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 Coating Ring-down Measurement Lab elog, Page 8 of 18 Not logged in
ID Date Author Type Category Subject
352   Thu Jun 22 15:37:20 2017 ZachElectronicsModelingBeginning modeling

# 2017-06-22

• Created the geometry of the ESD by creating blocks and joining them with Unions. I then created a block to serve as the domain and added air to that region
• This plot is a combination of a Surface plot of the potential and a Streamline plot of the electric field
• I created another model of the ESD with more accurate measurements to the real thing and added the silica disc to the model
353   Fri Jun 23 12:02:12 2017 ZachElectronicsModelingPlots

# 2017-06-23

• I created plots of the E field and potential from my rough model of the ESD. This model has 1mm electrode arm widths and spacings, the length of each arm is 16 mm, and the resulting total size is 38mm x 20 mm x 0.1 mm. One comb has ten arms while the other has nine to match the actual ESD currently in use in the lab.
• I set the ten arm comb to a potential of 100 V and the other to ground. I then used physics controlled mesh with an extremely fine element size to computer the simulations. With mesh sizes larger than extra fine, there was clearly non-physical error in the electric field and potential graphs that appeared as inexplicable field lines, spikes, and coarseness in the plots.
• To create readable plots of the potential I created a Cut Plane in the center of the ESD perpendicular to both the arms and the plane of the device. The plots are attached with a milimeter length scale. I created a filled contour plot of the potential that is very clean, I tried a couple of different options for the electric field because it is harder to represent well. I created a contour plot for the norm of the electric field as well as superimposing a streamline plot of the field lines over that. Everything behaves generally as expected though I do suspect the spikes in electric field at the edges of each electrode are due to the fact that they are sharp corners and not smooth edges.

Attachment 1: Potential.png
Attachment 2: E_w_Lines.png
Attachment 3: Mesh.png
354   Sat Jun 24 12:59:27 2017 GabrieleGeneralMeasurementsS1600541 S1600542 post annealing

## 2017-06-24

• 12:47pm in chamber
• S1600541 in CR1
• S1600542 in CR3
• 12:50pm roughing pump on
• 12:59pm turbo pump on
• Excitations
• Quiet time before excitation: 1182524202
Quiet time after excitation: 1182524262

• Quiet time before excitation: 1182535092
Quiet time after excitation: 1182535152

• Quiet time before excitation: 1182545982
Quiet time after excitation: 1182546042

• Quiet time before excitation: 1182556872
Quiet time after excitation: 1182556932

• Quiet time before excitation: 1182567762
Quiet time after excitation: 1182567822

• Quiet time before excitation: 1182578652
Quiet time after excitation: 1182578712

• Quiet time before excitation: 1182589542
Quiet time after excitation: 1182589602

• Quiet time before excitation: 1182600432
Quiet time after excitation: 1182600492

## 2017-06-28

• 3:36pm, valve closed, vented, pumps stopped
355   Tue Jun 27 09:20:16 2017 AlenaGeneralAnnealingAnnealing run (546-551) on 3" wafers - Crime 06/27/2017

Started annealing run https://dcc.ligo.org/T1700293

Will be ready by June 28th afternoon

356   Tue Jun 27 14:17:47 2017 ZachElectronicsModelingFurther plots and improving models

# 2017-06-27

• I built a new model of the ESD to determine whether or not the spikes in the electric field at the corners was affecting the results enough that it had to be accounted for in further models. To create the model, I created a 2D profile of the arm used in my original model and filleted the corners at a radius of .05 mm, since the electrode model is .1 mm thick, this made completely rounded edges. In creating this model I caught an earlier mistake in the original one, I only set one half of the surface of the electrodes to have a potential or to ground, the "bottom" was left with no charge. I fixed this mistake and then compared the two models at a potential of 1000 V. For speed of computation I ran both models with a finer mesh size and then calculated the electric field at approximately the middle of the ESD, 1mm above the fourth electrode arm. For the rounded electrodes the field had a value of 84024 V/m and for the rectangular electrodes the field had a value of 80728 V/m, which is less than a 4% difference in field magnitude. Furthermore, the field shapes appear nearly indistinguishable; I am confident from this test that I can proceed modelling the arms of the ESD as rectangles.
Attachment 1: E_field_corner.png
Attachment 2: E_field_round.png
357   Wed Jun 28 15:50:15 2017 GabrieleGeneralMeasurementsS1600541

## 2017-06-28

We plan to leave S1600541 in vacuum for a long period, and measure the Q's periodically.

• 3:48pm, S1600541 installed in CR0
• 3:50pm, roughing pump on
• 4:35pm turbo pump on
358   Thu Jun 29 13:15:01 2017 Alastair, GabrieleGeneralGeneralLaser polishing

We laser polished S1600546, 547, 548, 549, 550 and 551

359   Thu Jun 29 16:40:41 2017 ZachElectronicsModelingAccurate model and force profile

# 2017-06-29

• I created a much more accurate model of the current ESD setup from the technical drawings. My resulting ESD has dimensions of 21.3x24.3x.1mm with 1 mm spacings and 17.5 mm long electrode arms. The sample has a diameter of 75 mm and thickness of 1mm, the ESD is 1mm below the sample in the current model. I still have to compare the technical drawings to confirm that is the actual distance in the current lab setup.
• I was able to calculate the force profile on the disk from the ESD. COMSOL struggled to resolve the data with a small mesh size over the whole domain, so I created a region of extremely fine mesh around the ESD and the disk and then made the rest of the mesh size normal sized. Over the domain near the ESD my mesh size ranges from 2.5*10-3 to .25 mm and over the rest of the domain it's automatically setup at the normal size.
• The force on a single dipole is given as $F = (P \cdot \nabla)E$, since fused silica is isotropic it's polarization is proportional to E so $F = \chi_e \epsilon_0 \nabla (E^2)$. The electric suscepitibility of fused silica is 1.09, I plotted the profile of the force perpendicular to the plane of the disk and exported data files of the full vector quantity of the force for use with Matlab.

360   Fri Jun 30 11:02:18 2017 ZachElectronicsModelingMatching Forces

# 2017-06-30

• I adjusted the plot parameters slightly so that it only showed the actual force profile on the sample in the direction perpendicular to the sample surface. Additionally I compared the two methods of computing the force, as $\vec{F} = -(\vec{P}\cdot \nabla)\vec{E}$ and as $\vec{F} =- \chi_e \epsilon_0 \nabla \vec{E}^2$. The profile of the force in both instances appear equal, but they differ in magnitude by exactly a factor of 2, I plotted the force computed with the explicit polarization doubled and the force magnitudes matched exactly. I'm still not entirely sure where this factor of two could be coming from.

361   Fri Jun 30 16:27:56 2017 ZachElectronicsModelingDouble Checking Model

# 2017-06-30

• In order to confirm the accuracy of my model I checked some easily computable quantities between what real values and what COMSOL produced. My expected electric field magnitude between the electrodes is 106 V/m and COMSOL reads out 1.015*10which is less than a 2% error. When I went to compute the electric field gradient however, I discovered that I had been calculating my derivatives wrong, I was calculating full derivatives when I needed partial derivatives. Due to some subtleties of the numerics involving curl calculations are the order of the variables, in order to calculate a partial I belive that I have to map the results of the electric field to Lagrange elements.
362   Wed Jul 5 10:01:29 2017 GabrieleGeneralMeasurementsS1600547 S1600548 S1600549 S1600550

## 2017-07-05

• NOTE: at 9:40am switched off turbo pump in CR0 to avoid  vibrations
• NOTE: boxes are labeled as S1600546/547/548/549 but must be relabeled as S1600547/548/549/550
• 9:53am, in chamber
• S1600547 in CR1
• S1600548 in CR2
• S1600549 in CR3
• S1600550 in CR4
• 9:54am roughing pump on
• 10:02am turbo pump on
• Excitations:
• Quiet time before excitation: 1183323620
Quiet time after excitation: 1183323680

• Quiet time before excitation: 1183330910
Quiet time after excitation: 1183330970

• Quiet time before excitation: 1183338200
Quiet time after excitation: 1183338260

• Quiet time before excitation: 1183345490
Quiet time after excitation: 1183345550

• Quiet time before excitation: 1183352780
Quiet time after excitation: 1183352840

• Quiet time before excitation: 1183360070
Quiet time after excitation: 1183360130

• Quiet time before excitation: 1183367360
Quiet time after excitation: 1183367420

• Quiet time before excitation: 1183374650
Quiet time after excitation: 1183374710

## 2017-07-06

• 3:45pm, valve closed, vented, pumps stopped
363   Wed Jul 5 12:01:51 2017 ZachElectronicsModelingForce plots-Correct plots, force issue

# 2017-07-05

• I sorted out my mathematical lapse in logic and computed the correct force profiles in the perpendicular direction in both disks. The issue is that now the force profiles don't match up. The fact that there is a measured force distribution for the E^2 case outside the disk is only an artifact of the numerics because it is being calculated only from the electric field data which is defined outside the sample. It can be easily removed for final plots once the force distributions are matched by either redefining the cut plane or putting a data filter specifically on the E^2 plot. The jumps in the E^2 plot suggest that the meshing is still too large, I will try to fix this first, hopefully it will help resolve the difference.

364   Wed Jul 5 16:40:51 2017 ZachElectronicsModelingForce disparity-improvement

# 2017-07-05

• In order to improve my data I shrunk the region of the finer meshing slightly and made the mesh even smaller and then recalculated the force profiles. This time I tried sampling regions inside the disc rather than immediately at the surface. The attached graphs were sampled at the center of the disc. These two techniques vastly improved the data, now the profiles appear the same, but the magnitudes differ by a factor of 2 again. Previously this was due to an error in my calculation of the force, now I do not believe this to be the case. I will leave my work here for the purposes of my first report, it is an interesting result. I also restricted my data set to the finely meshed box which resolved the earlier data display issue.

365   Thu Jul 6 12:08:35 2017 ZachElectronicsModelingChecking physical parameters

# 2017-07-06

• I compared the electric field and the polarization to make sure that those calculations made sense. Since $P = \epsilon_0 \chi_e E$ due to the linear dielectric, I plotted the electric field and the polarization divided by the proportionality constant and they match exactly.
• This confirms both the constant value and the polarization distribution but gets me no closer to resolving the factor of two

366   Thu Jul 6 12:48:54 2017 ZachElectronicsModelingResolving the factor of two

# 2017-07-06

I resolved the factor of two from Griffiths' discussion of dipoles in non-uniform electric fields. The force on a dipole in a non-uniform field is $\textbf{F}=\textbf{F}_+ + \textbf{F}_-=q(\Delta \textbf{E})$ where $\Delta \textbf{E}$ is the difference in the field between the plus end and the minus end. Component wise, $\Delta E_x = (\nabla E_x) \cdot \textbf{d}$ where d is a unit vector. This holds for y and z, the whole thing can also be written as $\Delta \textbf{E} = (\textbf{d} \cdot \nabla) \textbf{E}$. Since p=qd, we can write $\textbf{F} = (\textbf{p} \cdot \nabla) \textbf{E}$

Jackson derives it differently by deriving the electrostatic energy of a dielectric from the energy of a collection of charges in free space. He then derives the change in energy of a dielectric placed in a fixed source electric field to derive that the energy density w is given by $w = -\frac{1}{2} \textbf{P} \cdot \textbf{E}_0$. This explicity explains the factor of two and is an interesting alternative explanation.

367   Wed Jul 12 15:08:59 2017 ZachElectronicsModelingModel of actuator and sample

# 2017-07-12

• I am attaching the first fully functioning model of the actuator and sample. I cleared both meshes and solutions to make the file a reasonable size, but they can quickly be built/solved again.
Attachment 1: Force_Model.mph
368   Fri Jul 14 16:43:24 2017 ZachElectronicsModelingForce profile matlab script

# 2017-07-14

• I have completed a rough, but functioning script that calculates the modal force profiles. The force values are still coming out incorrect (on the order of 10^14) but the script can take in my model as a .m file and return an array with a force value per mode. I am attaching both the .m file and the matlab script
• I have done very little work with the numerical integration itself, based on the 2D numerical integration code I received I just appended a z component and left it at that so when I return from Livingston I will  fix that component
Attachment 1: forces.m
par.a = 75e-3/2;    % radius [m]
par.h = 1.004e-3;   % thickness [m]
par.E = 73.2e9;     % Young's modulus [Pa]
par.nu = 0.155;     % Poisson's ratio
par.rho = 2202;     % density [kg/m^3]

%Calculate fundamental modes of the disk
[freqs, modes, shapes, x, y] = disk_frequencies(par, 10000, 1, 'shapes', 0.5e-3);

%Now we extract the force profile from the COMSOL model

... 41 more lines ...
Attachment 2: faster.m
function out = model
%
% faster.m
%
% Model exported on Jul 14 2017, 14:47 by COMSOL 5.2.1.262.

import com.comsol.model.*
import com.comsol.model.util.*

model = ModelUtil.create('Model');

... 403 more lines ...
369   Tue Jul 18 09:13:08 2017 GabrieleGeneralMeasurementsShear and bulk losses in tantala

S1600525 has been coated in Fort Collins with 480nm of pure tantala. I used the emasured loss angles (after deposition, before annealing) to estimate the shear and bulk loss angles.

## Model

First, my COMSOL simulation shows that even if I don’t include the drum-like modes, I still have a significant scatter of shear/bulk energy ratio. The top panel shows indeed the ratio shear/bulk for all the modes I can measure, and the variation is quite large. So, contrary to my expectation, there is some room for fitting here. The bottom panel just shows the usual dilution factors.

Then I tried to fit the total losses in my sample (the substrate is negligible) using four different models:
1) one single loss angle for both bulk and shear, constant in frequency
2) one single loss angle for both bulk and shear, linear in frequency
3) separate bulk and shear loss angles, constant
4) separate bulk and shear loss angels, linear in frequency

Instead of using Gregg harry's technique (taking pairs of losses together), I simply fit the whole datasets with the assumptions above. I derived the 95% confidence intervals for all parameters. I also weighed each data point with the experimental uncertainty. I’m not sure yet how to compare the performance of the various models and decide which is the best one, since clearly the more parameters I plug into the model, the better the fit gets.

If I use two different loss angles, but constant, I get numbers similar to what Gregg presented at the last Amaldi conference (G1701225), but inverted in bulk and shear. I cross checked that I didn’t do any mistake. Instead, if I allow linear dependency on frequency of bulk and shear, I get a trend similar to the one in Gregg's slides.

My plan is to have this sample annealed today or tomorrow and measure it again before the end of the week.

## Results

### One loss angle - constant

$\phi = (6.99 \pm 0.05) \times 10^{-4} \mbox{ rad}$

### One loss angle - linear in frequency

$\phi = (6.91 \pm 0.07) \times 10^{-4} +\frac{f-1 \mbox{ kHz}}{1 \mbox{ kHz}} \cdot (3.3 \pm 2.2) \times 10^{-6} \mbox{ rad}$

### Bulk and shear - constant

$\begin{matrix} \phi_{shear} = (6.79 \pm 0.12) \times 10^{-4} \mbox{ rad} \\ \phi_{bulk} = (8.54 \pm 0.98) \times 10^{-4} \mbox{ rad} \end{matrix}$

### Bulk and shear - linear in frequency

$\begin{matrix} \phi_{shear} = (6.9 \pm 0.4) \times 10^{-4} +\frac{f-1 \mbox{ kHz}}{1 \mbox{ kHz}} \cdot (9.9 \pm 7.4) \times 10^{-6} \mbox{ rad} \\ \phi_{bulk} = (6.4 \pm 3.7) \times 10^{-4} +\frac{f-1 \mbox{ kHz}}{1 \mbox{ kHz}} \cdot (-14 \pm 39) \times 10^{-6} \mbox{ rad} \end{matrix}$

370   Wed Jul 19 21:19:14 2017 GabrieleGeneralMeasurementsShear and bulk losses in tantala

To quantify which of the fit below is the most significant, I did a Bayesian analysis (thanks Rory for the help!).

In brief, I compute the Bayes factors for each of the models considered below. As always in any Bayesian analysis, I had to assume some prior distribution for the fit parameters. I used uniform distributions, between 0 and 20e-4 for the loss angles, and between -100e-6 and 100e-6 for the slope. I checked that the intervals I choose for the priors have only a small influence on the results.

The model that has the highest probability is the one that considers different bulk and shear frequency depent loss angles. The others have the following relative probabilities

One loss angle constant:                       1/13e+13
One loss angle linear in frequency:      1/5.5
Bulk/shear angles constant:                  1/48784
Bulk/shear angles linear in frequency: 1/1

So the constant loss angle models are excluded with large significance. The single frequency dependent loss angle is less probable that the bulk/shear frequency dependent model, but only by a factor of 5.5. According to the literature, this is considered a substantial evidence in favor of frequency dependent bulk/shear loss angles.

Quote:

Results

### One loss angle - constant

$\phi = (6.99 \pm 0.05) \times 10^{-4} \mbox{ rad}$

### One loss angle - linear in frequency

$\phi = (6.91 \pm 0.07) \times 10^{-4} +\frac{f-1 \mbox{ kHz}}{1 \mbox{ kHz}} \cdot (3.3 \pm 2.2) \times 10^{-6} \mbox{ rad}$

### Bulk and shear - constant

$\begin{matrix} \phi_{shear} = (6.79 \pm 0.12) \times 10^{-4} \mbox{ rad} \\ \phi_{bulk} = (8.54 \pm 0.98) \times 10^{-4} \mbox{ rad} \end{matrix}$

### Bulk and shear - linear in frequency

$\begin{matrix} \phi_{shear} = (6.9 \pm 0.4) \times 10^{-4} +\frac{f-1 \mbox{ kHz}}{1 \mbox{ kHz}} \cdot (9.9 \pm 7.4) \times 10^{-6} \mbox{ rad} \\ \phi_{bulk} = (6.4 \pm 3.7) \times 10^{-4} +\frac{f-1 \mbox{ kHz}}{1 \mbox{ kHz}} \cdot (-14 \pm 39) \times 10^{-6} \mbox{ rad} \end{matrix}$

371   Thu Jul 20 11:37:01 2017 ZachElectronicsModelingMatlab Script

# 2017-07-20

• I believe my MATLAB script successfully calculates the force distribution into each of the modes specified by the parameters. My previous error was caused by my neglecting the proportionality factor of $\frac{1}{2}\chi_e\epsilon_0$. Now the force order of magnitude is on the order of 103. I am currently unclear how to think about the units of the mode shapes from the disk_frequencies script, but I will pick it apart more carefully and try to figure that out. Then it will be a matter of converting units so that it matches with the N/m^3 from the COMSOL script and then comparing with real lab results. It seems to me that the error in force distribution should be inversely proportional to the number of modes calculated, in which case it would be useful to determine an appropriate number of modes to calculate.
Attachment 1: forces.m
par.a = 75e-3/2;    % radius [m]
par.h = 1.004e-3;   % thickness [m]
par.E = 73.2e9;     % Young's modulus [Pa]
par.nu = 0.155;     % Poisson's ratio
par.rho = 2202;     % density [kg/m^3]

%Calculate fundamental modes of the disk
[freqs, modes, shapes, x, y] = disk_frequencies(par, 10000, 1, 'shapes', 0.5e-3);

%Now we extract the force profile from the COMSOL model

... 27 more lines ...
372   Fri Jul 21 08:42:09 2017 GabrieleGeneralMeasurementsS1600525

## 2017-07-21

• 8:30am, in chamber (CR4)
• 8:32am, roughing pump on
• 8:41am, turbo pump on
• Excitations
• Quiet time before excitation: 1184697303
Quiet time after excitation: 1184697363

• Quiet time before excitation: 1184698593
Quiet time after excitation: 1184698653

• Quiet time before excitation: 1184699883
Quiet time after excitation: 1184699943

• Quiet time before excitation: 1184701173
Quiet time after excitation: 1184701233

• Quiet time before excitation: 1184702463
Quiet time after excitation: 1184702524

• Quiet time before excitation: 1184703754
Quiet time after excitation: 1184703814

• Quiet time before excitation: 1184705044
Quiet time after excitation: 1184705104

• Quiet time before excitation: 1184706334
Quiet time after excitation: 1184706394

## 2017-07-22

• 12:13pm, valve closed, pumps off
373   Fri Jul 21 14:55:02 2017 GabrieleGeneralMeasurementsShear and bulk losses in annealed tantala

I repeated the analysis for bulk and shear losses described in an early elog entry, with the same coating, but after annealing at 500C for 9 hours.

The COMSOL model is the same as before, so the dilution factors are the same, except that this time I could measure a few more modes at high frequency:

As in the previous analysis, I fitted four different models:
1) one single loss angle for both bulk and shear, constant in frequency
2) one single loss angle for both bulk and shear, linear in frequency
3) separate bulk and shear loss angles, constant
4) separate bulk and shear loss angles, linear in frequency

The data strongly favor the last model: two loss angles for shear and bulk, linearly dependent on frequency (Bayes factor -22.7 for the second best model, which is the frequency dependent single loss angle).

The results are below.

## Single constant loss angle

$\phi = (3.95 \pm 0.08) \times 10^{-4} \mbox{ rad}$

## Single loss angle, linearly dependent on frequency

$\phi = (3.69 \pm 0.17) \times 10^{-4} + \frac{f-1 kHz}{1 kHz} (4.6 \pm 0.3)\times 10^{-6} \mbox{ rad}$

## Bulk and shear loss angles, constant

$\begin{array}{l} \phi_{shear} = (3.4 \pm 0.5) \times 10^{-4} \mbox{ rad} \\ \phi_{bulk} = (7.3 \pm 3.3) \times 10^{-4} \mbox{ rad} \\ \end{array}$

## Bulk and shear loss angles, linearly dependent on frequency

$\begin{array}{l} \phi_{shear} = (3.58 \pm 0.15) \times 10^{-4} + \frac{f - 1 kHz}{1 kHz} (6.1 \pm 2.4) \times 10^{-6} \mbox{ rad} \\ \phi_{bulk} = (4.5 \pm 1.2) \times 10^{-4} + \frac{f - 1 kHz}{1 kHz} (-7 \pm 16) \times 10^{-6} \mbox{ rad} \\ \end{array}$

Attachment 7: postannealing_linear_bulk_shear.png
374   Sat Jul 22 13:05:46 2017 GabrieleGeneralMeasurementsS1600533 S1600535 S1600536 S1600547

## 2017-07-22

• 12:55pm in chamber
• S1600533 in CR1
• S1600535 in CR2
• S1600536 in CR3
• S1600547 in CR4
• 12:57pm roughing pump on
• 1:05pm turbo pump on
• Excitations
• Quiet time before excitation: 1184803575
Quiet time after excitation: 1184803636

• Quiet time before excitation: 1184804866
Quiet time after excitation: 1184804926

• Quiet time before excitation: 1184806156
Quiet time after excitation: 1184806216

• Quiet time before excitation: 1184807446
Quiet time after excitation: 1184807506

• Quiet time before excitation: 1184808736
Quiet time after excitation: 1184808796

• Quiet time before excitation: 1184810027
Quiet time after excitation: 1184810087

• Quiet time before excitation: 1184811317
Quiet time after excitation: 1184811377

• Quiet time before excitation: 1184812607
Quiet time after excitation: 1184812667

• More excitations

• Quiet time before excitation: 1184878758
Quiet time after excitation: 1184878819

• Quiet time before excitation: 1184880049
Quiet time after excitation: 1184880109

• Quiet time before excitation: 1184881339
Quiet time after excitation: 1184881399

• Quiet time before excitation: 1184882629
Quiet time after excitation: 1184882689

• Quiet time before excitation: 1184883919
Quiet time after excitation: 1184883979

• Quiet time before excitation: 1184885210
Quiet time after excitation: 1184885270

• Quiet time before excitation: 1184886500
Quiet time after excitation: 1184886561

• Quiet time before excitation: 1184887791
Quiet time after excitation: 1184887851

## 2017-07-24

• 3:28pm valve closed, venting

375   Mon Jul 24 09:13:45 2017 ZachElectronicsModelingParametric Sweep

# 2017-07-24

• I wrote a MATLAB script that is capable of sweeping parameters, the code is attached. The next step is to create nested loops so that I can sweep multiple parameters in a single run. I also should add a function in the script to eliminate the modes that cannot be measured by the experimental setup.
• My first sweep was for the gap between electrodes and swept from 1 to 2 mm. In the plot the gap grows from steps 1 to 6 and the only obvious effect in the plot is a decrease in force from the highest mode. Intuitively it makes sense that a wider gap would decrease the force because the electric field is diminished by spreading out the electrodes.
• I would like to add a parameter for the overlap of the electrodes, but this would require substantial redesigning of the COMSOL model due to the multilevel dependency on parameters.

Attachment 2: forcesweep.m
fpro = zeros(6, 27);
no = 1;
for count = 1:.2:2
gap = strcat(num2str(count), ' [mm]')
model = fst2(gap);
forces;
fpro(no, :)= product(:);
no = no + 1;
end
376   Mon Jul 24 16:06:11 2017 GabrieleGeneralMeasurementsS1600530 S1600532 S1600537 S1600539

## 2017-07-24

• 3:55pm installed in chamber
• S1600530 in CR1
• S1600532 in CR2
• S1600537 in CR3
• S1600539 in CR4
• 3:58pm roughing pump on
• 4:06pm turbo pump on
• Excitations:
• Quiet time before excitation: 1184986754
Quiet time after excitation: 1184986814

• Quiet time before excitation: 1184988044
Quiet time after excitation: 1184988104

• Quiet time before excitation: 1184989334
Quiet time after excitation: 1184989394

• Quiet time before excitation: 1184990625
Quiet time after excitation: 1184990685

• Quiet time before excitation: 1184991915
Quiet time after excitation: 1184991975

• Quiet time before excitation: 1184993205
Quiet time after excitation: 1184993265

• Quiet time before excitation: 1184994495
Quiet time after excitation: 1184994555

• Quiet time before excitation: 1184995785
Quiet time after excitation: 1184995845

## 2017-07-25

• 11:00am valve closed, pumps stopped, venting
377   Tue Jul 25 11:22:37 2017 GabrieleGeneralMeasurementsS1600548 S1600550 S1600538

## 2017-07-25

• 11:12am in chamber (non standard order is not a typo!!)
• S1600548 in CR1
• S1600550 in CR2
• S1600538 in CR3
• 11:13am roughing pump on
• 11:22am turbo pump on
• Excitations:
• Quiet time before excitation: 1185056320
Quiet time after excitation: 1185056380

• Quiet time before excitation: 1185057610
Quiet time after excitation: 1185057670

• Quiet time before excitation: 1185058900
Quiet time after excitation: 1185058960

• Quiet time before excitation: 1185060190
Quiet time after excitation: 1185060251

• Quiet time before excitation: 1185061481
Quiet time after excitation: 1185061541

• Quiet time before excitation: 1185062771
Quiet time after excitation: 1185062831

• Quiet time before excitation: 1185064061
Quiet time after excitation: 1185064121

• Quiet time before excitation: 1185065351
Quiet time after excitation: 1185065411

## 2017-07-26

• 4:05pm valve closed, pumps stopped, venting
378   Tue Jul 25 13:38:30 2017 ZachElectronicsModelingParametric Sweep of ESD gap

# 2017-07-25

• I completed a short sweep of the gap between the drive and the sample, between .5 and 1 mm in .1 mm increments. It appears that a 1 mm distance is the ideal distance by approximately a factor of two. I will next sweep larger distances and see how the force profile behaves at greater distances.

379   Wed Jul 26 09:27:40 2017 ZachElectronicsModelingSweeping the space between ESD and sample

# 2017-07-26

• I ran a sweep of the gap between the ESD and the sample, first from .5 mm to 1 mm. That sweep suggested that there is a significant jump in force across almost all of the modes at 1 mm. To confirm this I double checked the geometry and it appears that COMSOL is building everything as expected when changing the spacing parameter. Then I ran a finer sweep in .02 mm increments for the spacing between .9 and 1.1 mm. Once again it appears there is a large jump as the gap approaches 1 mm, but the behavior does not seem to be symmetric about that point, the force appears to diminish linearly as the gap increases beyond 1 mm. I will run a sweep of the ESD arm spacing along with the vertical gap to confirm that the jump occurs when the gap between the ESD and the sample is equivalent to the spacings between the ESD arms.

Attachment 1: Gap_near_one.jpg
380   Wed Jul 26 16:22:22 2017 GabrieleGeneralMeasurementsS1600528 S1600531

## 2017-07-26

• 4:14pm in chamber
• S1600528 in CR1
• S1600531 in CR2
• 4:16pm roughing pump on
• 4:23pm turbo pump on
• Excitations
• Quiet time before excitation: 1185160841
Quiet time after excitation: 1185160901

• Quiet time before excitation: 1185168131
Quiet time after excitation: 1185168192

• Quiet time before excitation: 1185175422
Quiet time after excitation: 1185175482

• Quiet time before excitation: 1185182712
Quiet time after excitation: 1185182772

• Quiet time before excitation: 1185190002
Quiet time after excitation: 1185190063

• Quiet time before excitation: 1185197293
Quiet time after excitation: 1185197354

## 2017-07-27

• 4:30pm, valve closed, pumps stopped, vented
381   Wed Jul 26 21:22:50 2017 ZachElectronicsModelingParametric Sweep Results

# 2017-07-26

• I resolved the major bugs in the parametric sweep scripts and ran low resolution sweeps of the gap between the ESD and sample (Gap Sweep) and the spacing between the ESD arms (ESD Arm Gap Sweep).
• The arm gap sweep largely behaved in a reasonable way with a maximum excitation at a 1.25 mm gap. However modes 14, 19, and 25 did not follow the general trends and had sharp drops and increases compared to the other modes.
• The sample gap sweep had less intuitive behavior, all of the modes followed the same general double peak trend that drops to zero when the gap is 1.5 mm. I cannot explain exactly why it is behaving that way, I will run a higher resolution sweep and examine the geometry in greater detail.

382   Thu Jul 27 13:37:31 2017 ZachElectronicsModelingCorrected sample gap sweep

# 2017-07-27

• I resolved a couple more data processing bugs and calculated a sweep of the ESD-Sample gap from a distance of .5 mm to 1.5 mm. The resulting data behaves far more like I would expect from a force generated by an electric field, it seems to drop off like distance squared. This is a very strong correlation with a good intuitive explanation, and would suggest that it is prudent to place the ESD as close to the sample as possible.
• I also computed a higher resolution sweep of the gap between the arms of the ESD. It did not resolve the strange behavior at all, so I will investigate coupling into the mode pairs as a possible source.

Attachment 1: Fine_sample_gap.jpg
Attachment 3: fine_arm_gap.jpg
383   Thu Jul 27 16:56:03 2017 ZachElectronicsModelingOffset Sweep

# 2017-07-27

• I ran a low resolution sweep of the offset in the arms of the ESD, the space between the end of the arm and base of the opposite combs. The trends are much more subtle and are not coherent across as many of the modes. The lower frequency modes decrease slightly, while the force in the higher frequency modes increase more drastically. This is an interesting parameter, I will definitely run another sweep once I have written code that accounts for the mode pairs. Assuming the apparent trends are physically accurate, this could be a useful parameter because a greater offset gives a greater relative increase to the higher order modes while still leaving a substantial force on the lower order modes that are excited more easily anyway.

Attachment 1: Offset.jpg
384   Mon Jul 31 13:21:37 2017 Gabriele, RosalieGeneralMeasurementsS1600520 S1600521 S1600523 S1600524

## 2017-07-31

• 1:20pm in chamber
• S1600520 in CR1
• S1600521 in CR2
• S1600523 in CR3
• S1600524 in CR4
• 1:21pm roughinp pump on
• 1:30pm turbo pump on
• Excitations:
• Quiet time before excitation: 1185582780
Quiet time after excitation: 1185582840

• Quiet time before excitation: 1185584070
Quiet time after excitation: 1185584130

• Quiet time before excitation: 1185585360
Quiet time after excitation: 1185585420

• Quiet time before excitation: 1185586650
Quiet time after excitation: 1185586710

• Quiet time before excitation: 1185587940
Quiet time after excitation: 1185588000

• Quiet time before excitation: 1185589230
Quiet time after excitation: 1185589290

• Quiet time before excitation: 1185590520
Quiet time after excitation: 1185590581

• Quiet time before excitation: 1185591811
Quiet time after excitation: 1185591871

## 2017-08-01

• 9:55am, valve closed, venting, pumps off
385   Tue Aug 1 10:19:39 2017 Gabriele, RosalieGeneralMeasurementsS1600519, S1600522

## 2017-08-01

• 10:05am, in chamber
• S1600519 in CR1
• S1600522 in CR2
• 10:11am, roughing pump on
• 10:19am, turbo pump on
• Excitations
• Quiet time before excitation: 1185649996
Quiet time after excitation: 1185650056

• Quiet time before excitation: 1185651286
Quiet time after excitation: 1185651346

• Quiet time before excitation: 1185652576
Quiet time after excitation: 1185652636

• Quiet time before excitation: 1185653866
Quiet time after excitation: 1185653926

• Quiet time before excitation: 1185655156
Quiet time after excitation: 1185655216

• Quiet time before excitation: 1185656446
Quiet time after excitation: 1185656506

• Quiet time before excitation: 1185657737
Quiet time after excitation: 1185657797

## 2017-08-02

• 11:25am valve closed, venting, pumps off
386   Tue Aug 1 16:10:42 2017 ZachElectronicsModelingImproved Gap Sweep

# 2017-08-01

• I completed an improved sweep of the gap between the ESD arms. I resolved some code issues, since it was passing the maximum value not the most extreme, smaller magnitude positive values were being included rather than the strongest force calculation.
• There are still three modes that show unique behavior relative to the others: 14, 19, and 25. Mode 14 is the (2,2), mode 19 is the (2,3) and mode 25 is (3,2).
• Plots of the mode shapes are included for reference. The black rectangle represents the region covered by the ESD.

387   Wed Aug 2 11:45:27 2017 Gabriele, RosalieGeneralMeasurementsS1600553, S1600554, S1600555, S1600556

## 2017-08-02

• 11:33am in chamber
• S1600553 in CR1
• S1600554 in CR2
• S1600555 in CR3
• S1600556 in CR4
• 11:35am roughing pump on
• 11:45am turbo pump on
• Excitations:
• Quiet time before excitation: 1185760223
Quiet time after excitation: 1185760283

• Quiet time before excitation: 1185767513
Quiet time after excitation: 1185767573

• Quiet time before excitation: 1185774804
Quiet time after excitation: 1185774864

• Quiet time before excitation: 1185782094
Quiet time after excitation: 1185782154

• Quiet time before excitation: 1185789384
Quiet time after excitation: 1185789444

• Quiet time before excitation: 1185796675
Quiet time after excitation: 1185796735

## 2017-08-03

• 11:00am valve closed, pumps stopped, venting
388   Wed Aug 2 13:47:47 2017 ZachElectronicsModelingArm width Sweep

# 2017-08-02

• I ran a sweep of the width of the ESD arms. There appears to be a linear relationship across the modes except for mode 25. Mode 25 exhibits a very similar behavior as in the arm gap sweep. I realized that the abrupt change in direction (also noticeable in mode 14) is likely caused by the fact that the force profile is calculated as absolute value, there might be an exponential relationship that gets converted into that shape by the absolute value function.

389   Wed Aug 2 15:40:00 2017 ZachElectronicsModelingParameter diagram

I am posting a diagram of the geometric parameters that I swept. The only one not included is the vertical space between the ESD and sample that sweeps perpendicularly out of the image

390   Thu Aug 3 11:55:18 2017 Gabriele, RosalieGeneralMeasurementsS1600520 S1600521 S1600523 S1600524

## 2017-08-03

• 11:43am in chamber
• S1600520 in CR1
• S1600521 in CR2
• S1600523 in CR3
• S1600524 in CR4
• 11:46am roughing pump on
• 11:55am turbo pump on
• Excitations:
• Quiet time before excitation: 1185835692
Quiet time after excitation: 1185835752

• Quiet time before excitation: 1185837582
Quiet time after excitation: 1185837642

• Quiet time before excitation: 1185839472
Quiet time after excitation: 1185839532

• Quiet time before excitation: 1185841362
Quiet time after excitation: 1185841422

• Quiet time before excitation: 1185843252
Quiet time after excitation: 1185843312

• Quiet time before excitation: 1185845143
Quiet time after excitation: 1185845203

• Quiet time before excitation: 1185847033
Quiet time after excitation: 1185847093

• Quiet time before excitation: 1185848923
Quiet time after excitation: 1185848983

## 2017-08-04

• 2:00pm valve closed, pumps off, venting
391   Fri Aug 4 14:15:16 2017 Gabriele, RosalieGeneralMeasurementsS1600535, S1600536, S1600537, S1600538

## 2017-08-04

• 2:04pm in chamber
• S1600535 in CR1
• S1600536 in CR2
• S1600537 in CR3
• S1600538 in CR4
• 2:06pm roughing pump on
• 2:15pm turbo pump on
• Excitations:
• Quiet time before excitation: 1185930952
Quiet time after excitation: 1185931013

• Quiet time before excitation: 1185932843
Quiet time after excitation: 1185932903

• Quiet time before excitation: 1185934733
Quiet time after excitation: 1185934793

• Quiet time before excitation: 1185936623
Quiet time after excitation: 1185936683

• Quiet time before excitation: 1185938513
Quiet time after excitation: 1185938573

• Quiet time before excitation: 1185940403
Quiet time after excitation: 1185940463

• Quiet time before excitation: 1185942293
Quiet time after excitation: 1185942353

• Quiet time before excitation: 1185944183
Quiet time after excitation: 1185944243

## 2017-08-05

• 1:23pm valve closed, pumps stopped, venting

392   Sat Aug 5 13:46:08 2017 GabrieleGeneralMeasurementsS1600539 S1600547 S1600548 S1600550

## 2017-08-05

• 1:37pm in chamber
• S1600539 in CR1
• S1600547 in CR2
• S1600548 in CR3
• S1600550 in CR4
• 1:39pm roughing pump on
• 1:47pm turbo pump on
• Excitations
• Quiet time before excitation: 1186015242
Quiet time after excitation: 1186015303

• Quiet time before excitation: 1186017133
Quiet time after excitation: 1186017193

• Quiet time before excitation: 1186019023
Quiet time after excitation: 1186019083

• Quiet time before excitation: 1186020913
Quiet time after excitation: 1186020973

• Quiet time before excitation: 1186022803
Quiet time after excitation: 1186022863

• Quiet time before excitation: 1186024694
Quiet time after excitation: 1186024754

• Quiet time before excitation: 1186026584
Quiet time after excitation: 1186026644

• Quiet time before excitation: 1186028474
Quiet time after excitation: 1186028534

## 2017-08-07

• 10:23am, valve closed, pumps off, venting
393   Mon Aug 7 10:44:53 2017 GabrieleGeneralMeasurementsS1600525 S1600530 S1600532 S1600533

## 2017-08-07

• 10:36am in chamber
• S1600525 in CR1
• S1600530 in CR2
• S1600532 in CR3
• S1600533 in CR4
• 10:38am roughing pump on
• 10:46am turbo pump on
• Excitations
• Quiet time before excitation: 1186171948
Quiet time after excitation: 1186172008

• Quiet time before excitation: 1186173838
Quiet time after excitation: 1186173899

• Quiet time before excitation: 1186175729
Quiet time after excitation: 1186175789

• Quiet time before excitation: 1186177619
Quiet time after excitation: 1186177679

• Quiet time before excitation: 1186179510
Quiet time after excitation: 1186179570

• Quiet time before excitation: 1186181400
Quiet time after excitation: 1186181460

• Quiet time before excitation: 1186183290
Quiet time after excitation: 1186183350

• Quiet time before excitation: 1186185180
Quiet time after excitation: 1186185240

## 2017-08-08

• 10:58am, valve closed, pumps stopped, venting
394   Mon Aug 7 13:19:48 2017 ZachElectronicsModelingNormalized data

# 2017-08-07

• I included the modal mass factors in the code and renormalized my data. The normalization has a noticeable impact, but does not change the general trends of the data
• In fact the impact is not even significant enough to warrant a change in the ideal parameters I picked for the rectangular ESD in my interim report

Attachment 1: Arm_gap.pdf
Attachment 2: Arm_width.pdf
Attachment 3: Offset.pdf
Attachment 4: Sample_Gap.pdf
395   Tue Aug 8 09:58:34 2017 GabrieleGeneralMeasurementsEffect of assist beam on tantala coatings - no post deposition annealing

## ntroduction

A set of substrates have been coated by the Colorado State University Fort Collins group, with ~500 nm tantala and various ion assist beam parameters. Here's a table summarizing the depositions parameter, by Le Yang

 substrate main ion source voltage / V main ion source current / mA main ion source Ar flow / sccm target oxygen flow / sccm assist ion source voltage / V assist ion source current / mA assist ion source gas/sccm thickness / nm abs / ppm notes Ar O2 s1600525 1250 600 18 49 100 100 12.5 0 480 s1600535 1250 600 18 49 100 100 12.5 0 541 7.2 s1600536 1250 600 18 49 100 100 3.5 9 532 20.2 s1600537 1250 600 18 49 100 100 6.5 6 534 damaged by holder s1600538 1250 600 18 49 100 100 6.5 6 524 scratch s1600547 1250 600 18 49 100 100 6.5 6 528 15.4 s1600532 1250 600 18 49 200 100 12.5 0 518 17.8 s1600539 1250 600 18 49 200 100 3.5 9 541 17.7 s1600533 1250 600 18 49 200 100 6.5 6 539 11.6 s1600530 1250 600 18 49 100 200 12.5 0 537 10.3 s1600550 1250 600 18 49 100 200 3.5 9 519 19.9 s1600548 1250 600 18 49 100 200 6.5 6 532 17.2

## Coating losses before annealing

The plot below shows the measured loss angle for all modes of all samples, before annealing. The error bars for the datapoints are from the 95% confidence intervals computed from 8 measurements each. The red line is the average value over frequencies, and the shaded red area gives the 95% confidence interval of the mean value. The loss angle seems reasonably indipendent of frequency.

The following pot then shows the averaged loss angle as a function of the serial number, for reference

There are three main parameters that are changed in the deposition: the assist beam voltage, the assist beam current and the content of oxygen in the assist beam. The plots below show the losses as a function of those parameters. The x axis changes in each of the four panels, and for each plot, the color code is linked to one of the process variables:

## Conclusions

Quoting Le Yang and Carmen Menoni

1. under certain conditions as oxygen flow increase and Ar flow decrease, the loss angle becomes worse
2. with existence of oxygen ions the loss is mitigated by increase of beam voltage
3. relatively small particle size of oxygen compared with argon the caused the less effective interaction between assist ions and coating adatoms on the surface
4. with increase of ion dose, the mechanical loss drops
396   Tue Aug 8 10:18:30 2017 GabrieleGeneralMeasurementsEffect of assist beam on tantala coatings - after post deposition annealing

## Introduction

The same set of samples described in the previous entry have been annealed at 500C for 9 hours. Then the loss angles have been measured again.

## Results

The plot below shows the measured loss angle for all modes and all samples. After annealing all loss angles are significantly decreased, and they also show an increasing trend with frequency. As before, the blue points are the measurement points (averages of 8 ring-downs each) and the error bars are computed from the statistical error of the measurments. The red line shows the average of the loss angles for frequencies below 15 kHz, weigthed with the data points uncertainties. The red shaded area shows the 95% confidence interval of the mean.

If we plot the frequency-averaged loss angle as a function of the serial number, we see that there isn't much of a spread in the values:

We can again plot the loss angle as a function of the process variables. There are three main parameters that are changed in the deposition: the assist beam voltage, the assist beam current and the content of oxygen in the assist beam. The plots below show the losses as a function of those parameters. The x axis changes in each of the four panels, and for each plot, the color code is linked to one of the process variables:

This time I can't see much of a trend anywhere in those plots.

## Linear fit

Since the loss angles show a clear increasing trend with frequency, instead of computing the mean value, I fit each dataset with a linear dependency on the frequency. To improve the fit I restricted the computations only to frequencies below 12 kHz. The results are shown below

The following plot shows the fitted loss angle at 1 kHz, as a function of the serial number. There is more spread in the results than when using the simple average:

And again, the dependency of the loss angle at 1 kHz on the process parameters:

The lowest loss angle is obtaine on sample S1600525, which was deposited without oxygen, low current and low voltage. But it's also the one sample that was deposited in a precedent separate run, and annealed twice at 500C.

397   Tue Aug 8 11:21:19 2017 GabrieleGeneralMeasurementsS1600557 S1600558 S1600559 S1600560

## 2017-08-08

• 11:10am in chamber
• S1600557 in CR1
• S1600558 in CR2
• S1600559 in CR3
• S1600560 in CR4
• 11:13am roughing pump on
• 11:21am turbo pump on
• Excitation:
• Quiet time before excitation: 1186262071
Quiet time after excitation: 1186262131

• Quiet time before excitation: 1186269362
Quiet time after excitation: 1186269422

• Quiet time before excitation: 1186276652
Quiet time after excitation: 1186276712

• Quiet time before excitation: 1186283942
Quiet time after excitation: 1186284002

• Quiet time before excitation: 1186291232
Quiet time after excitation: 1186291292

• Quiet time before excitation: 1186298522
Quiet time after excitation: 1186298582

## 2017-08-15

• 10:04am, pumps off, valve closed, venting

398   Tue Aug 8 16:20:24 2017 ZachElectronicsModelingRotated ESD

# 2017-08-08

• I rotated the ESD and calculated it's modal projections by rotating the data array that MATLAB extracts from COMSOL. I confirmed that this was properly done by plotting the profile and then computed and plotted both the rotated and normal projections.
• The rotated ESD actually increases the force in some of the modes but decreases the forces in others. It markedly improved the force in 7 of the modes: 3, 6, 12, 18, 19, 22, and 26 while being quite weaker in about 4 of the modes: 9, 13, 14, and 15. This suggests that it may actually be useful to rotate the ESD as it excites some of the higher order modes a noticeable amount more. I am including plots of both modal profiles as well as a chart with mode numbers, shapes, and frequencies.

Attachment 1: ESD.pdf
Attachment 2: Rotated.pdf
Attachment 3: resonantmodes.pdf
399   Wed Aug 9 12:10:47 2017 ZachElectronicsModelingPreliminary improvement from ESD optimization

# 2017-08-09

• I created a plot of the ratio of the force in the optimized design to the force in the original design. The improvement factor is huge, some modes are excited by more than a factor of 100. I took the same ratio keeping the gap between the ESD and the sample constant and it decreased the excitation by almost a factor of 10. Keeping that gap constant, the geometric modifications to the ESD give an improvement factor ranging from almost 2 to almost 4 for most of the modes. Modes 10 and 25 are outliers but in the original geometry they are barely excited at all, so this could easily be a numerical artifact where those modes were excited at a minimum in the original geometry.

Attachment 1: Ratio.jpg
400   Wed Aug 9 15:57:28 2017 ZachElectronicsModelingTriangular Geometry

# 2017-08-09

• I compared the triangular geometry to the original geometry and the excitation was only improved in 7 of the of 20 modes. In four of those modes the improvement factors ranged from almost 2 to over 3 while the other modes where only improved by about 25%. The other 13 modes were diminished drastically, 9 of them where less than half as excited. Given more time it may have been interesting to try and optimize the geometry of a triangular drive, but that would easily take the better part of a week.

401   Wed Aug 9 17:07:57 2017 ZacharyElectronicsModelingOptimization Summary

# 2017-08-09

• From the data I have gathered from a variety of MATLAB sweeps, I think that the optimal geometry I can produce has the parameters in the attached image. Neither the original or optimized drawing is to scale. The gap between the arms of the electrodes should be 1.25 mm, the arm width 0.55 mm, the arm length 16 mm, and the offset of the arms 3.5 mm.

• It is also optimal to place the ESD as close to the sample disk as can reasonably be achieved, at around 0.5 mm away. Since the force on the disk scales exponentially with the distance from the ESD, decreasing that gap is the most substantial way to impact the excitation. Decreasing the gap from 1 mm to .5 mm increases the excitation of the modes by approximately a factor of 8.

• From my simulations, the shift in geometry alone still has a useful impact on the excitation. Modes 1 and 3 are the only two modes that are less excited by the new geometry, mode 1 is 10% weaker  and mode 5 is 5% weaker. Modes 5 and 6 are nearly unaffected by the shift, mode 5 is 2% stronger and mode 6 is 5% stronger.  Modes 7, 18 and 19 are outliers, 7 is excited by a factor of 7, 18 by a factor of 4 and 19 by a factor of 17. The rest of the modes are improved by between a factor of 1.5 and 3. For mode numbers, shapes, and frequencies a plot is included.

Attachment 1: resonantmodes.pdf
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