08358116.pdf

Single Resonator, Time-switched, low Offset Drift z-axis FM MEMS Accelerometer Cristiano R. Marra, Filippo M. Ferrari, Giacomo Langfelder

Alessandro Tocchio, Francesco Rizzini

Dipartimento di Elettronica, Informazione e Bioingegneria Politecnico di Milano Italy Email: [email protected]

ST Microelectronics Cornaredo (MI), Italy Email: [email protected]

Abstract—The work presents principle of operation, design and test of a novel z-axis MEMS accelerometer realized through a single resonator, in which the differential readout is achieved sampling the two resonant frequency values obtained alternatively biasing suitable tuning electrodes in subsequent time intervals. An electronic oscillator sustains the MEMS resonator, providing a low-phase-noise signal to a frequency counter. The accelerometer shows a sensitivity of 1.3Hz/g, with linearity error lower√ than 1% up to 15g and a consumer-grade resolution of 160μg/ Hz. The key-feature of the proposed inertial sensor is that the ZGO (zero-g offset) thermal drift can be conceptually nulled. Preliminary demonstrations report values lower than 100 μg/K without post-acquisition compensation.

I. I NTRODUCTION Capacitive MEMS accelerometers have been dominating the market since few decades, showing, together with well known advantages, their limits in terms of dynamic range and offset thermal drift. In particular, 16-g-full-scale-range (FSR) consumer products exhibit offset drifts around 1mg/K [1], not suitable for future applications like inertial navigation and virtual reality. An attractive alternative to capacitive accelerometers is found in resonant (or frequency modulated, FM) accelerometers, mostly thanks to their high dynamic range and quasidigital output [2], [3]. More recently, the research attention moved on their thermal-stability performance, with few examples of low-offset-drift devices [4], [5]. Nevertheless, (i) these solutions do not deal with consumer applications requirements in terms of area and power dissipation; furthermore, (ii) these works are conceived exclusively for in-plane accelerations (z-axis resonant accelerometers were developed [6], but not targeting low-offset-drift applications); additionally, (iii) no conceptual operating principles for perfect offset drift zeroing was proposed. In this paper, the first out-of-plane, single-resonator, lowoffset-drift FM-accelerometer is described. The theory shows the conceptual possibility to null all offset drift components (stress-related and Young’s-modulus-related). Preliminary demonstration reaches sub-100 μg/K drift with other parameters (FSR, noise and prospective consumption) compatible with consumer applications.

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II. D EVICE DESCRIPTION A. Resonant frequency thermal drift The working principle of a FM accelerometer relies on a sustained oscillation of a vibrating structural part that, in presence of an external acceleration aext , varies its resonance frequency by an amount Δf (aext ): the sensor output can be thus written as fout = f0 + Δf (a). In this situation, a drift in the device resonance directly induces an analogous output drift. It is well known that the thermal drift of the resonant frequency of a Si/polySi MEMS resonator depends on the Young’s Modulus drift (described by its temperature coefficient T CE = −60ppm/K):   T CE ppm df0 = f0 · = f0 · − 30 dT 2 K

(1)

Thus, named S the output frequency variation per unit input acceleration (i.e. the scale factor), the input-referred drift is: df0 dT

S

=

  f0 ppm · − 30 S K

(2)

Proposed solutions to this issue are given by high-sensitivity differential readout topologies: the sensor includes two resonators that, under an external acceleration, vary their frequency with opposite sign. However, we note here that: (i) while subtracting the two frequency outputs, the commonmode term associated with the drift is erased only for perfectly matched resonators, both in terms of TCE and f0 ; (ii) as a rule of thumb, a high sensitivity S is obtained with small critical dimensions (e.g. thin resonating beams), which are hardly well-matched, due to unavoidable process nonuniformities. In realistic situations therefore, the two oscillating elements present a finite frequency and TCE mismatch at rest, resulting in a residual offset thermal drift: Δf dT

S

=

  T CE1 T CE2 1 f0,1 · − f0,2 · S 2 2

(3)

T CEi and f0,i corresponding to the two resonators. While the TCE differences among the two resonators can be minimized [5], the frequency mismatch is unavoidable.

Fig. 1. SEM top view, with highlighted electrodes for push-pull driving, differential readout and electrostatic tuning of the anti-phase oscillation. Mechanical elements as anchor points, tuning fork torsional springs and proof mass are also indicated. The overall area is (510 × 630)μm2

Fig. 2. Finite elements simulation showing the oscillating anti-phase mode (a) and the acceleration sensitive in-phase mode (b).

The approach proposed in this work relies on a singleresonator differential readout, achieved by periodically switching the sensor configuration in order to obtain, for a given input acceleration, opposite frequency shifts in subsequent time intervals. In other words, a single resonator is sampled twice in time, instead of having two resonator in space. Double sampling and subtracting the acquired frequency values brings a clear advantage that no mismatch between the resonant frequencies has to be considered, ideally erasing the equation (3) contribution. Even in presence of process nonuniformities, the two configurations in time can be chosen such that this contribution is canceled. A dual approach was already presented for in-plane accelerometers [7]: in the following, a z-axis MEMS device that implements the proposed solution is described in detail.

named tuning port #1 and #2, used to modulate the antiphase frequency in presence of accelerations, through the electrostatic softening effect. Indeed, when an external acceleration aext occurs (typically at frequencies << fip ), an in-phase torsion takes place: the rotor approaches one tuning port, e.g. port #1, moving away from the other one (#2). In a first time interval, here called ΔT1 , tuning port #1 is biased at a DC voltage, meanwhile port #2 is equipotential with the rotor. Being the gap between tuning port #1 and rotor e.g. diminished, the electrostatic contribution to the anti-phase torsional stiffness increases with respect to the rest value kel,0 by an amount kel (aext ), dependent on the input acceleration. The resulting anti-phase frequency in the considered first time interval is thus given by:

B. Working principle and design The proposed FM accelerometer (Fig. 1) is composed by a single torsional resonator, surrounded by a rigid frame-like structure that connects the centered anchor points to external torsional beams. The two halves through which the device is formed are coupled by a torsional tuning fork, resulting in a resonator with a coupled anti-phase mode (Fig. 2a), in addition to the in-phase mode (Fig. 2b) mode. The indicated figures refer to finite element simulations of a structure with an area of (510x600)μm2 with the anti-phase faph and the in-phase fip modes nominally designed at 25 kHz and 10 kHz. In operation, the device is kept in oscillation at its antiphase resonance through push-pull driving and differential sensing electrodes fabricated beneath the torsional structure, as depicted in Fig. 1. Further electrodes are also present,

 kmec − kel,0 − kel (aext ) 1 , t ∈ ΔT1 (4) faph,1 = 2π I where kmec is the mechanical contribution to the overall torsional stiffness and I is the moment of inertia associated with the anti-phase torsion. In the immediately following time interval ΔT2 , the voltages applied on the two tuning port are switched, thus inverting the sign of kel (aext ) and causing a positive shift of the anti-phase resonant frequency (with respect to its rest value):  kmec − kel,0 + kel (aext ) 1 , t ∈ ΔT2 (5) faph,2 = 2π I Subtracting the frequency values faph,1 and faph,2 acquired during ΔT1 and ΔT2 gives rise to a differential readout.

Fig. 3. Sketch of a system view including the voltages applied to each MEMS port, the designed discrete-component electronic oscillator and the off-theshelf frequency readout through a frequency counter.

In order to cope with overall sensor bandwidths of 50Hz, tuning intervals ΔT1 and ΔT2 were chosen to last 5ms. In this configuration tuning voltages are square waves at a frequency fsw = 100Hz. The resulting differential output signal, frequency-modulated around the rest anti-phase resonant frequency f0,aph , can be described with its first-harmonic approximation: faph (t) = f0,aph + (faph,2 − faph,1 ) · sin(2πfsw t)

(6)

The 100-Hz modulation of the FM signal bypasses slow temperature drifts. Conceptually, this working principle is similar to what is achieved by Lissajous FM gyroscopes [8]. III. E XPERIMENTAL RESULTS A. Electronics and experimental setup In order to keep the MEMS resonator in oscillation, the discrete-component electronic board sketched in Fig. 3 was designed and assembled. The sense current generated by the rotor oscillation is readout through a differential transcapacitance stage, converted in a single-ended signal by an instrumentation amplifier (INA) and shifted by 90◦ by an analog integrator, so to cope with Barkhausen criteria. The signal is then squared through an high-gain stage and then converted in a differential signal by a pair of buffers that drive the anti-phase resonator in push-pull mode. The frequency readout is performed sending the INA output to a frequency counter: an intermediate band-pass filtering stage has the task of limiting the wide-band noise at the counter input, mitigating noise folding issues related to the instrument measurement methodology.

Fig. 4. Differential frequency variation against input accelerations up to 15g(a), with associated percentage error with respect to a linear fitting of the obtained curve (b).

ramping up to 15g. The obtained sensitivity curve, reported in Fig. 4a, shows a scale factor of 1.3Hz/g with a linearity error lower than 1% at the 15-g full scale range (Fig. 4b). Note that observed fluctuations are likely due to board imbalance as no significant trend is visible, which indicates that nonlinearity is probably much lower than the indicated highest bound. For what concerns the resolution, the low-noise oscillator reaches a phase noise level of −116dBc/Hz (fig. 5) at a mismatch of 100Hz with respect to the carrier frequency

B. Sensitivity and resolution Sensitivity tests are performed mounting the electronic board coupled to the FM accelerometer on a rate table, in order to exploit the centrifugal acceleration arising while it sweeps the angular velocity, applying in this way input signals

Fig. 5. Measured phase noise √of the electronic oscillator, corresponding to a white noise floor of 160μg/ Hz.

Fig. 6. ZGO thermal drift (in gravity units) measured between 30o C and 70o C. The thermal drift coefficient corresponds to 32μg/K.

(i.e. where the FM signal is modulated), √ corresponding to an acceleration noise density of 160μg/ Hz, compatible with consumer accelerometers on the market [1]. C. Offset thermal drift Offset thermal drift measurement are carried out mounting the electronic board coupled with the device inside a climatic chamber, with no acceleration applied to the sensor. Once preheated, the climatic chamber is turned off in order to avoid spurious vibrations and, during the cool-down, temperature is monitored with a suitable temperature sensor while the offset is regularly acquired. Results shows a ZGO thermal drift coefficient below 100μg/K (fig. 6), the accuracy in the measured value (best linear fitting corresponding to 32μg/K) being limited by noise associated to the complicated setup mounting inside the climatic chamber. IV. C ONCLUSIONS The work presented the first single-resonator, ultra-lowoffset-drift, z-axis FM accelerometer. The shown architecture, designed to be coupled with low-noise, low-power integrated oscillators [9] meets consumer specifications in terms of area occupation, expected power dissipation, resolution and singlechip compatibility for planar, 3-axis solutions. Furthermore, through the time-switched differential readout, it is capable to erase the resonant frequency thermal drift, providing a measured sub 100μg/K consumer accelerometer, suitable for high-stability applications. V. ACKNOWLEDGMENTS The project is partially funded under the Cariplo/Regione Lombardia agreement 2016-0855 (Se-MEMS). R EFERENCES [1] Invensense, ICM-20600 High Performance 6-Axis MEMS Motion Tracking Device, www.invensense.com, Oct 2016. [2] X. Zou, and A. A. Seshia, A high-resolution resonant MEMS accelerometer, Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS) IEEE, Jun. 2015.

[3] C. Comi, A. Corigliano, G. Langfelder, A. Longoni, A. Tocchio, B. Simoni A Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit, Journal of microelectromechanical systems, vol.19, no. 5, pp. 1140-1152, Oct. 2010. [4] S. A. Zotov, B. R. Simon, A. A. Trusov, A. M. Shkel, High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation, IEEE Sensors Journal, vol. 15, no. 9, pp. 5045-5052, Sept. 2015. [5] D. D. Shin, C. H. Ahn, Y.Chen, D. L. Christensen, I. B. Flader, T. W. Kenny, Environmentally robust differential resonant accelerometer in a wafer-scale encapsulation process, 30th IEEE International Conference on Micro Electro Mechanical Systems (MEMS), pp 17-20, Jan. 2017. [6] C. Comi, A. Corigliano, V. Zega, S. Zerbini, Optimal design and nonlinearities in a z-axis resonant accelerometer, 16th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, Apr. 2015. [7] A. Tocchio, F. Rizzini, C. Valzasina, G. Langfelder, C.R. Marra, FM INERTIAL SENSOR AND METHOD FOR OPERATING THE FM INERTIAL SENSOR, Italian application patent n. 102017000097531, filed 30/08/2017. [8] I. I. Izyumin, M. H. Kline, Y. C. Yeh, B. Eminoglu, C. H. Ahn, V. A. Hong, Y. Yang, E. J. Ng, T. W. Kenny, and B. E. Boser, A 7ppm, 6o /hr frequency-output MEMS gyroscope, 28th IEEE International Conference on Micro Electro Mechanical Systems (MEMS), pp. 3336, Jan 2015, . [9] P. Minotti, G. Mussi, S. Dellea, A. Bonfanti, A. L. Lacaita, G. Langfelder, √ A. Tocchio, A 160 μA, 8 mdps/ Hz frequency-modulated MEMS yaw gyroscope, IEEE International Symposium on Inertial Sensors and Systems (INERTIAL), Mar. 2017.