CMUT Time of Flight Gas Sensor By Phase Shift Measurement
Authors: Iglesias Luis , Shanmugam Priyadarshini , Michaud Jean-François , Alquier Daniel , Certon Dominique , Dufour Isabelle 
Published: May 2020

Introduction

The most common approach to measure a gas concentration consists in coating the exposed part of a sensor with a functionalized film in order to absorb the targeted gas [1].
However, it is well known that a sensitive coating compromises the long term stability of the sensor mostly due to aging of such film [2]. This has resulted in an increasing interest in uncoated sensors, which rely on the change of the physical properties (mass density for instance) of their surrounding gas despite their lack of selectivity.
One example of uncoated sensors are time of flight sensors. Capacitive micromachined ultrasonic transducers (CMUTs) [3], have been previously used for time of flight gas sensing due to their easy integration capabilities. However, these methods rely on peak detection algorithms which can be very complex and hard to integrate.
In this study, we present a new simple approach using the phase shift of a continuous ultrasonic wave to measure the time of flight between two CMUT arrays. The principle of this method along with the experimental setup and results will be presented in the following sections.

Sensor

Figure 1 shows a picture of the sensor used in this study. It consists of an array of thousands of CMUTs as the one illustrated in Figure 2 fabricated according to [4]. By applying a bias Vdc
and an alternative voltage Vdc
between its electrodes, the top electrode vibrates generating an ultrasonic mechanical vibration in the gas (emitter mode). Similarly, when the membrane vibrates due to a mechanical vibration of the gas, the CMUT’s capacitance changes generating an electrical signal (receiver mode).

Principle

The experimental setup schematics are shown in Figure 3. One CMUT array working as emitter (1) generates a continuous ultrasonic wave at a given angular frequency (ω) through a network analyzer in gain/phase configuration (2). The wave propagates through the gas at a velocity (C) that depends on the gas composition. For this study the gas consists of N2 (similar to air) and either CO2 or H2. In the case of an ideal gas, its expression is given by Equation 1 where R = 8.314 J.K-1.mol-1, T = 20°C, x is the molar fraction of a gas (either N2 or the mixture), M is the corresponding molar mass and γ is the adiabatic index given by Equation 2 where cp
and cv
are, respectively, the isobar and isochoric heat capacitance per unit mass. After a delay τ, the wave reaches a second CMUT array (3) working in receiver mode. The generated signal is conditioned by a charge amplifier (4) and then injected back to the network analyzer. At a given time t, the phase difference φ between the emission and the reception is proportional to τ as shown in Equation 3. Therefore, the slope of the curve φ(ω
) changes when the gas composition changes. To verify this experimentally, the curves φ(
w) are shown for pure N2 (black), 4% of H2 in N2 (blue) and 4% of CO2 in N2 (green) in Figure 4.

Results

1-Sensitivity

Tests under H2 and CO2 in N2 at different concentrations (4%, 3%, 2% and 1%) were performed and are shown respectively in Figure 5 and Figure 6. From these measurements, the calibration curves were obtained with good linearity (Figure 7). The sensitivities (slope of the curves) to each gas were measured and their values are, respectively, S{H2,exp}=-92ns/% and S{CO2,exp}=55ns/%. Their corresponding theoretical values around a given concentration (xmix=4%) can be approximated by Equation 4. The obtained values are respectively, S{H2,th}=-135ns/% and S{CO2,th}=97ns/% which are consistent with the experiments.

2-Limit of Detection

Finally, knowing the sensitivity to a gas Sgas
, a theoretical limit of detection (LOD) can be estimated with Equation 5 where σ=1ns, is the noise standard deviation of the sensor. The obtained values for H2 and CO2 are, respectively, LODH2
=0.03%, LODCO
2
=0.05%.
In order to verify this experimentally, tests at low concentrations for H2 and CO2 were performed and are shown, respectively, in Figure 8 and Figure 9. The obtained results are consistent with the calculations.

Conclusion

In this study we presented a new way of determining the concentration of binary gas mixtures without a sensitive chemical coating through a time of flight measurement. We verified this method using N2 as a reference and both CO2 and H2 as analytes. Finally, we showed experimentally that the LOD in N2 is less than 0.03% for H2 and less than 0.05% for CO2 which, despite being worse than what has been reported with a coated sensor, remain comparable to the state of the art of uncoated sensors and to some commercial coated sensors.

References

[1] Göpel, W. New Materials and Transducers for Chemical Sensors. Sens. Actuators B Chem. 1994, 18 (1–3), 1–21. https://doi.org/10.1016/0925-4005(94)87049-7.
[2] Romain, A. C.; Nicolas, J. Long Term Stability of Metal Oxide-Based Gas Sensors for e-Nose Environmental Applications: An Overview. Sens. Actuators B Chem. 2010, 146 (2), 502–506. https://doi.org/10.1016/j.snb.2009.12.027.
[3] Shanmugam, P.; Iglesias, L.; Michaud, J.-F.; Dufour, I.; Alquier, D.; Colin, L.; Certon, D. CMUT Based Air Coupled Transducers for Gas-Mixture Analysis. In 2018 IEEE International Ultrasonics Symposium (IUS); IEEE: Kobe, 2018; pp 1–4. https://doi.org/10.1109/ULTSYM.2018.8579789.
[4] Heller, J.; Boulme, A.; Alquier, D.; Ngo, S.; Certon, D. Performance Evaluation of CMUT-Based Ultrasonic Transformers for Galvanic Isolation. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2018, 65 (4), 617–629. https://doi.org/10.1109/TUFFC.2018.2796303.

Figure 1