Microwave cavity-enhanced transduction for plug and play nanomechanics at room temperature

Transcription

1 Received 6 Sep 011 Accepted Fe 01 Pulished 6 Mr 01 DOI: /ncomms173 Microwve cvity-enhnced trnsduction for plug nd ply nnomechnics t room temperture T. Fust 1, P. Krenn 1, S. Mnus 1, J.P. Kotthus 1 & E.M. Weig 1 Following recent insights into energy storge nd loss mechnisms in nnoelectromechnicl systems (NEMS), nnomechnicl resontors with incresingly high qulity fctors re possile. Consequently, efficient, non-dissiptive trnsduction schemes re required to void the dominting influence of coupling losses. Here we present n integrted NEMS trnsducer sed on microwve cvity dielectriclly coupled to n rry of douly clmped pre-stressed silicon nitride em resontors. This cvity-enhnced detection scheme llows resolving of the resontors Brownin motion t room temperture while preserving their high mechnicl qulity fctor of 90,000 t 6.6 MHz. Furthermore, our pproch constitutes n opto - mechnicl system in which ckction effects of the microwve field re employed to lter the effective dmping of the resontors. In prticulr, cvity-pumped self-oscilltion yields linewidth of only 5 Hz. Therey, n djustement-free, ll-integrted nd self-driven nnoelectromechnicl resontor rry interfced y just two microwve connectors is relised, which is potentilly useful for pplictions in sensing nd signl processing. 1 Center for NnoScience (CeNS) nd Fkultät für Physik, Ludwig-Mximilins-Universität, Geschwister-Scholl-Pltz 1, München 80539, Germny. Correspondence nd requests for mterils should e ddressed to E.M.W. (emil: weig@lmu.de).

2 nture communictions DOI: /ncomms173 The incresing importnce of nnomechnicl resontors for oth fundmentl experiments 1 3 nd sensing pplictions 4,5 in recent yers is direct consequence of their high resonnce frequencies s well s low msses. However, ecuse of their smll size, they couple only wekly to their environment, which cn mke it difficult to efficiently trnsduce their motion. This coupling cn e strongly enhnced vi n opticl 6 11 or electricl microwve 1 17 cvity. While oth methods enle sensitive displcement detection, only the ltter is suitle for lrge-scle integrtion of mny resontors with single cvity. Up to now, nnoelectromechnicl trnsduction vi microwve cvities is predominntly performed t cryogenic tempertures to enefit from superconducting cvities cpcitively coupled to superconducting mechnicl resontors. With min focus on quntum mechnicl ground stte cooling, the potentil of cvity nnoelectromechnicl systems (NEMS) for integrted trnsduction t room temperture is yet to e exploited. To this end, we present n pproch sed on copper microstrip cvity operting t 300 K. While previous works 1 16 relied on cpcitive coupling etween cvity nd metllized resontor, we employ dielectric resontor mde of highly stressed silicon nitride. This voids dditionl dmping y losses in the metlliztion lyer, which frequently is one of the dominting sources of dissiption t room temperture 18,19. For trnsduction, we tke dvntge of dielectric grdient forces, which re ecoming more nd more estlished s powerful tool to control NEMS 0 3 : if dielectric em is plced in etween two verticlly offset electrodes, its virtion will induce periodic modultion of their mutul cpcitnce. We demonstrte tht this modultion lters the response of connected microwve cvity, which cn e demodulted to proe the displcement of the nnomechnicl resontor. The resulting heterodyne cvity-enhnced detection scheme llows proing of the resontor s Brownin motion with sensitivity of presently 4.4 pm/ Hz t 300 K. We hve tested the scheme to operte t tempertures etween 300 K nd low tempertures (4 K), t which superconducting cvities ecome superior. Furthermore, the coupled cvity-resontor device is microwve nlogy of n optomechnicl system: cvity electromechnics cn e employed to mplify or dmp the mechnicl virtion utilizing the dynmicl ckction of the microwve field. By strongly mplifying the motion, the regime of cvity-pumped self-oscilltion is reched. The resulting high-mplitude, nrrow-nd signl with linewidth of only 5 Hz cn e used to trck the resonnce frequency of the em, yielding n estimted mss resolution of out g. Results Device nd mesurement setup. Arrys of mechnicl em resontors of different length re fricted out of 100-nm-thick pre-stressed silicon nitride film deposited on fused silic wfer (see Fig. 1 for one element s well s Methods nd Supplementry Fig. S1). Ech nnomechnicl resontor is emedded in cpcitive structure, which is prt of the resonnt LC circuit s sketched in Fig. 1, nd c,d, respectively. One of the electrodes is connected to n externl λ/4 microstrip cvity (see Fig. 1d nd Methods) with resonnce frequency of f c = 3.44 GHz nd qulity fctor of 70, the trnsmission of which is shown in Fig. 1c. In contrst to the more common SiN films on silicon sustrtes, SiN on fused silic voids room temperture dissiption of microwve signls y moile chrge crriers nd genertes n even higher tensile stress in the SiN film 4. Mesuring the resonnce frequencies of severl hrmonic modes nd fitting these with simple theoreticl model 5 yields em stress of 1.46 ± 0.03 GP. Recently, it hs een demonstrted tht the tensile stress in nnomechnicl resontor enhnces its eigenfrequency nd qulity fctor 5,6. Thus, the oserved qulity fctors re higher thn the ones mesured with resontors of the sme eigenfrequency on silicon sustrte with prestress of 0.83 GP, nd ems of the sme length hve higher resonnce d Bond wire E Piezo drive B z Trnsmission (db) RF LO x frequencies. Wheres the descried scheme hs een employed on rnge of microwve cvities nd nnomechnicl resontor rrys, ll mesurements shown here hve een performed on one 55 µm long em with fundmentl mechnicl resonnce frequency of f m = 6.6 MHz nd room temperture qulity fctor Q m = 90,000. By coupling the mechnicl resontor to the microwve cvity, the electricl resonnce frequency f c is periodiclly modulted, cusing sidends t f c ± f m in the microwve trnsmission signl. These re demodulted, filtered nd mplified (see Fig. 1d, Fig. 5 nd Methods), then fed directly into vector network nlyser, the output of which cn e used to excite the mechnicl resontor vi piezo inertil drive 6. The resontor chip, glued onto the piezo trnsducer, s well s the cvity re operted in vcuum chmer t pressures elow mr t room temperture. Detection. The mplitude of the piezo-driven mechnicl resontor (Fig. ) is proed y monitoring the sidend signl vi the c IF LP VNA d Frequency f w (GHz) AMP Microwve source Figure 1 Smple nd setup. shows scnning electron microgrph of the 55 m long silicon nitride em (green) flnked y two gold electrodes (yellow). Scle r corresponds to 1 µm. The schemtic cross-section of the em nd electrodes in (scle r corresponds to 100 nm) exhiits symmetric gp of d = 60 nm nd includes simulted electric field lines. The em is plced just elow the electrodes, where its movement in the z direction induces the lrgest modultion of the cpcitnce. The electrodes re connected to n electricl λ/4 microwve cvity vi ond wires. c depicts its trnsmission spectrum (lck) with Lorentzin fit (green). The schemtic circuit digrm shown in d includes photo of the cvity circuit ord (8 8 mm ). It lso illustrtes mgnetic field lines (lue) indicting the inductive coupling etween the two side electrodes nd the centrl resontor, nd the electric field distriution (red) in the resontor. The cvity is pumped y microwve source, the rdio frequency trnsmission signl is mixed with reference signl (LO) such tht the mechnicl sidends (IF) re demodulted. A lowpss filter (LP) is used to remove higher-frequency components, nd the mplified (AMP) sidend signl is fed to vector network nlyser (VNA), which cn lso drive piezo to ctute the em. See Fig. 5 nd Methods for the detiled circuit. ~ ~

3 nture communictions DOI: /ncomms173 ARTICLE d Amplitude (nv Hz 1/ ) Amplitude (mv) Frequency (MHz) 8 pm Hz 1/ Frequency (MHz) Microwve power P w (dbm) Pek signl power (dbm) Microwve frequency f w (GHz) c Microwve power P w (dbm) Pek signl power (dbm) Figure Detection. The driven response of the 55 mm long em is shown in. It is virting with n mplitude of out 6 nm t piezo-driving power of 70 dbm mesured with microwve power of P µw = 18 dbm t f µw = 3.44 GHz. To determine the operting regime of the detection scheme s function of the cvity prmeters, microwve frequency nd power re systemticlly vried nd the mechnicl pek signl power reflecting the squred resonnce mplitude (tht is, the mximum of the resonnce in ) is plotted in for ech point. A cut long the microwve cvity resonnce (dshed line in ) shown in c depicts tht the detected signl is mximized t cvity powers etween 15 nd 18 dbm. The Brownin motion of the resontor in d is employed to deduce the sensitivity of the detection scheme from the noise floor. demodulted microwve trnsmission signl. Note tht ll mplitudes in this work re given s hlf-pek-to-pek vlues. A Lorentzin fit is used to extrct the mechnicl resonnce mplitude, which depends on the output power P µw nd frequency f µw of the microwve source. Figure shows how the operting rnge of the detection mechnism cn e mpped out y systemticlly vrying the microwve prmeters. The plot displys the colour-coded pek signl power of the mechnicl spectrum, plotted for every set of P µw nd f µw. Mximum sensitivity is chieved on resonnce with the microwve cvity (t f µw = f c = 3.44 GHz, dshed line), where the cvity field nd its sensitivity to frequency chnges re mximized. The pek signl power in Fig. c is directly proportionl to the microwve power t low levels, ut nonliner effects in the cvity cuse the detection efficiency to level off ove P µw = 15 dbm. Using the optiml operting point of f µw = f c nd P µw = 18 dbm, the thermlly induced Brownin motion of the resontor cn e esily resolved, s depicted in Fig. d. By clculting the therml mplitude of the em to e 8 pm/ Hz t room temperture, the oserved noise level corresponds to sensitivity of 4. 4 pm/ Hz (see lso Supplementry Methods). Thus, the full dynmic rnge of the resontor is ccessile s the detection scheme llows to chrcterize the resontor response from the therml motion until the onset of nonliner ehviour. As the detected signl is only proportionl to the chnge in cpcitnce dc/dz cused y displcement dz nd other geometricl prmeters, the displcement sensitivity is independent of the mechnicl frequency. However, higher-frequency ems imply reduced electrode length nd thus weker coupling for constnt cross-section of the detection cpcitor. The sme pplies to higher hrmonic modes, where only one ntinode of odd hrmonic modes genertes signl, s the other ntinodes cncel ech other. This results in 1/f scling of the sensitivity in the cse of stressed string, s oserved in other mesurements for ems with frequencies etween 6 nd 60 MHz. Furthermore, even the in-plne motion of the em cn e detected (not shown). Considering the electrode geometry displyed in Fig. 1, this seems to e suprising t first. Idelly, the cpcitnce grdient dc/dx is prol such tht oth displcement of the em in positive nd negtive x direction increses the cpcitnce symmetriclly. Thus, there should e no signl on the resonnce frequency of the mode. But even smll imperfections during smple friction led to slightly off-centre position of the em nd therey non-zero cpcitnce grdient in the x direction. Therefore, in-plne modes re ccessile, leit with lower sensitivity such tht the Brownin motion cnnot e resolved. Bckction effects. For detuned microwve cvity, the coupling etween the cvity nd the mechnicl resontor gives rise to opto - mechnicl effects such s ckction cooling nd pumping of the mechnicl mode,3,6 1,16,17,7,8. The signture of these cvity electromechnicl effects cn lredy e discerned in the red portion of Fig. nd is shown more clerly in Fig. 3. Comprison of the different mechnicl resonnce curves otined for negtive, positive nd no detuning (inset of Fig. 3) shows tht oth the resonnce mplitudes (Fig. 3) nd the mesured, effective Q( ) (Fig. 3, see Supplementry Methods) chnge with detuning. If the detuning = f µw f c etween microwve drive nd cvity resonnce frequency is negtive (red detuned), the electricl force produced y the cvity field countercts the virtionl motion, therey decresing its mplitude. For positive (lue) detuning, the mplitude is incresed. As the resonnce mplitude depicted in Fig. 3 is superimposed with the detuning-dependent sensitivity curve discussed in Fig. nd therefore distorted, we rther use the detuning dependence of the qulity fctor to nlyse the dt. The effective Q( ) in Fig. 3 clerly shows the expected ehviour: t negtive detuning, the dditionl cvity-induced dmping Γ( ) is positive, such tht the effective dmping exceeds the intrinsic vlue nd Q( ) decreses, wheres t positive detuning the opposite occurs, with n optiml detuning of opt = 9 MHz. Fitting the theoreticl model (refs 7 9 nd Supplementry Methods) to the dt mesured t severl cvity drive powers llows to extrct the verge coupling fctor g = fc / z = 75 ± 5 Hz/nm. The ckction effect is independent of piezo-driven em ctution s only the effective dmping is chnged. This is confirmed y repeting the experiment without piezo ctution (inset of Fig. 3). A comprison etween the wekly driven sitution depicted in Fig. 3 nd the Brownin motion in the inset only shows significnt increse of the noise in the ltter cse. Therefore, ll mesurements in Figs 3 nd 4

4 Resonnce mplitude (mv) Q( ) ( 10 5 ) Amplitude (mv) Q( )( 10 5 ) Offset (Hz) Detuning (MHz) Detuning (MHz) Detuning (MHz) Figure 3 Cvity electromechnics. Resonnce mplitude nd qulity fctor of the wekly driven (piezo power of 70 dbm) mechnicl mode re incresed or decresed depending on the microwve detuning = f w f c due to the ckction of the microwve field on the resontor. This is shown in the inset of, compring resonnce curves of the sme resonnce t microwve power of 1 dbm for red, lue or no (red, lue nd lck points, respectively) detuning. For clrity, the resonnce curves hve een plotted versus the frequency offset to the respective (detuning-dependent) resonnce frequency. Pnel shows the detuning dependence of the resonnce mplitude (tht is, mximum in inset) for different microwve powers of 18, 15 nd 1 dbm (green, red nd ornge dots). In, the detuning dependence of the qulity fctor for the sme power vlues is depicted, long with fit to the theoreticl model (lck line, see Supplementry Methods). The inset of shows the qulity fctor of the Brownin motion versus detuning t 18 dbm microwve power with identicl xes, the only difference to the min plot is the etter signl to noise rtio in the wekly driven cse. (except the inset in Fig. 3) were done with wek piezo ctution of 70 dbm to operte with n improved signl to noise rtio. Incresing the microwve power to 3 dbm, the qulity fctor cn e decresed to hlf its initil vlue with negtive s shown in Fig. 4, corresponding to n effective mode temperture of 150 K (ref. 6). For positive, the qulity fctor diverges. This reflects cvity-driven self-oscilltion of the em, once the intrinsic dmping is cncelled y the cvity ckction. The power spectrum of this oscilltion is shown in Fig. 4. Its linewidth of 5 Hz, corresponding to n effective qulity fctor 30 of 1.3 million, is limited y the stility of the oscilltion frequency, which is minly ffected y fluctutions of the cvity drive. This ultr-low linewidth is idelly suited for mss-sensing pplictions, giving rise to n estimted mss resolution of out g (see Supplementry Methods). In contrst to single cron nnotues, which hve een employed to proe msses of 10 g (refs 4,5), the presented scheme cn redily e scled up to lrge-scle friction process involving mny ems. Further improvements cn e expected y incresing the electromechnicl coupling constnt,13. Power (dbm Hz 1 ) Q( opt ) ( 10 3 ) nture communictions DOI: /ncomms173 1, Microwve power P w (dbm) Frequency (MHz) Figure 4 Cvity-induced dmping nd self-oscilltion. Using luedetuned (red-detuned) cvity drive, the mplitude of the em cn e mplified (dmped). This effect is controlled y the microwve power P µw, s shown in (lue squres: lue detuning, red tringles: red detuning) for the optiml opt of ± 9 MHz. By incresing the microwve power to 3 dbm, the ckction gin cused y the lue-detuned cvity exceeds the intrinsic dmping, nd self-oscilltion occurs. The respective power spectrum in shows linewidth reduced to 5 Hz. This cn e chieved y reduced gp size in the detection cpcitor. Bem electrode seprtions of 0 nm hve lredy een demonstrted 15, which should yield tenfold increse in coupling. Besides the ckction effects, there is qusisttic electric force cting on the resontor 1. The electric microwve field etween the electrodes polrizes the dielectric em, creting dipoles tht re ttrcted to high electric fields. This leds to n dditionl effective spring constnt tht scles with the squre of the field (tht is, with P µw ) nd leds to n incresed (decresed) restoring force for the out-of-plne (in-plne) mode. The resulting difference in resonnce frequency is clerly visile compring Fig. (P µw = 18 dbm) to Fig. 4 (P µw = 3 dbm) nd cn e employed to tune the mechnicl eigenfrequency. Discussion There re only few existing nnomechnicl trnsduction schemes t room temperture providing good integrtion nd sclility to lrge resontor rrys coupled to single redout cvity: photonic circuits offer extremely lrge displcement sensitivities, ut re limited y the precise lignment of externl components nd thus sensitive to virtions. On the other hnd, djustment-free schemes such s piezoelectric trnsduction 34 or cpcitive detection 13,35, which, in ddition, frequently require cryogenics, impose mteril constrints nd cn cuse dditionl dissiption 18,19. In contrst, the presented dielectric coupling of the nnomechnicl resontor to the microwve cvity llows to mintin lrge qulity fctor over wide temperture rnge (tested etween 4 nd 300 K). Accordingly, the reported room temperture Q m of 90,000 of the prestressed SiN-on-fused-silic nnoresontor is, to our knowledge, the highest ever otined in this frequency rnge. In conclusion, we present room temperture pltform for the sensitive redout, ctution nd tuning of nnomechnicl resontors. We chieve sensitivity well elow the Brownin motion for the fully integrle nd roust heterodyne redout of nnomechnicl resontor vi wekly coupled microwve cvity (g = fc / z = 75 ± 5 Hz/nm). This coupling constnt is significntly smller thn the one otined with cpcitively coupled

5 nture communictions DOI: /ncomms173 Piezo drive C 0 VNA C 1 dc 1 AMP ems 13 ut requires neither cryogenics nor em metlliztion. The reltive cvity frequency shift g/f c is comprle to typicl opticl experiments,36, s not only the coupling constnt g ut lso the cvity resonnce frequency f c re orders of mgnitude smller in the microwve regime. A mjor dvntge of the presented scheme is the prllel redout of mny ems nd mny modes (higher hrmonics s well s in- nd out-of-plne) using only single microwve setup. Additionlly, the cvity ckction cn e used to control the mplitude of the resontor, thus llowing to omit the piezo ctutor. By entering the regime of cvity-pumped self-oscilltion strong nd nrrownd signl is generted, perfectly suited for sensing pplictions requiring simple resonnce frequency redout. As oth resontor nd cvity re fricted reproducily using stndrd lithogrphic processes, inexpensive plug nd ply NEMS sensor modules using only two microwve connectors to interfce them with control electronics cn e developed. Methods Microwve setup. The microwve cvity is fricted on cermic sustrte suitle for high-frequency pplictions (Rogers TMM10) cut to smll chips. Stndrd opticl lithogrphy nd wet etch processes re employed to pttern the 17 µm thick top copper lyer, onto which 150 nm gold coting is evported to void corrosion. The design of the microwve cvity shown in Fig. 1d consists of n 8 mm long nd 0.64 mm wide centre strip tht forms the ctul λ/4 resontor. One end of the strip is grounded, while its other end is connected to the silic chip crrying the mechnicl resontors. Two djcent strips ner the grounded end re used to inductively couple the cvity to the feed lines nd mesure the trnsmission signl. We chose inductive coupling to seprte the interfce to the chip t the open end from the interfce to the feed lines t the grounded end of the λ/4 resontor. The length of the two feed lines (6 mm) nd the distnce etween the striplines (1. mm) were optimized using high-frequency circuit simultions with APLAC for trdeoff etween trnsmission nd qulity fctor of the cvity. Figure 5 shows detiled version of the simplified electricl circuit depicted in Fig. 1d. On the left, the electricl equivlent circuit of the λ/4 microstrip cvity including oth feed lines nd the coupling to the chip is depicted. The ctul cvity consists of the inductnce L 0 of the 8 mm long copper strip nd its cpcitnce C 0 to the ground plne on the ottom of the circuit ord. The inductive coupling etween L 0 nd the two feed lines with inductnces L c provides the externl interfce to the cvity. The resontor chip is connected to the open end of the cvity, it dds sttic cpcitnce C 1 nd time-dependent contriution dc 1 (t), which oscilltes with the ctul em displcement. A very rough estimte for L 0 nd C 0 cn e otined from microstrip theory, giving vlues of 1 pf nd 3 µh (this would result in fc = 1 /( p L0C0 ) =. 9 GHz), neglecting the effects of the microstrip ends. As the resonnce frequency of the re microwve cvity is out 5% higher thn with the ond wire nd chip connected, C 1 must e < 10% of C 0, s the ond wire lso dds some inductnce to the circuit. A microwve tone is pplied to one port of the cvity, thus creting phse-modulted signl t the other port of the cvity cused y the lternting cpcitnce dc 1. As the trnsmission through the cvity lso dds some detuningdependent phse to the microwve tone, directly mixing the cvity output with the drive tone would result in detuning-dependent phse difference etween the two signls. This difference would need to e compensted for y n dditionl phse RF RF LP 9 LO IF IF* LO* 9 Microwve drive Figure 5 Detiled electricl schemtic. Detiled version of Fig. 1d showing n electricl equivlent circuit of the microwve cvity (green ox) coupled to the resontor chip (lue ox) nd the complete IQ mixing circuit (red ox). The two signl pths offset y 9 re denoted LO/IF nd LO*/IF*, respectively. ARTICLE shifter, which hd to e djusted for mximum signl t every drive frequency. To void this tedious procedure, we use n IQ (in-phse/qudrture) mixer shown in the red ox in Fig. 5. It consists of / nd /9 power splitter s well s two mixers. The reference signl coming from the microwve genertor is split into two prts with 9 phse shift to ech other. By mixing these two signls (LO nd LO*) with the rdio frequency trnsmission signl of the cvity, two intermedite frequency signls (IF nd IF*) re creted. Depending on the phse of the two input signls of the IQ mixer, t lest one of these signls is lwys non-zero, nd their (phse-correct) sum is completely independent of the phse reltion of the input signls. Thus, y comining the two demodulted qudrture components with nother /9 power splitter nd locking the higher-frequency mixing products, mplitude nd phse of the mechnicl signl re reconstructed. The noise ckground of this signl is primrily cused y the phse noise of the frequency genertor driving the electricl cvity, cusing more ckground noise with incresing power. Therefore, we use Rohde nd Schwrz SMA100A signl genertor with extremely low phse noise elow 150 dbc t 10 MHz offset. In order to preserve the low noise level, the demodulted sidends re mplified with 35 db premplifier with noise figure of 1.3 db. The output of this mplifier is either directly connected to spectrum nlyser (to quntify the Brownin motion) or mplified y nother 30 db nd fed to network nlyser (in cse of the driven mesurements). Resontor friction. The smples re fricted on 500 µm thick fused silic wfers, which re coted with 100 nm thick commercil high-qulity LPCVD lyer of pre-stressed silicon nitride. Lrge chips of size 5 5 mm re cut from the wfer. To enle electron em lithogrphy on these non-conductive sustrtes, nm of chromium is evported onto the PMMA resist efore exposure nd removed efore developing. E-em lithogrphy nd stndrd lift-off processes re used to define the gold electrodes nd thin colt etch msk protecting the ems. The susequent inductively coupled plsm rective ion etch using SF 6 nd Ar removes the silicon nitride which is not protected y metl lyer. The finl hydrofluoric cid wet etch removes the colt nd releses the ems, while the gold electrodes use chromium s n dhesion lyer nd re not ttcked y the cid. Finlly, the chips re low-dried with nitrogen, glued to the piezo nd wire onder is used to connect them to the microwve cvity. All these processing steps use industry-stndrd techniques, so lrge-scle friction of inexpensive sensor modules should e within rech. Ech mechnicl resontor chip contins multiple ems with their respective electrodes, ll shunted etween two ond pds tht re used to connect the chip to the microwve cvity. One design with ig vritions in the em length is shown in Supplementry Fig. S1. It is lso possile to use designs with very smll length differences in the order of 100 nm, llowing to ddress mny mechnicl resonnces y frequency division multiplexing in nrrow frequency nd. Resontor chip design. In order to choose the smple design with the highest coupling etween the electricl cvity nd the mechnicl resontor, severl simultions of the electrode configurtion using COMSOL Multiphysics were conducted. The electrodes were ptterned directly onto the SiN film to induce mximl cpcitnce vrition with em displcement. We decided to put the gold electrodes on top of the silicon nitride lyer nd therey deposit them efore the rective ion etch step, in contrst to our erlier designs where the gold ws evported onto the remining silicon dioxide covering the silicon sustrte elow the resontor 1. In these previous designs, the verticl seprtion etween the em nd the silicon dioxide lyer hd to exceed 50 nm to chieve sufficient underetching of the em. Thus the new design llows for much smller overll em electrode seprtions, resulting in lrger effect of the em motion on the cpcitnce. Further simultions with this principl geometry vried severl other prmeters. These primrily show n 1/d scling etween the lterl em electrode distnce d (see Fig. 1) nd the cpcitnce chnge per nnometre em displcement, s expected for cpcitive interction. As the ems tend to stick to the side electrodes t very low gp sizes, the friction of smller defect-free gps y conventionl scnning electron microscopy lithogrphy nd dry nd wet etching ws not successful. We hve investigted devices with gp widths vrying etween 110 nm nd 60 nm. Supplementry Figure S shows the coupling strength (lck squres) extrcted from the qulity fctor versus microwve frequency curves, s shown in Fig. 3, for different vlues of d. The dotted red curve depicts the cpcitnce grdients otined from the simultion multiplied with scling fctor to fit the mesured coupling strength. The dependence of the coupling strength on the gp size in the mesurements is qulittively reproduced y the simultions. References 1. O Connell, A. D. et l. Quntum ground stte nd single-phonon control of mechnicl resontor. Nture 464, (010).. Teufel, J. D. et l. Sidend cooling of micromechnicl motion to the quntum ground stte. Nture 475, (011). 3. Chn, J. et l. Lser cooling of nnomechnicl oscilltor into its quntum ground stte. Nture 478, 89 9 (011). 4. Lssgne, B., Grci-Snchez, D., Agusc, A. & Bchtold, A. Ultrsensitive mss sensing with nnotue electromechnicl resontor. Nno Lett. 8, (008).

6 nture communictions DOI: /ncomms Jensen, K., Kim, K. & Zettl, A. An tomic-resolution nnomechnicl mss sensor. Nt. Nno. 3, 533 (008). 6. Metzger, C. H. & Krri, K. Cvity cooling of microlever. Nture 43, (004). 7. Gign, S. et l. Self-cooling of micromirror y rdition pressure. Nture 444, (006). 8. Arcizet, O., Cohdon, P.- F., Brint, T., Pinrd, M. & Heidmnn, A. Rditionpressure cooling nd optomechnicl instility of micromirror. Nture 444, (006). 9. Kleckner, D. & Bouwmeester, D. Su-kelvin opticl cooling of micromechnicl resontor. Nture 444, (006). 10. Schliesser, A., Riviere, R., Anetserger, G., Arcizet, O. & Kippenerg, T. J. Resolved-sidend cooling of micromechnicl oscilltor. Nt. Phys. 4, (008). 11. Eichenfield, M., Cmcho, R., Chn, J., Vhl, K. J. & Pinter, O. A picogrmnd nnometre-scle photonic-crystl optomechnicl cvity. Nture 459, (009). 1. Brown, K. R. et l. Pssive cooling of micromechnicl oscilltor with resonnt electric circuit. Phys. Rev. Lett. 99, (007). 13. Regl, C. A., Teufel, J. D. & Lehnert, K. W. Mesuring nnomechnicl motion with microwve cvity interferometer. Nt. Phys. 4, (008). 14. Sillnpää, M. A., Srkr, J., Sulkko, J., Muhonen, J. & Hkonen, P. J. Accessing nnomechnicl resontors vi fst microwve circuit. Appl. Phys. Lett. 95, (009). 15. Sulkko, J. et l. Strong gte coupling of high-q nnomechnicl resontors. Nno Lett. 10, (010). 16. Rocheleu, T. et l. Preprtion nd detection of mechnicl resontor ner the ground stte of motion. Nture 463, 7 75 (010). 17. Ho, L., Gllop, J. C. & Cox, D. Excittion, detection, nd pssive cooling of micromechnicl cntilever using ner-field of microwve resontor. Appl. Phys. Lett. 95, (009). 18. Sekric, L., Crr, D. W., Evoy, S., Prpi, J. M. & Crighed, H. G. Nnomechnicl resonnt structures in silicon nitride: friction, opertion nd dissiption issues. Sens. Actutors A: Phys. 101, (00). 19. Yu, P.- L., Purdy, T. P. & Regl, C. A. Control of mteril dmping in high-q memrne microresontors. Preprint t (011). 0. Schmid, S., Wendlndt, M., Junker, D. & Hierold, C. Nonconductive polymer microresontors ctuted y the kelvin polriztion force. Appl. Phys. Lett. 89, (006). 1. Unterreithmeier, Q. P., Weig, E. M. & Kotthus, J. P. Universl trnsduction scheme for nnomechnicl systems sed on dielectric forces. Nture 458, (009).. Anetserger, G. et l. Ner-field cvity optomechnics with nnomechnicl oscilltors. Nt. Phys. 5, (009). 3. McRe, T. G., Lee, K. H., Hrris, G. I., Knittel, J. & Bowen, W. P. Cvity optoelectromechnicl system comining strong electricl ctution with ultrsensitive trnsduction. Phys. Rev. A 8, 0385 (010). 4. Retjczyk, T. F. & Sinh, A. K. Elstic stiffness nd therml expnsion coefficients of vrious refrctory silicides nd silicon nitride films. Thin Solid Films 70, (1980). 5. Unterreithmeier, Q. P., Fust, T. & Kotthus, J. P. Dmping of nnomechnicl resontors. Phys. Rev. Lett. 105, 0705 (010). 6. Verridge, S. S., Prpi, J. M., Reichench, R. B., Belln, L. M. & Crighed, H. G. High qulity fctor resonnce t room temperture with nnostrings under high tensile stress. J. Appl. Phys. 99, (006). 7. Mrqurdt, F., Chen, J. P., Clerk, A. A. & Girvin, S. M. Quntum theory of cvity-ssisted sidend cooling of mechnicl motion. Phys. Rev. Lett. 99, (007). 8. Teufel, J. D., Regl, C. A. & Lehnert, K. W. Prospects for cooling nnomechnicl motion y coupling to superconducting microwve resontor. New J. Phys. 10, (008). 9. Clerk, A. A., Devoret, M. H., Girvin, S. M., Mrqurdt, F. & Schoelkopf, R. J. Introduction to quntum noise, mesurement, nd mplifiction. Rev. Mod. Phys. 8, (010). 30. Feng, X. L., White, C. J., Hjimiri, A. & Roukes, M. L. A self-sustining ultrhigh-frequency nnoelectromechnicl oscilltor. Nt. Nno 3, 34 (008). 31. Pernice, W. H. P., Li, M. & Tng, H. X. Optomechnicl coupling in photonic crystl supported nnomechnicl wveguides. Opt. Express 17, (009). 3. Lin, Q., Rosenerg, J., Jing, X., Vhl, K. J. & Pinter, O. Mechnicl oscilltion nd cooling ctuted y the opticl grdient force. Phys. Rev. Lett. 103, (009). 33. Eichenfield, M., Chn, J., Cmcho, R. M., Vhl, K. J. & Pinter, O. Optomechnicl crystls. Nture 46, 78 8 (009). 34. Mhoo, I. & Ymguchi, H. Prmetriclly pumped ultrhigh q electromechnicl resontor. Appl. Phys. Lett. 9, (008). 35. Knoel, R. G. & Clelnd, A. N. Nnometre-scle displcement sensing using single electron trnsistor. Nture 44, (003). 36. Thompson, J. D. et l. Strong dispersive coupling of high-finesse cvity to micromechnicl memrne. Nture 45, 7 75 (008). Acknowledgements The finncil support y the Deutsche Forschungsgemeinschft vi Project No. Ko 416/18, the Germn Excellence Inititive vi the Nnosystems Inititive Munich (NIM) (which lso contriuted the title illustrtion) nd LMUexcellent, the Germn- Isreli Foundtion (G.I.F.), s well s the Europen Commission under the FET-Open project QNEMS (3399) is grtefully cknowledged. We would like to thnk Florin Mrqurdt nd Johnnes Rieger for stimulting discussions. Author contriutions All uthors plnned the experiment nd discussed the dt. The smple ws fricted y P.K., the mesurement ws crried out y P.K. nd T.F. in setup uild y P.K., T.F. nd S.M., who especilly helped with the microwve mesurements. T.F. nd P.K. nlysed the dt, nd T.F., J.P.K. nd E.M.W. wrote the mnuscript. Additionl informtion Supplementry Informtion ccompnies this pper t nturecommunictions Competing finncil interests: The uthors declre no competing finncil interests. Reprints nd permission informtion is ville online t reprintsndpermissions/ How to cite this rticle: Fust, T. et l. Microwve cvity-enhnced trnsduction for plug nd ply nnomechnics t room temperture. Nt. Commun. 3:78 doi: /ncomms173 (01). License: This work is licensed under Cretive Commons Attriution-NonCommercil- NoDerivtive Works 3.0 Unported License. To view copy of this license, visit cretivecommons.org/licenses/y-nc-nd/3.0/