Superconducting nano-mechanical diamond resonators

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by  Tobias Bautze

Superconducting nano-mechanical diamond resonators
Tobias Bautze,1,2,∗ Soumen Mandal,1,2,† Oliver A. Williams,3,4
Pierre Rodi`ere,1,2 Tristan Meunier,1,2 and Christopher B¨auerle1,2,‡
1Univ. Grenoble Alpes, Inst. NEEL, F-38042 Grenoble, France
2CNRS, Inst. NEEL, F-38042 Grenoble, France
3Fraunhofer-Institut fu¨r Angewandte Festko¨rperphysik, Tullastraße 72, 79108 Freiburg, Germany
4University of Cardiff, School of Physics and Astronomy,
Queens Buildings, The Parade, Cardiff CF24 3AA, United Kingdom
4
(Dated: January 29, 2014)
1
0 Inthisworkwepresentthefabrication andcharacterization ofsuperconductingnano-mechanical
2 resonators made from nanocrystalline boron doped diamond (BDD). The oscillators can be driven
andreadoutintheirsuperconductingstateandshowqualityfactorsashighas40,000ataresonance
n
frequency of around 10 MHz. Mechanical damping is studied for magnetic fields up to 3 T where
a
J theresonatorsstillshowsuperconductingproperties. Duetotheirsimplefabricationprocedure,the
devicescaneasilybecoupledtoothersuperconductingcircuitsandtheirperformanceiscomparable
8
with state-of-the-art technology.
2

]
l I. INTRODUCTION II. FABRICATION
l
a
h
The nano-mechanical resonators have been fabricated
-
s Nano-mechanical resonators allow to explore a vari- from a superconducting nanocrystaline diamond film,
e
ety of physical phenomena. From a technological point grownona siliconwafer with a 500nm thick SiO layer.
m 2
of view, they can be used for ultra-sensitive mass1–3, TobeabletogrowdiamondontheSi/SiO surface,small
2
t. force4–6, charge7,8 and displacement detection. On the diamond particles of a diameter smaller than 6 nm are
a more fundamental side, they offer fascinating perspec- seeded onto the silica substrate with the highest possi-
m
tives for studying macroscopicquantum systems. Signif- bledensity24. Asubsequentmicrowaveplasmachemical-
- icantprogresshasbeenmadeinthelastfewyearsbycool- vapordeposition(CVD) allowsto growandcontrolvari-
d
n inganano-mechanicalresonatorintoitsgroundstate9–12. ouspropertiesofthe film. Itispossibleto varythe grain
o Couplings between nano-mechanical resonators and su- sizes from few nanometers to few microns by controlling
c perconducting circuits have been realized and even the the methane concentration. Furthermore one can add a
[ creation of entanglement with these macroscopic oscilla- variety of dopants to drastically change some of the key

1 torsseemsinreach13. Inordertoexploitsuchasystemin propertiesofpurediamond. Whileaddingborongasdur-
v quantum information technology, nano-mechanical sys- ingtheCVDprocessonecanturntheelsewiseinsulating
2 tems will have to be coupled to other quantum systems diamondfilm metallic and abovea criticalconcentration
6 suchaslight14orsuperconductingcircuits9,15–19andnew evensuperconducting25,26. A detaileddescriptionofthis
1 materials to improve the coupling for such hybrid sys- growth process can be found in reference24.
7
tems are of importance. In this respect diamond is an
.
1 extremely attractive material. Despite the fact that dia-
0 mond has exceptional mechanical properties20–23, it has
4 a relatively high refractive index which allows to couple
1
it to light. In addition when doped with boron, it can
:
v be rendered superconducting with remarkable electrical
i properties and makes it a promising material for fully
X
integrated hybrid nano-mechanicalsystems.
r
a
Inthisarticlewepresentthefabricationandcharacter- FIG. 1: Scanning electron micro-graph of a diamond res-
izationofnano-mechanicalresonatorsbuilt outofsuper- onator. The dimensions of the resonator are 480 nm x 300
conductingdiamond. Wedemonstrateasimpletopdown nm (width x thickness). Different resonators with different
lengths ranging from 5 to 30 µm havebeen fabricated.
processtofabricatetheseresonatorsbycommonelectron
beamlithographyandhenceofferasimple waytobeim-
plemented into superconducting circuits. We compare The nano-mechanicalstructures have been defined us-
their performance to state-of-the-art resonators and in- ing standard electron beam lithography. First, a 70 nm
vestigate the limits of their superconductivity. Quality thicknickeletchmaskwhichdefinesthesamplegeometry
factors around 40000 at around 10 MHz resonance fre- has been evaporated on top of the diamond film which
quency are demonstrated and it is shown that it is pos- has then been followed by anisotropic oxygen plasma
sible to directly readout a superconducting resonatorat etching27. The sample is cooled to 10oC while being ex-
a magnetic field as high as 3 Tesla. posedtotheoxygenplasmaforapproximately8minutes.
2
The anisotropy of the etching process leads to straight properties of the nano-mechanical resonators.
walls that broaden less than 5 nm after 300 nm of etch-
ing. After this process, the nickel mask is removed by
dipping the sample in a FeCl solution. To provide good B) 3 0 T
3 d 0.5 T
ohmic contacts, a tri-layer consisting of titanium, plat- n ( 6 1.0 T
inumandgoldhasbeenevaporatedfollowedbyannealing o 1.5 T
at 750oC. The structures have been suspended by etch- ssi 9 2.0 T
ingthesacrificialSiO layerusingHFvaporat50oCand mi
2
s 12
atmospheric pressure for about 10 minutes. Diamond it- n
a
self is inert to this chemical etching process. Due to the r 15
T
strong mechanical stiffness, tri-critical point drying has
60 40 20 1 2 3 4
not been necessary even for structures with lengths up
Input power (dBm) Temperature (K)
to 30 micrometers. Figure 1 displays a suspended dia-
mondstructurethathasbeenfabricatedbythismethod.
We have also fabricated superconducting diamond res- FIG.2: Superconductingcharacteristicsoftheresonator. The
onators that were covered with a 50 nm thick gold layer diamondresonator(sampleB)showsasuperconductingstate
in order to test the samples at temperatures above the at zero magnetic field at low input powers (left) and at low
temperatures (right) identified by the plateau region. With
superconducting transition temperature and at currents
increasing input power (temperature), the sample undergoes
above the superconducting critical current. This allows
atransition intoits normalstate, itsresistance increases and
for easy detection of the resonance conditions. For this
hence the transmitted signal decreases. The transition is
purpose a slightly modified technique was used. After
shifted to lower input powers (temperatures) at higher mag-
the e-beam process a metallic bilayer of 50 nm gold and netic fields.
50 nm of nickel was deposited instead of 70 nm nickel as
in the previous case. This bilayer acts as a mask for the
To verify whether our resonators show superconduc-
etching process. The nickel layer was subsequently re-
tivity, we first measured the superconducting transition
movedusing FeCl which does not attack the goldlayer.
3 as a function of the input power and temperature at a
Finally the combination of diamond and gold layer was
frequency of approximately 9 MHz close to the expected
exposed to HF gas for suspension. The etch rate of gold
resonance frequency. The input power can in principle
in HF at the temperatures used is negligible28.
be directly converted into a current using a perfectly 50
In the following, we mainly discuss the results of two
Ohm adapted circuit model. However, since this ap-
resonators, one with a geometry of 30 µm x 480 nm
proach neglects the change of sample impedance when
(length x width) and one with 25 µm x 350 nm with
sweeping through the resonance as well as contact resis-
a 50 nm gold layer on the top, referred to as sample
tances, it is more convenient to directly plot the input
A and sample B, respectively. The thickness of the di-
power instead of the bias current. Nevertheless, the cal-
amond film was estimated to 300 nm using an optical
culatedcriticalcurrentsareofthe orderoffew µA,simi-
profilometer.
lartowhathasbeenmeasuredwithDCmeasurementsof
similar nanostructures made from BDD30,31. The trans-
missionsignalofsampleBisplottedinfigure2. Onecan
III. MEASUREMENTS clearly identify a constant transmission plateau at low
input powers (left panel) and at low temperatures (right
The low temperature characterization of the nano- panel). A constanttransmissiondirectly goes with unal-
mechanical beams was done using the magneto-motive tered electrical properties for which we can identify the
detection scheme29. The radio frequency signal from a superconducting state of the beam. The device shows
networkanalyzer(Rohde-SchwarzZVL-13)wasfedinto an increase in impedance at high input powers (temper-
acoaxiallineatthetopofa3Hecryostatwithabasetem- atures), which leads to a reduction of the transmitted
peratureof500mK.Thesignalwasdeliveredtothesam- signalandeventuallyto thetransitionofthe sampleinto
ple through two attenuation stages: 20 dB at 4.2 K and its normal state. This impedance increase is associated
20 dB atthe 1.2 K stage. An ac-currentflowing through with the absorption of microwave power. The splitting
thesampleexposedtoaperpendicularexternalmagnetic of cooper-pairs leads to the creation of excess quasipar-
field B induces a Lorentz force that actuates the beam ticles and drastically alters the complex conductivity of
andleadstoadisplacementofthenano-mechanicalbeam our structure and hence the superconducting state32.
in plane to the diamond film. On resonance, the beam From the total transmissiondrop we can calculate the
dissipates energy changing its impedance and resulting approximatenormalstateresistancevaluestoaround300
in a dip in the transmission signal. The transmitted sig- Ohms for sample B. We have obtained similar data for
nal is amplified at 4.2 K with a gain of approximately sampleAandanormalstateresistancecloseto2.5kOhm
50 dB (Caltech CITLF1 SN120) and fed into the input (not displayed). The difference in resistance is due to
port of the network analyzer. The same electricalset-up the presence of the gold layer on top of sample B. At
also allows for characterization of the superconducting higher magnetic fields, the superconducting transition is
3
shifted to lower input powers and to lower temperatures 28
and a residual resistance appears which can be associ-
)
ated to the increase of quasiparticles in the supercon- 6
27
ductor. We obtained a superconducting transition tem- −0
1
perature of approximately 2.5 K at zero magnetic field (
in agreement with measurements on non-suspended dia- g 26
n
mond samples27,30,31. pi
We now turn to the mechanical properties of the dia- m 25
a
mondnano-mechanicalresonator. Byapplyingaperpen- D
dicular magnetic field and sweeping the RF frequency of 24
the bias, the resonators can be actuated and its charac- 0.0 0.5 1.0 1.5 2.0 2.5 3.0
teristics can be extracted. In figure 3 we show a typical Magnetic field (T)
transmission signal at resonance obtained from sample
A. The resonance frequency of resonator A and B are
FIG.4: DampingofthemechanicalresonatorAasafunction
9.39226 MHz and 8.77142 MHz respectively. Using
of magnetic field. The quadratic dependence indicates that
thedamping is governed by eddy-currents.
1 χ2 YI
y
f = (1)
res 2π l2 sρwt
A side effect of the magneto-motive detection tech-
with χ = 4.73 being a numerical factor for the beams’
nique is the circulationofeddy currentsinside the struc-
first flexual mode33, I being its moment of Inertia, w
y ture, which leads to an additional magnetic field that is
its width, l its length and ρ the density of diamond, we
opposed to the applied external magnetic field. This re-
can calculate the Young’s modulus to 950 and 810 GPa,
sults in an additive force that is opposed to the beam
respectively. The difference between the Young’s mod-
movement and leads to another damping term Q that
E
uli of sample A and B is simply due to the additional
adds linearly to the intrinsic mechanical damping.
metal layer of the latter. In addition, the fact that the
Young’s modulus is as high as the one observed for un- 1 1 1
= + (2)
dopednanocrystallinediamond34,35showsthattheboron Q Qmech QE
doping does not degrade the mechanical properties.
The eddy current damping39 scales with B2 and adds to
the inverse of the intrinsic quality factor which is inde-
0.0 pendent of the magnetic field and only depends on the
)
B intrinsic mechanical losses. Figure 4 shows the corre-
d 0.1
( sponding magnetic damping for sample A from which
n
o 0.2 we extract the intrinsic unloaded quality factor Qmech
si = 41000 at zero magnetic field. This mechanical qual-
s 0.3
mi ity factor is limited by the surface roughness of the di-
ns 0.4 amond and more importantly by clamping losses due to
a
r 0.5 the doubly-clamped beam design. The isotropic etching
T
of the sacrificial SiO layer leads to an undercut of the
2
anchorpadsoftheNEMS.Themoresurfaceundercutthe
9.3916 9.3920 9.3924 9.3928
moredissipationispossibleinthevibratingsurroundings
Frequency (MHz)
of the resonators’ clamps, the higher the losses. Possi-
ble solutions to increase this quality factor would be to
FIG.3: MechanicalresonanceofsampleArecordedat2Tesla use the so-called free-free beam design39, to reduce the
showing a loaded quality factor of 40000. The red line is a
surface losses by smoothing the surface with mechani-
Lorentzian fit. calorchemicalpolishingbeforenanofabrication40 andto
remove the undercut by means of a focused ion beam
From the transmission measurement we can also ex-
technique. Nevertheless,the observedquality factorsare
tract the loaded quality factor Q, which describes the
comparable with state-of-the art resonators22,41,42. A
rate ofenergy loss,comparedto the energystoredin the
commonly used value for comparison is the product of
resonator. For sample A and B we find Q = 40000 and
frequency and quality factor, fQ, for which we obtain
Q = 30000, respectively. From these measurements we
3.85 × 1011.
concludethattheYoung’smodulusaswellasthequality
To convince oneself that the measured resonance is of
factorofsampleBislowerduetoenhancedlossescaused
mechanical nature and not of some electrical resonance,
by the gold layer on top of the structure. The effect of
we plot the signal amplitude as a function of magnetic
the gold layer is to modify the mechanical properties in
field in figure 5. Following43, we can fit our curves using
terms of surface stress, additional mass, additional elas-
ticity and damping. Such effects have been studied in 2Z
0
detail in the literature36–38. S12 =−20βLog[αB2+2Z ] (3)
0
4
2.5 nano-mechanical oscillator. Assuming that this embed-
B) -56 dBm ding impedance changesslowlyoverthe resonancewidth
(d 2.0 -52 dBm which is justified in our case as the damping is low, we
e -48 dBm
d -44 dBm findthattheloadedresonancefrequencyshiftsaccording
tu 1.5 -40 dBm to43
pli
m 1.0
a ℜe(Zext)
nal 0.5 fl =f0s1+Θ(B−Bc)Zc |Ze2xt| (4)
g
Si 0.0 where f0 is the unshifted frequency at zero embedding
0 2 4 6 8 10 impedance. Assuming that the second term in equation
Magnetic field (T2) 4iszerobelowacriticalfieldB forthe superconducting
c
resonatorwe can fit our data of the resonance frequency
FIG.5: Thesignalamplitudeasafunctionofmagneticfieldat shift as shown in figure 6. From the fit we extract the
differentinputpowers. Alogarithmicscalingwiththesquared critical field to Bc = 0.996T which is consistent with
magnetic field accounts for a mechanical resonance. the onset of the residualresistance of sample A (not dis-
played).
)
z
H
9.39227
M
( IV. CONCLUSION
y
c 9.39226
n
e We have demonstrated that nano-mechanical res-
u
q 9.39225 onators made from boron doped diamond show super-
e
fr conducting properties up to magnetic fields of 3 Teslas.
e
c 9.39224 These resonators show high quality factors as high as
n
a 40000 at a resonance frequency of around 10 MHz. The
n
o 9.39223 simple fabrication process of superconducting diamond
es 0.0 0.5 1.0 1.5 2.0 2.5 3.0 resonators allows for easy implementation into fully su-
R
Magnetic field (T) perconductingdiamondcircuitssuchasmicro-cavitiesor
superconducting quantum interference devices. Due to
its remarkable mechanical, electrical as well as optical
FIG.6: Themechanical centerfrequencyisshifted duetoan
properties we conclude that nano-mechanical resonators
embeddingimpedancethatappearsaround1T.Thedatahas
been fitted with equation 4. made from boron doped diamond offer an extremely at-
tractive system in the growing field of quantum opto-
mechanics.
where αB2 = Z = ξl2B2 is the resonators impedance,
c ω0m
β adjusts the amplitude of the signal, Z is the line
0
impedance and ξ is a constant of order unity, depend- Acknowledgments
ing on the mode shape43.
The transmission signal of the resonator A shows a fi- C.B. acknowledges financial support from the French
niteresidualresistanceatfinitemagneticfieldasdepicted National Agency (ANR) in the frame of its program
in figure 2. This resistance can be seen as the real part in Nanosciences and Nanotechnologies (SUPERNEMS
of an external embedding impedance in series with the project no anr-08-nano-033).
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