Dual-gate junction-less FET-detection for in-plane nano-electro-mechanical resonators

Faezeh Arab Hassani, Hiroshi Mizuta School of Materials Science

JAIST Nomi, Japan

ahfaezeh@jaist.ac.jp

Yoshishige Tsuchiya, Hiroshi Mizuta School of Electronics and Computer Science

University of Southampton Southampton, United Kingdom

Cecilia Dupré, Eric Ollier The Laboratory for Electronics and Information Technology

CEA-Léti Grenoble, France

Sebastian T Bartsch, Adrian Mihai Ionescu Institute of Electrical Engineering

EPFL Lausanne, Switzerland

Abstract—This paper presents the high frequency

characterization of a fabricated in-plane nano-electro-mechanical

resonator in which the doubly clamped nano-wire acts as a

suspended channel for a dual gate junction-less field-effect-

transistor that is used for the resonance frequency detection. The

applied DC biases to gates of the transistor were optimized to

amplify the detected output signal of the resonator. The effects of

changes in the applied DC biases and radio-frequency power on

the resonance frequency and quality factor of the resonator have

been investigated. Reduction of thermoelestic quality factor,

QThermoelastic, is discussed in terms of elevated temperature in the

thermally oxidized nano-wires with an increase in the applied

radio-frequency power.

Keywords—Nano-electro-mechanical resonator; junction-less

field-effect-transistor; resonance frequency; quality factor

I. INTRODUCTION The detection of resonance frequency is the bottleneck of

nano-electro-mechanical (NEM) resonators due to the need of good signal to noise/background ratio (SNR/SBR) to single out very small output signals [1]. The usage of integrated transistors with resonators as the detection circuit is a solution to this issue [2]. However, the performance of this method can be improved further using the monolithically integrated transistors to reduce unwanted parasitic capacitances due to the long distance between NEM resonators and transistors [3,4]. The introduction of nano-wire (NW) transistors with no junctions and doping concentration gradients gives the full functionality of metal-oxide-semiconductor field-effect-transistor (MOSFET) as well as design simplicity and CMOS compatibility [3,5]. Recently, a resonant-body silicon NW FET without junctions has been proposed by S. T. Barstch et al. [6].

In this paper, a junction-less FET (JL FET) is used for the resonance frequency detection of a NEM resonator. In Sec. II, the design and fabrication process of the NEM resonator are

presented. Section III shows the optimization of the DC characterization of JL FET, followed by the high-frequency measurement technique and characterization of resonators in Sec. IV. Section V, discusses effects of changes in biasing on the high frequency characterization of resonators. The conclusion of this work is given in Sec. V.

II. DESIGN AND FABRICATION OF THE NEM RESONATOR The presented in-plane NEM resonator in this paper

consists of a NW that plays the role of the suspended channel for the JL FET (Fig. 1 (a)). The changes of displacement for the resonating NW causes changes in the current of JL FET that is used for the detection of the resonance frequency later. The resonator was fabricated on 40 nm-tick, t, silicon on insulator (SOI) platform with the uniform boron doping of 1019 cm-3. The NW with the width of w=45 nm was defined by e-beam lithography followed by deep ultra violet (DUV) for defining the pads. The NW was then suspended using vapor hydrofluoric acid. The metallization was done after the deposition of poly-silicon for protecting the NW. The final releasing of the NW was done at the end. A 15 nm-tick thermal oxide layer was grown around the NW as shown in Fig. 1 (b) for passivation of the NW. Two side gates with the initial gap of 120 nm were considered for the NW to increase the controllability of gates over the channel. The gap size was reduced to a smaller value due to the oxidization of the NW and side gates. The oxide layer shown in Fig. 1 (c) is defined in the fabrication process for further protection of the device.

(a) (b) (c)

Fig. 1. The NEM resonator: (a) Schematic, (b) cross section of NW, and top SEM view.

This work is financially supported by EUFP7 project NEMSIC (Hybrid nano-electro-mechanical/integrated circuit systems for sensing and power management applications).

Oxide Oxide

Gate1

Gate2

978-1-4673-4743-3/13/$31.00 ©2013 IEEE

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The resonance frequency of the NW, fr, is calculated by [4]:

fr =1

2π

kbm

mb

(1) where kbm is the mechanical spring stiffness and mb is the effective mass of the NW. kbm and mb for Fig. 1 (b) are derived by [4]:

kbm =30.78

l3 (Etw3 + Eoxide(tT wT

3 − tw3)) (2)

mb = 0.735l(ρwt + ρoxide (wTtT − wt)) (3)

where E and Eoxide is young’s modulus, ρ and ρoxide is density for silicon and oxide, respectively. l is the length of the NW.

Figure 2 shows how the existence of a 15 nm-thick layer of oxide affects fr of the silicon NW (left). We assume the original designed dimensions for the NW (left) are kept the same after the lithography and suspension of the NW, however further shrinkage of the original dimensions (right) shows much smaller value for the resonance frequency that is observed in the high frequency measurement later.

The analytical values for the resonance frequency of two resonators with the thin oxide layer (Fig. 2 (middle)) are given in TABLE I. The total Q-factor is calculated using the following formula [7]:

ticThermoelasAnchorAmbient QQQfactorQ

1111++=

− (4)

QAmbient is the damping due to the working environment of the resonator. This damping is ignored here because of considering the high vacuum environment for the resonator. QAnchor is due to the energy dissipation of the resonator through its anchors and QThermoelastic is due to the interaction of the normal mode of vibration of a resonator with the thermally-excited phonons. QAnchor are calculated by [8]:

3

2))(1)(3(43.22 ⎟⎠

⎞⎜⎝⎛

+−

×=

w

l

XQ

nn

Anchorβϑϑ

(5)

where ϑ is the Poisson’s ratio, Xn is the shape factor and βn is the mode constant, where n shows the mode number of the resonator. The inverse value of QThermoelastic for the NW without oxide layer is as following [9]:

⎟⎟⎠⎞⎜⎜⎝

⎛+

+−

′=−

ξξ

ξξ

ξξ

α

coscoshsinsinh66

32

21

C

TEQ ticThermoelas (6)

where ξ is silicon’s thermal expansion, T is the operating temperature and C is silicon’s heat capacity of the NW. ξ is defined by [9]:

χ

πξ

22 rfw= (7)

where χ is silicon’s thermal diffusivity.

Fig. 2. The impact of adding a 15 nm-thick oxide onto the 1.5 μm-length NW on its resonance frequency.

As QThermoelastic at T=300 oK is larger about two orders of magnitude than QAnchor, we only considered QAnchor as the dominant factor for calculation of Q-factor for the NW with oxide layer in TABLE I. The parameters used for the calculations are shown in TABLE II.

III. DC CHARACTERIZATION OF THE NEM RESONATOR The optimum gate voltage bias of the resonator for the

consequent frequency measurement should provide the highest transconductance, gm, as well as high ON current. By applying the same voltages to side gates, the channel is formed in the middle of the NW due to the symmetrical depletion regions from both sides. By resonating the center-based channel, changes of drain current due to changes of displacement in one period will be small that will cause difficulties in the detection of weak output current signal in the high frequency measurement. For this reason, different bias voltages were applied to the side gates to improve this issue. More explanation on this fact is given in the next section.

Figure 3 (a) shows the DC characteristics of the resonator with the length of 1.5 μm while applying same voltages to both gates. The effects of applying different gate biases on Id-Vg and gm-Vg (inset to Fig. 3 (b)) characteristics of the resonator are shown in Fig. 3 (b). In this figure, the asymmetrical applied voltages to gates (i.e Vg1=-20 V, Vg2=-5 V) shows higher ON current as well as high gm. We do not apply larger voltage than -20 V for the consequent high frequency measurement in order to avoid the possibility of breakage/pull-in of the NW. TABLE I. ANALYTICAL AND EXPERIMENTAL KEY PARAMETERS FOR RESONATORS WITH 15 NM-TICK OXIDE LAYER

TABLE II. PARAMETERS USED FOR CALCULATIONS OF Q-FACTORS

Length Analytical Experimental

Resonance

frequency Q- factor

Resonance

frequency Q- factor

1.5 μm 158.98 MHz 9762 108.03 MHz 502-900

2 μm 89.42 MHz 23141 49.82 MHz 553-662

Parameter Value Parameter Value

α′ 2.616×10-6 1/K ϑ 0.33 C 700 J/kgK β0 1.5056 χ 0.86 cm2/s Χ0 -0.983 E 130.18 GPa ρ

2331 kg/m3

Eoxide 70 GPa ρoxide

2150 kg/m3

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10-14

10-12

10-10

10-8

Vg (V)

Id (

A)

Vg=Vg1=Vg2, Vd=50 mV

-25 -20 -15 -10 -5 0 5-8

-6

-4

-2

0

2

gm

(nS

)

(a)

-20 -10 010

-15

10-10

Vg2 (V)

Id (A

)

Vg1=-15 V

Vg1=-10 V

Vg1=-5 V

(b)

Fig. 3. The 1.5 μm-length NEM resonator: (a) DC characteristics and (b) the effect of various Vg1 on DC characteristics at Vd=50 mV.

IV. HIGH FREQUENCY CHARACTERIZATION OF THE NEM RESONATOR

NEM resonators were characterized using a down-mixing technique [10,11] as shown in Fig. 4. The gates were biased at the optimum bias point and a signal generator was used to apply a frequency modulation (FM) signal, vin, with frequency of ωc<100 kHz to drain. The measurements were done at high vacuum (10-6 mbar) and room temperature, and a lock-in amplifier was used to detect the output current signal, iout, from source. iout is defined by [10]:

)(ωxx

ivgi DS

inmout∂

∂∝ (8)

where iDS is the drain current and x(ω) is the in-plane displacement at the frequency of ω.

Figure 5 shows the lock-in current versus the frequency of resonators. The measured resonance frequency for the resonators and their related Q-factors are less than the analytical values in TABLE I that may be explained due to changes of dimensions of NWs as shown earlier in Fig. 2. Moreover, in contrary to the analytical values, the Q-factor of shorter NW is higher than the longer one in Fig. 5 that might be due to the deformation of the NW as this issue was not seen for the NW in the other set of device.

Fig. 4. Down-mixing measurement setup.

Fig. 5. High frequency characteristics of NEM resonators.

V. DISCUSSION ON RESULTS In order to investigate the impact of gates’ bias voltages on

the resonance frequency, Vg1 was fixed to -20 V while Vg2 was changed. The lock-in current versus frequency characteristics for resonators by changing Vg2 are shown in Fig. 6. In both devices, an increase in |ΔVg=Vg2-Vg1| causes an increase in the electrical spring stiffness and reduces the total spring stiffness that leads to the reduction of the resonance frequency so called softening effect.

The Q-factor of resonators versus |ΔVg| are shown in Fig. 7. The reduction of Q-factor by increasing |ΔVg| can be seen for both devices. This reduction is higher for the shorter NW due to the higher applied voltages.

(a) (b)

Fig. 6. The impact of changing Vg1 on the resonance frequency and Q-factor of: (a) 2 μm-length and (b) 1.5 μm-length NEM resonators.

-20 -10 0-5

-4

-3

-2

-1

0

1

Vg2 (V)

gm

(n

S)

Increase of |ΔVg|

Increase of |ΔVg|

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14 16 18 20 22500

550

600

650

700

750

800

|ΔVg|

Q-f

acto

r

1.5 um

2 um

Fig. 7. Changes of Q-factor of the resonators versus |ΔVg|.

The lock-in current versus the frequency of resonators for various RF powers are shown in Fig. 8. In this figure, the resonance frequency of both resonators is stable by increasing the RF power. Q-factors of the measured devices versus various applied RF powers are shown in Fig. 9. Increasing of the applied RF power causes higher temperature in the shorter NW and consequently reduction of QThermoelastic using (6) and its dominance effect on the total Q-factor compared to QAnchor. The reason of increasing of temperature is mainly due to the existence of oxide layer around the NW as oxide has smaller thermal conductivity in comparison with silicon. This effect is not visible for the 2μm-length NW at the smaller applied RF powers. Furthermore, the longer NW transfers the produced heat to environment sooner that the shorter NW.

Figure 10 (a) shows how the consequent repeating of the frequency measurement for the 1.5μm-length NW causes a slight reduction of the resonance frequency. The similar reduction was found for the 2-length NW. The same measurement was done for the resonator at lower RF power (Fig. 10 (b)) and the reduction of the resonance frequency is negligible. The dependence of the resonance frequency of the resonator to the value of applied RF power shows the necessity of doing the measurement in low temperatures that is considered for our future work.

(a) (b)

Fig. 8. The effect of various RF power on the frequency characteristics of: (a) 1.5 μm-length and (b) 2 μm-length NEM resonator.

-40 -38 -36 -34 -32500

550

600

650

700

750

800

850

900

950

RF power (dBm)

Q-f

acto

r

1.5 um

2 um

Fig. 9. The Q-factor of resonators versus applied RF power.

(a) (b)

Fig. 10. Repeatability of the mixing measurement applying the RF power of: (a) -32 dBm and (b) -34 dBm.

VI. CONCLUSION High frequency characterizations of fabricated in-plane

NEM resonators have been presented using the monolithically integrated JL FET. The optimization of the applied DC voltage to both gates of JL FET provided higher current in the transistor for easier detection of the resonance frequency. Applying higher RF power as well as gate voltages result in smaller Q-factor. The reduction of the resonance frequency especially at higher applied RF power and by increasing the applied gate voltages have been investigated. Size and cost reduction, design and fabrication simplicity and easy detection are the benefits of introducing NEM resonator taking advantage of JL FET detection.

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resonators and their front-end co-integration with CMOS for high sensitivity applications,” 25th IEEE Int. Conf. Micro Electro Mechanical Systems, 2012.

[2] T. Ernst et al., “High performance miniaturized NEMS sensors toward co-integration with CMOS?,” 70th Annual Device Research Conf., 2012.

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[7] B. Chouvion, “Vibration transmission and support loss in MEMS sensors,” PhD Dissertation, University of Nottingham, pp. 1-25, January 2010.

[8] Z. Haoa, A. Erbil, and F. Ayazi, “An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations,” Sensor. Actuator. A, vol. 109, pp. 156-164, 2003.

[9] R. Lifshitz and M. L. Roukes “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B, vol. 61, no. 8, pp. 5600-5609, February 2000.

[10] S. T. Bartsch, A. Rusu, and A. M. Ionescu, “A single active nanoelectromechanical tuning fork front-end radio-frequency receiver,” Nanotechnol., vol. 23, pp. 225501 (7pp), May 2012.

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