JSSS | Articles | Volume 8, issue 1

J. Sens. Sens. Syst., 8, 37–48, 2019

https://doi.org/10.5194/jsss-8-37-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/jsss-8-37-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

Special issue: Sensors and Measurement Systems 2018

**Regular research article**
14 Jan 2019

**Regular research article** | 14 Jan 2019

Phase optimization of thermally actuated piezoresistive resonant MEMS cantilever sensors

^{1}Institute of Semiconductor Technology (IHT), Technische Universität Braunschweig, Hans-Sommer-Straße 66, 38106 Braunschweig, Germany^{2}Laboratory for Emerging Nanometrology (LENA), Technische Universität Braunschweig, Langer Kamp 6a, 38106 Braunschweig, Germany^{3}Research Centre for Physics, Indonesia Institute of Sciences (LIPI), Kawasan Puspiptek Serpong, 15314 Tangerang Selatan, Indonesia^{4}Department of Metrology, Kenya Bureau of Standards (KEBS), Popo Rd, 00200 Nairobi, Kenya

^{1}Institute of Semiconductor Technology (IHT), Technische Universität Braunschweig, Hans-Sommer-Straße 66, 38106 Braunschweig, Germany^{2}Laboratory for Emerging Nanometrology (LENA), Technische Universität Braunschweig, Langer Kamp 6a, 38106 Braunschweig, Germany^{3}Research Centre for Physics, Indonesia Institute of Sciences (LIPI), Kawasan Puspiptek Serpong, 15314 Tangerang Selatan, Indonesia^{4}Department of Metrology, Kenya Bureau of Standards (KEBS), Popo Rd, 00200 Nairobi, Kenya

**Correspondence**: Andi Setiono (a.setiono@tu-braunschweig.de)

**Correspondence**: Andi Setiono (a.setiono@tu-braunschweig.de)

Abstract

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The asymmetric resonance response in
thermally actuated piezoresistive cantilever sensors causes a need for
optimization, taking parasitic actuation–sensing effects into account. In
this work, two compensation methods based on Wheatstone bridge (WB) input
voltage (*V*_{WB_in}) adjustment and reference circuit involvement
were developed and investigated to diminish those unwanted coupling
influences. In the first approach, *V*_{WB_in} was increased,
resulting in a higher current flowing through the WB piezoresistors as well
as a temperature gradient reduction between the thermal actuator (heating
resistor: HR) and the WB, which can consequently minimize the parasitic
coupling. Nevertheless, increasing *V*_{WB_in} (e.g., from 1 to
3.3 V) may also yield an unwanted increase in power consumption by
more than 10 times. Therefore, a second compensation method was considered:
i.e., a reference electronic circuit is integrated with the cantilever
sensor. Here, an electronic reference circuit was developed, which mimics the
frequency behavior of the parasitic coupling. By subtracting the output of
this circuit from the output of the cantilever, the resonance response can
thus be improved. Both simulated and measured data show optimized amplitude
and phase characteristics around resonant frequencies of 190.17 and
202.32 kHz, respectively. With this phase optimization in place, a
phase-locked-loop (PLL) based system can be used to track the resonant
frequency in real time, even under changing conditions of temperature (*T*)
and relative humidity (RH), respectively. Finally, it is expected to enhance
the sensitivity of such piezoresistive electro-thermal cantilever sensors
under loading with any target analytes (e.g., particulate matter, gas, and
humidity).

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Setiono, A., Fahrbach, M., Xu, J., Bertke, M., Nyang'au, W. O., Hamdana, G., Wasisto, H. S., and Peiner, E.: Phase optimization of thermally actuated piezoresistive resonant MEMS cantilever sensors, J. Sens. Sens. Syst., 8, 37–48, https://doi.org/10.5194/jsss-8-37-2019, 2019.

1 Introduction

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Environmental conditions have a major impact on human well-being, comfort,
and productivity. High air pollution levels for example may cause adverse
health effects (Al horr et al., 2016; Moreno-Rangel et al., 2018). Therefore,
research and development of chemical sensors have been progressively
advanced, especially with the technological enhancement in
micro-electro-mechanical systems (MEMS), which has led to the realization of
highly sensitive and selective microscale sensors (Corigliano et al., 2014).
Additionally, MEMS resonators have become favorable devices for measuring
concentrations of the undesired chemical substances ubiquitously (e.g.,
airborne nanoparticles, toxic gases, and humidity) by monitoring their
responses in resonant frequency *f*_{0} (Bausells, 2015; Li and Lee, 2012;
Mathew and Ravi Sankar, 2018; Wasisto et al., 2016, 2015; Xu et al., 2018).
Most of these MEMS resonators are often actuated by electrostatic (Zhao et
al., 2017), piezoelectric (Hees et al., 2013), or electrothermal (Chu et al.,
2018) methods, in which the sensing mechanisms are based on capacitive
(Pérez Sanjurjo et al., 2017), piezoelectric (Sviličić et al.,
2014), or piezoresistive (Bertke et al., 2016) transductions. Nevertheless,
unfavorable direct parasitic coupling due to resistive, capacitive, and
thermal effects between the actuating and sensing components of MEMS
resonators has been reported (Wasisto et al., 2015; Xu et al., 2018; Chu et
al., 2018; Zuo et al., 2010; Bertke et al., 2017a). The parasitic coupling
effect of an in-plane thermally actuated silicon-based microcantilever is
shown in Fig. 1a, in which the heating resistor (HR, actuating part) induces
a direct thermal parasitic coupling to the Wheatstone bridge (WB, sensing
part). Subsequently, the thermal parasitic coupling affects the output
signal: amplitude (asymmetric) and phase (reversed), as shown in Fig. 1b. The
expected amplitude and phase responses should be symmetric and monotonic,
respectively, as demonstrated by the same piezoresistive cantilever resonator
with an external piezoactuator (Fig. 1c). The piezoelectric shear actuator
resulted in an in-plane base point excitation of the cantilever with a very
low direct coupling to the WB (i.e., a low parasitic effect). Hence, the
optimize signal responses were obtained in this case (Fig. 1d).

Mathematical approaches shown by Chu et al. (2018) indicate that de-embedding
and post data processing have succeeded in revealing a symmetric amplitude
shape from the measured asymmetric response of a MEMS resonator. The
de-embedding method implements a mathematical model of parasitic parameters
and then removes the parasitic characteristics from the overall measurement.
Another mathematical model appropriate for de-embedding involves the use of
the Fano resonance approach (Bertke et al., 2017a), in which the quality
factor (*Q*) and resonant frequency (*f*_{0}) are obtained by fitting the
measured asymmetric resonance curve using mathematical models shown in
Eqs. (1) and (2):

$$\begin{array}{}\text{(1)}& {\displaystyle}A& {\displaystyle}={\displaystyle \frac{{\left(\frac{f-{f}_{\mathrm{0}}}{g}+q\right)}^{\mathrm{2}}}{{\left(\frac{f-{f}_{\mathrm{0}}}{g}\right)}^{\mathrm{2}}+\mathrm{1}}}H+{A}_{\mathrm{0}}+cf,\text{(2)}& {\displaystyle}Q& {\displaystyle}={\displaystyle \frac{{f}_{\mathrm{0}}}{\mathrm{2}g\sqrt{\sqrt{\mathrm{2}}-\mathrm{1}}}}\left(\mathrm{1}-\sqrt{\left|q\right|}\right)+{\displaystyle \frac{{f}_{\mathrm{0}}^{\mathrm{2}}-{g}^{\mathrm{2}}}{\mathrm{2}g{f}_{\mathrm{0}}}}\sqrt{\left|q\right|},\end{array}$$

where *f*_{0}, *Q*, *A*, *q*, *g*, *H*, and *A*_{0} are center frequency,
quality factor, amplitude, asymmetry factor, line width, and gain parameters,
respectively. Furthermore, an offset proportional to frequency *f* is
considered with a constant *c*.

The proposed approaches are however still not feasible in fast tracking and
real-time frequency measurement. Phase-locked-loop (PLL)-based systems have
broadly been used to realize continuous online resonance tracking of resonant
sensors (Wasisto et al., 2014, 2015; Toledo et al., 2016). A PLL can be used
to derive characteristic frequencies of a system by tracking a given phase
difference between the input and output signals of the system. In the case of
cantilever sensors, the resonance phase difference ideally is independent of
the resonant frequency. Therefore, the resonant frequency can be monitored by
tracking the resonance phase. When the measured phase reaches the desired
phase difference, the output frequency of the PLL is interpreted as the
resonance frequency. Here, the resonance phase becomes an essential parameter
to lock the resonant frequency using PLL-based systems. Nevertheless, PLL
systems do not function properly in thermally actuated cantilever sensors due
to their reversed phase response. Resonance tracking cannot work in a
reversed phase response because there is an ambiguity in the phase response,
which subsequently leads to instability during the locking process of
resonant frequency. Therefore, there is a need to develop a technique that
can guarantee an utmost suppression of parasitic effects on the thermally
actuated cantilever sensors. The developed technique is then expected to be
able to obtain a symmetrical amplitude shape and optimize the phase
characteristic without ambiguity in the phase response (monotonically
decreasing). In this work, two methods of mitigating the asymmetric behavior
in thermally actuated piezoresistive cantilever sensors are proposed (i.e.,
Wheatstone bridge (WB) input voltage (*V*_{WB_in}) adjustment and
application (subtraction) of an external reference signal). These techniques
are subsequently intended to expedite the locking procedure of resonant
frequency based on the PLL mechanism.

2 Thermally actuated MEMS cantilever sensor

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A thermally actuated piezoresistive silicon cantilever resonator (Fig. 2a)
comprises two main parts (i.e., for mechanical actuation and electrical
sensing, respectively), in which both are realized as diffused *p*-type
silicon resistors (Fig. 2b). Mechanical (thermal) actuation is obtained by
applying an AC voltage *V*_{ac}cos(*ω**t*) superimposed to a DC
voltage *V*_{dc} on a heating resistor (HR), which is located at the
clamped end of the cantilever. The resulting power loss (dissipation) *P* can
be described as

$$\begin{array}{}\text{(3)}& P={\displaystyle \frac{{V}_{\mathrm{dc}}^{\mathrm{2}}}{R}}+{\displaystyle \frac{{V}_{\mathrm{ac}}^{\mathrm{2}}}{\mathrm{2}R}}+{\displaystyle \frac{\mathrm{2}{V}_{\mathrm{dc}}{V}_{\mathrm{ac}}}{R}}\mathrm{cos}\left(\mathit{\omega}t\right)+{\displaystyle \frac{{V}_{\mathrm{ac}}^{\mathrm{2}}}{\mathrm{2}R}}\mathrm{cos}\left(\mathrm{2}\mathit{\omega}t\right),\end{array}$$

where *R* is the resistance of HR, *V*_{dc} and *V*_{ac}
are the DC and AC voltage amplitudes, respectively, and *ω* is the
excitation frequency. This term will lead to the Joule heating effect
(Wasisto et al., 2015; Brand et al., 2015) yielding a lateral temperature
gradient around the HR, as shown in Fig. 2c.

After a strain gradient has been induced, it will finally result in a
cantilever bending in the lateral direction (in-plane mode). The DC component
is necessary to have a large excitation amplitude at the excitation frequency
*ω* (third term in Eq. 3). The response to this mechanical actuation is
sensed by four piezoresistors configured in a U-shape WB, where this design
has been adapted to the strain distribution at the cantilever top surface
during lateral bending. Lastly, the electrical signal generated by the WB is
amplified using an external instrumentation amplifier (Texas Instruments,
INA217), as depicted in Fig. 2d.

As shown in finite element modeling (FEM,
COMSOL Multiphysics 4.4b, cf. Fig. 2c), the sensing piezoresistors near the
heating resistor (i.e., *R*_{1} and *R*_{2}) are exposed to more thermal
heating than *R*_{3} and *R*_{4}. This parasitic thermal coupling, which is
expected to result in an asymmetric response around resonance, can be
described by

$$\begin{array}{}\text{(4)}& {V}_{\mathrm{HR}}\left(T\right)=\mathit{\lambda}P,\end{array}$$

where *T* and *λ* are the temperature and a coupling factor,
respectively. When using voltage supply, thermal coupling to the WB
contributes to the output voltage of the WB (*V*_{WB_out})
according to

$$\begin{array}{}\text{(5)}& {V}_{\mathrm{WB}\mathrm{\_}\mathrm{out}}={V}_{\mathrm{WB}\mathrm{\_}\mathrm{in}}{\displaystyle \frac{\mathrm{\Delta}R}{R}}={V}_{\mathrm{WB}\mathrm{\_}\mathrm{in}}\mathit{\pi}\mathit{\sigma},\end{array}$$

where *V*_{WB_in} is the supply voltage of the WB, *R*=*R*_{i}
(*i*=1, …, 4) is the resistance of the WB, *π* is the (effective)
piezoresistive coefficient of the *p*-type silicon WB, and *σ* is the
average stress acting on the cantilever surface at the position of the WB.
Ideally, the WB output voltage (*V*_{WB_out}) should be linearly
proportional only to the stress *σ* acting on the Wheatstone bridge,
which is caused by the cantilever deflection. However, the temperature
dependences of *π* and *σ* can cause additional parasitic effects on
*V*_{WB_out} according to

$$\begin{array}{}\text{(6)}& {\displaystyle}& {\displaystyle}\mathit{\pi}={\mathit{\pi}}_{\mathrm{0}}(\mathrm{1}+\mathit{\beta}\mathrm{\Delta}T),\text{(7)}& {\displaystyle}& {\displaystyle}\mathit{\sigma}={\mathit{\sigma}}_{\mathrm{0}}(\mathrm{1}+\mathit{\gamma}\mathrm{\Delta}T),\end{array}$$

where *π*_{0} and *σ*_{0} represent the piezoresistive coefficient and
the average stress, respectively, at zero temperature increase, i.e., the
average temperature increase induced by HR at WB $\mathrm{\Delta}T=T-{T}_{\mathrm{0}}=\mathrm{0}$. The
temperature coefficients of piezoresistivity and thermal expansion are given
by *β* and *γ*, respectively. Substituting Eqs. (6) and (7) in
Eq. (5) results in

$$\begin{array}{ll}{\displaystyle}{V}_{\mathrm{WB}\mathrm{\_}\mathrm{out}}& {\displaystyle}={V}_{\mathrm{WB}\mathrm{\_}\mathrm{in}}{\mathit{\pi}}_{\mathrm{0}}{\mathit{\sigma}}_{\mathrm{0}}\left(\mathrm{1}+\mathit{\beta}\mathrm{\Delta}T\right)\left(\mathrm{1}+\mathit{\gamma}\mathrm{\Delta}T\right)\\ \text{(8)}& {\displaystyle}& {\displaystyle}={V}_{\mathrm{WB}\mathrm{\_}\mathrm{in}}{\mathit{\pi}}_{\mathrm{0}}{\mathit{\sigma}}_{\mathrm{0}}\left[\mathrm{1}+\left(\mathit{\beta}+\mathit{\gamma}\right)\mathrm{\Delta}T+\mathit{\beta}\mathit{\gamma}\mathrm{\Delta}{T}^{\mathrm{2}}\right].\end{array}$$

Based on Eq. (8), we can expect a nonlinear dependence of the WB output
voltage on the temperature increase (Δ*T*). Furthermore, temperature
distribution across the WB is not uniform, but is biased towards the HR;
i.e., resistors *R*_{1} and *R*_{2} are expected to be exposed to a higher
Δ*T* than *R*_{3} and *R*_{4}. Increasing *V*_{WB_in} reduces
Δ*T*, while its absolute nonuniformity is only slightly lower, as will
be shown below.

3 Wheatstone bridge adjustments

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In principle, removing asymmetry from the resonance response of a MEMS-based
resonator can be carried out by cancellation or minimization of the parasitic
effects at the resonator output. In the first approach, the WB input voltage
(*V*_{WB_in}) was gradually increased (from 1 to 3.3 V),
thereby inducing an increasing heating effect on the WB. Consequently, the
temperature gradient towards HR should reduce and finally eliminate the
thermal parasitic coupling effect. We used FEM (COMSOL Multiphysics 4.4b;
cf. Fig. 3) to show the temperature increase at the WB induced by increasing
*V*_{WB_in} from 1 to 3.3 V. As shown in this simulation,
the voltages applied to HR (*V*_{HR}=5 V) and
*V*_{WB_in} generate the temperatures *T*_{1} and *T*_{2},
respectively. The resultant average temperature difference $\mathrm{\Delta}T={T}_{\mathrm{1}}-{T}_{\mathrm{2}}$ due to *V*_{WB_in}=3.3 V amounts to
1.25 K, which is lower compared to the 2.23 K obtained for
*V*_{WB_in}=1 V. Again, *T*_{2} is not uniformly
distributed at *V*_{WB_in}=3.3 V, as indicated by the
deviation of Δ*T* across the WB of ±0.480 K vs. ±0.493 K at *V*_{WB_in}=1 V. According to Eq. (8)
and the reduced Δ*T*, a smaller parasitic temperature coupling to the
WB may be expected at *V*_{WB_in}=3.3 V, which was
confirmed by the measurements shown in Fig. 4, yielding a symmetric amplitude
shape and a monotonic phase response. Accordingly, the phase difference shows
a nearly ideal shape with a 90^{∘} transition occurring at the frequency
corresponding to the amplitude maximum.

However, compared to that of *V*_{WB_in}=1 V, the power
consumption produced by *V*_{WB_in}=3.3 V is boosted by an
order of magnitude. To relieve the need for such a large increase in
*V*_{WB_in}, an optimized design of the actuating–sensing
components is necessary in such a way as to reduce the thermal coupling
effect. Stationary FEM simulation delineated in Fig. 5b, c, and d shows that
shifting HR away from WB yields a lower thermal distribution compared to the
current design (Fig. 5a) at otherwise equal operating conditions (i.e.,
*V*_{HR}=5 V and *V*_{WB_in}=1 V).
Nevertheless, lower thermal distribution is followed by less total
displacement (*D*_{t}) of the cantilever beam. In this simulation,
total displacement changes from 17.79 to 15.95, 13.04, and 10.18 nm,
respectively, resulted for distances of HR to WB of 33, 43, 58, and
73 µm. Correspondingly, redesigned cantilever structures will be
fabricated and investigated in the near future. Therefore, as an alternative
we proposed a second method that involves the subtraction of a reference from
the sensor output signal.

4 Subtraction of reference signal

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A reversed phase response often occurs simultaneously with an asymmetric amplitude shape, i.e., a Fano resonance. According to Bertke et al. (2017a), a Fano resonance is yielded by mixing a discrete state (Lorentzian line shape) with a constant continuum background. Therefore, in order to obtain a symmetrical amplitude shape (Lorentzian line shape), elimination of the continuum background should be done by subtracting a corresponding characteristic. Simultaneously, the symmetrical amplitude shape should then be accompanied by a monotonic phase response.

In this study, amplitude and phase responses of a reference signal were
subtracted from the outputs of the thermally actuated microcantilever as
shown in Fig. 6. The reference signal was created by an RCL (resistor,
capacitor, and inductor) high-pass filter (HPF) with a cut-off frequency of
∼50 kHz. In this case, the RCL-HPF yields a small slope of both
amplitude and phase responses corresponding to the frequency dependence of
the baseline of the cantilever signal around the working frequency (i.e.,
∼202 kHz). Hence, the RCL-HPF circuit was intended to generate
and provide a suitable characteristic reference signal, which could then be
subtracted from the cantilever signal. The variable resistors VR_{1} and
VR_{2} were tuned to control the level of reference amplitude and phase
responses, respectively. Furthermore, subtraction was performed using both
negative and positive voltage input terminals of a lock-in amplifier (MFLI,
Zurich Instruments). The positive (V+) and negative (V−) inputs of the
lock-in amplifier were connected to the output signals of the cantilever and
reference, respectively, and the resultant amplifier output voltage (*V*_{O})
was then determined internally in the MFLI lock-in amplifier.

In order to yield a symmetric line shape at the differential output, the
amplitude and phase of the reference signal should be placed close to the
out-of-resonance baselines of amplitude and phase of the thermally actuated
microcantilever. Subtracting the reference signal from an asymmetric
amplitude shape was simulated using LTspice, as depicted in Fig. 7. From the
simulation, it was found that the asymmetric amplitude response (Fig. 7a,
open-red line) and the reversed phase response (Fig. 7b, open-blue line) of a
circuit can be eliminated using a reference signal set close to the
asymmetric baseline. These configurations result in a resonant signal with a
symmetric amplitude shape about *f*_{0} and the phase difference is
90^{∘} as shown in Fig. 7c.

A mathematical model of polar and Cartesian equations was used to analyze the
amplitude (*A*) and phase (*φ*) of a differential output [*A*,*φ*].
Polar equations noted by Eq. (9) represent the amplitude and phase responses
of the sensor output (index “S”) and the reference signal (index “R”).
The polar form is then converted to the Cartesian form to obtain both sensor
[*x*_{1},*y*_{1}] and reference [*x*_{2},*y*_{2}] signals, as expressed in
Eqs. (10) and (11), respectively. Then, *x* and *y* components of a reference
signal are subtracted from the sensor signal (Eq. 12). Finally, the amplitude
of the differential output can be calculated by Eq. (13), while the phase
response is calculated using Eq. (14):

$$\begin{array}{}\text{(9)}& {\displaystyle}& {\displaystyle}{A}_{\mathrm{S}}\mathrm{\angle}{\mathit{\phi}}_{\mathrm{S}};\phantom{\rule{0.25em}{0ex}}{A}_{\mathrm{R}}\mathrm{\angle}{\mathit{\phi}}_{\mathrm{R}};\text{(10)}& {\displaystyle}& {\displaystyle}{x}_{\mathrm{1}}={A}_{\mathrm{S}}\mathrm{cos}{\mathit{\phi}}_{\mathrm{S}};\phantom{\rule{0.25em}{0ex}}{y}_{\mathrm{1}}={A}_{\mathrm{S}}\mathrm{sin}{\mathit{\phi}}_{\mathrm{S}};\text{(11)}& {\displaystyle}& {\displaystyle}{x}_{\mathrm{2}}={A}_{\mathrm{R}}\mathrm{cos}{\mathit{\phi}}_{\mathrm{R}};\phantom{\rule{0.25em}{0ex}}{y}_{\mathrm{2}}={A}_{\mathrm{R}}\mathrm{sin}{\mathit{\phi}}_{\mathrm{R}};\text{(12)}& {\displaystyle}& {\displaystyle}\mathrm{\Delta}x={x}_{\mathrm{1}}-{x}_{\mathrm{2}};\phantom{\rule{0.25em}{0ex}}\mathrm{\Delta}y={y}_{\mathrm{1}}-{y}_{\mathrm{2}};\text{(13)}& {\displaystyle}& {\displaystyle}A=\sqrt{\mathrm{\Delta}{x}^{\mathrm{2}}+\mathrm{\Delta}{y}^{\mathrm{2}}};\text{(14)}& {\displaystyle}& {\displaystyle}\mathit{\phi}=\mathrm{arctan}\mathrm{2}(\mathrm{\Delta}y,\phantom{\rule{0.125em}{0ex}}\mathrm{\Delta}x).\end{array}$$

Experimental results depicted in Fig. 8 show that the sensor amplitude (open
red line) has a baseline between ∼221.79 and ∼218.50 mV,
whilst the phase baseline (open blue line) ranges from ∼56.96 to ∼56.75^{∘} in the frequency range of 202.0 to 202.6 kHz. The
reference signal was then set closer to the baseline of the sensor signal by
adjusting VR_{1} and VR_{2} (shown in Fig. 6). In the same frequency
domain, the measured reference amplitude (solid red line) was observed to
increase from ∼219.99 to ∼220.84 mV, whereas the phase
response (solid blue line) decreases from ∼56.70 to ∼56.56^{∘}. The observed changes in the amplitude (increment) and phase
(decrement) of the reference signals are characteristic of an electronic
filter, which, in the case of RCL-HPF, covers an extended phase range of
$\mathrm{0}{}^{\circ}<\mathit{\theta}<\mathrm{90}{}^{\circ}$ and $\mathrm{90}{}^{\circ}<\mathit{\theta}<\mathrm{180}{}^{\circ}$.

Subtracting the reference from the sensor signal demonstrates a symmetric amplitude shape (Fig. 9a, solid red squares) and a monotonic phase response (solid blue squares, Fig. 9b) in the range of ∼94.48 to $\sim (-\mathrm{167.87}{}^{\circ})$. These experimental results are confirmed by calculation approaches, i.e., implementation of Eqs. (13) and (14) for the amplitude (black solid line, Fig. 9a) and phase (purple solid line, Fig. 9b), respectively. As a result, both experimental and calculated results generate symmetrical amplitude and monotonic phase with small deviations. The next step will be to generate a suitable reference signal by a programmed software to enable automatic reference adjustment.

5 Resonant frequency tracking

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Tracking of the resonance frequency is performed by implementing the PLL
technique, as shown in Fig. 10a. Reference subtraction from the cantilever
output results in a symmetric amplitude shape (red solid line) and a
monotonic phase response with no ambiguity (blue dashed line), as depicted in
Fig. 10b. The monotonic phase is applicable in the PLL-based system for
resonant frequency tracking. From the highest peak of amplitude, the
resonance phase *φ*_{0} is determined. It is subsequently used as a set
point of phase. The set point value is subtracted from the measured phase
difference, generating an error signal. This error signal is then used by the
PID (proportional, integral, derivative) controller to calculate a new output
frequency, which is expected to result in a smaller error signal. When the
error signal reaches zero, the resonance frequency *f*_{0} is found and will
be tracked henceforth. Setting of the parameters *K*_{p}
(proportional gain), *K*_{i} (integral gain), and *K*_{d}
(derivative gain) determines how quickly and how precisely the controller can
lock the resonant frequency. The *K*_{p} and *K*_{i} will
have the effect of reducing the rise time and eliminating the steady-state
error, respectively, while *K*_{d} is effective for decreasing the
overshoot. However, too-high values of *K*_{p}, *K*_{i},
and *K*_{d} will result in an unstable response; conversely, too-low
values will lead to sluggish steering. Therefore, optimization is needed for
these parameters to get the best tracking control, i.e., as fast and precise
as possible.

Two experimental setups shown in Figs. 11 and 12 were used to confirm the
performance of the monotonic phase response that is obtained by subtracting
the reference signal from the sensor output (i.e., the second method). In the
first case, a bare silicon cantilever is used, while in the second case the
cantilever was functionalized with a bilayer of ZnO and chitosan. Tracking of
the resonant frequency was realized by using a lock-in amplifier with an
integrated PLL system (MFLI, Zurich Instruments). For comparison, a
commercial instrument to measure relative humidity (RH) and temperature (*T*)
(Chauvin Arnoux, CA 1246 Thermo-hygrometer) was used simultaneously. By these
two experiments, we investigated whether the resultant monotonic phase
response will yield an improved response during the resonance frequency
tracking.

From the first test configuration, depicted in Fig. 11, both *T* and RH are
expected to generate a shift in resonant frequency. The temperature
coefficient of Young's modulus and the thermal expansion coefficient are the
main intrinsic parameters, which cause a change in the spring constant (*k*).
By increasing the temperature, the spring constant *k* decreases, thereby
causing the resonant frequency *f*_{0} to decrease. On the other hand, an
increase in humidity leads to an enhanced absorption of water molecules on
the cantilever, leading to an increase in its mass and a decrease in *f*_{0}.
Thus, the effects of temperature and humidity changes will cancel out each
other up to a certain level in resonance. This is evidently shown in Fig. 11,
in which the shift in resonance ($\mathrm{\Delta}{f}_{\mathrm{0}}<\pm \mathrm{80}$ Hz) is
relatively stable especially after 30 min of tracking. Previously,
larger resonant frequency shifts Δ*f*=7.275 kHz and Δ*f*=444 Hz corresponding to added masses of 0.20 µg and
38 ng under cigarette smoke exposure conditions were reported by
Bertke et al. (2017a, b). The small shift in resonance (i.e., $\mathrm{\Delta}{f}_{\mathrm{0}}<\pm \mathrm{80}$ Hz) realized in this study makes the MEMS sensor more
sensitive for the detection of particulate matter.

The second test configuration involved assessment of the resonance response and relative humidity using a cantilever and commercial sensor, respectively, under the same conditions. The cantilever is initially coated with ZnO film and chitosan. Both sensors were put in a bottle filled with chemical solutions under different saturation vapor pressures. These solutions release different humidity levels depending on the type of solution (i.e., potassium acetate: 23 %; potassium carbonate: 43 %; sodium chloride: 75.3 %; and potassium sulfate: 97.3 %). The experimental results (Fig. 12) show a good correlation between cantilever and commercial sensor in the ascending range of RH from 0 % to 60 %. Above this range, we find much worse agreement between cantilever and commercial sensor, which we assign to a slower response of the commercial sensor at large RH. In the case of the cantilever direct exposure and fast reaction of water molecules are possible with the ZnO/chitosan sensing layer, leading to an increase in adsorbed mass and thus a fast responding frequency shift. Correspondingly, on the descending part of the curve, desorption is much faster from the cantilever than indicated by the commercial hygrometer.

6 Conclusions

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Asymmetric resonance in thermally actuated piezoresistive cantilever sensors
has been successfully suppressed by adjusting the supply voltage
*V*_{WB_in} of the Wheatstone bridge (WB) and subtracting a
reference signal. Both methods reveal monotonic phase responses that are
suitable for implementation in a phase-locked-loop (PLL) system for tracking
the resonant frequency of the sensor. Adjustment of *V*_{WB_in} not
only directly reduces the parasitic coupling effect, but also leads to
increased power consumption. Further works will be necessarily done to
optimize the design of the actuating–sensing components (i.e., HR and WB) as
well as their operating conditions (i.e., *V*_{DC},
*V*_{AC}, and *V*_{WB_in}). By subtraction of a constant
reference, symmetric amplitude shapes can be effectively obtained from
measured asymmetric resonance signals. Monotonic phase responses earned by
this technique have been employed successfully in a PLL system, resulting in
effective frequency tracking under changing temperature (*T*) and relative
humidity (RH). However, further investigation is still necessary to implement
reference signals under a wide range of conditions (e.g., in humidity
measurement). Moreover, automatic adjustment of reference parameters, design
of an on-chip reference, and implementation of a symmetric heat actuator
design will become further challenges to be undertaken.

Biographies

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**Andi Setiono** obtained his Bachelor of Sciences
degree in electronics and instrumentation from the Department of Physics,
Gadjah Mada University (UGM), Yogyakarta, Indonesia, in 2009. In 2015, he
finished his masters study in electronics and photonics from the Department
of Electrical Engineering, University of Indonesia. Since 2010, he has been
part of the Optoelectronics Research Group at the Research Center for
Physics, Indonesia Institute of Sciences (LIPI), working in the field of
fiber Bragg grating sensors for landslide monitoring and weight measurement.
Since December 2016, he has been a PhD student at the Institute of
Semiconductor Technology (IHT), TU Braunschweig, Germany, in the IG-Nano
Project (i.e., Indonesian-German Center for Nano and Quantum Technologies)
supported by LENA and LIPI. His PhD study is funded by the Ministry of
Research, Technology and Higher Education of the Republic of Indonesia
(RISTEKDIKTI). His research interests include electronic systems for resonant
silicon MEMS/NEMS sensors.

**Michael Fahrbach** studied electrical engineering at Braunschweig
University of Technology and obtained his MSc degree in 2017. Currently,
he is working as a PhD student at the Institute of Semiconductor
Technology (IHT), TU Braunschweig and Laboratory for Emerging Nanometrology
(LENA), Germany. His research is focused on further developing MEMS-based
sensors and measurement systems for high-speed contact resonance
spectroscopy (CRS) measurements.

**Jiushuai Xu** studied applied chemistry and
biochemistry at Northwest A&F University in Yangling, China, and obtained
his MSc degree in 2015. Currently, he is pursuing his PhD degree at the
Institute of Semiconductor Technology at TU Braunschweig and Laboratory for
Emerging Nanometrology. His research interests are the fabrication of
nanostructures and thin films of metal oxides and organic materials, and
MEMS/NEMS piezoresistive silicon humidity and gas sensors.

**Maik Bertke** received a Master of Science degree in
electrical engineering from the Technische Universität Braunschweig,
Germany, in 2016. Currently, he is working towards a PhD degree at the
Institute of Semiconductor Technology (IHT), TU Braunschweig and Laboratory
for Emerging Nanometrology, Germany, where his main interests are in the
fields of resonant micro-/nano-electromechanical systems (MEMS/NEMS)-based
sensors.

**Wilson Ombati Nyang'au** received BSc and MSc degrees
in physics from the Jomo Kenyatta University of Agriculture and Technology,
Kenya, in 2008 and 2012, respectively. He has been working at the Department
of Metrology in the Kenya Bureau of Standards since 2011. Currently, he is
pursuing his PhD degree at the Institute of Semiconductor Technology (IHT),
TU Braunschweig, Germany. His research interests include
microcantilever-based sensors for liquid-borne particle detection, M/NEMS,
and mass metrology.

**Gerry Hamdana** received his Bachelor of Engineering
degree in mechanical engineering from the Esslingen University of Applied
Science in 2012 and his Master of Science degree in mechanical engineering,
specializing in mechatronic/microsystems technology, from the Braunschweig
University of Technology (TU Braunschweig), Germany, in 2015. He finished his
PhD work in 2018 at the Institute of Semiconductor Technology (IHT), TU
Braunschweig, Germany. His research interests include semiconductor
processing, microsystems technology and micro-/nano-electromechanical systems
(MEMS/NEMS).

**Hutomo Suryo Wasisto** received the Doktor-Ingenieur
(Dr.-Ing.) degree in Electrical Engineering (summa cum laude) from the
Technische Universität Braunschweig, Germany, in 2014. He was a
postdoctoral research fellow at the School of Electrical and Computer
Engineering (ECE), Georgia Institute of Technology, Atlanta, GA, USA, in
2015–2016. Since 2016, he has been head of the Optoelectromechanical
Integrated Nanosystems for Sensing (OptoSense) Group at the Laboratory for
Emerging Nanometrology (LENA) and Institute of Semiconductor Technology
(IHT), Technische Universität Braunschweig, as well as an initiator and
CEO of the Indonesian-German Center for Nano and Quantum Technologies
(IG-Nano), Braunschweig, Germany. His main research interests include
nano-opto-electro-mechanical systems (NOEMS), nanosensors, nanoelectronics,
nanoLEDs, nanogenerators, and nanometrology. He has received several
international scientific awards (i.e., the Young Materials Scientist Award at
MRS-id 2018, the Transducer Research Foundation (TRF) Travel Grant Award at
Transducers 2015, the Walter Kertz Study Award 2014 at TU Braunschweig, the
Best Paper Award at IEEE NEMS 2013, and the Best Young Scientist Poster Award
at Eurosensors 2012).

**Erwin Peiner** received diploma and Dr. rer. nat. degrees in physics from the University of Bonn, Germany, in 1985 and 1988,
respectively, and the Venia Legendi degree in semiconductor technology from
the Technical University (TU) Braunschweig, Braunschweig, Germany, in 2000.
In 2002 he did a professor internship at Volkswagen AG Headquarters,
Electronics Research Department, Wolfsburg, Germany. Since 2015 he has been
an associate professor at TU Braunschweig, where he is the leader of the
Semiconductor Sensors and Metrology Group at the Institute of Semiconductor
Technology (IHT) and the Laboratory for Emerging Nanometrology (LENA). His
current research interests include design, fabrication, assembly, and testing
of Micro/Nano Electro Mechanical Systems (M/NEMS) for industrial applications
like condition monitoring, tactile surface and force metrology, pollution
monitoring, environmental sensing, and energy harvesting. He has published
more than 300 papers in international journals and conference proceedings.

Data availability

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Data availability.

Research data are available upon request to the authors.

Author contributions

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Author contributions.

AS simulated and analyzed the FEM modeling; simulated, assembled, and fabricated the electronic circuit for the subtraction method; designed and performed all the tests and measurements; analyzed measurement data; and drafted the manuscript. MF contributed to realizing the data acquisition; analyzing and interpreting data of the bridge adjustment; and reviewing the principle of the PID controller. JX and MB designed and fabricated the cantilever sensors used for this study, discussed the results and contributed to interpreting the FEM simulation. WON and GH reviewed and discussed the simulation and experimental results and contributed to the manuscript. HSW critically revised the manuscript for important intellectual content. EP supervised the work; reviewed and discussed results; provided recommendations for improving the manuscript; and gave final approval of the version to be submitted and any revised version.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement

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Special issue statement.

This article is part of the special issue “Sensors and Measurement Systems 2018”. It is a result of the “Sensoren und Messsysteme 2018, 19. ITG-/GMA-Fachtagung”, Nürnberg, Germany, from 26 June 2018 to 27 June 2018.

Acknowledgements

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Acknowledgements.

This project has received funding from the EMPIR program co-financed by the
Participating States and from the European Union's Horizon 2020 research and
innovation program under no. 17IND05 MicroProbes. Andi Setiono would like to
thank the Ministry of Research, Technology and Higher Education of the
Republic of Indonesia (RISTEKDIKTI) for the PhD scholarship of RISET-Pro
under no. 343/RISET-Pro/FGS/VIII/2016 (World Bank loan no. 8245-ID) and the
Indonesian-German Center for Nano and Quantum Technologies (IG-Nano) for the
support. Jiushuai Xu, Maik Bertke, and Wilson Ombati Nyang'au are grateful
for funding from the China Scholarship Council (CSC) under grant CSC
no. 201506300019, from “Niedersächsisches Vorab”, Germany, through the
“Quantum- and Nanometrology (QUANOMET)” initiative within the project of
“NP 2-2”, and from the German Federal Ministry for Economic Cooperation and
Development (BMZ) within the Braunschweig International Graduate School of
Metrology, respectively. Hutomo Suryo Wasisto acknowledges the Lower Saxony
Ministry for Science and Culture (N-MWK) for funding of the LENA-OptoSense
group. We are also grateful to Angelika Schmidt, Maike Rühmann,
Aileen Michalski, Karl-Heinz Lachmund, Zhenshuo Ding, Xuejing Li, and
Ratna Indrawijaya for their assistance during preparation of research tools
as well as many fruitful discussions.

Edited
by: Walter Lang

Reviewed by: two anonymous referees

References

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Al horr, Y., Arif, M., Katafygiotou, M., Mazroei, A., Kaushik, A., and Elsarrag, E.: Impact of indoor environmental quality on occupant well-being and comfort: A review of the literature, International Journal of Sustainable Built Environment, 5, 1–11, https://doi.org/10.1016/j.ijsbe.2016.03.006, 2016.

Bausells, J.: Piezoresistive cantilevers for nanomechanical sensing, Microelectron. Eng., 145, 9–20, https://doi.org/10.1016/j.mee.2015.02.010, 2015.

Bertke, M., Hamdana, G., Wu, W., Marks, M., Wasisto, H. S., and Peiner, E.: Asymmetric resonance frequency analysis of in-plane electrothermal silicon cantilevers for nanoparticle sensors, J. Phys.-Conf. Ser., 757, 12006, https://doi.org/10.1088/1742-6596/757/1/012006, 2016.

Bertke, M., Hamdana, G., Wu, W., Wasisto, H. S., Uhde, E., and Peiner, E.: Analysis of asymmetric resonance response of thermally excited silicon micro-cantilevers for mass-sensitive nanoparticle detection, J. Micromech. Microeng., 27, 64001, https://doi.org/10.1088/1361-6439/aa6b0d, 2017a.

Bertke, M., Wu, W., Wasisto, H. S., Uhde, E., and Peiner, E.: Size-selective electrostatic sampling and removal of nanoparticles on silicon cantilever sensors for air-quality monitoring, in: 2017 19th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2017 19th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), Kaohsiung, Taiwan, IEEE, 1493–1496, 2017b.

Brand, O., Dufour, I., Heinrich, S. M., and Josse, F.: Resonant MEMS: Fundamentals, Implementation and Application, edited by: Brand, O., Dufour, I., Heinrich, S. M., and Josse, F., Advanced Micro & Nanosystems, Wiley-VCH, Weinheim, Germany, 2015.

Chu, C.-C., Dey, S., Liu, T.-Y., Chen, C.-C., and Li, S.-S.: Thermal-Piezoresistive SOI-MEMS Oscillators Based on a Fully Differential Mechanically Coupled Resonator Array for Mass Sensing Applications, J. Microelectromech. Syst., 27, 59–72, https://doi.org/10.1109/JMEMS.2017.2778307, 2018.

Corigliano, A., Ardito, R., Comi, C., Frangi, A., Ghisi, A., and Mariani, S.: Microsystems and Mechanics, Procedia IUTAM, 10, 138–160, https://doi.org/10.1016/j.piutam.2014.01.015, 2014.

Hees, J., Heidrich, N., Pletschen, W., Sah, R. E., Wolfer, M., Williams, O. A., Lebedev, V., Nebel, C. E., and Ambacher, O.: Piezoelectric actuated micro-resonators based on the growth of diamond on aluminum nitride thin films, Nanotechnology, 24, 25601, https://doi.org/10.1088/0957-4484/24/2/025601, 2013.

Li, X. and Lee, D.-W.: Integrated microcantilevers for high-resolution sensing and probing, Meas. Sci. Technol., 23, 22001, https://doi.org/10.1088/0957-0233/23/2/022001, 2012.

Mathew, R. and Ravi Sankar, A.: A Review on Surface Stress-Based Miniaturized Piezoresistive SU-8 Polymeric Cantilever Sensors, Nano-Micro Lett., 10, 25, https://doi.org/10.1007/s40820-018-0189-1, 2018.

Moreno-Rangel, A., Sharpe, T., Musau, F., and McGill, G.: Field evaluation of a low-cost indoor air quality monitor to quantify exposure to pollutants in residential environments, J. Sens. Sens. Syst., 7, 373–388, https://doi.org/10.5194/jsss-7-373-2018, 2018.

Pérez Sanjurjo, J., Prefasi, E., Buffa, C., and Gaggl, R.: A Capacitance-To-Digital Converter for MEMS Sensors for Smart Applications, Sensors (Basel, Switzerland), 17, 1312, https://doi.org/10.3390/s17061312, 2017.

Sviličić, B., Mastropaolo, E., and Cheung, R.: Piezoelectric sensing of electrothermally actuated silicon carbide MEMS resonators, Microelectron. Eng., 119, 24–27, https://doi.org/10.1016/j.mee.2014.01.007, 2014.

Toledo, J., Jiménez-Márquez, F., Úbeda, J., Ruiz-Díez, V., Pfusterschmied, G., Schmid, U., and Sánchez-Rojas, J. L.: Piezoelectric MEMS resonators for monitoring grape must fermentation, J. Phys.-Conf. Ser., 757, 12020, https://doi.org/10.1088/1742-6596/757/1/012020, 2016.

Wasisto, H. S., Zhang, Q., Merzsch, S., Waag, A., and Peiner, E.: A phase-locked loop frequency tracking system for portable microelectromechanical piezoresistive cantilever mass sensors, Microsyst. Technol., 20, 559–569, https://doi.org/10.1007/s00542-013-1991-9, 2014.

Wasisto, H. S., Merzsch, S., Uhde, E., Waag, A., and Peiner, E.: Handheld personal airborne nanoparticle detector based on microelectromechanical silicon resonant cantilever, Microelectron. Eng., 145, 96–103, https://doi.org/10.1016/j.mee.2015.03.037, 2015.

Wasisto, H. S., Uhde, E., and Peiner, E.: Enhanced performance of pocket-sized nanoparticle exposure monitor for healthy indoor environment, Build. Environ., 95, 13–20, https://doi.org/10.1016/j.buildenv.2015.09.013, 2016.

Xu, J., Bertke, M., Li, X., Mu, H., Yu, F., Schmidt, A., Bakin, A., and Peiner, E.: Self-actuating and self-sensing ZNO nanorods/chitosan coated piezoresistive silicon microcantilever for humidit Y sensing, in: 2018 IEEE Micro Electro Mechanical Systems (MEMS), 2018 IEEE Micro Electro Mechanical Systems (MEMS), Belfast, IEEE, 206–209, 2018.

Zhao, C., Wood, G. S., Pu, S. H., and Kraft, M.: A mode-localized MEMS electrical potential sensor based on three electrically coupled resonators, J. Sens. Sens. Syst., 6, 1–8, https://doi.org/10.5194/jsss-6-1-2017, 2017.

Zuo, C., Sinha, N., van der Spiegel, J., and Piazza, G.: Multifrequency Pierce Oscillators Based on Piezoelectric AlN Contour-Mode MEMS Technology, J. Microelectromech. Syst., 19, 570–580, https://doi.org/10.1109/JMEMS.2010.2045879, 2010.

Special issue

Short summary

In this work, methods to reveal a symmetrical amplitude shape from the asymmetric behavior in thermally actuated piezoresistive cantilever sensors are proposed. The symmetrical amplitude shape should then be accompanied by a monotonic phase response. With the monotonic phase response, real-time frequency tracking can be easier to implement using a phase-locked-loop (PLL) system.

In this work, methods to reveal a symmetrical amplitude shape from the asymmetric behavior in...

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