arXiv:1112.2196v1 [physics.optics] 9 Dec 2011
Ultra-high-Q wedge-resonator on a silicon chip
Hansuek Lee, Tong Chen, Jiang Li, Ki Youl Yang, Seokmin Jeon, Osk
ar Painter, and Kerry J. Vahala
T. J. Watson Laboratory of Applied Physics, California Institute of
Technology, Pasadena, California 91125, USA
(Dated: December 12, 2011)
Ultra-high-Q optical resonators are being studied
across a wide range of research subjects including
quantum information, nonlinear optics, cavity
optomechanics,
and
telecommunications
1–7
.
Here, we demonstrate a new, resonator on-a-chip
with a record Q factor of 875 million, surpassing
even microtoroids
8
. Significantly, these devices
avoid a highly specialized processing step that
has made it difficult to integrate microtoroids
with other photonic devices and to also precisely
control their size. Thus, these devices not only
set a new benchmark for Q factor on a chip, but
also provide, for the first time, full compatibility
of this important device class with conventional
semiconductor processing.
This feature will
greatly expand the possible kinds of system on a
chip functions enabled by ultra-high-Q devices.
Long photon storage time (high Q factor) in mi-
crocavities relies critically upon use of low absorption
dielectrics and creation of very smooth (low scattering)
dielectric interfaces. For chip-compatible devices, silica
has by far the lowest intrinsic material loss. Microtoroid
resonators combine this low material loss with a reflow
technique in which surface tension is used to smooth
lithographic and etch-related blemishes
8
. At the same
time, reflow smoothing makes it very challenging to
fabricate larger diameter UHQ resonators and likewise
to leverage the full range of integration tools and
devices available on silicon. The devices reported here
attain ultra-high-Q performance using only conventional
semiconductor processing methods on a silicon wafer.
Moreover, the best Q performance occurs for diameters
greater than 500 microns, a size range that is difficult to
access for microtoroids on account of the limitations of
the reflow process. Microcombs will benefit from such
a combination of UHQ and larger diameter resonators
(microwave-rate free-spectral-range) to create combs
that are both efficient in turn-on power and that can be
self-referenced
6
. Moreover, integrated reference cavities
and ring gyroscopes are two other applications that
can benefit from larger (1
−
50 mm diameter) UHQ
resonators. Fabrication control of the free-spectral
range to 1 : 20
,
000 is also demonstrated here, opening
the possibility of precision repetition rate control in
microcombs or precision spectral placement of modes in
certain nonlinear oscillators
9,10
.
Earlier work considered the Q factor in a wedge-
shaped resonator fabricated of silica on a silicon wafer.
Q factors as high as 50 million were obtained
11
. That
approach isolated the mode from the lithographic
blemishes near the outer rim of the resonator by using
a shallow wedge angle. In the current work, we have
boosted the optical Q by about 20X beyond these earlier
results through a combination of process improvements.
These improvements make it unnecessary to isolate the
mode from the resonator rim. Indeed, the highest Q
factor demonstrated uses the largest wedge angles. A
top-view optical micrograph is provided in figure 1 to
illustrate the basic geometry. The process flow begins
with thermal oxide on silicon, followed by lithography
and oxide etching with buffered hydrofluoric acid. In
the insets to figure 1, scanning electron micrographs of
devices featuring 12-degree and 27-degree wedge angles
are imaged. Empirically, the angle can be controlled
through adjustment of the photoresist adhesion using
commercially available adhesion promoters. The oxide
disk structures function as an etch mask for an isotropic
dry etch of the silicon using XeF
2
. During the dry etch,
the silicon undercut is set so as to reduce coupling of
the optical mode to the silicon support pillar. This
value is typically set to about 100 microns for 1 mm
diameter structures and over 150 microns for 7
.
5 mm
diameter disks, however, smaller undercuts are possible
while preserving ultra-high-Q performance. Further
information on the processing is given in the Methods
section.
To measure intrinsic Q factor, devices were coupled
to SMF-28 optical fiber using a fiber taper
12,13
and
spectral lineshape data were obtained by tuning an
external cavity semiconductor laser across the resonance
while monitoring transmission on an oscilloscope. To
accurately calibrate the laser scan in this measurement,
a portion of the laser output was also monitored af-
ter transmission through a calibrated Mach-Zehnder
interferometer having a free spectral range of 7
.
75
MHz. The inset in figure 2 shows a spectral scan
obtained on a device having a record Q factor of 875
million. In these measurements, the taper coupling was
applied on the upper surface of the resonator near the
center of the wedge region. Modeling shows that the
fundamental mode has its largest field amplitude in
this region. Moreover, this mode is expected to feature
the lowest overall scattering loss resulting from the
three, dielectric-air interfaces as well as from the silicon
support pillar. An additional test that can be performed
to verify the fundamental mode is to measure the mode
index by monitoring the free-spectral-range (FSR). The
fundamental mode features the largest mode index and
hence smallest FSR.
The typical coupled power in all measurements was
maintained around 1 microWatt to minimize thermal
effects. However, there was little or no evidence of
2
silicon
silica
FIG. 1:
Micrographs and mode renderings of the wedge resonator from
top and side views. (a)
An op-
tical micrograph shows a top view of a 1 mm diameter wedge resonato
r.
(b)
A scanning electron micrograph shows
the side-view of a resonator. The insets here give slightly magnified m
icrographs of resonators in which the wedge
angle is 12 degrees (upper inset) and 27 degrees (lower inset).
(c)
A rendering shows calculated fundamental mode
intensity profiles in 10 degree and 30 degree wedge angle resonator
s at two wavelengths. As a guide, the center-of-
motion of the mode is provided to illustrate how the wedge profile intro
duces normal dispersion that is larger for
smaller wedge angles.
thermal effects in the optical spectrum. Typically, these
appear as an asymmetry in the lineshape and also a
scan-direction dependent (to higher or lower frequency)
spectral linewidth. As a further check that thermal
effects were negligible, ring down measurements
14
were
also performed on a range of devices for comparison to
the spectral-based Q measurement. For these, the laser
was tuned into resonance with the cavity and a lithium
niobate modulator was used to abruptly switch off the
input. The output cavity decay rate was then monitored
to ascertain the cavity lifetime. Ring-down data and
spectral linewidths were consistently in good agreement.
This insensitivity to thermal effects is a result of the
larger mode volumes of these devices in comparison to
earlier work on microtoroids (for which thermal effects
must be carefully monitored). The mode volumes in the
present devices are typically 100
−
1000X larger.
Measurements showing the effects of oxide thickness
and device diameter on Q factor are presented in the
figure 2 main panel. Four, oxide thicknesses are shown
(2, 4, 7
.
5 and 10 microns) over diameters ranging from
0
.
2 mm to 7
.
5 mm. All data points, with the exception
of the red points, correspond to a wedge angle of
approximately 10 degrees. The upper most (highest
Q at a given diameter) data correspond to a wedge
angle of 27 degrees. The solid curves are a model of
optical loss caused by surface scattering on the upper,
wedge, and lower oxide-air interfaces and by bulk-oxide
loss. In the model, the surface roughness was measured
independently on each of these surfaces using an atomic
force microscope (AFM) (r.m.s. roughness values are
given in the Methods section). The bulk optical loss
of the thermal silica corresponds to a Q value of 2
.
5
billion by fit to the data. The data corresponding to
the 10 degree wedge angle show that Q increases for
thicker oxides and also larger diameters. Using the
model, this trend can be understood to result from loss
that is caused primarily by scattering at the oxide-air
interfaces. Specifically, both thicker oxides and larger
diameter structures feature a reduced field amplitude at
the dielectric-air interface, leading to reduced scattered
power. A slight, overall boost to the Q factor is possible
by increasing the wedge angle. In this case, the mode
experiences reduced upper and lower surface scattering
as compared to the smaller angle case. A record Q
factor of 875 million for any chip based resonators is
obtained under these conditions. In general, there is
reasonably good agreement between the model and the
data, except in the case of the thinner oxides. For these
thinner structures, there is a tendency for stress-induced
buckling to occur at larger radii. This is believed to
create the discrepancy with the model.
The ability to lithographically define ultra-high-Q
resonators as opposed to relying upon the reflow process
enables a multi-order-of-magnitude improvement in
precision control of resonator diameter and FSR. This
feature is especially important in microcombs and also
certain nonlinear sources
9,10
. As a preliminary test of
the practical limits of FSR control, two studies were
conducted. In the first, a series of resonator diameters
were set in a CAD file used to create a photo mask.
A plot of the measured FSR (fundamental mode)
versus CAD file target diameter is provided in figure 3
(main panel). The variance from ideal linear behavior
3
0.1
1
10
10
1
10
2
10
3
10
m
7.5
m
4
m
2
m
10
m (27 degree)
Q (M illio n )
Resonator Diameter (mm)
FIG. 2:
Data showing the measured Q factor
plotted versus resonator diameter with oxide
thickness as a parameter.
The solid lines show the
predicted Q factor from a model that accounts for sur-
face roughness induced scattering loss and also material
loss. The rms roughness is measured using an AFM
(see Methods section for values) and the fitted bulk
material loss corresponds to a Q value of 2
.
5 billion.
The red data points correspond to a wedge angle of
27 degrees. All other data are obtained using a wedge
angle of approximately 10 degrees. The inset shows a
spectral scan for the case of a record Q factor of 875
million. The sinusoidal curve accompanying the spec-
trum is a calibration scan performed using a fiber inter-
ferometer.
is 2
.
4 MHz, giving a relative variance of better than
1 : 4
,
500 (FSR
≈
11 GHz). The inset to figure 3 shows
that for separate devices having the same target CAD
file diameter, the variance is further improved to a value
of 0
.
45 MHz or 1 : 20
,
000.
The Q factor for these new resonators is not only
higher in an absolute sense than what has been possible
with microtoroids, but it also accesses an important
regime of resonator FSR that has not been possible
using microtoroids. To date, the smallest FSR achieved
with the toroid reflow process has been 86 GHz (D
= 750
μm
) and the corresponding Q factor was 20
million
15
. The present structures attain their best Q
factors for FSRs that are complementary to microtoroids
(FSRs less than 100 GHz). This range has become
increasingly important in applications like microcombs
where self-referencing is important. Specifically, low
turn-on power and microwave-rate repetition are con-
flicting requirements in these devices on account of
the inverse dependence of threshold power on FSR.
However, such increases can be compensated using
ultra-high-Q because turn-on power depends inverse
quadratically on Q
16
. The ability to manipulate normal
dispersion through the wedge angle (see figure 1) can
be shown to provide control over the zero dispersion
point in spectral regions where silica exhibits anomalous
dispersion. Ultra-high-Q performance in large area
resonators is also important in rotation sensing
17
and
for on-chip frequency references
18,19
. In the former case,
the larger resonator area enhances the Sagnac effect. In
the latter, the larger mode volume lowers the impact
of thermal fluctuations on the frequency noise of the
resonator
20
. The precision control of FSR is important
to determine repetition rate in microcombs, and also in
applications such as stimulated Brillouin lasers where
a precise match of FSR to the Brillouin shift is a
prerequisite for oscillation. Application of these devices
to low turn-on power, microwave-rate microcombs and
to high-efficiency SBS lasers will be reported elsewhere.
Finally, an upper bound to the material loss of thermal
silica was established in this work. The value of 2
.
5
billion bodes well for further application of thermal silica
to photonic devices.
Methods
Disks were fabricated on (100) prime grade float zone
silicon wafers. Photo-resist was patterned using a GCA
6300 stepper on thermally grown oxide of thickness in
the range of 2
−
10 microns. Post exposure bake followed
in order to cure the surface roughness of photo-resist
pattern which acted as an etch mask during immersion
in buffered hydrofluoric solution (Transene, buffer-HF
improved). Careful examination of the wet etch revealed
6000
6020
6040
6060
6080
6100
6120
10.70
10.75
10.80
10.85
10.90
10.95
11.00
F re e S p e c tra l R a n g e (G H z )
Target Disk diameter (
m)
Experimental value
Estimation (linear fit)
disk 1
disk 2
disk 3
disk 4
8.7060
8.7065
8.7070
8.7075
8.7080
Free Spectral R ange (G H z)
Disk ID
FIG. 3:
Plot of measured free spectral range
(FSR) versus the target design-value resonator
diameter on a lithographic mask.
The plot shows
one device at each size and five different sizes. The
rms variance is 2
.
4 MHz (relative variance of less than
1 : 4
,
500). The inset shows the FSR data measured on
four devices having the same target FSR. An improved
variance of 0
.
45 MHz is obtained (a relative variance of
1 : 20
,
000).
4
0
20
40
60
80
100
120
140
0
2
4
6
8
10
D e p th (
m )
Etching Time (minutes)
Etching depth
Foot region height
FIG. 4:
Data plot showing the effect of etch time
on appearance of the “foot” region in etching of
a
10
micron thick silica layer.
The foot region is a
separate etch front produced by wet etch of silica that
is empirically observed to adversely affect the optical
Q factor. The data show that by control of the etch
time the “foot” region can be eliminated. The upper-
left inset is an image of the foot region and the lower
right inset shows the foot region eliminated by increase
of the wet etch time.
that the vertex formed by the lower oxide and upper
surface contains an etch front that is distinct from
that associated with the upper surface (see “foot”
region in figure 4 inset). This region has a roughness
level that is higher than any other surface and is a
principle contributor to Q degradation. By extending
the etch time beyond what is necessary to reach the
silicon substrate, this foot region can be eliminated as
shown in figure 4. With elimination of the foot etch
front, the isotropic and uniform etching characteristic of
buffered hydrofluoric solution results in oxide disks and
waveguides having very smooth wedge-profiles which
enhance Q factors. After the conventional cleaning
process to remove photo-resist and organics, silicon was
isotropically etched by xenon difluoride to create an
air-cladding whispering gallery resonator. An atomic
force microscope was used to measure the surface
roughness of the three, silica-air dielectric surfaces. For
the lower surface, the resonators were detached by first
etching the silicon pillar to a few microns in diameter
and then removing the resonator using tape. The r.m.s.
roughness values on 10-degree wedge-angle devices are:
0
.
15 nm (upper), 0
.
46 nm (wedge), 0
.
70 nm (lower); and
for 27-degree wedge-angle devices are: 0
.
15 nm (upper),
0
.
75 nm (wedge), 0
.
70 nm (lower). The correlation length
is approximately a few hundred nm. The difference in
the wedge surface roughness obtained for the large and
small wedge angle cases is not presently understood.
Acknowledgments
We gratefully acknowledge the
Defense Advanced Research Projects Agency under
the iPhod and Orchid programs and also the Kavli
Nanoscience Institute at Caltech. H. L. thanks the Cen-
ter for the Physics of Information.
1
Vahala, K. J. Optical microcavities.
Nature
424
, 839–846
(2003).
2
Kippenberg, T. J. & Vahala, K. J. Cavity optomechan-
ics: Back-action at the mesoscale.
Science
321
, 1172–1176
(2008).
3
Kippenberg, T. J. & Vahala, K. J. Cavity opto-mechanics.
Optics Express
15
, 17172–17205 (2007).
4
Matsko, A. B. & Ilchenko, V. S. Optical resonators with
whispering-gallery modes-part I: basics.
IEEE J. Sel. Top.
Quant.
12
, 3–14 (2006).
5
Ilchenko, V. S. & Matsko, A. B. Optical resonators with
whispering-gallery modes-part II: applications.
IEEE J.
Sel. Top. Quant.
12
, 15–32 (2006).
6
Kippenberg, T. J., Holzwarth, R. & Diddams, S. A.
Microresonator-based optical frequency combs.
Science
332
, 555–559 (2011).
7
Aoki, T.
et al.
Observation of strong coupling between
one atom and a monolithic microresonator.
Nature
442
,
671–674 (2006).
8
Armani, D. K., Kippenberg, T. J., Spillane, S. M. & Va-
hala, K. J. Ultra-high-Q toroid microcavity on a chip.
Nature
421
, 925–929 (2003).
9
Tomes, M. & Carmon, T.
Photonic micro-
electromechanical systems vibrating at X-band (11-GHz)
rates.
Phys. Rev. Lett.
102
, 113601 (2009).
10
Grudinin, I. S., Yu, N. & Maleki, L. Brillouin lasing with a
CaF
2
whispering gallery mode resonator.
Phys. Rev. Lett.
102
, 043902 (2009).
11
Kippenberg, T. J., Kalkman, J., Polman, A. & Vahala,
K. J. Demonstration of an erbium-doped microdisk laser
on a silicon chip.
Phys. Rev. A
74
, 051802 (2006).
12
Cai, M., Painter, O. J. & Vahala, K. J. Observation of
critical coupling in a fiber taper to silica-microsphere whi
s-
pering gallery mode system.
Phys. Rev. Lett.
74
, 051802
(2006).
13
Spillane, S. M., Kippenberg, T. J., Painter, O. J. & Va-
hala, K. J. Ideality in a fiber-taper-coupled microresonato
r
system for application to cavity quantum electrodynamics.
Phys. Rev. Lett.
91
, 043902 (2003).
14
Vernooy, D. W., Ilchenko, V. S., Mabuchi, H., Streed,
E. W. & Kimble, H. J. High-Q measurements of fused-
silica microspheres in the near infrared.
Optics Letters
23
,
247–249 (1998).
15
Del’Haye, P., Arcizet, O., Schliesser, A., Holzwarth, R. &
Kippenberg, T. J. Full stabilization of a microresonator
frequency comb.
Phys. Rev. Lett.
101
, 053903 (2008).
5
16
Kippenberg, T. J., Spillane, S. M. & Vahala, K. J. Kerr-
nonlinearity optical parametric oscillation in an ultrahi
gh-
Q toroid microcavity.
Phys. Rev. Lett.
93
, 083904 (2004).
17
Ciminelli, C., Dell’Olio, F., Campanella, C. & Armenise,
M. Photonic technologies for angular velocity sensing.
Adv.
Opt. Photon.
2
, 370–404 (2010).
18
Matsko, A. B., Savchenkov, A. A., Yu, N. & Maleki,
L. Whispering-gallery-mode resonators as frequency ref-
erences. I. fundamental limitations.
J. Opt. Soc. Am. B
24
, 1324–1335 (2007).
19
Savchenkov, A. A., Matsko, A. B., Ilchenko, V. S., Yu,
N. & Maleki, L. Whispering-gallery-mode resonators as
frequency references. II. stabilization.
J. Opt. Soc. Am. B
24
, 2988–2997 (2007).
20
Gorodetsky, M. L. & Grudinin, I. S. Fundamental thermal
fluctuations in microspheres.
J. Opt. Soc. Am. B
21
, 697–
705 (2004).