2017-06-22

S1600541 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
  Excitation broadband: 1182524237
  Quiet time after excitation: 1182524262
- Quiet time before excitation: 1182535092
  Excitation broadband: 1182535127
  Quiet time after excitation: 1182535152
- Quiet time before excitation: 1182545982
  Excitation broadband: 1182546017
  Quiet time after excitation: 1182546042
- Quiet time before excitation: 1182556872
  Excitation broadband: 1182556907
  Quiet time after excitation: 1182556932
- Quiet time before excitation: 1182567762
  Excitation broadband: 1182567797
  Quiet time after excitation: 1182567822
- Quiet time before excitation: 1182578652
  Excitation broadband: 1182578687
  Quiet time after excitation: 1182578712
- Quiet time before excitation: 1182589542
  Excitation broadband: 1182589577
  Quiet time after excitation: 1182589602
- Quiet time before excitation: 1182600432
  Excitation broadband: 1182600467
  Quiet time after excitation: 1182600492

2017-06-28

3:36pm, valve closed, vented, pumps stopped

355

Tue Jun 27 09:20:16 2017

Alena

Annealing run (546-551) on 3" wafers - Crime 06/27/2017

Annealing

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

Will be ready by June 28th afternoon

356

Tue Jun 27 14:17:47 2017

Further 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

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, Gabriele

Laser polishing

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

359

Thu Jun 29 16:40:41 2017

Accurate 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

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

Double 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*10⁶which 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

S1600547 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
  Excitation broadband: 1183323655
  Quiet time after excitation: 1183323680
- Quiet time before excitation: 1183330910
  Excitation broadband: 1183330945
  Quiet time after excitation: 1183330970
- Quiet time before excitation: 1183338200
  Excitation broadband: 1183338235
  Quiet time after excitation: 1183338260
- Quiet time before excitation: 1183345490
  Excitation broadband: 1183345525
  Quiet time after excitation: 1183345550
- Quiet time before excitation: 1183352780
  Excitation broadband: 1183352815
  Quiet time after excitation: 1183352840
- Quiet time before excitation: 1183360070
  Excitation broadband: 1183360105
  Quiet time after excitation: 1183360130
- Quiet time before excitation: 1183367360
  Excitation broadband: 1183367395
  Quiet time after excitation: 1183367420
- Quiet time before excitation: 1183374650
  Excitation broadband: 1183374685
  Quiet time after excitation: 1183374710

2017-07-06

3:45pm, valve closed, vented, pumps stopped

363

Wed Jul 5 12:01:51 2017

Force 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

Force 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

Checking 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

Resolving 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

Model 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

Force 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

Shear 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

Shear 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

371

Thu Jul 20 11:37:01 2017

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

2017-07-21

8:30am, in chamber (CR4)
8:32am, roughing pump on
8:41am, turbo pump on
Excitations
- Quiet time before excitation: 1184697303
  Excitation broadband: 1184697338
  Quiet time after excitation: 1184697363
- Quiet time before excitation: 1184698593
  Excitation broadband: 1184698628
  Quiet time after excitation: 1184698653
- Quiet time before excitation: 1184699883
  Excitation broadband: 1184699918
  Quiet time after excitation: 1184699943
- Quiet time before excitation: 1184701173
  Excitation broadband: 1184701208
  Quiet time after excitation: 1184701233
- Quiet time before excitation: 1184702463
  Excitation broadband: 1184702499
  Quiet time after excitation: 1184702524
- Quiet time before excitation: 1184703754
  Excitation broadband: 1184703789
  Quiet time after excitation: 1184703814
- Quiet time before excitation: 1184705044
  Excitation broadband: 1184705079
  Quiet time after excitation: 1184705104
- Quiet time before excitation: 1184706334
  Excitation broadband: 1184706369
  Quiet time after excitation: 1184706394

2017-07-22

12:13pm, valve closed, pumps off

373

Fri Jul 21 14:55:02 2017

Shear 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

S1600533 S1600535 S1600536 S1600547

2017-07-22

12:55pm in chamber
- S1600533 in CR1
- S1600535 in CR2
- S1600536 in CR3
- S1600547 in CR4
Added neutral densities
12:57pm roughing pump on
1:05pm turbo pump on
Excitations
- Quiet time before excitation: 1184803575
  Excitation broadband: 1184803611
  Quiet time after excitation: 1184803636
- Quiet time before excitation: 1184804866
  Excitation broadband: 1184804901
  Quiet time after excitation: 1184804926
- Quiet time before excitation: 1184806156
  Excitation broadband: 1184806191
  Quiet time after excitation: 1184806216
- Quiet time before excitation: 1184807446
  Excitation broadband: 1184807481
  Quiet time after excitation: 1184807506
- Quiet time before excitation: 1184808736
  Excitation broadband: 1184808771
  Quiet time after excitation: 1184808796
- Quiet time before excitation: 1184810027
  Excitation broadband: 1184810062
  Quiet time after excitation: 1184810087
- Quiet time before excitation: 1184811317
  Excitation broadband: 1184811352
  Quiet time after excitation: 1184811377
- Quiet time before excitation: 1184812607
  Excitation broadband: 1184812642
  Quiet time after excitation: 1184812667
More excitations
- Quiet time before excitation: 1184878758
  Excitation broadband: 1184878794
  Quiet time after excitation: 1184878819
- Quiet time before excitation: 1184880049
  Excitation broadband: 1184880084
  Quiet time after excitation: 1184880109
- Quiet time before excitation: 1184881339
  Excitation broadband: 1184881374
  Quiet time after excitation: 1184881399
- Quiet time before excitation: 1184882629
  Excitation broadband: 1184882664
  Quiet time after excitation: 1184882689
- Quiet time before excitation: 1184883919
  Excitation broadband: 1184883954
  Quiet time after excitation: 1184883979
- Quiet time before excitation: 1184885210
  Excitation broadband: 1184885245
  Quiet time after excitation: 1184885270
- Quiet time before excitation: 1184886500
  Excitation broadband: 1184886536
  Quiet time after excitation: 1184886561
- Quiet time before excitation: 1184887791
  Excitation broadband: 1184887826
  Quiet time after excitation: 1184887851

2017-07-24

3:28pm valve closed, venting

375

Mon Jul 24 09:13:45 2017

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

S1600530 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
  Excitation broadband: 1184986789
  Quiet time after excitation: 1184986814
- Quiet time before excitation: 1184988044
  Excitation broadband: 1184988079
  Quiet time after excitation: 1184988104
- Quiet time before excitation: 1184989334
  Excitation broadband: 1184989369
  Quiet time after excitation: 1184989394
- Quiet time before excitation: 1184990625
  Excitation broadband: 1184990660
  Quiet time after excitation: 1184990685
- Quiet time before excitation: 1184991915
  Excitation broadband: 1184991950
  Quiet time after excitation: 1184991975
- Quiet time before excitation: 1184993205
  Excitation broadband: 1184993240
  Quiet time after excitation: 1184993265
- Quiet time before excitation: 1184994495
  Excitation broadband: 1184994530
  Quiet time after excitation: 1184994555
- Quiet time before excitation: 1184995785
  Excitation broadband: 1184995820
  Quiet time after excitation: 1184995845

2017-07-25

11:00am valve closed, pumps stopped, venting

377

Tue Jul 25 11:22:37 2017

S1600548 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
  Excitation broadband: 1185056355
  Quiet time after excitation: 1185056380
- Quiet time before excitation: 1185057610
  Excitation broadband: 1185057645
  Quiet time after excitation: 1185057670
- Quiet time before excitation: 1185058900
  Excitation broadband: 1185058935
  Quiet time after excitation: 1185058960
- Quiet time before excitation: 1185060190
  Excitation broadband: 1185060226
  Quiet time after excitation: 1185060251
- Quiet time before excitation: 1185061481
  Excitation broadband: 1185061516
  Quiet time after excitation: 1185061541
- Quiet time before excitation: 1185062771
  Excitation broadband: 1185062806
  Quiet time after excitation: 1185062831
- Quiet time before excitation: 1185064061
  Excitation broadband: 1185064096
  Quiet time after excitation: 1185064121
- Quiet time before excitation: 1185065351
  Excitation broadband: 1185065386
  Quiet time after excitation: 1185065411

2017-07-26

4:05pm valve closed, pumps stopped, venting

378

Tue Jul 25 13:38:30 2017

Parametric 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

Sweeping 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

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
  Excitation broadband: 1185160876
  Quiet time after excitation: 1185160901
- Quiet time before excitation: 1185168131
  Excitation broadband: 1185168167
  Quiet time after excitation: 1185168192
- Quiet time before excitation: 1185175422
  Excitation broadband: 1185175457
  Quiet time after excitation: 1185175482
- Quiet time before excitation: 1185182712
  Excitation broadband: 1185182747
  Quiet time after excitation: 1185182772
- Quiet time before excitation: 1185190002
  Excitation broadband: 1185190038
  Quiet time after excitation: 1185190063
- Quiet time before excitation: 1185197293
  Excitation broadband: 1185197329
  Quiet time after excitation: 1185197354

2017-07-27

4:30pm, valve closed, pumps stopped, vented

381

Wed Jul 26 21:22:50 2017

Parametric 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

Corrected 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

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

S1600520 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
  Excitation broadband: 1185582815
  Quiet time after excitation: 1185582840
- Quiet time before excitation: 1185584070
  Excitation broadband: 1185584105
  Quiet time after excitation: 1185584130
- Quiet time before excitation: 1185585360
  Excitation broadband: 1185585395
  Quiet time after excitation: 1185585420
- Quiet time before excitation: 1185586650
  Excitation broadband: 1185586685
  Quiet time after excitation: 1185586710
- Quiet time before excitation: 1185587940
  Excitation broadband: 1185587975
  Quiet time after excitation: 1185588000
- Quiet time before excitation: 1185589230
  Excitation broadband: 1185589265
  Quiet time after excitation: 1185589290
- Quiet time before excitation: 1185590520
  Excitation broadband: 1185590555
  Quiet time after excitation: 1185590581
- Quiet time before excitation: 1185591811
  Excitation broadband: 1185591846
  Quiet time after excitation: 1185591871

2017-08-01

9:55am, valve closed, venting, pumps off

385

Tue Aug 1 10:19:39 2017

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
  Excitation broadband: 1185650031
  Quiet time after excitation: 1185650056
- Quiet time before excitation: 1185651286
  Excitation broadband: 1185651321
  Quiet time after excitation: 1185651346
- Quiet time before excitation: 1185652576
  Excitation broadband: 1185652611
  Quiet time after excitation: 1185652636
- Quiet time before excitation: 1185653866
  Excitation broadband: 1185653901
  Quiet time after excitation: 1185653926
- Quiet time before excitation: 1185655156
  Excitation broadband: 1185655191
  Quiet time after excitation: 1185655216
- Quiet time before excitation: 1185656446
  Excitation broadband: 1185656481
  Quiet time after excitation: 1185656506
- Quiet time before excitation: 1185657737
  Excitation broadband: 1185657772
  Quiet time after excitation: 1185657797
- Quiet time before excitation: 1185659027
  Excitation broadband: 1185659062
  Quiet time after excitation: 1185659087

2017-08-02

11:25am valve closed, venting, pumps off

386

Tue Aug 1 16:10:42 2017

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

S1600553, 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
  Excitation broadband: 1185760258
  Quiet time after excitation: 1185760283
- Quiet time before excitation: 1185767513
  Excitation broadband: 1185767548
  Quiet time after excitation: 1185767573
- Quiet time before excitation: 1185774804
  Excitation broadband: 1185774839
  Quiet time after excitation: 1185774864
- Quiet time before excitation: 1185782094
  Excitation broadband: 1185782129
  Quiet time after excitation: 1185782154
- Quiet time before excitation: 1185789384
  Excitation broadband: 1185789419
  Quiet time after excitation: 1185789444
- Quiet time before excitation: 1185796675
  Excitation broadband: 1185796710
  Quiet time after excitation: 1185796735

2017-08-03

11:00am valve closed, pumps stopped, venting

388

Wed Aug 2 13:47:47 2017

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

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

S1600520 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
  Excitation broadband: 1185835727
  Quiet time after excitation: 1185835752
- Quiet time before excitation: 1185837582
  Excitation broadband: 1185837617
  Quiet time after excitation: 1185837642
- Quiet time before excitation: 1185839472
  Excitation broadband: 1185839507
  Quiet time after excitation: 1185839532
- Quiet time before excitation: 1185841362
  Excitation broadband: 1185841397
  Quiet time after excitation: 1185841422
- Quiet time before excitation: 1185843252
  Excitation broadband: 1185843287
  Quiet time after excitation: 1185843312
- Quiet time before excitation: 1185845143
  Excitation broadband: 1185845178
  Quiet time after excitation: 1185845203
- Quiet time before excitation: 1185847033
  Excitation broadband: 1185847068
  Quiet time after excitation: 1185847093
- Quiet time before excitation: 1185848923
  Excitation broadband: 1185848958
  Quiet time after excitation: 1185848983

2017-08-04

2:00pm valve closed, pumps off, venting

391

Fri Aug 4 14:15:16 2017

S1600535, 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
  Excitation broadband: 1185930987
  Quiet time after excitation: 1185931013
- Quiet time before excitation: 1185932843
  Excitation broadband: 1185932878
  Quiet time after excitation: 1185932903
- Quiet time before excitation: 1185934733
  Excitation broadband: 1185934768
  Quiet time after excitation: 1185934793
- Quiet time before excitation: 1185936623
  Excitation broadband: 1185936658
  Quiet time after excitation: 1185936683
- Quiet time before excitation: 1185938513
  Excitation broadband: 1185938548
  Quiet time after excitation: 1185938573
- Quiet time before excitation: 1185940403
  Excitation broadband: 1185940438
  Quiet time after excitation: 1185940463
- Quiet time before excitation: 1185942293
  Excitation broadband: 1185942328
  Quiet time after excitation: 1185942353
- Quiet time before excitation: 1185944183
  Excitation broadband: 1185944218
  Quiet time after excitation: 1185944243

2017-08-05

1:23pm valve closed, pumps stopped, venting

392

Sat Aug 5 13:46:08 2017

S1600539 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
  Excitation broadband: 1186015278
  Quiet time after excitation: 1186015303
- Quiet time before excitation: 1186017133
  Excitation broadband: 1186017168
  Quiet time after excitation: 1186017193
- Quiet time before excitation: 1186019023
  Excitation broadband: 1186019058
  Quiet time after excitation: 1186019083
- Quiet time before excitation: 1186020913
  Excitation broadband: 1186020948
  Quiet time after excitation: 1186020973
- Quiet time before excitation: 1186022803
  Excitation broadband: 1186022838
  Quiet time after excitation: 1186022863
- Quiet time before excitation: 1186024694
  Excitation broadband: 1186024729
  Quiet time after excitation: 1186024754
- Quiet time before excitation: 1186026584
  Excitation broadband: 1186026619
  Quiet time after excitation: 1186026644
- Quiet time before excitation: 1186028474
  Excitation broadband: 1186028509
  Quiet time after excitation: 1186028534

2017-08-07

10:23am, valve closed, pumps off, venting

393

Mon Aug 7 10:44:53 2017

S1600525 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
  Excitation broadband: 1186171983
  Quiet time after excitation: 1186172008
- Quiet time before excitation: 1186173838
  Excitation broadband: 1186173873
  Quiet time after excitation: 1186173899
- Quiet time before excitation: 1186175729
  Excitation broadband: 1186175764
  Quiet time after excitation: 1186175789
- Quiet time before excitation: 1186177619
  Excitation broadband: 1186177654
  Quiet time after excitation: 1186177679
- Quiet time before excitation: 1186179510
  Excitation broadband: 1186179545
  Quiet time after excitation: 1186179570
- Quiet time before excitation: 1186181400
  Excitation broadband: 1186181435
  Quiet time after excitation: 1186181460
- Quiet time before excitation: 1186183290
  Excitation broadband: 1186183325
  Quiet time after excitation: 1186183350
- Quiet time before excitation: 1186185180
  Excitation broadband: 1186185215
  Quiet time after excitation: 1186185240

2017-08-08

10:58am, valve closed, pumps stopped, venting

394

Mon Aug 7 13:19:48 2017

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

Effect 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
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	Ar	O₂	thickness / nm	abs / ppm	notes
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

under certain conditions as oxygen flow increase and Ar flow decrease, the loss angle becomes worse
with existence of oxygen ions the loss is mitigated by increase of beam voltage
relatively small particle size of oxygen compared with argon the caused the less effective interaction between assist ions and coating adatoms on the surface
with increase of ion dose, the mechanical loss drops

396

Tue Aug 8 10:18:30 2017

Effect 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

S1600557 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
  Excitation broadband: 1186262106
  Quiet time after excitation: 1186262131
- Quiet time before excitation: 1186269362
  Excitation broadband: 1186269397
  Quiet time after excitation: 1186269422
- Quiet time before excitation: 1186276652
  Excitation broadband: 1186276687
  Quiet time after excitation: 1186276712
- Quiet time before excitation: 1186283942
  Excitation broadband: 1186283977
  Quiet time after excitation: 1186284002
- Quiet time before excitation: 1186291232
  Excitation broadband: 1186291267
  Quiet time after excitation: 1186291292
- Quiet time before excitation: 1186298522
  Excitation broadband: 1186298557
  Quiet time after excitation: 1186298582

2017-08-15

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

398

Tue Aug 8 16:20:24 2017

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