arXiv:1401.7162v1 [cond-mat.mes-hall] 28 Jan 2014 esaeo motne nti epc imn san properties is dia- mechanical diamond that exceptional fact respect has the this sys- mond Despite In hybrid material. attractive such importance. extremely for of coupling are the tems improve to materials antcfil shg s3Tesla. 3 as at high pos- resonator as is superconducting field it a magnetic that out a fre- shown read is resonance directly it to MHz sible and 10 demonstrated around Quality are at quency superconductivity. 40000 their around in- of factors and limits resonators the compare state-of-the-art vestigate We to im- performance be circuits. to their way superconducting simple into a offer plemented hence electron and common lithography by beam resonators these down fabricate top to simple process a super- demonstrate We of out diamond. built conducting resonators nano-mechanical of ization fully for material promising can systems. a nano-mechanical it hybrid it boron, integrated makes with electrical remarkable and doped with when properties superconducting addition couple rendered In to be allows light. which to index it refractive high relatively a fve,te a eue o lr-estv mass ultra-sensitive for used be point can technological they a From view, of phenomena. physical of ety eswl aet eculdt te unu systems quantum other to coupled light be as such to have sys- will nano-mechanical tems technology, information quantum raino nageetwt hs arsoi oscilla- reach the in macroscopic even seems these tors and with entanglement realized of been creation su- have and circuits resonators perconducting nano-mechanical between Couplings n aomcaia eoao noisgon state ground cool- its by into years resonator few nano-mechanical last a the ing in made Signif- been perspec- has systems. progress quantum fascinating icant macroscopic offer studying for they tives side, fundamental more force nti ril epeettefbiainadcharacter- and fabrication the present we article this In aomcaia eoaosalwt xlr vari- a explore to allow resonators Nano-mechanical 4–6 charge , 14 eie a aiyb ope oohrsprodcigcirc superconducting technology. other state-of-the-art to fo coupled with studied be Due easily is properties. can damping superconducting devices Mechanical show still MHz. resonators quality the 10 show around and state of ( superconducting frequency diamond their in doped out boron read and nanocrystalline from made resonators 3 ruhfrIsiu ¨rAgwnt Festk¨orperphysik, f¨ur Angewandte Fraunhofer-Institut rsprodcigcircuits superconducting or nti okw rsn h arcto n characterizatio and fabrication the present we work this In 7,8 .INTRODUCTION I. 13 n ipaeetdtcin nthe On detection. displacement and nodrt xli uhasse in system a such exploit to order In . uecnutn aomcaia imn resonators diamond nano-mechanical Superconducting ireRodi`ere,Pierre oisBautze, Tobias uesBidns h aae adffC2 A,Uie Kingd United 3AA, CF24 Cardiff Parade, The Buildings, Queens 1 nv rnbeAps nt EL -84 rnbe France Grenoble, F-38042 NEEL, Inst. Alpes, Grenoble Univ. 4 nvriyo adff colo hsc n Astronomy, and Physics of School Cardiff, of University 2 NS nt EL -84 rnbe France Grenoble, F-38042 NEEL, Inst. CNRS, ,2 1, ,2, 1, 9,15–19 rsa Meunier, Tristan ∗ 20–23 omnMandal, Soumen Dtd coe ,2018) 9, October (Dated: n new and thas it , 9–12 1–3 . , ,2 1, rw naslcnwfrwt 0 mtikSiO thick nm 500 a film, with wafer diamond silicon nanocrystaline a on superconducting grown a from ob bet rwdaodo h Si/SiO the on diamond grow to able be To rwhpoescnb on nreference in found be can process growth concentration critical a insulating superconducting above even elsewise and the metallic turn film can one diamond dur- process gas key CVD boron the the adding While of ing some diamond. pure change a of drastically properties add to can dopants one controlling of Furthermore by variety grain microns the concentration. vary few methane to to the possible nanometers is few It from film. vari- sizes control the and of grow properties to ous possi- allows highest (CVD) deposition are the vapor nm with 6 substrate density than silica ble smaller the diameter onto a seeded of particles diamond ntr h iesoso h eoao r 8 mx300 different x with 30 nm to resonators res- 5 480 Different from are diamond ranging thickness). resonator a lengths x the of (width of micro-graph nm dimensions electron The Scanning onator. 1: FIG. a hnbe olwdb nstoi xgnplasma oxygen anisotropic which film by diamond followed the etching been of then top on has evaporated nm geometry sample 70 been the a has defines which First, mask etch lithography. nickel thick beam electron standard ing oe oteoye lsafrapoiaey8minutes. 8 approximately for plasma oxygen the to posed h aomcaia eoaoshv enfabricated been have resonators nano-mechanical The h aomcaia tutrshv endfie us- defined been have structures nano-mechanical The ,2, 1, n hitpe B¨auerle Christopher and ulsrß 2 90 riug Germany Freiburg, 79108 72, Tullastraße otersml arcto rcdr,the procedure, fabrication simple their to isadterpromnei comparable is performance their and uits † 27 atr shg s4,0 taresonance a at 40,000 as high as factors fsprodcignano-mechanical superconducting of n lvrA Williams, A. Oliver h apei oldt 10 to cooled is sample The . D) h siltr a edriven be can oscillators The BDD). 24 antcfilsu o3Twhere T 3 to up fields magnetic r usqetmcoaepam chemical- plasma microwave subsequent A . I FABRICATION II. 25,26 ealddsrpino this of description detailed A . µ om ,2, 1, aebe fabricated. been have m ,4 3, ‡ o hl en ex- being while C 24 2 . ufc,small surface, 2 layer. 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 3 0 T dipping the sample in a FeCl3 solution. To provide good 0.5 T ohmic contacts, a tri-layer consisting of titanium, plat- 6 1.0 T 1.5 T inum and gold has been evaporated followed by annealing 2.0 T at 750oC. The structures have been suspended by etch- 9 ing the sacrificial SiO layer using HF vapor at 50oC and 2 12 atmospheric pressure for about 10 minutes. Diamond it- self is inert to this chemical etching process. Due to the 15 Transmission (dB) 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- mond structure that has been fabricated by this method. We have also fabricated superconducting diamond res- FIG. 2: Superconducting characteristics of the resonator. The onators that were covered with a 50 nm thick gold layer diamond resonator (sample B) shows a superconducting state in order to test the samples at temperatures above the at zero magnetic field at low input powers (left) and at low superconducting transition temperature and at currents temperatures (right) identified by the plateau region. With increasing input power (temperature), the sample undergoes above the superconducting critical current. This allows a transition into its normal state, its resistance 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 moved using FeCl which does not attack the gold layer. 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 culated critical currents are of the order of few µA, simi- profilometer. lar to what has been measured with DC measurements of similar nanostructures made from BDD30,31. The trans- mission signal of sample B is plotted in figure 2. One can 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 constant transmission directly 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 network analyzer (Rohde - Schwarz ZVL-13) was fed into an increase in impedance at high input powers (temper- a coaxial line at the top of a 3He cryostat with a base tem- atures), which leads to a reduction of the transmitted perature of 500 mK. The signal was delivered to the sam- signal and eventually to the transition of the sample into ple through two attenuation stages: 20 dB at 4.2 K and its normal state. This impedance increase is associated 20 dB at the 1.2 K stage. An ac-current flowing through with the absorption of microwave power. The splitting the sample exposed to a perpendicular external magnetic 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 and leads to a displacement of the nano-mechanical beam our structure and hence the superconducting state32. in plane to the diamond film. On resonance, the beam From the total transmission drop we can calculate the dissipates energy changing its impedance and resulting approximate normal state resistance values to around 300 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 sample A and a normal state resistance close to 2.5 kOhm 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 electrical set-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- − perature of approximately 2.5 K at zero magnetic field 26 in agreement with measurements on non-suspended dia- mond samples27,30,31. We now turn to the mechanical properties of the dia- 25 mond nano-mechanical resonator. By applying a perpen- (10 Damping 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: Damping of the mechanical resonator A as a function 9.39226 MHz and 8.77142 MHz respectively. Using of magnetic field. The quadratic dependence indicates that 2 the damping is governed by eddy-currents. 1 χ Y Iy fres = (1) 2π l2 s ρwt A side effect of the magneto-motive detection tech- with χ = 4.73 being a numerical factor for the beams’ 33 nique is the circulation of eddy currents inside the struc- first flexual mode , Iy being its moment of Inertia, w 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 QE that 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 34,35 = + (2) doped nanocrystalline diamond shows that the boron 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 intrinsic mechanical losses. Figure 4 shows the corre- 0.1 sponding magnetic damping for sample A from which 0.2 we extract the intrinsic unloaded quality factor Qmech 0.3 = 41000 at zero magnetic field. This mechanical qual- ity factor is limited by the surface roughness of the di- 0.4 amond and more importantly by clamping losses due to 0.5 the doubly-clamped beam design. The isotropic etching Transmission (dB) of the sacrificial SiO2 layer leads to an undercut of the 9.3916 9.3920 9.3924 9.3928 anchor pads of the NEMS. The more surface undercut the Frequency (MHz) more dissipation is possible in the vibrating surroundings of the resonators’ clamps, the higher the losses. Possi- ble solutions to increase this quality factor would be to FIG. 3: Mechanical resonance of sample A recorded at 2 Tesla use the so-called free-free beam design39, to reduce the showing a loaded quality factor of 40 000. The red line is a surface losses by smoothing the surface with mechani- Lorentzian fit. cal or chemical polishing before nanofabrication40 and to remove the undercut by means of a focused ion beam From the transmission measurement we can also ex- technique. Nevertheless, the observed quality factors are tract the loaded quality factor Q, which describes the comparable with state-of-the art resonators22,41,42. A rate of energy loss, compared to the energy stored in 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. conclude that the Young’s modulus as well as the quality To convince oneself that the measured resonance is of factor of sample B is lower due to enhanced losses caused 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 2Z0 36–38 S12 = −20βLog[ 2 ] (3) detail in the literature . αB +2Z0 4

2.5 nano-mechanical oscillator. Assuming that this embed- -56 dBm ding impedance changes slowly over the resonance width 2.0 -52 dBm -48 dBm which is justified in our case as the damping is low, we -44 dBm find that the loaded resonance frequency shifts according 1.5 -40 dBm to43

1.0 ℜe(Zext) fl = f0 1+Θ(B − Bc)Zc 2 (4) 0.5 s |Zext| Signal amplitude (dB) 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 2 Magnetic field (T ) 4 is zero below a critical field Bc for the superconducting resonator we can fit our data of the resonance frequency FIG. 5: The signal amplitude as a function of magnetic field at shift as shown in figure 6. From the fit we extract the different input powers. A logarithmic scaling with the squared critical field to Bc = 0.996T which is consistent with magnetic field accounts for a mechanical resonance. the onset of the residual resistance of sample A (not dis- played).

9.39227 IV. CONCLUSION 9.39226 We have demonstrated that nano-mechanical res- 9.39225 onators made from boron doped diamond show super- conducting properties up to magnetic fields of 3 Teslas. 9.39224 These resonators show high quality factors as high as 40000 at a resonance frequency of around 10 MHz. The 9.39223 simple fabrication process of superconducting diamond 0.0 0.5 1.0 1.5 2.0 2.5 3.0 resonators allows for easy implementation into fully su- Resonance frequency (MHz) Magnetic field (T) perconducting diamond circuits such as micro-cavities or superconducting quantum interference devices. Due to FIG. 6: The mechanical center frequency is shifted due to an its remarkable mechanical, electrical as well as optical embedding impedance that appears around 1T. The data has properties we conclude that nano-mechanical resonators been fitted with equation 4. made from boron doped diamond offer an extremely at- tractive system in the growing field of quantum opto- mechanics. 2 2 αB2 Z ξl B where = c = ω0m is the resonators impedance, β adjusts the amplitude of the signal, Z0 is the line 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 nite residual resistance at finite magnetic field as depicted 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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