface of the "half moon" is rougher than the surface of the inner circle. On average, the roughness is $1.7 \pm 0.4$ times higher. This could be due to the \ce{Pb} preferring already established particle sites to diffuse and grow near another possible reason is a chronology of events where the growth happens first on the outer circle and then on the elliptical shape, as previously looked at.\\
 
@@ -351,11 +354,11 @@ Lead or in general any deposited material deposits more easily, when there is al
     	\caption{}
 		\label{fig:evaporation_simulation_rejection_comparison}
 	\end{subfigure}
-	\caption{Simulated evaporation dots without (\subref{fig:evaporation_simulation_rejection_prev}) and with (\subref{fig:evaporation_simulation_rejection_after}) $90$ \% probability to reject a deposition, when no previous deposition happened on the target pixel. (\subref{fig:evaporation_simulation_rejection_comparison}) shows the AFM image parameters for simulation were obtained from for comparison. The parameters of the ellipse are the same as in Figure \ref{fig:evaporation_simulation_first_compare}.}
+	\caption{Simulated evaporation dots without (\subref{fig:evaporation_simulation_rejection_prev}) and with (\subref{fig:evaporation_simulation_rejection_after}) $90$ \% probability to reject a deposition, when no previous deposition happened on the target pixel. (\subref{fig:evaporation_simulation_rejection_comparison}) shows the AFM image from which the parameters for the simulation were obtained. The parameters of the ellipse are the same as in Figure \ref{fig:evaporation_simulation_first_compare}.}
     \label{fig:evaporation_simulation_rejection}
 \end{figure}
 
-The results of adding this penalty for initial deposition are shown in Figure \ref{fig:evaporation_simulation_rejection_after}. As compared to the previous simulation step in Figure \ref{fig:evaporation_simulation_rejection_prev} the dot appears more rough and the height has decreases. The outer tail of the ellipse disappears nearly completely, these parameters match the deposition in the actual AFM image more closely, but crucially the decreased roughness of the elliptical part of the dot is not mirrored in the simulation, where the dot also appears rough. Typically, growth prefers to occur at grains, since these function as nucleation sites. Particles impinging on the surface will diffuse to a nearby large nucleation site. The simulation does not take this effect into account at all. Though it could be implemented, by having each pixel interact with neighboring pixels. \\
+The results of adding this penalty for initial deposition are shown in Figure \ref{fig:evaporation_simulation_rejection_after}. As compared to the previous simulation step in Figure \ref{fig:evaporation_simulation_rejection_prev} the dot appears more rough and the height has decreases. The outer tail of the ellipse disappears nearly completely, these parameters match the deposition in the actual AFM image more closely, but crucially the decreased roughness of the elliptical part of the dot is not mirrored in the simulation, where the dot also appears rough. Typically, growth prefers to occur at grains, since these function as nucleation sites. Particles impinging on the surface will diffuse to a nearby large nucleation site. The simulation does not take this effect into account at all. But it could be implemented, by having each pixel interact with neighboring pixels. \\
 
 The simulation image matches the one given by the AFM measurement pretty well, which shows that vibrations bending the hole pattern of the mask induced by the vibrations of the turbomolecular pump are a plausible explanation for the abberant penumbra of the measured dots. Particularly it shows that a mixture of deformation on the mask edge and lateral vibrations can cause the artifacts seen in the AFM images.
 
@@ -366,14 +369,14 @@ The simulation image matches the one given by the AFM measurement pretty well, w
     \label{fig:evaporation_simulation_progression}
 \end{figure}
 
-The simulation allows for taking in progress images at specified time intervals, with this a progression of the evaporation can be created. An example for the previously discussed example can be seen in Figure \ref{fig:evaporation_simulation_progression}. With this, the chronology of events can be made visible more easily and visualizations could easily be created. \\
+The simulation allows for taking in progress images at specified time intervals, with this a progression of the evaporation can be created. An example for the previously discussed case can be seen in Figure \ref{fig:evaporation_simulation_progression}. With this, the chronology of events can be made visible more easily and visualizations could easily be created. \\
 
-\paragraph{Software improvements}
+\subsection{Software improvements}
 The simulation is accurate in geometrical configuration of the Mask Aligner setup, but it assumes each particle hitting the surface either sticks to it or is rejected with a certain probability, which is a reasonable approximation as it follows the linear behavior from the Knudsen equation (Eq. \ref{eq:hertz_knudsen}), but it does not currently take into account grain size and diffusion of particles, which makes the graininess of the image resolution dependent.\\
 The current way of implementing the simulation using Godot allowed for very quick implementation and bug fixing, but lacks in performance. Each ray is cast sequentially on the CPU and significant overhead is caused by the game engine computing things necessary for games, but unnecessary for the purposes of this simple simulation. This causes the render time of each image to be in the minute to hour range for images of higher resolutions. \\
-In order to improve performance, a dedicated ray tracing engine with support for threading and maybe even parallel deployment on the \textbf{G}raphics \textbf{P}rocessing \textbf{U}nit (GPU) using \textbf{A}pplication \textbf{P}rogramming \textbf{I}nterfaces (APIs) like for example CUDA or OpenCL could give massive performance improvements since rays many thousands of rays could be cast in parallel this way. This would most likely boost generation times by several orders of magnitude. \\
-Since Godot uses its own units for length measurement, which are stored as $32$-bit floating point numbers, this also causes unit conversion from real world units to Godot's units to be time-consuming and can potentially cause float point rounding issues. With a dedicated ray casting engine, real world units could be used and accuracy of the simulation could be improved by using higher precision floating point numbers. \\
+In order to improve performance, a dedicated ray tracing engine with support for threading and maybe even parallel deployment on the \textbf{G}raphics \textbf{P}rocessing \textbf{U}nit (GPU) using \textbf{A}pplication \textbf{P}rogramming \textbf{I}nterfaces (APIs) like for example CUDA or OpenCL could give significant performance improvements since many thousands of rays could be cast in parallel this way. This would most likely shorten generation times by several orders of magnitude. \\
+Since Godot uses its own units for length measurement, which are stored as $32$-bit floating point numbers, this also causes unit conversion from real world units to Godot's units to be time-consuming and can potentially cause floating point rounding issues. With a dedicated ray casting engine, real world units could be used and accuracy of the simulation could be improved by using higher precision floating point numbers. \\
 
-\paragraph{Conclusion}
+\subsection{Final Remark}
 
-The results of the simulation show that a x-y-z vibration with a component of "bending" simulated as a strong tilt can explain the shape of the penumbra obtained in the AFM, and that its peak to peak amplitude is within the expected for this system. This also shows that the sharper penumbra edge, which for this evaporation was measured to be $\approx 60$ nm is penumbras that would likely be obtained had there been no vibrational influence on the experiment. This shows that the Mask Aligner is capable of creating sharp interfaces, that fall within the superconductors coherence length. \\
\ No newline at end of file
+The results of the simulation show that a x-y-z vibration with a component of "bending" simulated as a strong tilt can explain the shape of the penumbra obtained in the AFM, and that its peak to peak amplitude is within the expected range for this system. This also shows that the sharper penumbra edge, which for this evaporation was measured to be $\approx 60$ nm is the penumbra that would likely be obtained had there been no vibrational influence on the experiment. This shows that the Mask Aligner is capable of creating sharp interfaces, that fall within a superconductor's coherence length. \\
\ No newline at end of file
diff --git a/conclusion.aux b/conclusion.aux
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diff --git a/conclusion.tex b/conclusion.tex
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--- a/conclusion.tex
+++ b/conclusion.tex
@@ -1,22 +1,22 @@
-\chapter*{Conclusions and Outlook}
+\chapter*{Conclusion and Outlook}
 \addcontentsline{toc}{chapter}{Conclusions and Outlook}
 In this thesis, the function of a mask aligner operating in UHV was optimized and its capabilities were analyzed. 
 
 Mask Aligner functionality was restored and measures were taken to prevent further failure in the future. 
-Maintenance procedures for certain potential faults of the Mask Aligner system were established and applied to the Mask Aligner. With this, the initially failing performance of the Mask Aligner was restored. 
+Maintenance procedures for certain potential faults of the Mask Aligner system were established and applied to the Mask Aligner. With this, the initially failing performance of the Mask Aligner was improved. 
 Potential sources of cross capacitances on the Mask Aligner were investigated and likely candidates for sources of cross capacitance were found on the Mask holders/shuttles, with the Mask Aligner itself found to be negligible in the creation of cross capacitance. \\
 
 Further research will have to be done on the prevention of faults in the mask preparation procedure, as issues with leakage currents created in the process of mask bonding were found to be the likely reason for large correlations in the capacitance sensors of the Mask Aligner. \\
 
-A new controller for the Mask Aligner was created by the electronics workshop. Programming of the new electronic was done, and initial performance tests showed favorable results over the old driver electronics. The new controller, however, still suffers from hardware issues, which is why tests under load could not be performed. A final performance test with calibration is still outstanding. \\
+A new controller for the Mask Aligner was created by the electronics workshop. Programming of the new electronic was done, and initial performance tests showed favorable results over the old driver electronics. The new controller, however, still suffers from hardware issues, which is why tests under load could not be performed. A final performance test with calibration is still pending. \\
 
 The new controller will have to be tested under load for its driving behavior in comparison to the old driver and hardware instability issues will have to be resolved before larger scale evaporation, can be performed.
 In order to adapt voltage output per channel, during approach, a control script with the Mask Aligner will also have to be created and a new calibration as a function of voltage will have to be recorded. \\
 
 It was shown that sharp interfaces on the sub-$60$ nm scale can be created using the Mask Aligner and that under good conditions sharp pristine interfaces can be created using the previously established alignment procedure. Ellipsoidal artifacts on the resulting evaporation could be explained using a simulation approach as a result of vibrations that created bending and x-y shifting of the mask with regard to the sample. \\
 
-In future the Mask Aligner will be first used to test evaporation properties of \ce{Pb} on \ce{Au} with this it will be established if \ce{Pb} is a good candidate for a superconductor/topological insulator interface and if the previously established alignment process transfers to other types of sample. 
+In future the Mask Aligner will be first used to test evaporation properties of \ce{Pb} on \ce{Au}. With this it will be established if \ce{Pb} is a good candidate for a superconductor/topological insulator interface and if the previously established alignment process transfers to other types of sample. 
 Characterization of these new samples using a low temperature STM to record a superconducting gap is also a subject of future research. The determination of properties, such as appearance of a wetting layer is another important factor that will be done in STM analysis, as the appearance of a wetting layer across the sample's surface would make \ce{Pb} a bad candidate for Majorana Zero Mode research.\\
 
-Another possible candidate for evaporation on a topological insulator seems to be \ce{Pd}. As recent papers have shown it to have interesting self epitaxial growth properties when evaporated on the topological insulator \ce{(Bi_{1-x}Sb_{x})2Te3}.\cite{self_epitaxy} This could be a good candidate for further research. The current evaporator attached is unable to perform palladium evaporation. If \ce{Pd} were chosen over \ce{Pb} a new evaporator need to be connected to the Mask Aligner system.
+Another possible candidate for evaporation on a topological insulator seems to be \ce{Pd}. As recent papers have shown it to have interesting self epitaxial growth properties when evaporated on the topological insulator \ce{(Bi_{1-x}Sb_{x})2Te3}~\cite{self_epitaxy}. This could be a good candidate for further research. The current evaporator attached is unable to perform palladium evaporation. If \ce{Pd} would be chosen over \ce{Pb} a new evaporator would need to be connected to the Mask Aligner system.
 
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diff --git a/preface.tex b/preface.tex
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@@ -1,10 +1,10 @@
 \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 among others. 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 the small patterns, that are smaller than the coherence length ($<100$ nm) of the superconductor, required to create the vortices need high accuracy. \\
-Atmospheric conditions typically damage 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 often required. \\
-Many substrate patterning methods like \textbf{E}lectron \textbf{B}eam \textbf{L}ithography or \textbf{E}xtreme \linebreak \textbf{U}ltra\textbf{V}iolet \textbf{L}ithography (EUVL) or sometimes (EUV) give the required precision needed for patterning sample at the sub $100$ nm scale,\cite{euv} but require resists, which typically contain 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 and thus may damage the sample further. \\
-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 that require 
+In condensed matter physics, precise fabrication of nanostructures with sharp patterns is paramount for research in various fields like electronics, photonics and quantum computing among others. 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 the small patterns, that are smaller than the coherence length ($<100$ nm) of the superconductor, required to create the vortices need high accuracy. \\
+Atmospheric conditions typically damage 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 substrate patterning methods like \textbf{E}lectron \textbf{B}eam \textbf{L}ithography or \textbf{E}xtreme \linebreak \textbf{U}ltra\textbf{V}iolet \textbf{L}ithography (EUVL) or sometimes (EUV) give the required precision needed for patterning sample at the sub $100$ nm scale,~\cite{euv} but require resists, which typically contain 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 and thus may damage the sample further. \\
+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 that require 
 long timescales and expensive equipment. Additionally, many Scanning Probe approaches still require resists and development, leading to the same issues as previously mentioned lithography methods.\\
-A simple and inexpensive approach is given by stencil lithography and \textbf{P}hysical \textbf{V}apor \textbf{D}eposition (PVD), where a stencil (mask) is used to mask off a section of the sample. When the sample is hit with a molecular vapor beam, the masked off areas are protected from the impinging material and stay pristine, while the ones not protected by the stencil built patterned structures. In this method, no resist is required, and the procedure is required to be performed at UHV conditions. Resolutions of sub-$50$ nm have been achieved using stencil lithography.\cite{stencil_resolution} \\
+A simple and inexpensive approach is given by stencil lithography and \textbf{P}hysical \textbf{V}apor \textbf{D}eposition (PVD), where a stencil (mask) is used to mask off a section of the sample. When the sample is hit with a molecular vapor beam, the masked off areas are protected from the impinging material and stay pristine, while the ones not protected by the stencil built patterned structures. In this method, no resist is required, and the procedure is required to be performed at UHV conditions. Resolutions of sub-$50$ nm have been achieved using stencil lithography~\cite{stencil_resolution}. \\
 Stencil lithography however has its own downside. In order to get very high resolution, the mask and the sample have to be very close together as otherwise the aperture of the mask creates a "penumbra", which can affect the final resolution of the pattern on the sample negatively. The simple and often used approach is to simply bring mask and sample into direct contact, ensuring minimal distance. This however is for the case of the creation of many interfaces not possible, since the damage the sample sustains when brought into contact with the mask would damage the condition of the sample. \\
-For this reason the Mask Aligner, the subject of this work, was designed.\cite{Olschewski, Bhaskar} The Mask Aligner is a tool to use capacitive measurement to ensure minimal mask sample distance during PVD, while avoiding full contact with the sample, thus preserving the samples condition. This work concerns the optimization, improvement and analysis of the Mask Aligner and its capabilities, as well as work on the creation of additional electronics and software to drive the Mask Aligners operation. 
\ No newline at end of file
+For this reason the Mask Aligner, the subject of this work, was designed~\cite{Olschewski, Bhaskar}. The Mask Aligner is a tool to use capacitive measurement to ensure minimal mask sample distance during PVD, while avoiding full contact with the sample, thus preserving the samples condition. This work concerns the optimization, improvement and analysis of the Mask Aligner and its capabilities, 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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diff --git a/thesis.pdf b/thesis.pdf
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Binary files a/thesis.pdf and b/thesis.pdf differ
diff --git a/thesis.synctex.gz b/thesis.synctex.gz
index 9dc26f8b807d7ec266128618ff9acecb0eb402de..0c3acd03026641953887ea30388030eda709e832 100644
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diff --git a/thesis.toc b/thesis.toc
index 8ab4e17b533758af149cbcd9c57a7f26a4b7db3b..50f15cc81fac3163f53407fe0434aa3421da220f 100644
--- a/thesis.toc
+++ b/thesis.toc
@@ -67,50 +67,52 @@
 \contentsline {section}{\numberline {4.7}Final test}{68}{section.4.7}%
 \contentsline {chapter}{\numberline {5}Evaporations and measurement}{70}{chapter.5}%
 \contentsline {section}{\numberline {5.1}Evaporation configuration}{70}{section.5.1}%
-\contentsline {section}{\numberline {5.2}Contamination}{72}{section.5.2}%
-\contentsline {section}{\numberline {5.3}Penumbra}{73}{section.5.3}%
+\contentsline {section}{\numberline {5.2}Contamination}{73}{section.5.2}%
+\contentsline {section}{\numberline {5.3}Penumbra}{74}{section.5.3}%
 \contentsline {section}{\numberline {5.4}Tilt and deformation}{79}{section.5.4}%
 \contentsline {section}{\numberline {5.5}Simulation}{81}{section.5.5}%
-\contentsline {paragraph}{Software improvements}{87}{section*.88}%
-\contentsline {paragraph}{Conclusion}{88}{section*.89}%
-\contentsline {chapter}{Conclusions and Outlook}{89}{chapter*.90}%
-\contentsline {chapter}{Bibliography}{91}{chapter*.91}%
-\contentsline {chapter}{List of Abbreviations}{94}{chapter*.92}%
-\contentsline {chapter}{Appendix}{i}{chapter*.93}%
+\contentsline {subsection}{\numberline {5.5.1}Overview and principle}{81}{subsection.5.5.1}%
+\contentsline {subsection}{\numberline {5.5.2}Results}{83}{subsection.5.5.2}%
+\contentsline {subsection}{\numberline {5.5.3}Software improvements}{87}{subsection.5.5.3}%
+\contentsline {subsection}{\numberline {5.5.4}Final Remark}{88}{subsection.5.5.4}%
+\contentsline {chapter}{Conclusions and Outlook}{89}{chapter*.88}%
+\contentsline {chapter}{Bibliography}{91}{chapter*.89}%
+\contentsline {chapter}{List of Abbreviations}{94}{chapter*.90}%
+\contentsline {chapter}{Appendix}{i}{chapter*.91}%
 \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*.94}%
+\contentsline {paragraph}{pol x}{vi}{section*.95}%
+\contentsline {paragraph}{amp x}{vi}{section*.96}%
+\contentsline {paragraph}{volt x}{vi}{section*.97}%
+\contentsline {paragraph}{channel x}{vi}{section*.98}%
+\contentsline {paragraph}{maxmstep x}{vi}{section*.99}%
+\contentsline {paragraph}{step x}{vi}{section*.100}%
+\contentsline {paragraph}{mstep x}{vi}{section*.101}%
+\contentsline {paragraph}{cancel}{vii}{section*.102}%
+\contentsline {paragraph}{help}{vii}{section*.103}%
 \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*.104}%
+\contentsline {paragraph}{angle}{vii}{section*.105}%
+\contentsline {paragraph}{radius\_mask}{vii}{section*.106}%
+\contentsline {paragraph}{distance\_circle\_mask}{vii}{section*.107}%
+\contentsline {paragraph}{distance\_sample}{vii}{section*.108}%
+\contentsline {paragraph}{rays\_per\_frame}{vii}{section*.109}%
+\contentsline {paragraph}{running\_time}{vii}{section*.110}%
+\contentsline {paragraph}{deposition\_gain}{vii}{section*.111}%
+\contentsline {paragraph}{penalize\_deposition}{vii}{section*.112}%
+\contentsline {paragraph}{first\_layer\_deposition\_prob}{vii}{section*.113}%
+\contentsline {paragraph}{oscillation\_period}{vii}{section*.114}%
+\contentsline {paragraph}{delay\_oscill\_time}{viii}{section*.115}%
+\contentsline {paragraph}{save\_in\_progress\_images}{viii}{section*.116}%
+\contentsline {paragraph}{save\_intervall}{viii}{section*.117}%
+\contentsline {paragraph}{oscillation\_dir}{viii}{section*.118}%
+\contentsline {paragraph}{oscillation\_rot\_s}{viii}{section*.119}%
+\contentsline {paragraph}{oscillation\_rot\_e}{viii}{section*.120}%
+\contentsline {paragraph}{random\_seed}{viii}{section*.121}%
+\contentsline {paragraph}{x\_min, x\_max, y\_min, y\_max}{viii}{section*.122}%
+\contentsline {paragraph}{resolution}{viii}{section*.123}%
+\contentsline {paragraph}{path}{viii}{section*.124}%
+\contentsline {chapter}{Acknowledgments}{ix}{chapter*.125}%