The Vibrating Body Transistor - IEEE Xplore

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 7, JULY 2011

2113

The Vibrating Body Transistor Daniel Grogg, Member, IEEE, and Adrian Mihai Ionescu, Senior Member, IEEE

Abstract—This paper presents a hybrid resonator architecture called the vibrating body field-effect transistor (VB-FET), which combines a silicon microelectromechanical (MEM) resonator and a FET in a single device. The active device provides improved motion sensing at the mechanical resonance based on charge- and/or piezoresistive-drain-current modulations. We detail the principles of the VB-FET for a clamped-clamped-beam resonator design. The different transduction mechanisms occurring in this structure are discussed, and the benefit of the FET detection with respect to the capacitive transduction in terms of reduced motional resistance is highlighted. The experimental characteristics of the resulting devices are detailed, including a full scattering-parameter characterization and temperature characterizations. An increase in the signal transmission by more than +30 dB over the conventional capacitive transduction is demonstrated under equivalent biasing conditions at 2 MHz. Intrinsic signal amplification in a hybrid MEM resonator is another unique property of active resonators demonstrated in this paper for VB-FET resonators. Index Terms—Field-effect transistor, hybrid microelectromechanical field-effect-transistor (MEM-FET) device, microelectromechanical-system (MEMS) device, quality factor (Q-factor), resonator, transistor.

I. I NTRODUCTION

M

ICROELECTROMECHANICAL (MEM) resonators have attracted interest for time and frequency reference applications due to their small size, high quality factor (Q-factor), low cost, and improved integration perspectives [1]. Since their first introduction in 1967 [2], their transduction properties have been studied, and significant improvements by design [3], by technology, or by more radical changes of the detection mechanisms have been proposed. The widely used capacitive transduction has been optimized to achieve low motional resistances at high frequencies [4], [5], but the nanoscale miniaturization of their principle remains a challenge. The piezoelectric transduction offers benefits in terms of electromechanical coupling and is suitable for high frequencies [6], but the reported Q-factors are lower than in monocrystalline-

Manuscript received October 8, 2010; revised February 4, 2011 and March 27, 2011; accepted April 5, 2011. Date of current version June 22, 2011. This work was supported in part by Microsystems Platform for Mobile Services and Applications Project, by the Micro–Nano Integrated Platform for Transverse Ambient Intelligence Applications Project, and by the Hybrid Nano-Electro-Mechanical/Integrated Circuit Systems for Sensing and Power Management Applications Project. The review of this paper was arranged by Editor Z. Celik-Butler. D. Grogg was with the Nanoelectronic Devices Laboratory, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. He is now with the IBM Zurich Research Laboratory, 8803 Rüschlikon, Switzerland. A. M. Ionescu is with the Nanoelectronic Devices Laboratory, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland (e-mail: dgr@ zurich.ibm.com; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2011.2147786

silicon resonators. To overcome the inherent limitations of the capacitive transduction, different mechanisms have been proposed, including piezoresistive current modulation [7]–[9], dielectric actuation with a solid gap [10], [11], field-effect transistor (FET)-based current modulation [12]–[16], depletionmode actuators [17], [18], and combinations of the different mechanisms. Nanoscale integrated resonators with high signalto-feedthrough and signal-to-noise ratios need significant improvements of their input and output transduction mechanisms in order to be interfaced with complementary metal–oxide– semiconductor (MOS) integrated circuits. The vibrating body transistor presented in this paper provides high output-signal levels suitable for integrated micro- and nanoscale resonators. Beyond radio-frequency (RF) applications, scaled vibrating body FETs (VB-FETs) can be foreseen as candidates for sensing applications (e.g., mass, force, gas, and biosensing) due to their extreme sensitivities to mass loading or electrical charges [19], [20]. This paper reports the detailed experimental characteristics of the VB-FET resonators in addition to the previous publications of our group [15], [21], [22]. These experimental results are discussed based on a small-signal equivalent circuit suitable to model the device transmission proposed within this paper. We discuss the combined charge-and-piezoresistive-current modulation showing that the device is effectively exploiting the FET to achieve its remarkable characteristics. These results are somehow in contrast with the resonant body transistor [16], where the piezoresistive modulation seems to be the uniquely important effect. The experimental results of the in-plane VB-FET demonstrated for the first time in 2008 follow the predicted device behavior, including an improvement of the transmission characteristics at resonance by more than +30 dB. A signal gain at resonance under adequate biasing conditions is reported. II. D EVICE D ESCRIPTION The concept of the VB-FET is inspired by the resonant gate FET (RG-FET) [2], but the configuration of the transistor has two main differences: First, the body of the transistor is suspended, and the gates are fixed, and second, the FET layout is adapted to detect the in-plane motion of the resonator. More importantly, the working principle of the VB-FET differs from the RG-FET by the combination of stress- (piezoresistive) and amplitude- (field effect and capacitive) dependent transduction mechanisms, which can exist simultaneously. Fig. 1 shows a schematic of a VB-FET resonator with a suspended double-clamped beam having an integrated transistor channel in the center of the beam and a gate on either side (i.e., an independent double-gate FET). The operating principle of the VB-FET is similar with that of a single- or double-gate

0018-9383/$26.00 © 2011 IEEE

2114


Fig. 1. Perspective view of the double-clamped-beam VB-FET resonator in a double-gate configuration.

Fig. 3. (a) SEM micrograph of a beam VB-FET with lb: 100 μm and wb: 3 μm. The 1-μm-long FET body is indicated with a red square in the center of the beam. The two electrodes on either side are used to modulate the current and actuate the beam. The RF measurement setup is indicated around the SEM image for a single-gate actuation and double-gate modulation. (b) Schematic representation of the electrical equivalent to the VB-FET, indicating the drainbiased potential of (VD + VS )/2 in the body region. Fig. 2. Cross section of a beam VB-FET device obtained using FIB milling on the final resonator. The beam is 1.25-μm thick and 3.5-μm wide, and the air gaps between the beam and the electrodes are quasi-identical on both sides and measure ∼180 nm.

silicon-on-insulator (SOI) MOSFET with a partially or fully depleted body. The channel is placed on the lateral sides; consequently, its width is limited by the substrate thickness tb , and the junction depth of the source and drain implants is given by the width of the beam (wb ) and not by the depth of the implantation. In this paper, depletion-mode VB-FETs are reported with designed lengths of 30–100 μm and widths of 3 and 4 μm fabricated on a SOI substrate (i.e., a 1.25-μm silicon film with a 3-μm buried oxide) using a six-mask process [23]. By aggressively scaling the film thickness and/or the width of the beam, fully depleted fin-shaped FETs can be obtained [16], [20]. The FET channel is placed in the center of the resonator beam and is n-type (with a concentration of 1.8 × 1016 atoms/cm3 ), and the drain and source regions are n+ silicon (concentration < 3.7 × 1019 atoms/cm3 ). The channel length lchan is shorter than the beam length lb , whereas the electrode length is maximized for an efficient electrostatic transduction and has large gate-tosource and gate-to-drain overlap regions. All silicon surfaces are covered with a 20-nm thin SiO2 layer. Note that both the accumulation and the depletion of carriers in the channel region can be exploited and both modes are used to maximize the current modulation in the VB-FET. In this paper, the term accumulation mode is used to refer to the device type, without limiting the mode of operation to depletion or accumulation. The beam width of the resonators is in the micrometer range, and the center region of the beam cannot be modulated in the case of such a large width of the beam. Fig. 2 shows a focused-ion-beam (FIB) cross section of the double-clamped beam resonator through the FET region with

two quasi-equal gaps of 180 nm. The 20-nm oxide layer is clearly visible at the bottom as a thin bright line. Below the structures, some residues are visible, which are caused by material redeposition during the FIB milling. A scanning-electronmicroscopic image of a typical clamped-clamped-beam VB-FET resonator is shown in Fig. 3(a). The FET body region indicated with a red square is only a projection of the body volume; the carrier modulation takes place on the lateral sidewalls facing the gate electrodes. III. T HEORY In this section, we summarize the electromechanical modeling, and we propose a small-signal equivalent circuit for the VB-FET. Note that the proposed analysis corresponds to the single-gate operation. The electromechanical properties of the beam resonator are not detailed here. A. Small-Signal Equivalent Circuit In order to design and simulate circuits based on MEM resonators, equivalent-electrical-circuit models are needed. For conventional (passive) MEM resonators in the case of linear operation, such a model includes a resonant circuit with the mo , Lm , Cm ) and the following electrical tional impedances (Rm parasitic capacitances: the series feedthrough capacitance C0 and the parallel capacitance Cp [24]. This model is very convenient and can be used to compare different types of resonators . by directly comparing their equivalent motional resistance Rm However, it has some limitations: 1) It does not include the gain mechanism; 2) it cannot predict the phase of multiple current sources; and 3) it has only two terminals. Fig. 4 depicts the equivalent-circuit model proposed in this paper for an active single-gate VB-FET resonator. Three

GROGG AND IONESCU: VIBRATING BODY TRANSISTOR

2115

Fig. 4. Small-signal equivalent circuit for a VB-FET resonator. The input is coupled to the mechanical resonator electrostatically, whereas the output is a combination of the capacitive current (icap, GD ) and from charge (iFE ) and piezoresistive (ipiezo ) modulations in the channel.

main effects that contribute to the output current of an active resonator are identified: 1) the electrostatic input impedance and the corresponding capacitive currents igate1 = icap, 0 + icap, m ; 2) the voltage-controlled current source (VCCS) representing the field-effect modulation iFE = iFE, 0 + iFE, m ; and 3) the VCCS representing the piezoresistive modulation ipiezo, m , where subscript “0” stands for static currents and “m” for the currents generated by the resonator motion. The output current itot can be written as the sum of the different current components in the VB-FET as follows: itot = iFE, 0 + iFE, m + ipiezo, m + icap, 0 + icap, m .

(1)

Additional elements are the output impedance of the transistor (RDS ) and the series resistances given by the anchors (Ranchor ). In the next sections, we describe the basic analytical calculations of the current components and the associated device parameters. B. Input Impedance and Capacitive Current The actuation of the resonator is based on the electrostatic force created in the air gap separating the fixed electrode and the resonator. The input impedance of a VB-FET is given by the electrostatic-transduction parameters and the static capacitance, i.e., similar with capacitive resonators. The coupling factor η1 = ηGD1 + ηGS1 is determined by the electrostatic coupling between the gate and the beam. The two coupling factors for gate-to-source (ηGS1 ) and gate-to-drain (ηGD1 ) couplings are ηGD1 ≈ − ηGS1 ≈ −

ε2ox ε0 lel tb (VG1 − VD ) (εox gap + 2tox )2

(2)

ε2ox ε0 lel tb (VG1 − VS ). (εox gap + 2tox )2

(3)

The gate current is composed of the motional current through the resonator and the current through the different parasitic capacitances. This corresponds exactly to the case of a capacitive beam resonator with no channel resistance (lchan = 0 and VD = VS ). The motional current through the drain terminal is icap, m, GD1 = vin

ηGD1 (ηGD1 + ηGS1 ) √ keff meff Q

(4)

where vin is the applied alternating-current (ac) voltage, Q is the Q-factor, keff is the effective spring constant, and meff is the effective mass. Note that the capacitive currents of the source and the drain are dependent on the velocity of the lumped parameter system and, therefore, on the actuation through η1 and that their sum is equivalent to the motional current in the gate. Capacitances Cgs1 and Cgd1 present in parallel with the transformers include the direct capacitance through the narrow gap (gate-to-source-and-gate-to-drain overlap), the parasitic capacitance through the substrate, and the fringing capacitance through the air. The combination of the electrostatic actuation and the polarization of the channel in one electrode leads therefore to a tradeoff between the coupling factor and the parasitic gate-to-drain capacitance. C. FET Current The total current modulation due to the field effect is composed of two different components: 1) the modulation due to the applied ac voltage with a constant gap size; and 2) the modulation due to the change of the gap under constant gate voltage as follows: iFE =

∂ID ∂ID u vin + ∂VG ∂gap

(5)

where u is the amplitude of motion. The current modulation due to a varying gap under static biasing conditions can be interpreted qualitatively as a modulation of the threshold voltage (varying gate capacitance) or as a modulation of the field in the gap around a point of operation. The voltage variation is proportional to the field and the amplitude ((V /gap)u for tox = 0 [2]). First, we analyze the linear accumulation-mode operation of the VB-FET. In this simpler case, the current is given by the current in the beam (invariable) and the current through the accumulated carriers in the channel (depending on VG1 and the gap). A text-book equation [25] for the accumulation-mode device can be used, where the gate-to-channel voltage VG, dc depends also on the flatband voltage. Rewriting (5) for the effective transconductance gm, FE gives gm, FE = gm, FE, 0 ⎛ ⎜ × ⎝1 −

η1 r, ox VG, dc r, ox gap + 2tox keff

⎞ 1−

ω ω0

1 2 +

1 j ωω0 Q Q

⎟ ⎠

(6)

where gm, FE, 0 = dID /dVG is the static transconductance of the FET and ω is the frequency around the resonance frequency ω. To achieve high gm, FE , it is beneficial to design a transistor with a short length and high channel mobility, that create conditions for a strong field (e.g., small gap), and that maximize the electrostatic coupling used for the actuation. The advantage of the FET-based motion detection comes from the independent optimization of the transistor and the electromechanical coupling offering the possibility to increase the device performance.

2116


D. Piezoresistive Current

Fig. 5. Experimental transconductance versus frequency for a 50-μm-long VB-FET resonator in accumulation- and depletion-mode operation (single gate). The transconductance at resonance extracted from the measurement is one order of magnitude higher in depletion-mode operation at same |VG1 | = 30 V and reaches 0.84 mS at VD = 1 V.

For the depletion-mode operation, the current in the beam can be written as IFE, dep =

qμn ND tb (wb − xdep ) VD lchan

(7)

where q is the elementary charge, μn is the bulk electron mobility, ND is the doping concentration, and xdep is the depletion width. The transconductance is given by the variation of the depletion region by VG, dc and the gap. The total ac output current for the depletion case is therefore a function of the surface potential φs and can be written as iFE, dep

qμn ND tb VD = lchan

∂xdep ∂xdep ∂φS u . (8) vin + ∂VG, dc ∂φS ∂gap

The complex dependence of the surface potential φS on the gap and the applied potential can be derived based on the analytical expressions proposed in [25] and needs numerical calculations. Therefore, an explicit analytical formulation linking the applied voltages to the expected transconductance at resonance is not derived in this paper. Fig. 5 gives the transconductance in the depletion and accumulation modes of a 50-μm-long VB-FET. The transconductance has been extracted from S-parameter measurements using gm = Y21 − Y12 and shows close to one order of magnitude higher gm, FE for the depletion-mode operation. The unique behavior of the VB-FET transconductance gm, FE is its extremely high increase at resonance, i.e., by orders of magnitude, compared with the low value of the static transconductance (i.e., gm, FE, 0 ≈ 1 μS for VD = 1.5 V in the single-gate configuration) corresponding to relaxed equivalent oxide thickness due to the air gap. This remains true for both modes of operation but does not explain the difference between the two modes of operation. Possible reasons for this difference are: 1) the difference in mobility between the accumulation channel and the bulk conduction (depletion); and 2) the nonlinear change of φS when going from the flatband condition toward inversion.

The piezoresistive effect in silicon has been proposed as a readout mechanism for a wide range of MEM-system (MEMS) devices [26]. Piezoresistive-current modulation has been demonstrated on bulk-mode resonators [27], [28] at the resonance frequency ω0 and for flexural-mode resonators at ω0 [29] and 2ω0 [8]. Two important sources of time-dependent strain exist in the flexural-mode beam resonator: 1) strain due to the bending moment; and 2) strain due to the elongation of the wire under deflection. The latter has been used for the vibration detection in silicon nanowires [8], but the elongation effect is proportional to the square of the amplitude of motion, and the output signal is therefore at 2ω0 . In this section, we analyze the piezoresistive-current modulation in a double-clamped-beam VB-FET caused by the bending moment under asymmetric gate biasing to quantify the piezoresistive effect in the equivalent circuit in Fig. 4. Strain due to the bending moment is symmetric around the neutral axis, and the effect on the total resistance is zero if the beam is uniformly doped. However, the strain due to the bending moment gives a nonzero change of the resistance for asymmetric doping profiles [29] or in transistors, for asymmetric carrier distribution. This change of the resistance results in a current component at ω0 . The first-order calculations of the piezoresistive effect in the VB-FETs show that the piezoresistive effect plays a secondary role in long VB-FETs due to the dependence of the average strain y in the depletion region on the displacement given as y =

16us lb2

(9)

where s = (wb − xdep )/2 is the average distance from the neutral axis of the beam [30]. Because the depletion width is limited to a small fraction of the beam width, only a small part of the the total current can be modulated effectively. The piezoresistive transconductance in the FET channel is expressed as gm, piezo = KIeq

16s η1 lb2 k0 1 −

1 ω ω0

1 + j ωω0 Q

(10)

where K is the piezoresistive gauge factor and Ieq = Ib (xdep /wb ) is the current flowing through the nonsymmetric region. IV. S TATIC E LECTRICAL C HARACTERISTICS The accumulation-mode (or normally on) FET cannot be fully depleted by the two lateral gates (with a maximum depletion width of 230 nm); therefore, it cannot be turned off. An electrical equivalent of the VB-FET is given in Fig. 3(b) where the FETs are connected in parallel with a rather low resistance. The FET body is drain biased through this parallel resistance to a potential of (VD + VS )/2. The measured ID –VD and ID –VG characteristics of the VB-FET are shown in Fig. 6. A rather high current is observed with a small influence of the gate voltage corresponding to the proposed electrical equivalent schematic.


Fig. 6. ID –VD and ID –VG characteristics of a 100-μm-long and 3-μm-wide VB-FET structure. The electrostatic pull-in and pull-out events onto gate 1 are visible as abrupt steps in the drain current.

The ID –VD characteristics show a linear behavior for low VD ; at higher VD , the saturation of the carrier velocity starts to limit the drain current. The impact of the gate voltage on the total drain current can be distinguished clearly, but the control is limited. Qualitatively, three regimes of operation are distinguished: the channel is either in depletion (VG + VF B < 0), in a combined depletion/accumulation state (0 < VG + VF B < VD ), or in an accumulation state (VG + VF B > VD ). For long beams with low spring constants, a symmetric pull-in and pullout characteristic is observed for the negative and positive values of VG (see also [31]). V. VB-FET R ESONATOR C HARACTERIZATION The frequency characterization of the VB-FET resonators is comparable with capacitive-mode resonators and is performed using a HP 8753D vector network analyzer (VNA) to evaluate the S-parameter of the devices using the setup, as shown in Fig. 3(a). Measurements are performed inside a Süss Microtec cryogenic probe station at a pressure below 10−5 mbar to reduce air damping. The high bias voltages needed for the actuation and the polarization of the transistor are applied using external voltage sources and commercially available bias tees. A. FET and Capacitive Sensing The advantage of the FET-based sensing with respect to the capacitive sensing has been discussed theoretically above and is demonstrated experimentally with transmission measurements in Fig. 7. A two-port capacitive measurement is shown on the right side (“3”) where the gate electrodes have been used as input and output electrodes. The transmitted signal is hardly above the noise floor of the measurement setup, and the characterization of the resonator is difficult. A motional resistance of 16 kΩ is extracted corresponding well with the theoretically expected value, but the Q-factor cannot be estimated for this measurement. An increase by more than +30 dB is observed when using the FET-based sensing (double-gate sensing) with single-gate actuation (see the transmission characteristic in the center in Fig. 7, “2”). The amplitude of motion in this setup is nearly equal with the one in the capacitive measurement, which is

2117

Fig. 7. VB-FET (lb: 100 μm, wb: 4 μm) shows a strong increase in the output signal using the FET detection compared with the capacitive two-port setup. The measured increase in the signal magnitude for single-gate actuation is approximately 31 dB and can be further increased to 37 dB using the doublegate actuation.

only affected by the additional applied potential VD . An asymmetric polarization of the two gate electrodes gives the best results as the gaps change with opposite sign. This increases the effective channel width of the FET sensing (parallel operation, gm, FE, 0 = gm,acc + gm,dep ) and the transconductance compared with the single-gate setup. The equivalent motional = vin /id for the purpose resistance, which is defined as Rm of comparison, is reduced to 330 Ω in this configuration. Further improvements can be obtained by applying a differential driving scheme, doubling the amplitude of motion and improving the transmission by another 6 dB (“1”). The motional resistance drops in this case to 31 Ω. It is worth noting that all measurements in Fig. 7 are strongly impedance mismatched (i.e., 50 Ω load of the VNA). The output resistance of the VB-FET is determined by the source–drain resistance. For this device, values in the range of 2–5 kΩ have been measured, which is lower than the 16 kΩ of the capacitive case. B. Signal Amplification in a MEMS Resonator Unlike passive resonators, which always show a finite loss, active resonators can act as MEMS amplifiers due to their builtin gain [15], [27]. This attribute (S21, max > 0 dB) makes them extremely attractive for a series of innovative design approaches such as self-oscillating VB-FETs or filters with integrated signal amplification [32]. The left side in Fig. 8 shows the gain measured in a double-gate setup. In this configuration, several advantages are combined: High direct-current (dc) bias voltages are possible without pull-in, the two channels work in parallel, and the differential driving increases the amplitude of motion. Although self-heating and drain-current saturation are present at high VD levels, the gain is strongly dependent on the drain voltage. Gain is measured in a large voltage range starting from VD = 1.45 V and increases with increasing VD [15]. Above VD = 1.85 V, the saturation of the voltage gain is observed, being attributed to the negative influence of the self-heating and a reduction of the loaded Q-factor due to the external electrical resistances and the high dc voltage. The right side in Fig. 8 reports the voltage gain in a singlegate setup for negative gate voltage. In the single-gate configuration, the effective gap size is a direct function of VG due

2118

Fig. 8. Signal gain (+2.5 dB) of the VB-FET resonator (lb: 100 μm, wb: 4 μm) at 2.044 MHz measured with double-gate actuation setup under high drain and gate voltages and with single-gate operation (+2.3 dB) at 4.2 MHz (lb: 60 μm, wb: 3 μm).

Fig. 9. S-parameters of the VB-FET (lb: 50 μm, wb: 4 μm) resonator. The magnitude and the phase of the reflection from the gate (S11 ) and the drain (S22 ) are shown.

to the mechanical deformation of the beam and can be used to increase the transconductance of the built-in FET. Electrical nonlinearity, which is caused by the amplitude of 3.7 nm and the high electrical field in the narrow gap, is visible in this measurement and limits the gain. C. Transmission and Reflection The measurements of the VB-FET reported in the previous sections have been measured without calibration; the highimpedance mismatch between the MEM resonator and a 50-Ω termination of the VNA leads to S-parameter measurements that depend mainly on the signal reflection and not on the internal losses of the resonator. The high Q-factors of MEM resonators are related to the low losses in such devices. However, the information of the phase is lost when measuring the VB-FET without calibration. In this section, we report calibrated measurements for a VB-FET using a commercial short–open–load–thru technique for the calibration; the contactpad parasitics have not been deembedded. Fig. 9 reports the magnitude and the phase of the reflection measurement, and full reflection from the gate S11 is observed with only a very slight change at resonance, corresponding to the reduction of the input impedance. The phase is also constant


Fig. 10. S-parameters of a VB-FET (lb: 50 μm, wb: 4 μm) resonator. The magnitude and the phase of the transmission from the gate to the drain (S21 ) and from the drain to the gate (S12 ) are shown.

at 0◦ , as can be expected from the high input impedance of the VB-FET. The reflection from the drain S22 is lower, in agreement to the lower impedance level (RDS < 1/(jωCpad )). Around resonance, S22 shows an interesting behavior, which is not studied in the small-signal analysis. The ac signal applied on the drain actuates the beam by the electrostatic force. This periodic change of the gap results in a modulation of the channel and drain currents. The drain-current modulation adds to the reflected signal and thus increases the reflected signal level. If the drain-current modulation is strong, this can result even in a gain on the reflected signal. However, note that the gain and the corresponding phase change are small as the reflected signal is dominant. This is an important difference to the transmitted-signal characteristic, where a full 180◦ phase change is measured around resonance. Fig. 10 shows the magnitude and the phase of the transmitted signal from the gate to the drain (S21 ) and in the opposite direction. The forward transmission S21 benefits from the FET detection and results in a +30-dB-higher S-parameter at resonance than the S12 measurement. The signal transmission from the drain to the gate is purely capacitive and does not benefit from the FET. This is also seen on the phase of the two transmitted signals, where the capacitive signal lags the FET-based signal by 90◦ . No antiresonance is visible in the shown frequency range under the chosen conditions (high gm, FE around resonance) for the active transduction, but the antiresonance is visible for the passive transduction. For the lower levels of gm, FE , the theoretical antiresonance is often masked by the parasitic series capacitance CGD . The limits of the proposed small-signal model concern mainly the actuation of the beam when the ac signal is applied on the drain terminal, which has not been investigated. The behavior of the VB-FET, when the ac signal is applied on the gate, is correctly described by the model and can be used to predict the frequency and the magnitude of the output current. D. Drain- and Gate-Voltage Control 1) Gate-Voltage Influence: Fig. 11 shows the transmission characteristics of the VB-FET in accumulation operation and depletion operation with constant drain voltage and the gate


Fig. 11. Transmission characteristics of the VB-FET device (lb: 30 μm, wb: 3 μm) around resonance with VG1 as a parameter, for VG2 = 0 V and VD = −1 V.

2119

Fig. 12. a) Drain-voltage dependence of the VB-FET (lb: 50 μm, wb: 4 μm) transmission characteristics at low VD values, where a linear increase in the transmission characteristics is measured (20 × log(5) ≈ 14 dB).

voltage VG1 as a parameter (single-gate operation). From the 2 theory, the VG, dc dependence of the output current is expected for the accumulation case because the amplitude and gm, FE, 0 are proportional to VG, dc . For the depletion mode, the depen dence of gm, FE, 0 is proportional to VG, dc ; therefore, de3/2

pendence close to the VG, dc of the transmission characteristics on the gate voltage is expected. The experimental results in Fig. 11 shows systematically higher transmission peaks for the operation in depletion compared with accumulation. In contrast, the static measurements indicate a higher gm, FE, 0 value of 770 nS at 30 V in accumulation, whereas only 570 nS are measured in depletion at −30 V. Assuming positive VFB would result in a more important field in the case of the depletion-mode operation than for the accumulation mode. This could explain in part the overall stronger transduction for the depletion mode and, in addition, the different dependence of the increase in the peak with VG . Additionally, in depletion, the surface potential can vary strongly with the changing gap at high amplitudes of motion, making the transduction more efficient. We have investigated this phenomenon on different beams (i.e., different frequencies) and have always found a stronger modulation in the case of the depletion-mode operation. 2) Drain-Voltage Influence: Three main effects related to the drain-voltage level are identified: 1) The transconductance of the FET increases with increasing drain voltage; 2) the electrostatic spring constant changes with the drain voltage; and 3) the self-heating occurs at high drain-current levels. Fig. 12 shows the transmission characteristics with VD as a parameter for drain voltages varying between 0 (capacitive oneport transmission) and 1 V. A linear increase in the transmission level at resonance is measured in accordance with the linear operation of the FET. The increase of +14 dB corresponds to a multiplication of VD by five times (from 0.2 to 1 V). E. Self-Heating and Temperature Dependence The self-heating effect (SHE) in the VB-FET is due to the high thermal resistances specific to suspended or SOI devices and can occur for high drain-current levels leading to heat dissipation and local temperature gradients in the channel region.

Fig. 13. Self-heating in the long VB-FET (lb: 100 μm, wb: 3 μm), where the increasing drain voltages lowers the electrical spring constant (increase in the resonance frequency) and self-heating starts to dominate above 0.6 V, lowering the resonance frequency.

Fig. 13 visualizes the impact of the SHE for the case of a singlegate measurement. Both gate and drain voltages are positive, reducing the electrical spring constant for increasing drainvoltage levels. For low VDS levels, the electrical spring constant dominates the frequency shift, but above VD = 0.6 V, the SHE starts to dominate through two effects: 1) Young’s modulus is decreasing with the temperature increase; and 2) the linear thermal expansion of the beam results in a compressive stress, reducing the frequency [33]. The sensitivity of the resonance frequency on temperature is increased strongly when the SHE occurs. Frequency temperature coefficient (TCf) values as high as 300 ppm/◦ C have been obtained in the case of the SHE. Note that a similar increase in the TCf values has also been reported for piezoresistive resonators [34]. Temperature does not only influence the frequency behavior of the VB-FET by modifying the mechanical material properties but also affects its electrical transport parameters such as the threshold voltage Vth and mobility μ. The temperature dependence of mobility can be described by the following approximation:

− γ1 μ(T ) T = (11) μ(Tr ) Tr

2120


ACKNOWLEDGMENT The authors would like to thank all collaborators who have been involved in this paper, particularly H.C. Tekin, M. Mazza, D. Tsamados, and S. Ayöz. The authors would also like to thank the Center of Micro- and Nanotechnology at the Swiss Federal Institute of Technology(http://cmi.epfl.ch) for technical support and to Comelec SA (http://www.comelec.ch) for the parylene deposition. R EFERENCES

Fig. 14. Normalized transconductance (gm (T )/gm (Tr ))1/1.2 and output signal ((10Smax (T )/20 )/(10Smax (Tr )/20 ))1/1.2 of a VB-FET resonator (lb: 100 μm, wb: 4 μm) versus temperature. Both parameters show a linear decrease with increasing temperature, and the total performance decreases by 14% over the 56 ◦ C range.

where T is the absolute temperature, Tr is the room temperature, and γ is a constant in the range of 1.2–2 [25]. Fig. 14 reports the normalized transconductance and the linear S21 measured at different temperatures. gm, FE, 0 is proportional to μn , and the temperature behavior of gm, FE, 0 can be expressed using the same model (gm, FE, 0 (T )/gm, FE, 0 (Tr ))−1/γ , where a value of 1.2 for γ is used. The magnitude of the transmission characteristics at resonance for the same structures is reported in the same graph using the normalization as ((10Smax (T )/20 )/(10Smax (Tr )/20 ))−1/γ . A linear characteristic is observed for both normalized gm, FE, 0 and normalized S21 in the given temperature range, demonstrating the direct dependence of the output-signal amplitude on the gm, FE, 0 of the integrated transistor. A reduction of gm, FE, 0 and the output signal by 14% over a 56 ◦ C temperature span is extracted from this measurement. VI. C ONCLUSION In this paper, we have presented a complete investigation of an accumulation-mode VB-FET, including theoretical background and extensive experimental characterization in static and dynamic regimes. This device can exploit both charge and piezoresistive modulations to provide the MEMSbased amplification of signals at the resonance frequency. An increase in the output current by +30 dB has been experimentally demonstrated for the conditions of equivalent amplitude using the FET detection (active mode) compared with the capacitive (passive mode) one. This is equivalent to a reduction of the motional resistance from 16 kΩ to 330 Ω. The superior transmission characteristics obtained with the FET detection and the dependence on the applied voltages are demonstrated for a wide range of gate- and drain-voltage values. The influence of temperature on the resonator frequency and transmission characteristics is also detailed. Furthermore, signal amplification in VB-FET structures (S21 > 0 dB) has been demonstrated for single- and double-gate setups at 2 and 3.5 MHz, offering novel approaches to oscillators and filter applications.

[1] C. T. C. Nguyen, “MEMS technology for timing and frequency control,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 54, no. 2, pp. 251– 270, Feb. 2007. [2] H. C. Nathanson, W. E. Newell, R. A. Wickstrom, and J. R. Davis, Jr., “The resonant gate transistor,” IEEE Trans. Electron Devices, vol. ED-14, no. 3, pp. 117–133, Mar. 1967. [3] A. M. Ionescu, V. Pott, R. Fritschi, K. Banerjee, M. J. Declercq, P. Renaud, C. Hibert, P. Fluckiger, and G. A. Racine, “Modeling and design of a lowvoltage SOI suspended-gate MOSFET (SG-MOSFET) with a metal-overgate architecture,” in Proc. Int. Symp. Quality Electron. Des., 2002, pp. 496–501. [4] T. J. Cheng and S. A. Bhave, “High-Q, low impedance polysilicon resonators with 10 nm air gaps,” in Proc. IEEE 23rd Int. MEMS Conf., 2010, pp. 695–698. [5] A. K. Samarao and F. Ayazi, “Self-polarized capacitive silicon micromechanical resonators via charge trapping,” in IEDM Tech. Dig., 2010, pp. 7.4.1–7.4.4. [6] M. Rinaldi, C. Zuniga, C. Zuo, and G. Piazza, “Super-high-frequency two-port AlN contour-mode resonators for RF applications,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 57, no. 1, pp. 38–45, Jan. 2010. [7] J. T. M. van Beek, P. G. Steeneken, and B. Giesbers, “A 10 MHz piezoresistive MEMS resonator with high Q,” in Proc. IEEE Int. Freq. Control Symp. Expo., 2006, pp. 475–480. [8] R. He, X. L. Feng, M. L. Roukes, and P. Yang, “Self-transducing silicon nanowire electromechanical systems at room temperature,” Nano Lett., vol. 8, no. 6, pp. 1756–1761, Jun. 2008. [9] A. T.-H. Lin, J. E.-Y. Lee, J. Yan, and A. A. Seshia, “Enhanced transduction methods for electrostatically driven MEMS resonators,” in Proc. Int. Solid-State Sens., Actuators Microsyst. Conf., TRANSDUCERS, Jun. 21–25, 2009, pp. 561–564. [10] S. A. Bhave and R. T. Howe, “Internal electrostatic transduction for bulkmode MEMS resonators,” in Proc. Solid-State Sens., Actuator Microsyst. Workshop, Hilton Head Island, SC, Jun. 6–10, 2004. [11] Y.-W. Lin, S.-S. Li, Y. Xie, Z. Ren, and C. T. C. Nguyen, “Vibrating micromechanical resonators with solid dielectric capacitive transducer gaps,” in Proc. IEEE Int. Freq. Control Symp. Expo., 2005, pp. 128–134. [12] N. Abele, R. Fritschi, K. Boucart, F. Casset, P. Ancey, and A. M. Ionescu, “Suspended-gate MOSFET: Bringing new MEMS functionality into solid-state MOS transistor,” in IEDM Tech. Dig., 2005, pp. 479–481. [13] D. Grogg, D. Tsamados, N. D. Badila, and A. M. Ionescu, “Integration of MOSFET transistors in MEMS resonators for improved output detection,” in Proc. Int. Solid-State Sens., Actuators Microsyst. Conf., TRANSDUCERS, D. Tsamados, Ed., 2007, pp. 1709–1712. [14] C. Durand, F. Casset, P. Renaux, N. Abele, B. Legrand, D. Renaud, E. Ollier, P. Ancey, A. M. Ionescu, and L. Buchaillot, “In-plane siliconon-nothing nanometer-scale resonant suspended gate MOSFET for In-IC integration perspectives,” IEEE Electron Device Lett., vol. 29, no. 5, pp. 494–496, May 2008. [15] D. Grogg, M. Mazza, D. Tsamados, and A. Ionescu, “Multi-gate vibrating-body field effect transistors (VB-FETs),” in IEDM Tech. Dig., 2008, pp. 663–666. [16] D. Weinstein and S. A. Bhave, “The resonant body transistor,” Nano Lett., vol. 10, no. 4, pp. 1234–1237, Apr. 2010. [17] J. H. T. Ransley, A. Aziz, C. Durkan, and A. A. Seshia, “Silicon depletion layer actuators,” Appl. Phys. Lett., vol. 92, no. 18, pp. 184 103-1– 184 103-3, May 2008. [18] E. Hwang and S. Bhave, “PN-diode transduced 3.7-GHz silicon resonator,” in Proc. IEEE 23rd Int. Conf. MEMS, 2010, pp. 208–211. [19] E. Mile, G. Jourdan, I. Bargatin, S. Labarthe, C. Marcoux, P. Andreucci, S. Hentz, C. Kharrat, E. Colinet, and L. Duraffourg. (2010, Apr.). In-plane nanoelectromechanical resonators based on silicon nanowire piezoresistive detection. Nanotechnology. [Online]. 21(16), p. 165 504. Available: http://stacks.iop.org/0957-4484/21/i=16/a=165504


[20] D. Grogg, A. Lovera, and A. M. Ionescu, “Nano-electro-mechanical vibrating body FET resonator for high frequency integrated oscillators,” in Proc. DRC, 2010, pp. 183–184. [21] D. Grogg, H. C. Tekin, N. D. Badila-Ciressan, M. Mazza, D. Tsamados, and A. M. Ionescu, “Laterally vibrating-body double gate MOSFET with improved signal detection,” in Proc. Device Res. Conf., Jun. 23–25, 2008, pp. 155–156. [22] D. Grogg, S. Ayoz, D. Tsamados, and A. M. Ionescu, “Small signal modeling of charge and piezoresistive modulations in active MEM resonators,” in Proc. ESSDERC, Sep. 14–18, 2009, pp. 379–382. [23] D. Grogg, H. C. Tekin, N. D. Ciressan-Badila, D. Tsamados, M. Mazza, and A. M. Ionescu, “Bulk lateral MEM resonator on thin SOI with high Q-factor,” J. Microelectromech. Syst., vol. 18, no. 2, pp. 466–479, Apr. 2009. [24] H. A. C. Tilmans, “Equivalent circuit representation of electromechanical transducers: I. Lumped-parameter systems,” J. Micromech. Microeng., vol. 6, no. 1, pp. 157–176, 1996. [25] Y. Tsividis, Operation and Modeling of the MOS Transistor. Boston, MA: WCB/McGraw-Hill, 1999. [26] A. Barlian, W.-T. Park, J. Mallon, A. Rastegar, and B. Pruitt, “Review: Semiconductor piezoresistance for microsystems,” Proc. IEEE, vol. 97, no. 3, pp. 513–552, Mar. 2009. [27] J. T. M. van Beek, K. L. Phan, G. J. A. M. Verheijden, G. E. J. Koops, C. van der Avoort, J. van Wingerden, D. E. Badaroglu, J. J. M. Bontemps, and R. Puers, “A piezo-resistive resonant MEMS amplifier,” in IEDM Tech. Dig., 2008, pp. 1–4. [28] D. Weinstein and S. A. Bhave, “Piezoresistive sensing of a dielectrically actuated silicon BAR resonator,” in Proc. Solid-State Sens., Actuators, Microsyst. Workshop, Hilton Head Island, SC, Jun. 1–5, 2008, pp. 368–371. [29] K. L. Phan, J. T. M. van Beek, and G. E. J. Koops, “Piezoresistive ring-shaped MEMS resonator,” in Proc. Int. Solid-State Sens., Actuators Microsyst. Conf., TRANSDUCERS, Jun. 21–25, 2009, pp. 1413–1416. [30] W. D. Pilkey, Formulas for Stress, Strain, and Structural Matrices, 2nd ed. Hoboken, NJ: Wiley, 2005. [31] D. Grogg, C. Meinen, D. Tsamados, H. C. Tekin, M. Kayal, and A. M. Ionescu, “Double gate movable body micro-electro-mechanical FET as hysteretic switch: Application to data transmission systems,” in Proc. 38th ESSDERC, 2008, pp. 302–305. [32] A. Lovera, S. Bartsch, D. Grogg, S. Ayöz, R. Kaunisto, and A. Ionescu, “Active NEM filters for communications applications based on vibrating body transistors,” in Proc. ESSDERC, 2010, pp. 472–475. [33] W.-T. Hsu, J. R. Clark, and C. T. C. Nguyen, “Mechanically temperatu recompensated flexural-mode micromechanical resonators,” in IEDM Tech. Dig., 2000, pp. 399–402. [34] S. Bendida, J. Koning, J. Bontemps, J. van Beek, D. Wu, M. van Gils, and S. Nath, “Temperature stability of a piezoresistive MEMS resonator including self-heating,” Microelectron. Reliab., vol. 48, no. 8/9, pp. 1227– 1231, Aug. 2008.

2121

Daniel Grogg (S’08–M’11) received the M.S. degree in microengineering and the Ph.D. degree in microsystems and microelectronics from the Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, in 2004 and 2010, respectively. In 2011, he joined the IBM Research Laboratory Zurich, Rüschlikon, Switzerland, where he is currently working as a Postdoctoral Researcher. His research interests include micro- and nanofabrication, microelectromechanical (MEM) systems, micromechanical resonators and hybrid MEM complementary metal–oxide–semiconductor technology.

Adrian M. Ionescu He received the B.S. and M.S. degrees from the Polytechnic Institute of Bucharest, Bucharest, Romania, in 1989 and 1994, respectively, and the Ph.D. degree from the National Polytechnic Institute of Grenoble, Grenoble, France, in 1997. He has held staff and visiting positions with the Atomic Energy Commission Electronics and Information Technology Laboratory (CEA-Leti), Grenoble, with the Laboratoire de Physique des Composants à Semiconducteurs (LPCS), Ecole Nationale Supérieure d’Electronique et de Radioélectricité de Grenoble (ENSERG), Grenoble, and with Stanford University, Stanford, CA. He is currently an Associate Professor with the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland. He is also currently the Director with the Laboratory of Micro/Nanoelectronic Devices and the Head of the Doctoral School in Microsystems and Microelectronics, EPFL. He is the author of more than 250 articles in international journals and conferences. Dr. Ionescu was a member of the technical committees of IEEE Electronic Devices Meeting and was the Technical Program Committee Chair of the European Solid-State Device Research Conference in 2006. He has been appointed as the national representative of Switzerland for the European Nanoelectronics Initiative Advisory Council and a member of the Scientific Committee of the Cluster for Application and Technology Research in Europe on Nanoelectronics. He is the European Chapter Chair of the International Technology Roadmap for Semiconductors Emerging Research Devices Working Group. He was the recipient of the Blondel Medal 2009 of the French Society of Electricity and Electronics for his contributions to the progress of science in electrical engineering, three Best Paper Awards in international conferences, and the Annual Award 1994 of the Technical Section of the Romanian Academy of Sciences.