of 8
Supplemental Document
In situ
tuning of optomechanical crystals with
nano-oxidation: supplement
U
TKU
H
ATIPOGLU
,
1,2,†
S
AMEER
S
ONAR
,
1,2,†
D
AVID
P. L
AKE
,
1,2
S
RUJAN
M
EESALA
,
1,2
AND
O
SKAR
P
AINTER
1,2,3,
1
Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California
91125, USA
2
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied Physics, California
Institute of Technology, Pasadena, California 91125, USA
3
AWS Center for Quantum Computing, Pasadena, California 91125, USA
These authors contributed equally to this work.
opainter@caltech.edu
This supplement published with Optica Publishing Group on 8 March 2024 by The Authors
under the terms of the Creative Commons Attribution 4.0 License in the format provided by the
authors and unedited. Further distribution of this work must maintain attribution to the author(s)
and the published article’s title, journal citation, and DOI.
Supplement DOI: https://doi.org/10.6084/m9.figshare.25189322
Parent Article DOI: https://doi.org/10.1364/OPTICA.516479
In-situ tuning of optomechanical
1
crystals with nano-oxidation:
2
supplemental document
3
4
A. Experimental setup
5
Dimpled fiber
positioner
AFM head and
cantilever
Dimpled Fiber
OMC chip
AFM
Stage
Fig. S1.
AFM integrated with an optical test setup.
A dimpled fiber positioning stage is inte-
grated into an AFM, allowing for real-time oxidation and optical testing. Image on the right
shows a close-up view of the AFM cantilever, the dimpled fiber and the OMC chip.
To enable in-situ nano-oxidation and real-time tuning of OMC cavities, an optical test setup
6
has been integrated into the enclosure of an AFM as shown in Fig. S1. The system has three
7
sub-parts that are controlled independently: 1) the optical fiber positioning system, comprising a
8
three-axes linear motorized positioning stage and two rotational positioning stages, 2) the sample
9
mount of the AFM with x and y motional degrees of freedom, and 3) the AFM cantilever with z
10
motional degree of freedom. Additionally, the AFM enclosure is equipped with a temperature
11
and humidity sensor to ensure that environmental conditions are within the desired regime. The
12
entire assembly sits on an optical table to minimize vibrations during the oxidation process.
13
B. Characterization of nano-oxidation
14
The nano-oxidation process generates oxide beneath and above the surface of silicon. Here we
15
describe the procedure used to assess the ratio of oxide height and depth above and below the
16
silicon surface, respectively. We first measure the post-oxidation height by performing AFM
17
scans in the tapping mode. Subsequently, we etch the oxide in an anhydrous hydrofluoric acid
18
vapor etching tool (SPTS PRImaxx uEtch), and perform AFM scans of the resulting trenches in
19
silicon. The data obtained, as depicted in Figure S2a, indicates that the oxide thickness beneath
20
the surface is approximately 70
%
of the total measured thickness above the surface. Figure S2b
21
shows the characterization of a single oxide pixel generated in the mild oxidation mode. The
22
size of the pixel is approximately 25nm along both x and y axes. We utilize such oxide pixels for
23
fine-tuning of both optical and acoustic resonances in real-time as discussed in the main text.
24
C. Optical scattering due to nano-oxidation
25
In addition to altering the mechanical and optical characteristics of the local silicon surface, the
26
nano-oxidation process can introduce roughness and additional scattering sites. Consequently,
27
we observe an increase in the intrinsic optical scattering rate (
κ
i
/
2
π
) during our coarse tuning
28
experiments. As shown in Figure S3, the change in
κ
i
/
2
π
is more pronounced upon increasing
29
the size of the oxidation patterns and the thickness of the oxide layer. For optics-focused patterns
30
0
10
20
30
40
50
60
70
80
x (nm)
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Oxide thickness (nm)
Vertical
Horizontal
0
50
100
150
200
250
300
x (nm)
-1.5
-1
-0.5
0
0.5
1
1.5
2
Oxide height (nm)
After oxidation
After HF dip
Oxide
thickness
(
nm
)
0
50
100
150
200
250
300
x (nm)
-1.5
-1
-0.5
0
0.5
1
1.5
2
Oxide height (nm)
After oxidation
After HF dip
0
1
0.5
1.5
2
-
0.5
-
1
-
1.5
0
100
200
300
(
nm
)
Si
50
푛푚
Si
50
푛푚
50
150
250
30
푛푚
0
20
40
60
(
nm
)
10
30
50
80
70
Oxide
thickness
(
nm
)
0
0.4
0.8
1.2
0.2
0.6
1
a
b
Fig. S2.
Characterization of nano-oxidation on a silicon chip. a,
Height profile of the oxide
slab created by nano-oxidation (blue trace), and the depth profile obtained after removal of the
oxide slab using a hydrofluoric acid etch (red trace). Insets show the AFM scan of the oxide
slab (top) and the etched trench (bottom) along with horizontal line cuts used to sample the
traces on the main plot.
b,
Height profile of an oxide pixel along x and y axes indicating a
lateral size of
25 nm. Inset shows the AFM scan of the oxide pixel along with x and y line
cuts used to sample the traces on the main plot.
generated in regions with high electric field intensity, we observe a substantial increase in
κ
i
/
2
π
.
31
A maximum change in
κ
i
/
2
π
of approximately 440 MHz is noted for the aggressive oxidation
32
case when
w
<
350 nm. For the mild oxidation case, the change in
κ
i
/
2
π
is less than 200 MHz. In
33
the case of the acoustics-focused pattern, the change in
κ
i
/
2
π
is less than 400 MHz for aggressive
34
oxidation case, and less than 150 MHz for mild oxidation case when
l
<
1.6
μ
m.
35
D. FEM simulations for pixel-by-pixel oxidation and selectivity analysis
36
Figure S4a and b show the results of FEM simulations where we mapped out how the location of
37
a single oxidation pixel affects the optical wavelength and acoustic frequency, respectively. These
38
profiles closely match the optical intensity and acoustic displacement profiles shown in Fig. 1 of
39
the main text. This is expected because oxidation at points with larger optical field concentration
40
leads to larger change in optical energy, and thereby in the optical resonance wavelength. Similarly,
41
oxidation at the points of maximum displacement leads to a larger fractional change in effective
42
mass of the acoustic mode, and thereby in the acoustic resonance frequency. The exact material
43
properties of the thin film oxide such as the density, Young’s modulus and relative permittivity are
44
specific to the oxidation process. In our approach, we use these material properties as variables
45
and then we find what scaling allows us to match the coarse tuning experiment (Fig. 2 of the
46
main text) and simulations. This way, we found that the density, Young’s modulus and relative
47
permittivity of oxide are 3500 kg/
m
3
, 70 GPa and 2, respectively. In the acoustic simulations, we
48
use the anisotropic elasticity tensor of silicon with (
C
11
,
C
12
,
C
44
) = (166, 64, 80) GPa and assume a
49
[110] crystallographic orientation for the x-axis.
50
In Figure S4c and d, we plot the normalized optical selectivity,
δλ
/
δ
and normalized acoustic
51
selectivity,
δ
/
δλ
. Here,
δλ
and
δ
are normalized with respect to the maximum value calculated
52
in the pixel-by-pixel oxidation profiles in Figure S4a, b. In the case of fine tuning experiments
53
where we seek small frequency shifts, we concentrate on the high selectivity regions. However,
54
the locations with maximum optical selectivity,
δλ
/
δ
do not coincide with those that produce
55
maximum optical tuning
δλ
. Likewise, the regions with maximum acoustic selectivity are
56
relatively small and localized at the edge of the silicon-air boundary. As a result, for coarse tuning
57
experiments, it is more practical to use large oxide patches as opposed to individual pixels to
58
achieve large tuning at the expense of selectivity. Details of the pattern generation algorithm used
59
to generate the large oxide patches are given in Appendix E.
60
E. Nano-oxidation pattern generation algorithm.
61
The results from coarse tuning experiments in Fig. 2 of the main text show frequency shifts
62
generated by either the optics-focused or the acoustic-focused pattern type. In practice, we require
63
2