Electromagnetic Performance of RF NEMS Graphene Capacitive Switches

70 IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 13, NO. 1, JANUARY 2014

Electromagnetic Performance of RF NEMSGraphene Capacitive Switches

Pankaj Sharma, Student Member, IEEE, Julien Perruisseau-Carrier, Senior Member, IEEE, Clara Moldovan,and Adrian Mihai Ionescu, Senior Member, IEEE

Abstract—The RF performance of a nanoelectromechanical sys-tems (NEMS) capacitive switch based on graphene is evaluated.Our results show that graphene can be a good candidate for themembrane of RF NEMS switches in applications where low ac-tuation voltage and fast switching are required. The conductivityof the membrane is accurately modeled in the up- and down-statepositions of the switch by considering the field effect of graphene.Rigorous full-wave simulations are then performed to obtain thescattering parameters of the switch. It is shown that graphene’sconductivity variation due to electric field effect has a limited yetbeneficial impact on the performance of the switch. It is also demon-strated that while monolayer graphene results in quite high switchlosses at high frequency, the use of multilayer graphene, can consid-erably reduce the switch losses and improve the RF performance.Finally, an equivalent circuit model for the graphene-based RFNEMS switch is extracted and the results are compared with thefull-wave 3-D electromagnetic simulation. These results motivatefurther efforts in the fabrication and characterization of grapheneRF NEMS.

Index Terms—Graphene, microelectromechanical systems(MEMS), microwave, millimeter waves, nanoelectromechanicalswitch, RF nanoelectromechanical systems (NEMS).

I. INTRODUCTION

GRAPHENE is a flat monolayer of carbon atoms arrangedin a honeycomb lattice and has attracted great interest in

electronic devices since the demonstration of field-effect carriermodulation in 2004 [1]. It has remarkably unique mechanical(Young’s modulus up to 1 TPa) [2], electrical (electron mobilityup to 200 000 cm2 /Vs for suspended graphene) [3], and thermal(thermal conductivity up to 5000 W/mK) [4] properties. The ex-periments in fabricating suspended graphene, have considerably

Manuscript received December 15, 2012; accepted November 4, 2013. Dateof publication November 14, 2013; date of current version January 6, 2014.This work was supported by the European FP7 Grafol Project and by the SwissNational Science Foundation under Grant 133583. The review of this paper wasarranged by Associate Editor M. R. Stan.

P. Sharma is with the Nanoelectronics devices laboratory, Nanolab, andthe Adaptive MicroNanoWave Systems, LEMA/Nanolab, Ecole PolytechniqueFederale de Lausanne, 1015 Lausanne, Switzerland (e-mail: [email protected]).

J. Perruisseau-Carrier is with the Adaptive MicroNanoWave Systems,LEMA/Nanolab, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne,Switzerland (e-mail: [email protected]).

C. Moldovan and A. M. Ionescu are with the Nanoelectronics devices lab-oratory, Nanolab, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne,Switzerland (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TNANO.2013.2290945

increased the attention on this material in the field of nanoelec-tromechanical systems (NEMS). Research on graphene-basedNEMS has focused mainly on resonators [5]–[9], and some on dcswitches [10]–[14]. Furthermore, the possibility of large-scalesynthesis of graphene by chemical vapor deposition (CVD) [15]makes the fabrication of graphene-based RF NEMS switches,as discussed in this paper, a realistic short-term technologicalprospect.

RF microelectromechanical systems (MEMS) switches havebeen extensively researched as they offer a far superior high-frequency performance and high linearity compared to solid-state switches such as p-i-n diodes or field effect transistors(FET) [16]. Additionally, electrostatically actuated MEMSswitches require almost zero dc power, are low cost, and of-fer high isolation and zero insertion losses, which makes themsuitable candidate for a variety of applications from mobile com-munication to advanced radar systems. However, RF MEMSswitches based on metal membranes suffer from a tradeoff be-tween high-frequency performance and actuation voltage. Typ-ical MEMS actuation voltage (>10 V) are higher than theoperational voltages of current integrated circuit technology.Graphene-based RF NEMS capacitive switches could enablelower actuation voltages by taking advantage of its outstand-ing mechanical properties [11]. Graphene-based RF NEMSswitches also have an edge over carbon nanotube-based NEMS[17], [18] in terms of the ease of fabrication and higher compat-ibility with the device geometry. Moreover, Graphene-based RFNEMS switches, which are suitable for monolithic integrationwith graphene RF nanoelectronics, are extremely promising ascomponents for future all-graphene transceivers [19].

The idea of a doubly clamped RF NEMS switch based ongraphene was previously proposed in [20] but no details aboutfundamental issues such as the value of graphene conductiv-ity used for the electromagnetic simulation or the equivalentcircuit parameters of the shunt switch, were provided. In thispaper, we assess the RF performance in the doubly clampedsuspended shunt capacitive switches based on graphene via adetailed modeling and design. In graphene-based NEMS, theapplied bias (Vbias) across the membrane and central conductornot only performs the function of actuating the switch but alsotunes the conductivity of the membrane in the down state, whichimpacts the RF performance of the switch. We first model theconductivity of the graphene membrane in the up- and down-state position, then study the impact of this tunable conductivityon the scattering parameters of the switch. For the simulation, weuse the lowest reported [15] sheet resistivity value of graphene sothat the ultimate RF performance of graphene-based RF NEMS

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SHARMA et al.: ELECTROMAGNETIC PERFORMANCE OF RF NEMS GRAPHENE CAPACITIVE SWITCHES 71

Fig. 1. Schematic of graphene-based RF NEMS switch.

can be projected. Furthermore, the model and evaluation arealso presented for multilayer graphene. It is generally seen thatwith an increase in the number of layers of graphene, a low sheetresistivity value can be achieved, which is beneficial for the RFperformance of the switch.

Fig. 1 schematically shows the proposed graphene-based RFNEMS device. The switch consists of a conductive membrane(graphene in this case) suspended over the central conductor ofa coplanar waveguide (CPW) and fixed to the ground conduc-tor of the CPW. The central and ground conductors are high-conductivity metals (such as gold) on the low loss substrate(such as high-resistivity silicon). A dielectric layer is used todc isolate the switch from the CPW center conductor. Whena dc voltage is applied across the membrane and the centralconductor with the RF signal, the electrostatic force causes themembrane to snap down on the dielectric surface, forming a lowimpedance mainly capacitive RF path to the ground.

One interesting property of an atomically thin carbon filmsuch as graphene is its electric field effect [1], i.e., its conduc-tivity can be tuned by applying a transverse electric field viaa gated structure. In order to understand the relevance of thiseffect for the proposed device, we discuss the operation of thedevice which is shown in Fig. 2. When the switch is not actuated[see Fig. 2(a)], the membrane remains suspended in the originalposition and has certain intrinsic conductivity (σup ). When theswitch is actuated [see Fig. 2(b)], the membrane snaps downwith a portion of it in direct contact with the bottom dielectric.In this situation, a part of the graphene membrane [Region 2in Fig. 2(b)] experiences a perpendicular electric field from thebottom electrode which tunes its conductivity (σdown ). The con-ductivities in regions 1 and 3 can be approximated to have thesame value as in up-state (σup ). The situation is similar to thegraphene FET whereby the gate controls the channel’s currentin the on- and off-state except that the gate does not completelycover the channel.

The paper is organized as follows. Section II presents themodel to compute the conductivities of the membrane in up-and down-state positions, providing analytical expressions forthe chemical potential and scattering rate. Then, in Section III,we discuss certain considerations for the design of Graphene-based RF NEMS capacitive switch. Section IV presents thesimulation results and analysis of the RF performance of theswitch. Section V states some of the expected problems on

(b)

(a)

Fig. 2. Graphene membrane in (a) unactuated and (b) actuated case.

the performance of the switch based on the present experienceon the fabrication of suspended graphene. Finally, Section VIconcludes the paper.

II. MODELING

A. Frequency-Dependent Conductivity

The complex conductivity of graphene can be computed usingKubo’s formula [21]. This formula takes into account grapheneintraband and interband contributions. However, since the opera-tion of the device is far below the terahertz regime, the interbandcontributions are negligible and graphene conductivity may berepresented as [22]

σ(ω, μc ,Γ, T ) ≈ − jq2e kB T

π�2(ω − jΓ)

×(

|μc |kB T

+ 2 ln(e−|μc |/(kB T ) + 1))

(1)

where ω is the angular frequency, Γ is the phenomenologicalscattering rate (inverse of the relaxation time τ , Γ = τ−1), T =300 K is the temperature, � is the reduced Planck’s constant,kB is Boltzmann’s constant, and μc is the chemical potential.In order to compute the conductivity of graphene membranein up- and down-state position, it is essential to determine theparameters Γ and μc as they can take different values in thesetwo positions.


B. Conductivities in Up- and Down-State Positions

1) Chemical Potential: The chemical potential μc of themonolayer graphene is related to the hole (electron) carrier den-sity nh (ne ) by [23]

ne − nh = sign(μc)1π

(|μc |�vf

)2

(2)

where vf (= 106 ms−1) is the Fermi velocity in graphene. Incase of multilayer graphene, the relationship is given by [24]

ne − nh =2m∗μc

π�2 (3)

where m∗ is the effective mass of multilayer graphene. m∗ ≈0.052 me (for 3, 4 layers) [25], me being the effective mass ofthe electron.

Let us now consider the up-state position of the switch, wheregraphene membrane has an initial hole (electron) carrier densitynhup (neup ). In this case, the chemical potential, μcupMono inthe up-state position for monolayer graphene [from (2)] can bewritten as

μcupMono = sign(neup − nhup)�vf

√|neup − nhup |π. (4)

Similarly, the chemical potential μcupMulti in the up-state po-sition for the multilayer graphene [from (3)] can be expressedas

μcupMulti =π�

2

2m∗ (neup − nhup). (5)

We now consider the down-state position of the switch, whichis achieved by applying a dc voltage Vbias between the centralconductor and ground. The resulting electrostatic forces pull themembrane toward the center conductor and the voltage at whichelectrostatic forces overwhelm the restoring force is known asthe pull-in voltage Vpull−in . At this voltage or greater (|Vbias | ≥|Vpull−in |), the membrane is in direct contact with the bottomdielectric layer. In this position, a part of the membrane inregion 2 [see Fig. 2(b)] experiences the field effect from thecentral conductor. In order to compute the carrier density in thisregion, the charge balance relationship from [24] is employed,which is given as

Vbias − VDirac =q(nedown − nhdown)

Cox(6)

where q is the elementary charge, nhdown (nedown ) is hole(electron) carrier density in the down-state position, Cox isthe capacitance of the dielectric between the central conduc-tor and the membrane in down-state position, which is givenby Cox = εr ε0

td, where εr is the relative permittivity of the di-

electric, ε0 is vacuum permittivity, and td is the thickness ofthe dielectric, and VDirac is the bias voltage at the Dirac point.It has a nonzero value for the predoped graphene and its mag-nitude also depends upon the dielectric constant and thicknessof the supporting substrate. For the initial hole (electron) car-rier density of nhup (neup ), the value of VDirac can be writtenas [26] VDirac = −q(neup − nhup))/Cox . Thus, from (6), the

down-state carrier density can be expressed as

nedown − nhdown =Cox

qVbias + neup − nhup . (7)

As a result, the chemical potential in the down state for mono-layer graphene, μcdnMono (8), and for multilayer graphene,μcdnMulti (9), can be expressed as

μcdownMono = sign

(Cox

qVbias + neup − nhup

)�vf

×√∣∣∣∣Cox


∣∣∣∣π (8)

μcdownMulti =π�

2

2m∗

(Cox


). (9)

Note that we have ignored the effect of the quantum capaci-tance [27] in our model because its impact is negligible for thevalues of Vbias and the thickness of dielectric applicable for RFNEMS switches.

2) Scattering Rate: Graphene’s scattering rate is a substrate-dependent parameter. Indeed, in addition to the scattering phe-nomena due to defects in graphene, the substrate contributesto the scattering rate via the thermally excited surface polarphonon present at the substrate/graphene interface [24], [28].The total scattering rate can be expressed by Matthiessen’srule [24] as τ−1 = τgr

−1 + τsub−1 , where τgr

−1 is the scat-tering rate of graphene without the influence of substrate andτsub

−1 is the surface polar phonon scattering rate due to thesubstrate, which is proportional to the phonon occupationNop . Nop =

∑i

ci/[exp(�ωop i/kB T ) − 1], where �ωop is the

phonon energy of the substrate material and ci is the weightedcoefficient if more than one phonon mode is present. Accord-ing to Zhu et al. [24], the mobility, μsub , which is dominatedby surface polar phonon scattering mechanism, is related to thephonon occupation, Nop and carrier density, n by

μsub = SoxnαNop−1 (10)

where the constants α (= 0.04) and Sox (= 0.141) have beencalculated from the experimental reported data [24], [29]. τsubcan then be calculated from (10) by employing the relationshipbelow for both monolayer [30] (11a) and multilayer graphene[24] (11b), respectively,

τsub−1 =

1μsub

qvf

�√

πn=

q2vf

σ�

√n

π(11a)

τsub−1 =

1μsub

q

m∗ =q2

σ

n

m∗ . (11b)

Hence, the scattering rate of membrane in the up-state, Γup ,where there is no influence of substrate and in the down state,Γdown , where graphene is directly over the dielectric layer, can,respectively, be approximated as

Γup = τgr−1 (12a)

Γdown = τgr−1 + τsub

−1 . (12b)


Carrier scattering by ionized impurities [31] and the electron–hole puddle effect [32] are not considered, assuming such non-idealities can be overcome by annealing the sample [33].

III. DESIGN CONSIDERATIONS OF RF NEMS CAPACITIVE

SHUNT SWITCH

A. Actuation Mechanism

A widely used formula [34] for calculating the pull-in voltageof doubly clamped beams is

Vpull−in =√

8k

27ε0Wwg0

3 (13)

where k is the effective spring constant of the membrane, W isthe CPW center conductor width, w is the membrane’s width,and g0 is the height of the suspended membrane above the dielec-tric layer over the central conductor. According to continuummechanics, the effective spring constant of the doubly clampedmembrane with load applied at the center of the membrane andunder axial tension, is given by [35] and [36]

k = 32Ew(t/L)3 + 17T/L (14)

where E is Young’s modulus, T is the tension in the beam,and t and L are the thickness and length of the membrane,respectively.

Here, it is worth mentioning that for p-doped graphene as fur-ther explained, it is preferable to apply a negative pull-in volt-age (Vbias = −Vpull−in ). Indeed, a negative (positive) voltageinduces holes (electrons) in graphene. Therefore, for a p-dopedgraphene, the chemical potential at−Vpull−in will be higher thanat +Vpull−in (8), (9). A high chemical potential leads to highconductivity (1), which translates into an improved isolation inthe down state.

The switching time is approximated using the equation [11],[37]

ts = 3.67Vpull−in

Vsω0(15)

where Vs � 1.3 Vpull−in [11] and ω0 is the angular resonant

frequency which can be calculated as ω0 =√

km e f f

(meff =0.735Lwtρ [5], where ρ is the mass density).

B. Switch Design

The cross section and top view of the NEMS shunt switch areshown in Figs. 2 and 3, respectively. The suspended graphenemembrane is L =20 μm long and w=30 μm wide, and is sus-pended at a height g0= 300 nm. These dimensions are chosento be the same as the experimentally implemented dc NEMSswitch by Kim et al. [11], where no attempt was made to in-vestigate the microwave properties in a CPW configuration.Furthermore, a wide central conductor width (W = 15 μm)below the membrane is used. This is to achieve a maximumfield effect of the membrane in the down state. The substrate ishigh-resistivity silicon (10 kΩ·cm), and the ground and centralconductor are treated as perfect conductors for the full-wave

Fig. 3. (a) Top view of graphene-based capacitive shunt switch used for simu-lation. (b) Equivalent circuit model of graphene-based NEMS capacitive switch.

simulation (as loss in the metals is negligible with respect tographene membrane.).

A thin dielectric layer (td =20 nm) over the central conductoris considered to achieve a high capacitance ratio of the switch.A high-K dielectric HfO2 is chosen as a material for the dielec-tric layer, for two main reasons. First, High-K dielectrics likeHfO2 are known to reduce the impurity scattering [38], [39] ingraphene as compared to other dielectrics like SiO2 . Second, itshigher dielectric constant (εr = 25) and a low loss tangent (tanδ= 0.0098) [40], lead to a better switch performance at high fre-quency. Furthermore, it is noted that the maximum Vbias whichcan be applied without causing dielectric breakdown of HfO2 is0.85 V/nm [41] × td . In this case, for td = 20 nm, the maximumVbias which can be applied is 17 V, which is much larger thanthe maximum actuation voltage needed as shown later.

IV. RESULTS

We perform the full-wave simulation of graphene-based RFNEMS switch using Ansys high-frequency structure simulator(HFSS). In the full-wave simulation, the graphene membraneis modeled as an infinitesimally thin sheet characterized by fre-quency ω and bias Vbias-dependent surface conductivity accord-ing to Section II. In the up-state, a conductivity σup (ω, Vbias) isassigned to the whole membrane. In the down state, a membraneis divided into three regions, as shown in Fig. 2. In regions 1 and


TABLE IEXTRACTED PARAMETERS FROM THE MODEL

3, σup (ω, Vbias) is assigned and in region 2, σdown (ω, Vbias).The proposed model is used to compute σup and σdown . Usingthe sheet resistivity and carrier density data provided in [15], weextract the rest of the parameters based on our model required tocompute the conductivities. It is noted that the model presentedin Section II is generalized and can be applied to any sheet re-sistivity value of monolayer and multilayer graphene and is notlimited to the example shown in this paper. Table I summarizesthe extracted model parameters used for the simulation. Lowpull-in voltages <2 V based on the analytical expressions arecloser to the experimentally demonstrated values [11]. Switch-ing time of 0.24–0.43 μs have been obtained which is an orderof magnitude below the typical values (2–50 μs) for state-of-the-art MEMS switches [37]. It should be noted that we havenot considered the effect of contact resistance which exists be-tween graphene and ground conductor in our simulation as itseffect is almost negligible at higher frequencies (explained inAppendix).

An example of typical frequency-dependent surfaceimpedance (Zs = 1/σ) of graphene based on (1) is shown inFig. 4 both for monolayer and multilayer graphene. At a givenfrequency, the application of Vbias allows to increase μc , thusreducing the surface resistance. Note a Vbias corresponding to+Vpull−in has a higher surface resistance compared to the sur-face resistance at −Vpull−in because the considered sample isinitially p-doped as explained in Section III-B. There is also aweak inductive reactance contribution to the surface impedancewhich was also observed in experiments conducted for sheetcharacterization of graphene at the microwaves and millimeter-wave [42], [43].

The S-parameters of the switch are then computed in thefrequency range from 1 to 60 GHz. Fig. 5(a) shows theS-parameters in the up-state position of the switch. The inser-tion loss is 0.01–0.3 dB and 0.01–0.2 dB for monolayer andmultilayer graphene, respectively. The S-parameters in thedown-state position are shown in Fig. 5(b) and (c). The iso-lation of >10 dB for monolayer and >20 dB for multilayergraphene is obtained. The multilayer graphene switch offersa superior isolation as compared to the monolayer because ofthe lower surface resistance of the multilayer graphene. The

10 20 30 40 50 600

50

100

150

V = 0 V

− 2 V

− 4 V

− 7 V

− 0.3 V (− V )

0.3 V (+ V )

Frequency (GHz)

Sur

face

Impe

danc

e (Ω

)

(a)

10 20 30 40 50 600

5

10

15

20

25

30

35

40

V = 0 V

− 1.4 V (− V )

− 2 V

− 4 V

− 7 V

1.4 V (+ V )

Frequency (GHz)

Sur

face

Impe

danc

e (Ω

)

(b)

Fig. 4. Surface impedance versus frequency of (a) monolayer graphene and(b) multilayer graphene using the parameters in Table I. The cases Vbias =0 and Vbias �= 0 correspond to the up-state surface impedance (1/σup ) anddown-state surface impedances (1/σdown ) respectively.

isolation can further be improved by increasing the bias voltage(Vbias). This is due to the reduced resistance of the membranewith increasing Vbias .


Fig. 5. S-parameters of RF-NEMS switch shown in Fig. 3(a) in (a) up-stateboth for monolayer and multilayer graphene, (b) down state for monolayergraphene, and (c) down state for multilayer graphene.

It should be noted that changing Vbias has a negligible impacton the shunt capacitance of the device. In the ideal case, thetotal capacitance in the down state is the parallel combination ofquantum capacitance, CQ and COX . CQ is proportional to thecarrier density in graphene [27], which can be tuned by Vbiasin the down state. Therefore, the total capacitance, CQ‖ COX

will be the function of Vbias . Hence, total capacitance will be

Fig. 6. Comparison of loss versus S-parameters in the up-state position. Thereference planes are 20 μm from the edge of NEMS switch (width of membrane= 30 μm).

affected after |Vbias | ≥ |Vpull−in | through the quantum capaci-tance. However, the effect of quantum capacitance can generallybe ignored for two main reasons: 1) CQ is dominant only whenCOX CQ which usually the case for thin oxides (< 5 nm). 2)When the graphene considered has a very low carrier density.But for graphene NEMS switches, a highly conductive grapheneis desirable which usually has a high carrier density (throughchemical doping), a high carrier density means higher CQ =>COX CQ => CQ‖ COX ≈ COX . Therefore, changing Vbiaswill have a negligible impact on the capacitance–voltage char-acteristics of this device.

The lower insertion loss and isolation obtained for mono-layer graphene as compared to multilayer, and the subsequentimprovement in isolation with increasing Vbias , can be betterunderstood by observing the contribution of thermal losses tothe S-parameters. By energy conservation, the loss of a two-port network is simply derived from the S-parameters as Loss= 1 − |S11 |2 − |S12 |2 . The up-state position corresponds to theon-state of the switch, where S12 = 0 dB would be obtainedfor an ideal switch. As can be seen from Fig. 6(a), the de-crease in S12 is not solely due to the increase in the reflectedpower because of mismatch, but is also due to thermal loss inthe switch. By comparing the different curves, it is easily seenthat the better performance of the multilayer implementation isrelated to reduced losses rather than smaller mismatch. The sim-ilar argument applies for the superior performance of multilayergraphene in down-state position because of its reduces losses.

Finally, the equivalent circuit parameters are extracted (seeTable II) from the S-parameters based on the T-circuit modelshown in Fig. 3(b). In the circuit model of metal membraneMEMS, the capacitance (CP ) is the only variable component.However, in the present case, RP is also a variable compo-nent due to the variable resistivity behavior of the graphenemembrane in up- and down-state positions. �LS and �RS

are corrective series elements in order to keep the length ofthe discontinuity to zero in the modeling. This choice of zerolength (dref = 0) for the extraction procedure is arbitrary butfully rigorous, namely just a choice of reference planes [44].


TABLE IIT-MODEL CIRCUIT PARAMETER EXTRACTION FROM SIMULATED

S-PARAMETERS

We observed that the shunt impedance is well modeled by acapacitance (CP ) in series with resistance (RP ) alone. Indeed,there is obviously an inductive component linked with the cur-rent flowing through the membrane. However, its contributionis small and can be neglected, which can be inferred from thefact that the S-parameters reconstructed from the extracted pa-rameters (RP and CP alone) in Table II agrees well with theHFSS full-wave simulations as shown in Fig. 7. Furthermore,it can be seen from Table II that the extracted up-state capaci-tance [16.05–16.38 fF] is slightly higher than the parallel plateup-state capacitance[ ε0 wW

g0 + t dε r

=13.23 fF]. This is expected as a

result of some contribution of fringing field capacitance. Theextracted down-state capacitance[4.41–4.62 pF] from Table IIis also in good agreement with the parallel plate down-statecapacitance [ εr ε0

tdwW = 4.9 pF].

V. DISCUSSIONS

A number of practical problems still exists toward the suc-cessful and reliable operation of graphene RF NEMS. In partic-ular, in spite of the significant progress in the large scale CVDgrowth of graphene, the uniformity of multilayer graphene isstill questionable [45]–[47]. This nonuniformity will cause twomain problems: 1) Variation of sheet resistance among differentareas on the wafer. 2) Up- and down-state capacitance disper-sion due to different stress level over the wafer. This eventuallywould lead to variability issues among the performances ofthe NEMS switches of similar specifications across the wafer.Next, the pull-in voltage of graphene NEMS switch [11] wasnot found to be consistent among the successive switching op-erations. This was mainly due to the different air-gap height andphysical point of contact between graphene–substrate amongthe successive switching operations.

The fabrication of graphene capacitive shunt NEMS switch(without the central conductor) was recently demonstrated [48].In this paper, however, mainly the measurement of pull-in volt-age was carried out based on the Raman spectrum method. Adoubly clamped NEMS based on graphene with the central con-ductor [9], a structure very similar to the device proposed in thepaper except the dielectric layer on top of central conductor, wasalso demonstrated for the application of mechanical resonators.In addition, several other groups successfully fabricated doublyclamped [10], [11], [48] and cantilever [12] dc contact NEMS

Fig. 7. Comparison of S-parameters reconstructed from the T-circuit Modeland simulated from HFSS in (a) up-state for both monolayer and multilayergraphene, (b) down state for monolayer graphene, and (c) down state for mul-tilayer graphene. For the sake of clarity in graph, down-state S-parameters areshown only for two bias voltages, Vbias = − 2 V and Vbias = − 7 V.

switches based on graphene. These results support the viabilityof graphene RF-NEMS and it is expected that our predictionswill soon be tested in experiments on capacitive shunt grapheneRF NEMS switches.

VI. CONCLUSION

Our results demonstrated that graphene can be used for RFNEMS switches in applications where low actuation voltage andfast switching are required, at the cost of larger electromagneticlosses when compared to metal-based RF-MEMS. It was shownthat multilayer graphene can deliver superior isolation and re-duced losses at microwave and millimeter-wave frequency, andisolation can also be tuned with the bias voltage. Nevertheless,


Fig. 8. Equivalent circuit model of NEMS capacitive switch (a) with and(b) without contact impedance. (c) Schematic diagram of charge carrier injectionfrom graphene to metal electrode. (d) Dipole barrier at metal–graphene interface.Comparison of S-parameters between the circuits with and without contactimpedance in (e) up-state and (f) down-state positions.

monolayer graphene with low sheet resistivity value can also beconsidered in applications where even lower actuation voltageis required.

APPENDIX

The graphene–metal interface is modeled by a contact re-sistance in parallel with a contact capacitance [49], [50]. Theequivalent circuit model with and without contact impedanceis shown in Fig. 8(a) and (b), respectively. The typical valueof metal–graphene specific contact resistivity, ρc is 5 × 10−6

Ωcm2 [51]. The contact resistance can then be calculated asRC = 0.5×ρc/(wLT ) (the factor 0.5 is due to two branches ofcurrent flow from central conductor to ground, hence two resis-tances in parallel). LT is the transfer length which is defined asthe length it takes underneath the contact for the current to flowfrom the semiconductor (graphene in this case) to the contact[see Fig. 8(c)]. LT can be calculated as LT =

√ρc/ρgraphene =

4 μm (ρgraphene = 30 Ω/�). This gives a contact resistance, RC

of 2.08 Ω for the current design.The contact capacitance arises from the physical separa-

tion between metal and graphene. Xia et al. [52] attributethis physical separation to the dipole formation at the metal–graphene interface as shown in Fig. 8(d). The contact capaci-tance linked to this electrostatic separation can thus be calculatedas CC = 2 × εr ε0wLT /d1 , (the factor 2 is due to two branchesof current flow from central conductor to ground, hence two

capacitances in parallel) where d1 is the effective distance be-tween the charge sheets in the graphene and metal, and its typicalvalue is d1=1 A [52]. The relative dielectric constant of this thininterfacial layer is rather complex to determine [50]. Neverthe-less, the minimum value of this capacitance can be calculatedas CC = 2ε0wLT /d1 = 21.2 pF.

The circuits shown in Fig. 8(a) and (b) are then simulatedusing the RC and CC values calculated previously and othercircuit parameters values from Table I (multilayer graphene inup and down states). The simulated S-parameters, as shown inFig. 8(e). Fig. 8(f) indicates that the contact resistance plays anegligible impact at our frequency of interest. This is due to thepresence of the contact capacitance in parallel which shorts thecontact resistance at high frequencies. For example, at 10 GHz,the value of 1/jωCc(0.74Ω) RC (2.08Ω). The similar effectwas also demonstrated experimentally in [49] and [53].

ACKNOWLEDGMENT

The authors would like to thank A. Bazigos from Ecole Poly-technique Federale de Lausanne, Lausanne, Switzerland for thefruitful discussion.

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Pankaj Sharma (S’12) was born in India, 1986. Hereceived the Bachelor’s degree in electrical engineer-ing from National Institute of Technology Rourkela,Rourkela, India, in 2007 and the Master’s degree inmicroelectonics from the National University of Sin-gapore, Singapore, in 2011. He is currently workingtoward the Ph.D. in the NANOLAB group under theguidance of Prof. Adrian Ionescu jointly with Prof.Julien Perruisseau-Carrier of GR-JPC at Ecole Poly-technique Federale de Lausanne (EPFL), Lausanne,Switzerland.

For his Masters project on Silicon Nanowire Circuit Fabrication and VES-FET SONOS, he worked at Institute of Microelectronics, A-Star Singapore for ayear. After receiving the Master’s degree, he joined ST Microelectronics, Singa-pore where he worked as a Device Engineer. During this period he was attractedby the nanotechnology research at EPFL. His main research interests includedevelopment of graphene NEMS devices and novel graphene based circuits formillimeter-wave applications.

Julien Perruisseau-Carrier (S’07–M’09–SM’13)was born in Lausanne, Switzerland, in 1979. He re-ceived the M.Sc. and Ph.D. degrees from the EcolePolytechnique Federale de Lausanne (EPFL), Lau-sanne, Switzerland, in 2003 and 2007, respectively.During 2004–2007, he completed the Ph.D. degreefrom the Laboratory of Electromagnetics and Acous-tics, EPFL, while working on various EU fundedprojects.

In 2003, he was with the University of Birming-ham, Birmingham, U.K., first as a Visiting Student

and then as a Short-term Researcher. From 2007 to 2011, he was with theCentre Tecnologic de Telecomunicacions de Catalunya, Barcelona, Spain, asan Associate Researcher. Since June 2011, he has been a Professor at EPFLfunded by the Swiss National Science Foundation, where he leads the groupfor Adaptive MicroNano Wave Systems. He has led various projects at theNational, European Space Agency, European Union, and industrial levels. Hismain research interest include interdisciplinary topics related to electromag-netic waves from microwave to terahertz: dynamic reconfiguration, applicationof micro/nanotechnology, joint antenna-coding techniques, and metamaterials.He has authored +90 and +50 conference and journal papers in these fields,respectively.

Dr. Perruisseau-Carrier received the Raj Mittra Travel Grant 2010 presentedby the IEEE Antennas and Propagation Society, and of the Young ScientistAward of the URSI International Symposium on Electromagnetic Theory, bothin 2007 and in 2013. He currently serves as an Associate Editor of the IEEETRANSACTIONS ON ANTENNAS AND PROPAGATION, as the Swiss representativeto URSI’s commission B “Fields and waves,” and as a member of the Technicalcommittee on RF Nanotechnology (MTT-25) of the IEEE Microwave Theoryand Techniques Society. He is the chair of the Working Group on “EnablingTechnologies” of the EU COST Action IC1102.

Clara Moldovan received the B.S. degree in mi-croelectronics from the Polytechnic University ofBucharest, Bucharest, Romania, in 2009, and theM.S. degree in microengineering from the EcolePolytechnique Federale de Lausanne, Lausanne,Switzerland, in 2011, where she is currently workingtoward the Ph.D. degree in microsystems and micro-electronics, focusing on graphene nanoelectronics.

Adrian Mihai Ionescu (SM’06) received the B.S.,M.S., and Ph.D. degrees from the Polytechnic Insti-tute of Bucharest, Bucharest, Romania, and the Na-tional Polytechnic Institute of Grenoble, Grenoble,France, in 1989 and 1997, respectively.

He is currently a Professor at the Swiss Fed-eral Institute of Technology, Lausanne, Switzerland.He has held staff and/or visiting positions at LETI-CEA, Grenoble, France, LPCS-ENSERG, Grenoble,France and Stanford University, Stanford, CA, USA,in 1998 and 1999. He is the Director of the Labora-

tory of Micro/Nanoelectronic Devices. He has published more than 250 articlesin international journals and conferences.

Dr. Ionescu is appointed as the National Representative of Switzerland forthe European Nanoelectronics Initiative Advisory Council and member of theScientific Committee of CATRENE. He is the European Chapter Chair of theITRS Emerging Research Devices Working Group. He received three Best Pa-per Awards in international conferences and the Annual Award of the TechnicalSection of the Romanian Academy of Sciences in 1994. He served in the Interna-tional Symposium on Quality Electronic Design and the International ElectronDevices Meeting conference technical committees in 2003 and 2004, and asthe Technical Program Committee Chair of the European Solid-State DeviceResearch Conference in 2006.

Electromagnetic Performance of RF NEMS Graphene Capacitive Switches

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