Interconnect-free parallel logic circuits in a single mechanical resonator

Transcription

1 RTICLE Reeived ug 1 epted 19 Jn 11 Pulished 15 Fe 11 DOI: 1.18/nomms11 Interonnet-free prllel logi iruits in single mehnil resontor I. Mhoo 1, E. Flurin 1, K. Nishiguhi 1,. Fujiwr 1 & H. Ymguhi 1 In onventionl omputers, wiring etween trnsistors is required to enle the exeution of oolen logi funtions. This hs resulted in proessors in whih illions of trnsistors re physilly interonneted, whih limits integrtion densities, gives rise to huge power onsumption nd restrits proessing speeds. method to eliminte wiring mongst trnsistors y ondensing oolen logi into single tive element is thus highly desirle. Here, we demonstrte novel logi rhiteture using only single eletromehnil prmetri resontor into whih multiple hnnels of inry informtion re enoded s mehnil osilltions t different frequenies. The prmetri resontor n mix these hnnels, resulting in new mehnil osilltion sttes tht enle the onstrution of ND, OR nd XOR logi gtes s well s multiit logi iruits. Moreover, the mehnil logi gtes nd iruits n e exeuted simultneously, giving rise to the prospet of prllel logi proessor in just single mehnil resontor. 1 NTT si Reserh Lortories, NTT Corportion, tsugi-shi, Kngw -198, Jpn. Correspondene nd requests for mterils should e ddressed to I.M. (emil: imrn@will.rl.ntt.o.jp) or to H.Y. (emil: hiroshi@will.rl.ntt.o.jp). nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.

2 RTICLE nture ommunitions DOI: 1.18/nomms11 The onept of enoding multiple signls with different frequenies ws originlly pioneered in optil re networks to inrese their pity 1. To hieve this, wvelength division multiplexing (WDM) ws developed, whih enles single optil re to operte s it were undle of res. Stte-ofthe-rt WDM n enle more thn 1, different wvelengths of light to propgte in prllel through single re, yielding drmti inrese in signl throughput in n optil re network. Coneptully, WDM n e regrded s not ddressing rel spe, tht is, the hoie of prtiulr optil re, ut rther s ddressing frequeny spe, tht is, the hoie of wvelength in given optil re. On the sis of this priniple, here, we demonstrte the oolen logi nlogue where inry informtion is not enoded in physilly distint devies, ut is insted enoded s different osilltion frequenies in single devie the inresingly ommon eletromehnil resontor 5,6. This novel pproh llows single devie to not only operte s it were fully integrted logi iruit ut lso to operte s prllel logi proessor enling the simultneous exeution of multiple oolen funtions where ruilly ll interonnets hve een eliminted. Results Devie. The Gs/lGs-sed mehnil resontor used in this study is shown nd desried in Figures 1 nd 1, nd hs fundmentl mode t f = ω /π = 155,7 Hz with qulity ftor Q = 1, (Fig. 1 nd Methods) 7. The piezoeletri effet in the Gs/lGs heterostruture n enle eletril tution nd detetion of mehnil motion s well s the prmetri mplition vi fore onstnt modultion 8 1. mong the 1 independent eletril ontts, single twodimensionl eletron gs (DEG) ontt is used for inry informtion input with frequeny round f, nd the gte loted diretly ove (gte 1) is used for injeting n exittion round f. Heneforth, these exittions re termed pump nd signl, respetively, in nlogy with frequeny onversion in optil prmetri mpliers 11. The signl n diretly exite mehnil osilltion nd is neessry for funtionlizing logi opertions. In ontrst, the K K K s1 s Lok-in p p pc r Idler, = f p -f s nd so on (logi output) 1 m mplitude (1 11 ) , ,76 155,7 Frequeny (Hz) Pump, f p (logi input) Signl, f s (referene) Figure 1 The eletromehnil prmetri resontor. () shemti of the experimentl setup where the mehnil resontor is in the geometry of douly lmped em (grey) with length, width nd thikness of 6, 8, nd 1.5 µm, respetively, nd it hosts n out-of-plne osilltion mode. The mehnil osilltor hs Shottky u-eletrodes (ornge) loted ove oth lmping points, elow whih DEG is loted (red). pplition of.. is to either the DEG or the u-eletrodes n trigger oth hrmoni nd prmetri resonnes where the mehnil motion is monitored y deteting in either lok-in mplier or spetrum nlyser the motion-indued piezovoltge, whih is mplied y n on-hip mplier (red tringle) nd room temperture trnsimpedne mplier (lk tringle). In ll ses, the signls s1 nd s re pplied to the lrge u-eletrode with 5 µv rms tution mplitude nd the pumps p, p nd pc re pplied to the DEG with mv rms tution mplitude where the referene r is used for the lok-in mesurements. () flse-olour snning eletron mirosopi imge of the eletromehnil resontor where the pump (logi input), signl exittion (to funtionlize logi opertions) nd the idler (logi output) re mrked. () The eletromehnil resonne (dots) mesured vi the lok-in mplier nd tted with hrmoni osilltor response (line). nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.

3 nture ommunitions DOI: 1.18/nomms11 RTICLE 155,7 Detuning, δ (Hz) f s 1st 1st f s 155,7 n n nd 155,7 f n d + n 155, ,7 155,7 155,7 155,7 Signl frequeny, f s (Hz) Figure The mehnil idler dynmis. () The response of the mehnil osilltor mesured vi the lok-in mplier with f p = f + where = Hz nd f s = f + δ revels the fundmentl mode f s nd the idler = f δ. () The orresponding theoretil response generted from eqution (9) (Methods). () The response of the mehnil osilltor mesured vi the lok-in mplier, with f p = f + nd f p = f where =.5 Hz, nd f s = f + δ revels, in ddition to f s, the two rst-order idlers 1st nd 1st nd two seond-order idlers nd tht n e used to implement mehnil logi gtes. (d) The orresponding numeril simultion exept eqution (9) is modied to inlude two pumps, nd ll the higher order idlers re lelled (Methods). In ll ses, the experimentl response is roder thn the numeril simultions euse of n experimentl resolution nd width (RW) of 5 mhz. pump nnot diretly exite mehnil motion s its mplitude is elow the prmetri resonne threshold 7. However, the intertion etween signl nd pump results in the exittion of mehnil motion s shown elow. Within the resonne ndwidth, multiple osilltions t different frequenies n e simultneously exited y injeting multiple pumps with slightly different frequenies. In ll ses, the motion ws eletrilly deteted vi gte, tht is, this gte is used for the redout of oolen funtions s shown in Figure 1. Mehnil idler genertion. Prmetri frequeny onversion hs n essentil role in the exeution of logi funtions in this rhiteture nd its opertion is rst desried here 1,1. pump with xed frequeny, f p = f, is injeted into the DEG, while signl t frequeny f s = f + δ, where δ is vrile, is pplied to gte 1. The frequeny response mesured vi gte is shown in Figure s funtion of f s nd the orresponding theoretil response is shown in Figure (Methods). In ddition to the input signl (lue rrow), n dditionl osilltion with negtive slope (green rrow) is oserved. This exittion rises euse of mixing etween f p nd f s resulting in the retion of n idler t = f p f s = f δ, thus demonstrting mehnil prmetri frequeny onversion for the rst time (Supplementry Note 1 nd Supplementry Figure S1). Logi gtes. To demonstrte the ND ( ) opertion, two pump exittions with frequeny f p = f + nd f p = f with xed detuning re injeted into the DEG, whih orrespond to inry inputs nd, respetively, where the sene (presene) of the pump yields the inry input (1). The frequeny response mesured vi gte nd shown in Figure (long with the orresponding theoretil response in Fig. d) now revels not only the ove rst-order idlers = f + δ nd = f δ (green rrows) orresponding to the two pumps ut lso two seond-order idlers (purple rrows). The seond-order idlers rise euse of mixing etween the rst-order idlers nd, nd the two pumps f p nd f p, resulting in f p = f + + δ nd f p = f + δ (Methods). It should e emphsized tht the seond-order idlers n only e reted when the two pumps p nd p re tive, thus enling the exeution of the logi gte where the sene (presene) of the idlers orresponds to the inry output (1). Next, to demonstrte the OR ( ) opertion, the mehnil resontor is injeted with two signls t f s1 = f + + δ nd f s = f + δ, whih results in the referene virtions eing exited y oth s1 nd s (Supplementry Note nd Supplementry Figure S). The omplete set odlers reted when ll the signls nd pumps re tivted is shown in Figure. tivting only f p yields two rstorder idlers f δ (green rrow) nd f δ + (lk rrow ). tivting only f p yields f δ (red rrow ) nd f δ (green rrow). From these mesurements, it is seen tht the f δ idler n e exited y either pump or pump, whih enles the reliztion of the gte. The mehnil frequeny response otined nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.

4 RTICLE nture ommunitions DOI: 1.18/nomms11 Detuning, δ (Hz) 155,7 155,7 Line Line 1 n n 155,7 155,7 Signl frequeny, f s (Hz) Output mplitude (nhz.5 ) iv i 155,7 155,7 iv i Normlized output mplitude Reltive phse, φ (deg) 6 d Output mplitude (nhz.5 ) 1.5 iv iv i 155,7 i 155,7 Figure Mehnil logi gtes. () The mehnil resontor s response mesured vi the lok-in mplier with two signl exittions t f s1 = f + + δ nd f s = f + δ nd two pump exittions t f p = f + nd f p = f where =.5 Hz. Using this response, n gte n e relized y ny seondorder idler (lue rrows), the gte n e relized vi the degenerte rst-order idler (green rrow) nd the gte n e relized vi the degenerte idler t extly f r = f (purple irle). () Two-it inry input hnnels nd n e enoded vi f p nd f p where the nd logi gtes n e relized y mesuring the response of the mehnil resontor long the line 1 in s funtion of pump nd, while oth signl exittions re tive. The resulting response mesured vi spetrum nlyser with RW of 5 mhz revels oth nd gtes in prllel in single mehnil resontor. () The gte n lso e relized vi the degenerte idler t extly f r = f (purple irle in ) y vrying the phse differene etween s1 nd s, whih n led to oth onstrutive nd destrutive interferene. The destrutive interferene n e used to relize logi gte when φ = 9 where the dots re from the experimentl mesurement nd the line is the result of numeril simultion (Methods). (d) The gte is demonstrted long line in t f r = f y mesuring the response of the mehnil resontor in spetrum nlyser with RW = 5 mhz s funtion of p nd p when the phse differene etween s1 nd s is 9 with n on/off rtio of 1:1. ll the spetr re offset for lrity nd re numered (romn numerls) to orrelte with the numered truth omintions in their orresponding truth tles where the vrious inputs nd gtes hve een olour oded. t xed signl frequeny (long line 1 in Fig. ) s funtion of pump exittion is shown in Figure nd it lerly demonstrtes the ND nd OR opertion. It should e emphsized tht the two logi outputs n e otined in prllel with only single devie in ontrst to onventionl logi devies where only sequentil opertion is ville. To implement the XOR ( ) gte, we exploit the interferene etween the two idlers long f δ y simply djusting the reltive phse φ etween s1 nd s. t n pproprite vlue of φ, the f δ idler n e ompletely nelled t f s = f when oth pumps nd re tive s shown in Figure, whih enles the reliztion of the gte s funtion of pump exittion (long line in Fig. ) s shown in Figure d. The reliztion of universl eletromehnil logi gte in single devie with ND, OR nd XOR funtions n enle the onstrution of ny other logi gte. Logi iruits. eyond the implementtion of fundmentl two-it logi gtes, we lso investigte the prospet of multiit logi iruits in single mehnil resontor. To do this, third pump is injeted into the system t f pc = f +, whih is used to enode third-it lelled s C. The resulting response of the system mesured s ove vi gte s funtion of f s is shown in Figure long with the orresponding theoretil response in Figure (Methods). To demonstrte multiit logi iruit, we implement the sequene ( C), where, nd C re the inry input hnnels t f p, f p nd f pc, respetively. This logi iruit n e deomposed s nd C, whih n e mthemtilly represented y two seondorder idlers f p (f p f s ) nd f p (f pc f s ), where f s is either due to s1 or s. To hieve mximum delity for this logi iruit, the idlers must only interset with eh other nd their visiility will e mximized t f. Rewriting the signl nd pump exittions s f s1 = f + s1, f s = f + s, f p = f + p, f p = f + p nd f pc = f + pc n enle these oundry onditions to e expressed s = p p + s(1 or ) nd = p pc + s(1 or ), where p p pc. From these expressions, the detunings for the signl nd pump exittions tht led to 1% delity for the ( C) logi iruit n e extrted, nd the resulting iruit is exeuted in Figure. Using similr nlytil pproh, vrious -it logi iruits n e onstruted in prllel inluding ( ) ( C) (C ), tht is, the mjority gte whih is shown in Figure d (Supplementry Figure S for dditionl iruits). ll logi opertions inluding multiit logi iruits n e reprodued y numeril simultions, nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.

5 nture ommunitions DOI: 1.18/nomms11 RTICLE Detuning, δ (Hz) 155,7 155,7 n n 155,7 155,7 155,7 155,7 Signl frequeny, f s (Hz) Output mplitude (nhz.5 ) 8 6 C C v v 1 1 vi 1 v iv 1 1 i v v vi v iv i d 6 155,7 155,7 C C v v vi C v iv v vi 1 1 v iv 1 1 i i v Figure Multiit mehnil logi iruits. () The response of the mehnil resontor mesured vi the lok-in mplier with two signl exittions t f s1 = f + + δ nd f s = f + δ nd three pumps f p = f +, f p = f nd f pc = f + where =.5 Hz. () The orresponding numeril simultion exept eqution (9) is modied to inlude three pumps nd two signls (Methods). () The -it ( C) logi iruit is onstruted with the two seond-order idlers f p (f p f s ) nd f p (f pc f s ) where s1 = s =.5 Hz, p =.5 Hz, p =.5 Hz nd pc =.75 Hz. (d) The ( C) nd ( ) ( C) (C ) logi iruits re onstruted in prllel from rst nd seond-order idlers f p = f s, f p (f pc f s ) nd three seond-order idlers f p (f p f s ), f p (f pc f s ) nd f pc (f p f s ), respetively, with s1 =.5 Hz, s = 1 Hz, p =.5 Hz, p =.5 Hz nd pc =.75 Hz. In oth ses, the mehnil prmetri resontor ws smpled vi spetrum nlyser with n RW = 1.5 mhz. ll the spetr re offset for lrity nd re numered (romn numerls) to orrelte with the numered truth omintions in their orresponding truth tles where the vrious inputs nd iruits hve een olour oded. thus enling more dvned logi iruits to e esily designed (Methods). generlized formulism to implement multiit logi iruits for ritrry oolen funtions will e reported elsewhere. Disussion The rst progrmmle omputer ws pioneered in mehnil rhiteture lmost two enturies go 1. However, mehnil omputtion ws rendered osolete with the dvent of the trnsistor 15, whih gve rise to n eletril inry-unit (it) for oolen logi. With the reent emergene of eletromehnil resontors 5,6, the onept of mehnil omputer hs een revived s this offers the tntlizing prospet of low power onsumption 16. In spite of some reent experimentl effort, universl eletromehnil logi gte sed on oolen lger hs remined eyond reh 7,17. The prmetri frequeny onversion demonstrted here not only permits the reliztion of ll the primry logi gtes in n eletromehnil resontor for the rst time 16,18 1 ut it lso enles multiit logi iruits to e exeuted in single mehnil resontor s well s providing n rhiteture in whih prllel logi iruits n e esily onstruted. Consequently, mehnil omputer sed on these onepts offers the prospet of unrivlled integrtion density, low power onsumption 7,16 nd potentilly high speed, s informtion does not hve to e pssed etween multiple trnsistors s in onventionl sequentil logi iruits. Moreover, this onept ontriutes signintly to the eyond trnsistor-sed omputtion dete. To trnslte this proof-of-priniple prototype into more prtil devie, oth room temperture nd tmospheri opertion is neessry prerequisite. lthough the present devie n operte t room temperture, the visous dmping present t tmospheri pressure degrdes its performne. The effets of visous dmping ould e redued y utilizing on-hip vuum pkging or y employing nnomehnil resontors 5. The use of nnomehnil resontors would lso result in higher opertion frequenies nd integrtion densities, for exmple, 1 GHz mehnil em osilltor ould e relized with length nd width of 1 µm nd 1 nm, respetively, leding to integrtion densities s high s 1 8 osilltors per m (ref. 7). The outstnding ostle in the reliztion of the ove mehnil omputer is 1 GHz piezoeletri nnomehnil resontor with Q sufiently high to yield good signlto-noise rtios nd the ility to host the prmetri mplition nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.

6 RTICLE nture ommunitions DOI: 1.18/nomms11 funtionlity. potentil pth to these requirements might e found vi piezoeletri ulk ousti wve resontors 6. Wheres the performne of the urrent devie is typilly ~1 Hz per logi opertion, it is instrutive to estimte the prospets of this tehnology, for exmple, with 1 GHz resontor with Q = 1, yielding n opertion ndwidth of 1 MHz (ref. 7). Using stte-of-the-rt omputer word size of 6 its with 6 prllel proesses would result in its logi opertions per seond with only single nnomehnil devie. If suh nnomehnil proessors were ssemled on to hip with the ove desried integrtion density, it ould result in dt-proessing pity of 1 1 Hz m. Even higher proessing pity would e ville in grphene memrne resontors with dimensions of few nnometers, in whih resonne frequenies s high s GHz ould e hieved 8. nnomehnil omputer relized in this mould would yield unpreedented dt-proessing power mking it highly tntlizing prospet, whih merits further investigtion. Methods Experimentl. The eletromehnil resontor ws frited vi onventionl miromhining proesses from Gs/lGs modultion-doped heterostruture sustining DEG 9 nm elow the surfe. The smple ws mounted in high vuum insert (8 1 8 mr), whih ws then pled in He ryostt t K. The mehnil response ws mesured using stndrd low-frequeny lok-in nd mplition tehniques. The signl, pump nd referene (for the lok-in mesurements) exittions were generted vi six signl genertors (NF Wveftory 197), whih were oupled nd synhronized vi their internl 1 MHz referene lok. The eletromehnil osilltor s response ws mplied y n on-hip Si-nnoeld-effet trnsistor with d gin, followed y trnsimpedne mplier (Femto DLPC-) with gin of 1 7 V 1 nd mesured in either lok-in mplier (metek 765) or spetrum nlyser (gilent 891). Multiple idler genertion. The mehnil osilltor response when injeted with two detuned pumps with xed frequeny, f p = f + nd f p = f, while the system is lso exited y f s = f + δ is shown in Figure. This mesurement revels striking response from the mehnil osilltor with the oservtion of two rst-order idlers two seond-order idlers s well s two third-order idlers + = fp fs + d = fp fs d ++ + = fp + d = fs + + = fp + d + = fp + + d = fp + d = fs = fp + d = = fp d = ++ + = fp + d = fp + d = ++ + = fp d = + + = fp d + + = fp + d = = fp d = whih rise euse of the mixing of the pumps with rst nd seond-order idlers (Fig. d shows ll the idlers mrked). Moreover, y vrying, the idlers n e detuned round f where lrger vlues of result in the higher order idlers eoming less visile s shown in Supplementry Figure S1, tht is, the idlers n only e oserved within the ndwidth of the fundmentl mode (Supplementry Note nd Supplementry Figure S). Numeril simultions. The experimentl mesurements n e veried y simulting the response of the non-degenerte prmetri osilltor with n eqution of motion given y (1) () () d d + w g + w (1 + x( t) Γos( wpt)) x( t) = Λ os( ws1t ) dt dt where x(t) is the resontor s position with dmping γ = 1/Q nd n effetive spring onstnt w (1 + x( t) Γos( wp t)) ontining Dufng type nonlinerity prmeterized y β nd the prmetri nonlinerity where Γ is the mplitude of the prmetri modultion (pump) nd is the mplitude of the hrmoni exittion (signl) where the signl nd pump frequenies re given y ws1 = w + pd wp = w + p. Eqution () is solved in the rotting frme t ω y deomposing the resontor s position into in-phse nd qudrture omponents x( t) = X( t) sin( wt) + Y( t) os( wt) where X(t) nd Y(t) re slowly vrying ompred with ω. Eqution () n thus e expressed s w[ + X + gwx wγ( X os( p t) + Y sin( p t)) + w ( X + Y ) X] os( wt) + w[ Y gwy + wγ( X sin( p t) Y os( p t)) + w ( X + Y ) Y] sin( wt) + [ Y + pdwy ] os( wt) + [ Y + pdwx ] sin( wt) + [...] os( wt) + [...] sin( wt) = Λ( os( pdt) sin( wt) + sin( pdt) os( wt)). Negleting the off-resonne oefients yields two rst-order nonliner differentil equtions X = g X + Γ[ X os( p t) + Y sin( p t)] w ( X + Y ) Λ X + w sin( pdt) Y = gy + Γ[ Xsin( p t) Y os( p t)] w ( + X + Y ) Λ Y w os( pdt). Eqution (9) n e redily modied to introdue n dditionl pumps s Γn[ X os( p nt) + Y sin( p nt)] n Γn[ Xsin( p nt) Y os( p nt)]. n dditionl signl exittions n lso e introdued into eqution (9) s Λs1 Λs sin pds sin pds f w 1 ( t) + w ( t + ) +... Λs1 Λ os pds w ( 1 t) s ( )... os pds t + f w where φ is the phse differene etween the signl exittions s1 nd s. Eqution (9) n e numerilly solved using Euler s lgorithm nd the resulting mplitude t f + δ is extrted y tking the Fourier trnsform F of X nd Y s (F(X) if(y))/. Numeril simultions using this formulism n reprodue ll the experimentl results with β = nd Γ =.9γ, tht is, just elow the prmetri resonne threshold where mixing etween the signls nd pumps is medited y the prmetri term (mixing medited y the Dufng term, tht is, β is disussed in Supplementry Note nd is shown in Supplementry Figure S5). () (5) (6) (7) (8) (9) (1) (11) nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.

7 nture ommunitions DOI: 1.18/nomms11 RTICLE Referenes 1. Hork, R. Teleommunitions nd Dt Communitions Hndook (Wiley, 7).. rkett, C.. Dense wvelength division multiplexing networks: priniples nd pplitions. IEEE J. Sel. res Commun. 8, (199).. Yoo, S. J.. Wvelength onversion tehnologies for wdm network pplitions. J. Lightwve Tehnol. 1, (1996).. oole, G. n Investigtion of the Lws of Thought (Prometheus ooks, ), originlly pulished in Roukes, M. Nnoeletromehnil systems fe the future. Phys. World 1, 5 1 (1). 6. Ekini, K. L. & Roukes, M. L. Nnoeletromehnil systems. Rev. Si. Instrum. 76, 6111 (5). 7. Mhoo, I. & Ymguhi, H. it storge nd it flip opertions in n eletromehnil osilltor. Nt. Nnotehnol., (8). 8. Hyshi, C. Nonliner Osilltions in Physil Systems (Prineton University Press, 1986). 9. Rugr, D. & Grütter, P. Mehnil prmetri mplition nd thermomehnil noise squeezing. Phys. Rev. Lett. 67, (1991). 1. Mhoo, I. & Ymguhi, H. Piezoeletrilly pumped prmetri mplition nd Q enhnement in n eletromehnil osilltor. ppl. Phys. Lett. 9, 1719 (8). 11. Shen, Y. R. The Prples of Nonliner Optis (Wiley, 198). 1. rmstrong, J.., loemergen, N., Duuing, J. & Pershn, P. S. Intertions etween light wves in nonliner dieletri. Phys. Rev. 17, 1918 (196). 1. Giordmine, J.. & Miller, R. C. Tunle oherent prmetri osilltion in LiNO t optil frequenies. Phys. Rev. Lett. 1, (1965). 1. Swde, D. The Differene Engine: Chrles ge nd the Quest to uild the First Computer (Viking, 1). 15. rdeen, J. & rttin, W. H. The trnsistor, semi-ondutor triode. Phys. Rev. 7, 1 (198). 16. Roukes, M. L. Mehnil omputtion, redux? IEEE IEDM Tehn. Digest 59 5 (). 17. dzey, R. L., Zolfghrkhni, G., Gidrzhy,. & Mohnty, P. Controllle nnomehnil memory element. ppl. Phys. Lett. 85, (). 18. lik, R. H., Qin, H., Kim, H.- S. & Mrslnd, R. nnomehnil omputerexploring new venues of omputing. N. J. Phys. 9, 1 (7). 19. Msmnidis, S. C. et l. Multifuntionl nnomehnil systems vi tunly oupled piezoeletri tution. Siene 17, (7).. Guerr, D. N. et l. noise-ssisted reprogrmmle nnomehnil logi gte. Nno Lett. 1, (1). 1. Unterreithmeier, Q. P., Fust, T. & Kotthus, J. P. Nonliner swithing dynmis in nnomehnil resontor. Phys. Rev. 81, 15(R) (1).. Interntionl Tehnology Rodmp for Semiondutors, 9 Edition, Emerging Reserh Devies. Mhoo, I., Nishiguhi, K., Fujiwr,. & Ymguhi, H. Room temperture piezoeletri displement detetion vi silion eld effet trnsistor. ppl. Phys. Lett. 95, 1 (9).. Rhmn, M. S. et l. Devie-level vuum pkging for RF MEMS. J. Miroeletromeh. Syst. 19, (1). 5. Verridge, S. S., Ili, R., Crighed, H. G. & Prpi, J. M. Size nd frequeny dependent gs dmping of nnomehnil resontors. ppl. Phys. Lett. 9, 111 (8). 6. O Connell,. D. et l. Quntum ground stte nd single-phonon ontrol of mehnil resontor. Nture 6, (1). 7. Hung, X. M. H., Zormn, C.., Mehregny, M. & Roukes, M. L. Nnodevie motion t mirowve frequenies. Nture 1, 96 (). 8. Mshoff, T. et l. istility nd osilltory motion of nturl nnomemrnes ppering within monolyer grphene on silion dioxide. Nno Lett. 1, (1). knowledgments We re grteful to S. Miyshit for synthesizing the heterostruture, nd N Lmert, H Tkesue nd S Cmou for omments. This work ws prtly supported y JSPS KKENHI (66). uthor ontriutions I.M. oneived the ide, designed nd frited the eletromehnil resontor nd onstruted the mesurement. I.M. nd E.F. performed the mesurements nd nlysed the dt. K.N. nd.f. frited the Si-nnoFET mpliers. I.M., E.F. nd H.Y. developed the logi gtes nd iruits. ll uthors disussed the results, I.M. nd H.Y. wrote the pper nd H.Y. plnned the projet. dditionl informtion Supplementry Informtion ompnies this pper t ntureommunitions Competing nnil interests: The uthors delre no ompeting nnil interests. Reprints nd permission informtion is ville online t reprintsndpermissions/ How to ite this rtile: Mhoo, I. et l. Interonnet-free prllel logi iruits in single mehnil resontor. Nt. Commun. :198 doi: 1.18/nomms11 (11). Liense: This work is liensed under Cretive Commons ttriution-noncommeril- Shre like. Unported Liense. To view opy of this liense, visit retiveommons.org/lienses/y-n-s/./ nture ommunitions :198 DOI: 1.18/nomms Mmilln Pulishers Limited. ll rights reserved.