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{chapter}{Bibliography}{87}{chapter*.97}\protected@file@percent } \bibcite{sputter_damage}{{13}{}{{}}{{}}} \bibcite{florian_forster}{{14}{}{{}}{{}}} \bibcite{afm_physics}{{15}{}{{}}{{}}} @@ -59,7 +59,7 @@ \setcounter{subfigure}{0} \setcounter{subtable}{0} \setcounter{lstnumber}{1} -\setcounter{@todonotes@numberoftodonotes}{9} +\setcounter{@todonotes@numberoftodonotes}{8} \setcounter{float@type}{8} \setcounter{AM@survey}{0} \setcounter{thm}{0} diff --git a/chap02.aux b/chap02.aux index b073f8a47bab1f4e31ebd52afd689e482d712cf0..3acc2e0bc03d3511e42fe40519e40aa755aecba2 100644 --- a/chap02.aux +++ b/chap02.aux @@ -41,16 +41,28 @@ \newlabel{sub@fig:calibration_uhv_points_of_interest_z1}{{a}{24}{\relax }{figure.caption.23}{}} \newlabel{fig:calibration_uhv_points_of_interest_z2z3}{{2.8b}{24}{\relax }{figure.caption.23}{}} \newlabel{sub@fig:calibration_uhv_points_of_interest_z2z3}{{b}{24}{\relax }{figure.caption.23}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2.8}{\ignorespaces Points of interest for the calibration of the 3 piezo motors ion UHV. 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(a) motor Z1, \textcolor {tab_red}{red:} top of sapphire prism, \textcolor {tab_green}{green:} end of top plate used for step size determination (b) motors Z2/Z3, \textcolor {tab_red}{red:} screws on the motor plate that are close to motor Z2 and Z3 respectively, \textcolor {tab_green}{green:} lines used for step size determination.}}{24}{figure.caption.23}\protected@file@percent } +\newlabel{fig:calibration_uhv_points_of_interest}{{2.8}{24}{Points of interest for the calibration of the step size of the 3 piezo motors in UHV. (a) motor Z1, \textcolor {tab_red}{red:} top of sapphire prism, \textcolor {tab_green}{green:} end of top plate used for step size determination (b) motors Z2/Z3, \textcolor {tab_red}{red:} screws on the motor plate that are close to motor Z2 and Z3 respectively, \textcolor {tab_green}{green:} lines used for step size determination}{figure.caption.23}{}} \@writefile{lof}{\contentsline {figure}{\numberline {2.9}{\ignorespaces Upper curves: Measured distance of motors traveled as a function of steps driven with linear fit and marked results step size. $+$ is retract $-$ is approach (see Fig. \ref {fig:mask_aligner_nomenclature_motors}). Lower curves: deviation of the data points from fit.}}{25}{figure.caption.24}\protected@file@percent } \newlabel{fig:calibration_example}{{2.9}{25}{Upper curves: Measured distance of motors traveled as a function of steps driven with linear fit and marked results step size. $+$ is retract $-$ is approach (see Fig. \ref {fig:mask_aligner_nomenclature_motors}). 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Larger fluctuations in the signal visible on the \textcolor {tab_blue}{Blue} curve are due to an accidental change in time constant of the LockIn Amplifier}{figure.caption.36}{}} -\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.6}Cross capacitances}{34}{subsection.2.3.6}\protected@file@percent } -\newlabel{subsec:cross_cap}{{2.3.6}{34}{Cross capacitances}{subsection.2.3.6}{}} -\newlabel{fig:cross_cap_approach_difference}{{2.18a}{34}{\relax }{figure.caption.37}{}} -\newlabel{sub@fig:cross_cap_approach_difference}{{a}{34}{\relax }{figure.caption.37}{}} -\newlabel{fig:cross_cap_approach_difference_2}{{2.18b}{34}{\relax }{figure.caption.37}{}} -\newlabel{sub@fig:cross_cap_approach_difference_2}{{b}{34}{\relax }{figure.caption.37}{}} -\newlabel{fig:cross_cap_approach_sim}{{2.18c}{34}{\relax }{figure.caption.37}{}} -\newlabel{sub@fig:cross_cap_approach_sim}{{c}{34}{\relax }{figure.caption.37}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2.18}{\ignorespaces (\subref {fig:cross_cap_approach_difference}, \subref {fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure same scale. (\subref {fig:cross_cap_approach_sim}) shows a simple simulation of how the approach with tilted sample would look in an ideal case.}}{34}{figure.caption.37}\protected@file@percent } -\newlabel{fig:cross_cap_approach}{{2.18}{34}{(\subref {fig:cross_cap_approach_difference}, \subref {fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure same scale. (\subref {fig:cross_cap_approach_sim}) shows a simple simulation of how the approach with tilted sample would look in an ideal case}{figure.caption.37}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2.19}{\ignorespaces Diagram showing a cross section of the mask at a gold pad location. A small Tear in the \ce {SiNi} layer removes insulation between the gold wire and the Si of the mask, causing a leakage current. Parallel black lines are meant to illustrate plate capacitors. Larger plate shows larger capacitance. }}{35}{figure.caption.38}\protected@file@percent } -\newlabel{fig:leakage_current}{{2.19}{35}{Diagram showing a cross section of the mask at a gold pad location. A small Tear in the \ce {SiNi} layer removes insulation between the gold wire and the Si of the mask, causing a leakage current. Parallel black lines are meant to illustrate plate capacitors. Larger plate shows larger capacitance}{figure.caption.38}{}} -\@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.}}{36}{table.caption.39}\protected@file@percent } -\newlabel{tab:cross_cap}{{2.1}{36}{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.39}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2.20}{\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.}}{37}{figure.caption.40}\protected@file@percent } -\newlabel{fig:mask_old_caps}{{2.20}{37}{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}{figure.caption.40}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2.21}{\ignorespaces The 3 capacitance curves of the Mask labeled "old" scaled to be within same range, via normalization and subsequent fit of offset parameter, first to C2 and C3 fit to C1 and then C3 fit to C2. The lower plots show residuals. The residuals show the variation to be well within the error bars and overall within less than $1$ \%.}}{38}{figure.caption.41}\protected@file@percent } -\newlabel{fig:mask_old_correl}{{2.21}{38}{The 3 capacitance curves of the Mask labeled "old" scaled to be within same range, via normalization and subsequent fit of offset parameter, first to C2 and C3 fit to C1 and then C3 fit to C2. The lower plots show residuals. The residuals show the variation to be well within the error bars and overall within less than $1$ \%}{figure.caption.41}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {2.22}{\ignorespaces Circuit diagram of the measurement setup with the cross capacitances and parasitic capacitances for the mask shuttle. The $C_i$ refer to the main capacitances that are used for mask alignment. $C_{ij}$ refers to a cross capacitance between capacitance sensor $i$ and sensor $j$. $C_{mask-sample}$ refers to the capacitance between the Si of the Mask and the Si of the Sample, usually this should not be measured since the Si of the Mask is separated from the gold pads with a SiN layer, but should that layer be pierced or otherwise allow a leakage current (if the resistances $R_{i, Leak}$ are small enough) this will be measured instead of $C_i$, since it is an order of magnitude larger.}}{39}{figure.caption.42}\protected@file@percent } -\newlabel{fig:cross_cap_diagramm}{{2.22}{39}{Circuit diagram of the measurement setup with the cross capacitances and parasitic capacitances for the mask shuttle. The $C_i$ refer to the main capacitances that are used for mask alignment. $C_{ij}$ refers to a cross capacitance between capacitance sensor $i$ and sensor $j$. $C_{mask-sample}$ refers to the capacitance between the Si of the Mask and the Si of the Sample, usually this should not be measured since the Si of the Mask is separated from the gold pads with a SiN layer, but should that layer be pierced or otherwise allow a leakage current (if the resistances $R_{i, Leak}$ are small enough) this will be measured instead of $C_i$, since it is an order of magnitude larger}{figure.caption.42}{}} -\@writefile{toc}{\contentsline {paragraph}{Leakage current}{39}{section*.43}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{Improved gold pin fitting}{39}{section*.44}\protected@file@percent } -\@writefile{tdo}{\contentsline {todo}{Image of gold pins}{39}{section*.45}\protected@file@percent } +\newlabel{fig:approach_replicability_cap}{{2.17a}{33}{\relax }{figure.caption.35}{}} +\newlabel{sub@fig:approach_replicability_cap}{{a}{33}{\relax }{figure.caption.35}{}} +\newlabel{fig:approach_replicability_cap_diff}{{2.17b}{33}{\relax }{figure.caption.35}{}} +\newlabel{sub@fig:approach_replicability_cap_diff}{{b}{33}{\relax }{figure.caption.35}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2.17}{\ignorespaces \subref {fig:approach_replicability_cap} 3 subsequent approach curves. \subref {fig:approach_replicability_cap_diff} corresponding differences in capacitance. \textcolor {tab_green}{Green} is the initial curve. The \textcolor {tab_blue}{blue} curve is after sample has been carefully removed and reinserted. For the \textcolor {tab_red}{red} curve the mask was removed and reinserted. Larger fluctuations in the signal visible on the \textcolor {tab_blue}{Blue} curve are due to an accidental change in time constant of the LockIn Amplifier.}}{33}{figure.caption.35}\protected@file@percent } +\newlabel{fig:approach_replicability}{{2.17}{33}{\subref {fig:approach_replicability_cap} 3 subsequent approach curves. \subref {fig:approach_replicability_cap_diff} corresponding differences in capacitance. \textcolor {tab_green}{Green} is the initial curve. The \textcolor {tab_blue}{blue} curve is after sample has been carefully removed and reinserted. For the \textcolor {tab_red}{red} curve the mask was removed and reinserted. Larger fluctuations in the signal visible on the \textcolor {tab_blue}{Blue} curve are due to an accidental change in time constant of the LockIn Amplifier}{figure.caption.35}{}} +\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.6}Cross capacitances}{33}{subsection.2.3.6}\protected@file@percent } +\newlabel{subsec:cross_cap}{{2.3.6}{33}{Cross capacitances}{subsection.2.3.6}{}} +\newlabel{fig:cross_cap_approach_difference}{{2.18a}{34}{\relax }{figure.caption.36}{}} +\newlabel{sub@fig:cross_cap_approach_difference}{{a}{34}{\relax }{figure.caption.36}{}} +\newlabel{fig:cross_cap_approach_difference_2}{{2.18b}{34}{\relax }{figure.caption.36}{}} +\newlabel{sub@fig:cross_cap_approach_difference_2}{{b}{34}{\relax }{figure.caption.36}{}} +\newlabel{fig:cross_cap_approach_sim}{{2.18c}{34}{\relax }{figure.caption.36}{}} +\newlabel{sub@fig:cross_cap_approach_sim}{{c}{34}{\relax }{figure.caption.36}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2.18}{\ignorespaces (\subref {fig:cross_cap_approach_difference}, \subref {fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure the same scale. (\subref {fig:cross_cap_approach_sim}) shows a simple simulation of the approach with tilted sample.}}{34}{figure.caption.36}\protected@file@percent } +\newlabel{fig:cross_cap_approach}{{2.18}{34}{(\subref {fig:cross_cap_approach_difference}, \subref {fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure the same scale. (\subref {fig:cross_cap_approach_sim}) shows a simple simulation of the approach with tilted sample}{figure.caption.36}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2.19}{\ignorespaces Diagram showing a cross section of the mask at a gold pad location. A small tear in the \ce {SiO2} layer removes insulation between the gold wire and the Si of the mask. Parallel black lines depict plate capacitors illustratively. Larger plate shows larger capacitance. }}{35}{figure.caption.37}\protected@file@percent } +\newlabel{fig:leakage_current}{{2.19}{35}{Diagram showing a cross section of the mask at a gold pad location. A small tear in the \ce {SiO2} layer removes insulation between the gold wire and the Si of the mask. Parallel black lines depict plate capacitors illustratively. Larger plate shows larger capacitance}{figure.caption.37}{}} +\@writefile{lot}{\contentsline {table}{\numberline {2.1}{\ignorespaces Table of cross capacitance measurement results. All measurements were carried out with the mask shuttle the Mask Aligner and sample at $0.3$ mm distance. The distance was determined optically with Bresser MicroCam II and MikroCamLabII.}}{36}{table.caption.38}\protected@file@percent } +\newlabel{tab:cross_cap}{{2.1}{36}{Table of cross capacitance measurement results. All measurements were carried out with the mask shuttle the Mask Aligner and sample at $0.3$ mm distance. The distance was determined optically with Bresser MicroCam II and MikroCamLabII}{table.caption.38}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2.20}{\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.}}{37}{figure.caption.39}\protected@file@percent } +\newlabel{fig:mask_old_caps}{{2.20}{37}{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}{figure.caption.39}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2.21}{\ignorespaces The 3 capacitance curves of the Mask labeled "old" scaled to be within same range, via normalization and subsequent fit of offset parameter, first to C2 and C3 fit to C1 and then C3 fit to C2. The lower plots show residuals. The residuals show the variation to be well within the error bars and overall within less than $1$ \%.}}{38}{figure.caption.40}\protected@file@percent } +\newlabel{fig:mask_old_correl}{{2.21}{38}{The 3 capacitance curves of the Mask labeled "old" scaled to be within same range, via normalization and subsequent fit of offset parameter, first to C2 and C3 fit to C1 and then C3 fit to C2. The lower plots show residuals. The residuals show the variation to be well within the error bars and overall within less than $1$ \%}{figure.caption.40}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {2.22}{\ignorespaces Circuit diagram of the measurement setup with the cross capacitances and parasitic capacitances for the mask shuttle. The $C_i$ refer to the main capacitances that are used for mask alignment. $C_{ij}$ refers to a cross capacitance between capacitance sensor $i$ and sensor $j$. $C_{mask-sample}$ refers to the capacitance between the Si of the Mask and the Si of the Sample, usually this should not be measured since the Si of the Mask is separated from the gold pads with a SiN layer, but should that layer be pierced or otherwise allow a leakage current (if the resistances $R_{i, Leak}$ are small enough) this will be measured instead of $C_i$, since it is an order of magnitude larger.}}{39}{figure.caption.41}\protected@file@percent } +\newlabel{fig:cross_cap_diagramm}{{2.22}{39}{Circuit diagram of the measurement setup with the cross capacitances and parasitic capacitances for the mask shuttle. The $C_i$ refer to the main capacitances that are used for mask alignment. $C_{ij}$ refers to a cross capacitance between capacitance sensor $i$ and sensor $j$. $C_{mask-sample}$ refers to the capacitance between the Si of the Mask and the Si of the Sample, usually this should not be measured since the Si of the Mask is separated from the gold pads with a SiN layer, but should that layer be pierced or otherwise allow a leakage current (if the resistances $R_{i, Leak}$ are small enough) this will be measured instead of $C_i$, since it is an order of magnitude larger}{figure.caption.41}{}} +\@writefile{toc}{\contentsline {paragraph}{Leakage current}{39}{section*.42}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{Improved gold pin fitting}{39}{section*.43}\protected@file@percent } +\@writefile{tdo}{\contentsline {todo}{Image of gold pins}{39}{section*.44}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {2.3.7}Stop Conditions}{40}{subsection.2.3.7}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{High correlation between capacitance curves}{40}{section*.46}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{Low correlation between capacitance curves}{40}{section*.47}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{High correlation between capacitance curves}{40}{section*.45}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{Low correlation between capacitance curves}{40}{section*.46}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {2.4}Mask Aligner operation}{40}{section.2.4}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}Sample preparation}{40}{subsection.2.4.1}\protected@file@percent } \newlabel{sec:sample_prep}{{2.4.1}{40}{Sample preparation}{subsection.2.4.1}{}} @@ -150,7 +161,7 @@ \setcounter{subfigure}{0} \setcounter{subtable}{0} \setcounter{lstnumber}{1} -\setcounter{@todonotes@numberoftodonotes}{5} +\setcounter{@todonotes@numberoftodonotes}{4} \setcounter{float@type}{8} \setcounter{AM@survey}{0} \setcounter{thm}{0} diff --git a/chap02.tex b/chap02.tex index 67046964c521aef014e0c1f085a5eaf6491a60df..65caa78cc00dcfaf35ac7685dbe79427e3e121c3 100644 --- a/chap02.tex +++ b/chap02.tex @@ -152,23 +152,22 @@ With this one gets that for each unit of distance the motor moves, the screws mo \begin{figure}[H] \centering \begin{subfigure}{0.45\textwidth} - \includegraphics[width=\linewidth]{img/CalibrationUHV_Z1.png} + \includegraphics[width=\linewidth]{img/CalibrationUHV_Z1.pdf} \caption{} \label{fig:calibration_uhv_points_of_interest_z1} \end{subfigure} \begin{subfigure}{0.45\textwidth} - \includegraphics[width=\linewidth]{img/CalibrationUHV_Z2_Z3.png} + \includegraphics[width=\linewidth]{img/CalibrationUHV_Z2_Z3.pdf} \caption{} \label{fig:calibration_uhv_points_of_interest_z2z3} \end{subfigure} - \caption{Points of interest for the calibration of the 3 piezo motors ion -UHV. (a) shows measurement point \textcolor{tab_green}{green} and object that is -chosen for measurement \textcolor{tab_green}{red} for calibration of Z1. (b) -shows the same for Z2 and Z3.} + \caption{Points of interest for the calibration of the step size of the 3 piezo motors in +UHV. (a) motor Z1, \textcolor{tab_red}{red:} top of sapphire prism, \textcolor{tab_green}{green:} end of top plate used for step size determination (b) +motors Z2/Z3, \textcolor{tab_red}{red:} screws on the motor plate that are close to motor Z2 and Z3 respectively, \textcolor{tab_green}{green:} lines used for step size determination.} \label{fig:calibration_uhv_points_of_interest} \end{figure} -A linear fit is performed for the given data and from the slope of the fit the step size for a single step is determined. The results are shown in Figure \ref{fig:calibration_example}. After each set of steps it has to be ensured, that the mask frame is not tilted. Excessive tilt will affect the step size. It should also be taken care that the movement range of the piezos is not exceeded. The \ce{Nd} magnets should not detach from the frame. Moreover, the sapphire prism can fall out of the motor if it is driven too far down. The measurement has to be done for both driving directions separately, since the step sizes will be different. Indeed in Fig. \ref{fig:calibration_example} it can be seen, that the positive retract direction has consistently larger step sizes. The Z3 motor also shows a larger difference in step size for approach and retract than the other $2$ motors. +A linear fit is performed for the given data and from the slope of the fit the step size for a single step is determined. The results are shown in Figure \ref{fig:calibration_example}. After each set of steps it has to be ensured, that the mask frame is not tilted. Excessive tilt will affect the step size. It should also be taken care that the movement range of the piezos is not exceeded. The \ce{Nd} magnets should not detach from the frame. Moreover, the sapphire prism can fall out of the motor if it is driven too far down. The measurement has to be done for both driving directions separately, since the step sizes will be different. Indeed, in Fig. \ref{fig:calibration_example} shows that the positive retract direction has consistently larger step sizes. The Z3 motor also shows a larger difference in step size for approach and retract than the other $2$ motors. \begin{figure}[H] \centering @@ -194,18 +193,20 @@ Z3. Z3 is much more influenced by voltage than the other motors, where the step size/V is larger by $\approx 0.3$. Variations in motor behavior can be compensated using this data. To do this different voltages would have to be applied to each channel. However, the current setup does not allow for this. Due to this new driving electronics are required.\\ \subsection{Optical alignment} -To align mask and sample, it is first necessary to get the sample aligned and -within a distance of at least $50$ $\mu$m optically. This is -necessary since the capacitance sensors give only +To align mask and sample one starts optically down to a precision of $50$ $\mu$m. The capacitance sensors provide only small signals, at large distances.\\ -To do this, a Bresser MicroCam II camera with a resolution of $20$ megapixel is +In order to achieve this, a Bresser MicroCam II camera with a resolution of $20$ megapixel is mounted on a frame in front of the window of the mask aligner chamber. The frame can be positioned via 3 micrometer screws in x, y and z direction. Additionally, the camera can be rotated around $2$ axes allowing full control of the camera angle. The sample has to be aligned so that its surface normal is perpendicular to the camera's view direction. No sample surface can be -seen in camera view and no upwards tilt can be observed when viewing the side -edge of the sample, and the upper side of the sample holder, cannot be observed. +seen in camera view. No upwards tilt can be observed when viewing the side +edge of the sample, and the upper side of the sample holder, cannot be observed. \\ + +In Fig. \ref{fig:camera_alignment_example_low}, the surface of the sample can be seen, which means the camera is not in line +with the sample, but rather positioned too far up or tilted upward. In Fig. \ref{fig:camera_alignment_example_high}, one +can see the surface of the sample holder. Additionally, the side of the sample is tilted upwards in the image. The camera is positioned too high up or tilted downward. \\ \begin{figure}[H] @@ -213,48 +214,46 @@ edge of the sample, and the upper side of the sample holder, cannot be observed. \begin{subfigure}{0.32\textwidth} \includegraphics[width=\linewidth]{img/CameraAlignment_bad_low.pdf} \caption{} + \label{fig:camera_alignment_example_low} \end{subfigure} \begin{subfigure}{0.32\textwidth} \includegraphics[width=\linewidth]{img/CameraAlignment_high.png} \caption{} + \label{fig:camera_alignment_example_high} \end{subfigure} \begin{subfigure}{0.32\textwidth} \includegraphics[width=\linewidth]{img/CameraAlignment_good.png} \caption{} + \label{fig:camera_alignment_example_good} \end{subfigure} \caption{Examples of camera views for different alignment situations. (a) camera -placed or angled too low, (b) too high and (c) placed in good alignment. In -(a), the surface of the sample can be seen, which means the camera is not in line -with the sample, but rather tilted too far up or too low. In (b), one -can see the surface of the sample holder on the upper side as well as an upwards -shift on the side of the sample, indicating that the sample is tilted with -respect to the camera, this is caused by a camera too high up or tilted too far -down.} +placed or angled too low, (b) too high and (c) placed in good alignment. } \label{fig:camera_alignment_example} \end{figure} \todo{Fix} -When the camera is aligned with the sample, the mask can now be moved close to -the sample leaving a gap between mask and sample still. Now the -mask is aligned until only a very small gap can be seen. The size of the gap can -be optically estimated using the Bresser software. Direct contact of the sample has to be avoided at this stage. This might require retraction and subsequent approach since the motors are not located directly beneath the mask. A known length can be used to -calibrate lengths within the software. As an object of known length ($5940 \pm 20 $ $\mu$m), the sample is chosen. +When the camera is aligned with the sample, the mask can be moved close to +the sample. A visible gap must remain between sample and mask (Fig. \ref{fig:optical_approach_a}). Then the mask is moved toward the sample until only a very small gap remains (Fig. \ref{fig:optical_approach}\subref{fig:optical_approach_b}, \subref{fig:optical_approach_c}). The length of the gap can +be optically estimated using the Bresser software. Direct contact of the sample has to be avoided at this stage. This might require retraction and subsequent approach since the motors are not located directly beneath the mask. To calibrate the length scale of the camera the sample ($5940 \pm 20 $ $\mu$m) is chosen. In camera view direction, the mask and sample should now be aligned within -achievable optical accuracy. The progression of this can be seen in Figure \ref{fig:optical_approach} +achievable optical accuracy. \begin{figure}[H] \centering - \begin{subfigure}{0.3\textwidth} + \begin{subfigure}{0.32\textwidth} \includegraphics[width=\linewidth]{img/OpticalAlign01.png} \caption{} + \label{fig:optical_approach_a} \end{subfigure} - \begin{subfigure}{0.3\textwidth} + \begin{subfigure}{0.32\textwidth} \includegraphics[width=\linewidth]{img/OpticalAlign02.png} \caption{} + \label{fig:optical_approach_b} \end{subfigure} - \begin{subfigure}{0.3\textwidth} + \begin{subfigure}{0.32\textwidth} \includegraphics[width=\linewidth]{img/OpticalAlign03.png} \caption{} + \label{fig:optical_approach_c} \end{subfigure} \caption{The progression of optical alignment up from $65 \pm 5$ $\mu$m (a) to $25 \pm 5$ $\mu$m (c) mask sample distance. Measurement was obtained optically using measurement software and the sample's edge as a reference length.} \label{fig:optical_approach} @@ -264,8 +263,8 @@ achievable optical accuracy. The progression of this can be seen in Figure \ref{ \todo{Start here} \subsection{Approach curves} -After optical alignment, the mask is aligned to the sample via capacitive measurement. The 3 -capacitive sensors on the mask are for most masks setup in correspondance with the 3 motors of the Mask Aligner. They are labeled as seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_motors}. Note that this diagram is not true for all masks, since some are assembled misaligned on the mask stage. The mask consist of a $200$ $\mu$m thick \ce{Si} body. A small $100\times100$ $\mu$m \ce{SiN} membrane, with $3$ $\mu$m holes each $10$ $\mu$m apart, is situated in the center. The \ce{SiN} covers the whole mask and is $1$ $\mu$m thick. Below the center of the mask a trench is carved in the \ce{Si}. Around the hole membrane are $3$ gold pads, that function as capacitive sensors. The \ce{Au} of the gold pads is placed below an insulating $\approx 100$ nm layer of \ce{SiO2} at the bottom of a trench in the \ce{Si} body. They are at a distance of $0.7$ mm from the hole membrane and are located in an equilateral triangle around it. The dimensions of the mask and the capacitive sensors on the mask can be seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_mask}. +After optical alignment, the mask is further aligned to the sample via capacitive measurement. The 3 +capacitive sensors on the mask are setup in correspondence with the 3 motors of the Mask Aligner. They are labeled as seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_motors}. Note that this is not true for all masks. Some of the ones provided are assembled incorrectly. The mask consist of a $200$ $\mu$m thick \ce{Si} body. A $100\times100$ $\mu$m \ce{SiN} membrane, with circular $3$ $\mu$m diameter holes, $10$ $\mu$m apart from each other, is situated in the center. The \ce{SiN} covers the whole mask and is $1$ $\mu$m thick. Below the center of the mask a trench is carved in the \ce{Si}. Around the hole membrane are $3$ gold pads, that function as capacitive sensors. The \ce{Au} of the gold pads is placed below an insulating $\approx 100$ nm layer of \ce{SiO2} at the bottom of a trench in the \ce{Si} body. They are at a distance of $0.7$ mm from the hole membrane and are located in an equilateral triangle around it. The dimensions of the mask and the capacitive sensors on the mask can be seen in Figure \ref{fig:mask_aligner_nomenclature_capacitances_mask}. \begin{figure}[H] \centering @@ -280,10 +279,10 @@ capacitive sensors on the mask are for most masks setup in correspondance with t \label{fig:mask_aligner_nomenclature_capacitances_mask} \end{subfigure} \label{fig:mask_aligner_nomenclature_capacitances} - \caption{(\subref{fig:mask_aligner_nomenclature_capacitances_motors}) shows a cross-section of the Mask Aligner showing the labeling and rough positioning of the capacitance sensors on the mask (inner \textcolor{tab_red}{red} triangle) in relation to the $3$ piezo motor stacks. (\subref{fig:mask_aligner_nomenclature_capacitances_mask}) shows a diagram of the mask's dimensions as well as labeling of the mask's sensors. The inset shows the dimensions of the holey part of the mask, which is actually used to create patterns.} + \caption{(\subref{fig:mask_aligner_nomenclature_capacitances_motors}) shows a cross-section of the Mask Aligner showing the labeling and rough positioning of the capacitance sensors on the mask (inner \textcolor{tab_red}{red} triangle) in relation to the $3$ piezo motor stacks. (\subref{fig:mask_aligner_nomenclature_capacitances_mask}) shows a diagram of the mask's dimensions as well as labeling of the mask's sensors. The inset shows the dimensions of the holey part of the mask, which is used to create patterns.} \end{figure} -The readout of the capacitance sensors is performed with a Lock-in amplifier. The piezo motors are controlled with pulses from the RHK piezo motor controller. Communication with both the RHK and the Lock-in amplifier is done with a Matlab script. The communication with the RHK is done via a network interface, while the Lock-in uses a serial interface. Figure \ref{fig:diagram_MA_circ} shows a diagram of the communication circuit. Settings of the Lock-in amplifier are available in Appendix \ref{app:lock_in}. +The readout of the capacitance sensors is carried out with a Lock-in amplifier. The piezo motors are controlled with pulses from the RHK piezo motor controller. Communication with both the RHK and the Lock-in amplifier is done with a Matlab script. The communication with the RHK is done via a network interface, while the Lock-in uses a serial interface. Figure \ref{fig:diagram_MA_circ} shows a diagram of the communication circuit. Settings of the Lock-in amplifier are available in Appendix \ref{app:lock_in}. \begin{figure}[H] \centering @@ -295,9 +294,9 @@ The readout of the capacitance sensors is performed with a Lock-in amplifier. Th The capacitance of each of the $3$ sensors can be approximated using a simple plate capacitor model. The gold pad is one plate of the capacitor and the overlap of its bounds with the \ce{Si} sample can be seen as the other plate of -the capacitor. +the capacitor: \begin{equation} - C = \epsilon_0 \epsilon_r \frac{A}{r} + C = \epsilon_0 \epsilon_r(r) \frac{A}{r} \label{eq:plate_capacitor} \end{equation} where $C$ is the capacitance, $\epsilon_0$ is the vacuum permittivity, $\epsilon_r$ is the relative permittivity between the capacitor plates, $A$ is @@ -305,14 +304,14 @@ the area of overlap of the capacitor plates, which in this case corresponds to the area of the gold pad and $r$ is the distance between the gold pad and the \ce{Si} of the sample. $r$ is both the distance of $1$ $\mu$m of \ce{SiN} on the mask's surface and the mask sample distance in vacuum. \\ If any of the gold pads move a distance $r'$ closer to the sample the -capacitance increases by: +capacitance increases by (disregarding \ce{SiN}): \begin{equation} C' = \epsilon_0 \epsilon_r \frac{A}{r + r'} \Rightarrow \frac{1}{C'} = \frac{1}{C} + \epsilon_0 \epsilon_r \frac{A}{r'} \end{equation} The $\epsilon_r$ value for \ce{SiN} is $6.06$ (for a thin film of $437$ nm)~\cite{SiN_dielectric}. The value of $\epsilon_r$ in UHV is $\approx 1$, since the system is at a pressure of at least $10^{-8}$ mbar. The capacitance increases with a $\frac{1}{r}$ dependence. This holds true until -the mask's surface makes contact with the sample. Contamination particles can also cause indirect contact of mask and sample. +the mask's surface gets in contact with the sample. Contamination particles can also cause indirect contact of mask and sample. \begin{figure}[H] \centering @@ -344,24 +343,24 @@ the mask's surface makes contact with the sample. Contamination particles can al \caption{} \label{fig:approach_curve_example_full} \end{subfigure} - \caption{(a) A capacitance (approach) curve. (b) the difference of each capacitance value to the last. -Only one sensor is pictured. Marked with blue dashed lines are the important points where the slope of the $\frac{1}{r}$ curve changes. Below are images of the geometry between mask and -sample at First (c), Second (d) and Full contact (e). Red lines or points mark + \caption{(a) A capacitance (approach) curve. (b) the difference of each capacitance value. +Only one sensor is shown. Marked with blue dashed lines are the important points where the slope of the $\frac{1}{r}$ curve changes. Below are images of the geometry between mask and +sample at First (c), Second (d) and Full contact (e). Red lines or points indicate where the mask is touching the sample.} \label{fig:approach_curve_example} \end{figure} The curve obtained from approaching the sample is called an approach curve. An -example can be seen in Figure \ref{fig:approach_curve_example_cap} The same -curve when retracting mask from sample is called a retract curve. \\ +example is shown in Figure \ref{fig:approach_curve_example_cap}. The corresponding +curve for retraction is called a retract curve. \\ -When the alignment is not perfect, the mask will start contacting the sample with one point (or potentially an edge) first. An illustration of -this is seen in Figure \ref{fig:approach_curve_example_first} This will inhibit -the movement of the mask on associated motor. This results in a changed +Usually the mask will start contacting the sample with one point (or potentially an edge) first. An illustration of +this is shown in Figure \ref{fig:approach_curve_example_first}. This inhibits +the movement of the mask on the associated motor. This results in a changed step size. Since all motors move the mask frame this will affect all motors step sizes, albeit to different degrees. Due to -this step size change, the slope of the approach curve changes (shown in Eq. +this step size change, the slope of the approach curve changes (Eq. \ref{eq:cap_slope_change}), as seen in Figure -\ref{fig:approach_curve_example_cap} with the label "First contact". +\ref{fig:approach_curve_example_cap} at the label "First contact". \begin{equation} C'' = \epsilon_0 \epsilon_r \frac{A}{r + r' * d} \Rightarrow \frac{1}{C'} = @@ -370,11 +369,11 @@ this step size change, the slope of the approach curve changes (shown in Eq. \label{eq:cap_slope_change} \end{equation} -Where $C''$ is the final capacitance, $r$ is the distance to first contact, $r'$ is the distance since first contact and $d$ is the parameter by which the step size changes. -When approaching the surface further, the mask will then contact the surface +Where $C''$ is the resulting capacitance, $r$ is the distance to first contact, $r'$ is the distance since first contact and $d$ is the parameter by which the step size changes. +When approaching the surface further, the mask will contact the surface with an edge (see Figure \ref{fig:approach_curve_example_second}). This will have the same effect -of changing the slope of the curve again. This is labeled in Figure +as before. This is labeled in Figure \ref{fig:approach_curve_example_cap} as "Second contact". If the sample is approached further, the only axis of movement left for the mask is the one aligning the mask to the sample perfectly (Figure @@ -383,23 +382,21 @@ longer changes since the distance between mask and sample can no longer be decreased. This point is labeled "Full contact" in Figure \ref{fig:approach_curve_example_cap}. \\ -Another way of looking at this is to not consider the absolute capacitance -values, but instead their differences: +Another way of looking at this is to consider the differences between $2$ capacitance values: \begin{equation} C_2 - C_1 = \epsilon_0 \epsilon_r \frac{A}{r + r'} - \epsilon_0 \epsilon_r \frac{A}{r} < C_3 - C_2 = \epsilon_0 \epsilon_r \frac{A}{r + 2r'} - \epsilon_0 \epsilon_r \frac{A}{r + r'} \end{equation} Where $C_1$, $C_2$ and $C_3$ are $3$ different capacitance values where $C_1 < C_2 < C_3$. They are $r'$ apart in distance. -The values increase monotonically, when however the slope changes, the difference will suddenly drop. This can be seen in Figure \ref{fig:approach_curve_example_cap_diff}. When -the peak value of this graph is known one can predict the contact before it happens and stop the approach before the sample is contacted. This peak value of capacitance difference is called a "stop condition". The stop condition has to be determined using a calibration approach. \\ +The values increase monotonically, when however the slope changes, the difference will suddenly drop (Figure \ref{fig:approach_curve_example_cap_diff}). When +the peak value of this graph is known one can predict the contact before it happens and stop the approach before the sample is contacted. This peak value can be used to define a "stop condition". The stop condition has to be determined using a calibration approach. In practice the stop condition has to be chosen a few steps before the peak due to noise. \\ -When mask is perfect and the only capacitance values -to consider are from gold pads to the sample, the distance to the +The distance to the sample can be read off from the capacitance value via Eq. -\ref{eq:plate_capacitor}. However, with real masks the capacitance values can -deviate drastically from the expected ones. Without any point of -reference, no statement about the absolute distance can be made. +\ref{eq:plate_capacitor} in principle. However, with real masks the capacitance values can +deviate drastically from the model. Without any point of +reference, no assessment of the absolute distance can be made. For this reason, the approach curve of any mask sample combination has to be recorded first as a calibration curve. This requires contacting the sample at least once. Absolute distance can still not be measured since upon retraction and subsequent @@ -415,23 +412,21 @@ capacitance is used. The stop condition is used to determine good alignment \centering \includegraphics[width=0.95\linewidth]{img/MA/SubsequentApproachDeviation.pdf} - \caption{Plot of data of approach curves recorded on two different days. The + \caption{Approach curves recorded on two different days. The second curve was recorded after retraction and subsequent approach. The 2 curves -do not start at the same distance away from sample, which is why they are not -aligned on the x-axis. Both are driven until full contact.} +do not start at the same distance away from sample, therefore they are not +aligned on the x-axis. Both are driven until full contact. Capacitance 3 exhibits noisy signal. The reason for this is unknown.} \label{fig:approach_subsequent} \end{figure} \subsection{Reproducibility} -Reproducibility of approach curves with regard to different samples and masks is important for the future use of the Mask Aligner. In the master’s thesis of Jonas Beeker the +Reproducibility of approach curves with regard to different samples and masks is important for the future use of the Mask Aligner. In the master thesis of Jonas Beeker the reproducibility of different masks, different locations, different approaches and a comparison before and after evaporation were discussed~\cite{Beeker}. \subsubsection{Reproducibility when removing sample/mask} -\todo{Here} - -One question concerning reproducibility is whether the approach curve is strongly affected by the exchange of mask or sample, or even just the reinsertion of mask or sample. This is important since an exchange of sample to perform a new evaporation is a common operation in the creation of patterned samples. +One question concerning reproducibility is whether the approach curve is strongly affected by the exchange of mask or sample, or even just the reinsertion of mask or sample. This is important since an exchange of sample to perform a new evaporation is a common operation in the production of patterned samples. \begin{figure}[H] \centering @@ -445,24 +440,22 @@ One question concerning reproducibility is whether the approach curve is strongl \caption{} \label{fig:approach_replicability_cap_diff} \end{subfigure} - \caption{3 subsequent approach curves \subref{fig:approach_replicability_cap} and differences in capacitance for each step \subref{fig:approach_replicability_cap_diff} recorded. \textcolor{tab_green}{Green} is initial curve. \textcolor{tab_blue}{Blue} curve is after sample has been carefully removed and reinserted. For \textcolor{tab_red}{red} curve the mask was removed and reinserted. Larger fluctuations in the signal visible on the \textcolor{tab_blue}{Blue} curve are due to an accidental change in time constant of the LockIn Amplifier.} + \caption{\subref{fig:approach_replicability_cap} 3 subsequent approach curves. \subref{fig:approach_replicability_cap_diff} corresponding differences in capacitance. \textcolor{tab_green}{Green} is the initial curve. The \textcolor{tab_blue}{blue} curve is after sample has been carefully removed and reinserted. For the \textcolor{tab_red}{red} curve the mask was removed and reinserted. Larger fluctuations in the signal visible on the \textcolor{tab_blue}{Blue} curve are due to an accidental change in time constant of the LockIn Amplifier.} \label{fig:approach_replicability} \end{figure} -The reproducibility when exchanging just the mask and sample and reinserting it is looked at. When reinserting the mask, the approach curve changed drastically, which can likely be attributed to newly induced tilt on the mask. This can be seen in the shift between the \textcolor{tab_green}{green} and \textcolor{tab_red}{red} curves in Figure \ref{fig:approach_replicability}. This might be a feature of the particular batch of masks this thesis worked with, as the gold pins connecting the mask holder and mask stage do not have fully stable contact between the male and female side and allow for a certain level of movement. The process of moving the mask out and back in to the mask frame might induce enough perturbation to the mask holder to move it slightly in the mask. This fault could potentially be fixed with better gold pin design, when designing newer mask mentioned further in \ref{subsec:cross_cap}\\ - +The reproducibility when exchanging just the mask or sample and reinserting it is discussed in the following. When reinserting the mask, the approach curve changed drastically, which can likely be attributed to newly induced tilt on the mask. This can be seen in the shift between the \textcolor{tab_green}{green} and \textcolor{tab_red}{red} curves in Figure \ref{fig:approach_replicability}. The process of moving the mask out and back in to the mask frame might induce enough perturbation to the mask holder to move it slightly in the mask. This fault could potentially be fixed by better gold pin design, when designing newer mask discussed further in \ref{subsec:cross_cap}\\ -Another reason might be small movement of the mask frame on the \ce{Nd} magnets tilting the mask, when reinserting the mask. This problem cannot be fixed without a complete redesign of the Mask Aligner. \\ +Another reason might be small movement of the mask frame on the \ce{Nd} magnets tilting the mask. This problem cannot be fixed without a complete redesign of the Mask Aligner. \\ -Reinserting the sample also induced a difference in approach curves, but the difference is much smaller as can be seen in \textcolor{tab_blue}{blue} and \textcolor{tab_green}{green}, but the same curve is followed and the point of first contact has only shifted upwards slightly. In the difference curve, it is clear that the stop condition however changed by some amount. A stop condition developed on the peak of the \textcolor{tab_green}{green} curve (for example $0.04$ pF) would overshoot the point of first contact on the \textcolor{tab_blue}{blue} curve and the stop condition would never trigger. If left unsupervised, the mask would in this instance eventually crash into the sample, unless a point near the point of second or full contact satisfies the stop condition as well. This should be taken into account when deciding on a stop condition. \\ +Reinserting the sample also induced a difference in approach curves, but this difference is much smaller as can be seen in Figure \ref{fig:approach_replicability} (\textcolor{tab_blue}{blue} and \textcolor{tab_green}{green}). The trend of the curve remains the same, but the absolute value changes slightly. However, the peak in $dC$ changed significantly. A stop condition determined on the \textcolor{tab_green}{green} curve (for example $0.04$ pF) would overshoot the point of first contact on the \textcolor{tab_blue}{blue} curve. This means that after switching a conservative stop condition has to be chosen. \\ \subsection{Cross capacitances} \label{subsec:cross_cap} -The biggest alignment problem with current set of masks is the heavy correlation -between mask sensors, $C_i$ see Figure \ref{fig:cross_cap_approach}~\subref{fig:cross_cap_approach_difference}-\subref{fig:cross_cap_approach_difference_2}. If +The biggest alignment problem with the current set of masks is heavy correlation +between mask sensors, $C_i$ see Figure \ref{fig:cross_cap_approach}~\subref{fig:cross_cap_approach_difference}-\subref{fig:cross_cap_approach_difference_2}. If the alignment were perfect, these curves should indeed appear to be very similar -since moving any of the motors affects all capacitance sensors, but each of the capacitance sensors should independently give a curve, which follows a $\frac{1}{r}$ behavior. From this -follows, that if the distances from the \ce{Si} is different for each sensor. Their approach curves should be distinct. A simulated approach curve for a difference of $440$ nm between $C_1$ and $C_2$ and $560$ nm between $C_1$ and $C_3$ is shown in Figure \ref{fig:cross_cap_approach_sim}. The model assumes no capacitance between the 3 capacitance sensors and no capacitance to the environment. Additionally, the model assumes all motors drive exactly the same. It also assumes the mask first makes contact with the sample at the corner that is aligned with $C_1$ such that the motor aligned with $C_1$ stops moving. After that, the same happens for $C_2$. +since moving any of the motors affects all capacitance sensors. If the distances from the \ce{Si} is different for each sensor, their approach curves should be distinct. A simulated approach curve for a difference of $440$ nm between $C_1$ and $C_2$ and $560$ nm between $C_1$ and $C_3$ is shown in Figure \ref{fig:cross_cap_approach_sim}. The model assumes no capacitance between the 3 capacitance sensors and to the environment. Additionally, the model assumes all motors drive exactly the same. It also assumes the mask first makes contact with the sample at the corner that is aligned with $C_1$ such that the motor aligned with $C_1$ stops moving. After that, the same happens for $C_2$. \begin{figure}[H] \centering @@ -484,19 +477,17 @@ follows, that if the distances from the \ce{Si} is different for each sensor. Th \caption{} \label{fig:cross_cap_approach_sim} \end{subfigure} - \caption{(\subref{fig:cross_cap_approach_difference}, \subref{fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure same scale. (\subref{fig:cross_cap_approach_sim}) shows a simple simulation of how the approach with tilted sample would look in an ideal case.} + \caption{(\subref{fig:cross_cap_approach_difference}, \subref{fig:cross_cap_approach_difference_2}) approach curves of two example measurements of 2 different masks normalized to ensure the same scale. (\subref{fig:cross_cap_approach_sim}) shows a simple simulation of the approach with tilted sample.} \label{fig:cross_cap_approach} \end{figure} -The model in Figure \ref{fig:cross_cap_approach_sim} assumes a distance between the sensors on the z-axis of $440$ nm for C1-C2 and $220$ nm for C2-C3. A distance that is well within the optical accuracy of $\approx 5$ $\mu$m for maximum zoom and resolution. Even for such a small difference, the deviance between the curves, is very visible. \\ +The model in Figure \ref{fig:cross_cap_approach_sim} assumes a distance between the sensors on the z-axis of $440$ nm for C1-C2 and $220$ nm for C2-C3. A distance that is well within the optical accuracy of $\approx 5$ $\mu$m for maximum zoom and resolution. Even for such a small difference, the deviance between the curves, is easily visible. \\ +However, measured capacitances show a deviation in behavior from the model (Fig. \ref{fig:cross_cap_approach_difference}). The different capacitances vary by $1$-$2$ order of magnitude. The largest capacitance was measured to $19.12$ pF. The curves (Fig. \ref{fig:cross_cap_approach_difference}) start with large deviation and converge near full contact. This is the opposite to the expected behavior (Fig. \ref{fig:cross_cap_approach_sim}). The general shape of the curves is identical for all $3$, while it is expected that the first contact affects the $3$ capacitances differently. \\ -However, the curves measured for capacitance show a deviation in behavior from the model. Figure \ref{fig:cross_cap_approach_difference} shows this. The curves of the 3 capacitances were normalized to bring them into the same range. The different capacitances vary by $1$-$2$ order of magnitude. The largest capacitance was measured to $19.12$ pF. The curves start with large deviation and seem to converge. This is the opposite to the expected behavior (Fig. \ref{fig:cross_cap_approach_sim}). The general shape of the curve also is identical between all $3$, while it is expected that first contact affects the $3$ capacitances differently. \\ +Another mask (Figure \ref{fig:cross_cap_approach_difference_2}) shows behavior more close to the expected, with a difference for the $3$ capacitances at first contact. However, $C_2$ and $C_3$ behave identically again. The largest capacitance was measured to be $19.78$ pF and $C_2$ and $C_3$ varied by $2$ orders of magnitude from $C_1$. \\ -Another mask (Figure \ref{fig:cross_cap_approach_difference_2}) shows behavior more close to the expected, with a difference for the $3$ capacitances at first contact. However, $C_2$ and $C_3$ behave identically again. The largest capacitance was measured to be $19.78$ pF and $C_2$ and $C_3$ varied by $2$ orders of magnitude from $C_1$. -For the gold pads, this would give a capacitance value of $\approx 0.40$ fF at a -distance of $50$ micron, at a distance of $\approx 50$ micron, as was measured -optically. The capacitance values of the curve $C_1$ was $\approx 2.4$ +For the gold pads, this would result in a capacitance of $\approx 0.40$ fF, at a distance of $\approx 50$ micron (measured optically). The capacitance values of the curve $C_1$ was $\approx 2.4$ pF, which deviates by $4$ orders of magnitude. This corresponds more closely to the value expected for capacitance from the \ce{Si} of the mask to the \ce{Si} of the sample. The expected value for a plate capacitor would be $\approx @@ -513,19 +504,19 @@ might have. \\ %\todo{Plot of heavily correlated approach curves} The reason for this large deviation is most likely a leakage current from the cable connecting -the gold pads to the Si of the Mask. This leakage current is most likely -due to errors in the mask preparation process. These cause the \ce{SiNi} layer -insulating the Si to tear. This is depicted in Figure \ref{fig:leakage_current}. These -small tears that can happen due to small errors, when gluing the gold wire. This causes a path to be available from the gold wire to the \ce{Si} of the sample. The capacitance, which is now measured is dominated by the leakage capacitance from \ce{Si$_\text{Sample}$} to \ce{Si$_\text{Mask}$} (Figure \ref{fig:leakage_current}). +the gold pads to the Si of the Mask. This most likely happens +due to accidental piercing of the insulating \ce{SiO2} layer during assembly of the gold cable. This is depicted in Figure \ref{fig:leakage_current}. The capacitance measured is in this case dominated by the leakage capacitance from \ce{Si$_\text{Sample}$} to \ce{Si$_\text{Mask}$} (Figure \ref{fig:leakage_current}). \begin{figure}[H] \centering \includegraphics[width=0.5\linewidth]{img/LeakageCurrent.pdf} - \caption{Diagram showing a cross section of the mask at a gold pad location. A small Tear in the \ce{SiNi} layer removes insulation between the gold wire and the Si of the mask, causing a leakage current. Parallel black lines are meant to illustrate plate capacitors. Larger plate shows larger capacitance. + \caption{Diagram showing a cross section of the mask at a gold pad location. A small tear in the \ce{SiO2} layer removes insulation between the gold wire and the Si of the mask. Parallel black lines depict plate capacitors illustratively. Larger plate shows larger capacitance. } \label{fig:leakage_current} \end{figure} -Another reason for the correlation of capacitances are cross capacitances between the gold pad sensors. \\ +\newpage + +Another reason for the correlation of capacitances are cross capacitances between the gold pad sensors. \\ \begin{table}[H] \centering @@ -538,35 +529,36 @@ Mask 2 & $0.64 \pm 0.06$ & $0.64 \pm 0.06$ & $0.85 \pm 0.02$ \\ \hline Mask 3 & $3.33 \pm 0.04$ & $3.94 \pm 0.07$ & $0.86 \pm 0.02$ \\ \hline -Mask Old & $0.50 \pm 0.02$ & $0.29 \pm 0.09$ & $0.35 \pm +Mask old & $0.50 \pm 0.02$ & $0.29 \pm 0.09$ & $0.35 \pm 0.14$ \\ \hline \hline -Mask Shuttle 1 & $0.24 \pm 0.02$ & $0.25 \pm 0.02$ & $0.041 \pm +Mask shuttle 1 & $0.24 \pm 0.02$ & $0.25 \pm 0.02$ & $0.041 \pm 0.004$ \\ \hline -Mask Shuttle 2 & $0.30 \pm 0.04$ & $0.29 \pm 0.03$ & $0.041 \pm 0.004$ +Mask shuttle 2 & $0.30 \pm 0.04$ & $0.29 \pm 0.03$ & $0.041 \pm 0.004$ \\ \hline -Mask Shuttle 3 & $0.23 \pm 0.02$ & $0.25 \pm 0.02$ & $0.049 \pm +Mask shuttle 3 & $0.23 \pm 0.02$ & $0.25 \pm 0.02$ & $0.049 \pm 0.004$ \\ \hline \hline -Shuttles Average & $0.26 \pm 0.03$ & $0.26 \pm 0.02$ & $0.043 \pm 0.004$ +Shuttles average & $0.26 \pm 0.03$ & $0.26 \pm 0.02$ & $0.043 \pm 0.004$ \\ \hline \end{tabular} -\caption{Table of cross capacitance measurement 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.} +\caption{Table of cross capacitance measurement results. All measurements were carried out with the mask shuttle the +Mask Aligner and sample at $0.3$ mm distance. The distance was determined optically with Bresser MicroCam II and MikroCamLabII.} \label{tab:cross_cap} \end{table} -In order to check for the effect of this source, cross capacitances were measured directly between $3$ masks holders inside mask shuttles, as well as -3 empty shuttles. This is accomplished replacing the connection from the Lock-in amplifier to the sample in Figure \ref{fig:diagram_MA_circ} with one to one of the capacitive sensors. Measurements were performed inside the Mask Aligner with Sample inserted. Additionally, mask shuttles without any mask inserted were tested for cross capacitance. The results are shown in Table \ref{tab:cross_cap} +In order to quantify the effect of this source, cross capacitances were measured directly between $3$ masks holders inside mask shuttles, as well as +3 empty shuttles. This was accomplished by replacing the connection from the Lock-in amplifier to the sample in Figure \ref{fig:diagram_MA_circ} with one to one of the capacitive sensors. Measurements were performed inside the Mask Aligner with a sample inserted. Additionally, mask shuttles without any mask inserted were tested for cross capacitance. The results are shown in Table \ref{tab:cross_cap} \\ + +The shuttles themselves have large cross capacitance values. It is of the same order of magnitude as the capacitance expected from gold pad to sample. When adding the mask +the cross capacitances increase, often by an order of magnitude. This shows that cross capacitance is an important in the correlation. \\ + +To check if this is also the dominant cause of correlation, the mask labeled "old" is looked at more closely. The cross capacitance values for this mask were small compared with the other masks (Table \ref{tab:cross_cap}). The approach curve of this mask however, shows the heaviest correlation of all masks tested. This indicates that in this case a leakage current from gold to mask \ce{Si} is the main cause. \\ -The shuttles on their own have a cross capacitance values. It is of the same order of magnitude as the capacitance expected from gold pad to sample. When adding the mask -the cross capacitances increases, often by an order of magnitude. This shows that cross capacitance is a large factor in the correlation. \\ +To confirm the similarity between the different capacitance sensors signals, the data of each was overlaid over one another. The data was normalized to allow for comparison. Then an offset was fitted. The result of this can be seen in Figure \ref{fig:mask_old_correl}. The $3$ different capacitance sensors give the same signal. Systematic deviations in the residuals are only visible near the jump in capacitance signal, which is of unknown cause. The deviations are within $0.1$~\%, which is on the same order as the expected measurement error for the given LockIn parameters. \begin{figure}[H] \centering \includegraphics[width=0.9\linewidth]{img/Plots/Mask_Old_Caps.pdf} - \caption{The 3 capacitance curves of the Mask labeled "old", 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.} + \caption{The 3 capacitance curves of the Mask labeled "old". Of note is the difference in scale of the capacitance signal.} \label{fig:mask_old_caps} \end{figure} @@ -574,19 +566,16 @@ scale of the y-axis, and due to this the scale of the uncertainty.} \centering \includegraphics[width=0.95\linewidth]{img/Plots/Mask_Old_Correl.pdf} \caption{The 3 capacitance curves of the Mask labeled "old" scaled to be -within same range, via normalization and subsequent fit of offset parameter, first to C2 and C3 fit to C1 and then C3 fit -to C2. The lower plots show residuals. The residuals show the variation to be well within the error bars -and overall within less than $1$ \%.} +within the same range. The lower plots show deviations from comparison curve. } \label{fig:mask_old_correl} \end{figure} -To check if this is also the dominant cause of correlation, the mask labeled "old" is looked at more closely. The cross capacitance values for this mask were small compared with the other masks, but the approach curve of this mask shows the heaviest correlation of all masks tested. This indicates that in this case a leakage current from gold to mask \ce{Si} is the probable cause here. \\ -To further corroborate the similarity between the different capacitance sensors signals, the data of each was overlaid over one another. Since the capacitance ranges vary between sensors, the signals have to first be normalized to fall in the same range. Then additionally an offset has to be fitted, since they are also offset by each other. The result of this can be seen in Figure \ref{fig:mask_old_correl}. This shows even more clearly that the $3$ different capacitances give the same signal within error. Systematic deviations in the residuals are only visible near the jump in capacitance signal, which is of unknown cause. The deviations are within $0.1$ \%, which is on the same order as the expected measurement error for the given LockIn parameters. +This leads to the conclusion that while the cross capacitances have a strong influence on +the correlation, they are not the dominating +factor. Both leakage currents and cross capacitances have to be considered and their sources minimized. \\ -This suggests, that while the cross capacitances have a strong influence on -the correlation of the $3$ capacitance measurements, they are not the dominating -factor. Both leakage currents and cross capacitances have to be considered and their sources minimized. Figure \ref{fig:cross_cap_diagramm} shows a circuit diagram for the known sources of capacitance correlation. +Figure \ref{fig:cross_cap_diagramm} shows a circuit diagram for the known sources of capacitance correlation. \begin{figure}[H] \centering @@ -615,24 +604,21 @@ this thesis. \paragraph{Improved gold pin fitting} The gold pins for the current set of masks were cut to correct size by hand. -This causes a problem with the fit between male and female side of the gold pins, which causes -the contact between male and female gold pins to be loose. This allows the mask stage inside the holder to move slightly, changing both distance to sample and giving loose contact. -Instead, they should be machined with precision by a workshop. Additionally, a stable fit should be tested beforehand. +This causes a problem with the fit between male and female side of the gold pins. +The mask stage can move inside the holder slightly. This changes both distance to sample and gives a loose contact. +Instead, they should be machined with precision by a workshop. The stability of the fit should be tested after assembly. \todo{Image of gold pins} -The large cross capacitance of the mask holders should also be reduced. No proposal is made in this thesis about how to accomplish this, because the cause is undetermined. The other $2$ factors play a larger role and should be improved first. +The cross capacitances of the mask holders should also be reduced. No proposal is made in this thesis about how to accomplish this, because the cause is undetermined. The other $2$ factors play a larger role and should be improved first. \subsection{Stop Conditions} -When doing an approach for evaporation. As a first step an approach curve has to be -recorded as a calibration. Here, two different scenarios can arise: +During recording of a calibration approach curve two different scenarios can arise: \paragraph{High correlation between capacitance curves} When all 3 capacitance curves are heavily correlated, no alignment information -can be derived from the 3 different curves. Effectively only one curve can be -worked with. The stop condition in this case is a single peak in the derivative of the -capacitance curve. This peak in the capacitance curve happens right before first -contact. By picking a condition close to the peak good alignment can be achieved. +can be derived from the 3 different curves. Effectively only one curve is measured. The stop condition in this case is a single peak in the derivative of that one +capacitance curve. By picking a condition close to the peak good alignment can be achieved. By performing one approach until full contact between mask and sample the mask can be aligned at the cost of possibly damaging mask and sample. This has to be done on the first curve. @@ -640,32 +626,31 @@ Furthermore, the values of capacitance at full contact will afterward be known. \paragraph{Low correlation between capacitance curves} When all 3 capacitance curves are mostly uncorrelated, information of the mask sample can be gathered directly from the value of each -curve. It can be used to determine how close each sensor to the sample is. +curve. In this case the absolute value of the $3$ capacitance curves can be used to determine when to stop the approach. Optimal values can be iteratively reached, by moving the $3$ motors separately. \\ This is the easier and safer of the two scenarios, but it requires a good mask holder and mask stage. \section{Mask Aligner operation} \subsection{Sample preparation} \label{sec:sample_prep} -In order to get a clean interface, when evaporating a superconductor on any -material, a clean and contamination free sample surface is required. In this thesis, only \ce{Si} samples were used. To clean a \ce{Si} sample, the following steps have to be taken: +The evaporation of a superconductor onto any material requires a clean sample surface. In this thesis, only \ce{Si} samples were used. To clean a \ce{Si} sample, the following steps have to be taken: \begin{enumerate} \item Select chips from a \ce{Si} wafer and place them into a petri dish. The petri dish should be cleaned using acetone and then IPA in an ultrasonic bath. - \item Carefully grab the silicon chip with a soft tip tweezer and while -ensuring stable grip, carefully blow any coarse particles from the surface of the + \item Carefully grab a silicon chip with a soft tip tweezer and while +maintaining stable grip, carefully blow any coarse particles from the surface of the chip using pressurized nitrogen. Do not blow the nitrogen at the surface, but -across it, as otherwise the chip will just fall from the tweezer. - \item Place the chip in a beaker filled with pure acetone and put it in an +across it, as otherwise the chip will just fall from the tweezer. Do this for every chip. + \item Place the chips in a beaker filled with pure acetone and put it in an ultrasonic bath. Heat the acetone using the heating function of the ultrasonic -bath, ensuring however that $55^\circ$ C are never exceeded, for 10 minutes. - \item Take the chips out of the acetone with a soft tip tweezer and rinse them with IPA. Then submerge them in a beaker filled with IPA and clean them again in the ultrasonic bath for 10 minutes. No heating required this time. +bath for 10 minutes, ensuring however that $55^\circ$ C are never exceeded. + \item Take the chips out of the acetone with a soft tip tweezer and rinse them with IPA. Then submerge them in a beaker filled with IPA and clean them again in the ultrasonic bath for 10 minutes. No heating required. \item Take the chip out again and repeat the last step with demineralized water. While waiting, combine the hardener and resin of the 2 part epoxy EPO-TEK E4110-LV to ensure it is ready for a later step. \item Take the chip out and blow it dry with pressurized nitrogen, following the same procedure as step 2. - \item Place 4 dots of mixed epoxy EPO-TEK E4110-LV into the grooves of the sample holder at the edges. Carefully grab the chip and place it from the top as straight as possible onto the sample holder. If necessary, gently nudge the chips from the sides that stick out to ensure it is sitting straight in the sample holder. Avoid contaminating the surface with epoxy resin! + \item Place 4 dots of mixed epoxy EPO-TEK E4110-LV into the grooves of the sample holder at the edges. Carefully grab the chip and place it from the top as straight as possible onto the sample holder. If necessary, gently nudge the chip from the sides that stick out to ensure it is sitting straight in the sample holder. Avoid contaminating the surface with epoxy resin! \item Carefully place the sample holder in an oven heated to $150^\circ$ C and let the resin cure for $15$ minutes. \item Document the sample's surface cleanliness using an optical microscope image and an AFM image \item Place the sample as quickly as possible in the Mask Aligner Load Lock and pump the system down to avoid further contamination. \end{enumerate} -If the sample is intended to be analyzed in an STM, the sample preparation should happen in a UHV environment to ensure further cleanliness and the sample should be transported directly via the Load Lock UHV suitcase attached to the Mask Aligner Chamber. \ No newline at end of file +If the sample is intended to be analyzed in an STM, the sample preparation should happen in an UHV environment to ensure further cleanliness and the sample should be transported directly via the Load Lock UHV suitcase attached to the Mask Aligner Chamber. \ No newline at end of file diff --git a/chap03.aux b/chap03.aux index d082a371e1dfb0528bb12d6c22bceaf3bebcab6a..7b0399fa35bdb1f68197b130c6c1bda270a4465e 100644 --- a/chap03.aux +++ b/chap03.aux @@ -5,70 +5,70 @@ \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {3.1}RHK piezo motor controller}{42}{section.3.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}Overview}{42}{subsection.3.1.1}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{amplitude}{42}{section*.48}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{sweep period}{42}{section*.49}\protected@file@percent } -\@writefile{toc}{\contentsline {paragraph}{time between sweeps}{42}{section*.50}\protected@file@percent } -\@writefile{tdo}{\contentsline {todo}{Maybe image explanation}{42}{section*.51}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{amplitude}{42}{section*.47}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{sweep period}{42}{section*.48}\protected@file@percent } +\@writefile{toc}{\contentsline {paragraph}{time between sweeps}{42}{section*.49}\protected@file@percent } +\@writefile{tdo}{\contentsline {todo}{Maybe image explanation}{42}{section*.50}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {3.1.2}Pulse shape}{42}{subsection.3.1.2}\protected@file@percent } -\newlabel{fig:RHK_pulse_shape_approach}{{3.1a}{42}{\relax }{figure.caption.52}{}} -\newlabel{sub@fig:RHK_pulse_shape_approach}{{a}{42}{\relax }{figure.caption.52}{}} -\newlabel{fig:RHK_pulse_shape_retract}{{3.1b}{42}{\relax }{figure.caption.52}{}} -\newlabel{sub@fig:RHK_pulse_shape_retract}{{b}{42}{\relax }{figure.caption.52}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces Oscilloscope data showing both an approach step (\subref {fig:RHK_pulse_shape_approach}) and a retract step (\subref {fig:RHK_pulse_shape_retract}) for the RHK Piezo motor controller given at a voltage of $80$ V, as specified per setting. }}{42}{figure.caption.52}\protected@file@percent } -\newlabel{fig:RHK_pulse_shape}{{3.1}{42}{Oscilloscope data showing both an approach step (\subref {fig:RHK_pulse_shape_approach}) and a retract step (\subref {fig:RHK_pulse_shape_retract}) for the RHK Piezo motor controller given at a voltage of $80$ V, as specified per setting}{figure.caption.52}{}} -\newlabel{fig:RHK_pulse_shape_fast_flank_z1}{{3.2a}{43}{\relax }{figure.caption.53}{}} -\newlabel{sub@fig:RHK_pulse_shape_fast_flank_z1}{{a}{43}{\relax }{figure.caption.53}{}} -\newlabel{fig:RHK_pulse_shape_fast_flank_z2}{{3.2b}{43}{\relax }{figure.caption.53}{}} -\newlabel{sub@fig:RHK_pulse_shape_fast_flank_z2}{{b}{43}{\relax }{figure.caption.53}{}} -\@writefile{lof}{\contentsline {figure}{\numberline {3.2}{\ignorespaces Plots showing the fast flank of the RHK signal, set to 80 V. 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(\subref {fig:evaporation_simulation_rejection_comparison}) shows the AFM image from which the parameters were obtained. The parameters of the ellipse are the same as in Figure \ref {fig:evaporation_simulation_first_compare}.}}{82}{figure.caption.95}\protected@file@percent } -\newlabel{fig:evaporation_simulation_rejection}{{5.14}{82}{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 were obtained. 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{2.3.5}Reproducibility}{32}{subsection.2.3.5}% \contentsline {subsubsection}{Reproducibility when removing sample/mask}{32}{section*.34}% -\contentsline {subsection}{\numberline {2.3.6}Cross capacitances}{34}{subsection.2.3.6}% -\contentsline {paragraph}{Leakage current}{39}{section*.43}% -\contentsline {paragraph}{Improved gold pin fitting}{39}{section*.44}% +\contentsline {subsection}{\numberline {2.3.6}Cross capacitances}{33}{subsection.2.3.6}% +\contentsline {paragraph}{Leakage current}{39}{section*.42}% +\contentsline {paragraph}{Improved gold pin fitting}{39}{section*.43}% \contentsline {subsection}{\numberline {2.3.7}Stop Conditions}{40}{subsection.2.3.7}% -\contentsline {paragraph}{High correlation between capacitance curves}{40}{section*.46}% -\contentsline {paragraph}{Low correlation between capacitance curves}{40}{section*.47}% +\contentsline {paragraph}{High correlation between capacitance curves}{40}{section*.45}% +\contentsline {paragraph}{Low correlation between capacitance curves}{40}{section*.46}% \contentsline {section}{\numberline {2.4}Mask Aligner operation}{40}{section.2.4}% \contentsline {subsection}{\numberline {2.4.1}Sample preparation}{40}{subsection.2.4.1}% \contentsline {chapter}{\numberline {3}Electronics}{42}{chapter.3}% \contentsline {section}{\numberline {3.1}RHK piezo motor controller}{42}{section.3.1}% \contentsline {subsection}{\numberline {3.1.1}Overview}{42}{subsection.3.1.1}% -\contentsline {paragraph}{amplitude}{42}{section*.48}% -\contentsline {paragraph}{sweep period}{42}{section*.49}% -\contentsline {paragraph}{time between sweeps}{42}{section*.50}% +\contentsline {paragraph}{amplitude}{42}{section*.47}% +\contentsline {paragraph}{sweep period}{42}{section*.48}% +\contentsline {paragraph}{time between sweeps}{42}{section*.49}% \contentsline {subsection}{\numberline {3.1.2}Pulse shape}{42}{subsection.3.1.2}% \contentsline {section}{\numberline {3.2}KIM001}{43}{section.3.2}% \contentsline {subsection}{\numberline {3.2.1}Overview}{43}{subsection.3.2.1}% @@ -47,11 +47,11 @@ \contentsline {subsection}{\numberline {3.3.3}Fast flank}{47}{subsection.3.3.3}% \contentsline {subsection}{\numberline {3.3.4}Amplification}{47}{subsection.3.3.4}% \contentsline {subsection}{\numberline {3.3.5}Parameters}{48}{subsection.3.3.5}% -\contentsline {paragraph}{Amplitude (amp)}{48}{section*.59}% -\contentsline {paragraph}{Voltage (volt)}{48}{section*.60}% -\contentsline {paragraph}{Channel}{48}{section*.61}% -\contentsline {paragraph}{Max Step}{48}{section*.62}% -\contentsline {paragraph}{Polarity}{48}{section*.63}% +\contentsline {paragraph}{Amplitude (amp)}{48}{section*.58}% +\contentsline {paragraph}{Voltage (volt)}{48}{section*.59}% +\contentsline {paragraph}{Channel}{48}{section*.60}% +\contentsline {paragraph}{Max Step}{48}{section*.61}% +\contentsline {paragraph}{Polarity}{48}{section*.62}% \contentsline {subsection}{\numberline {3.3.6}Measured pulse shape}{48}{subsection.3.3.6}% \contentsline {subsection}{\numberline {3.3.7}Driving the Mask Aligner}{50}{subsection.3.3.7}% \contentsline {chapter}{\numberline {4}Mask Aligner repairs and optimizations}{52}{chapter.4}% @@ -76,44 +76,44 @@ \contentsline {subsection}{\numberline {5.5.2}Results}{79}{subsection.5.5.2}% \contentsline {subsection}{\numberline {5.5.3}Software improvements}{83}{subsection.5.5.3}% \contentsline {subsection}{\numberline {5.5.4}Final Remark}{84}{subsection.5.5.4}% -\contentsline {chapter}{Conclusions and Outlook}{85}{chapter*.97}% -\contentsline {chapter}{Bibliography}{87}{chapter*.98}% -\contentsline {chapter}{List of Abbreviations}{90}{chapter*.99}% -\contentsline {chapter}{Appendix}{i}{chapter*.100}% +\contentsline {chapter}{Conclusions and Outlook}{85}{chapter*.96}% +\contentsline {chapter}{Bibliography}{87}{chapter*.97}% +\contentsline {chapter}{List of Abbreviations}{90}{chapter*.98}% +\contentsline {chapter}{Appendix}{i}{chapter*.99}% \contentsline {section}{\numberline {A}LockIn amplifier 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