**3. Results and Discussion**

Using the setup described in the previous section, we measured and analyzed the sensor sample at six different absorption lengths (3.0 mm to 15.5 mm in intervals of 2.5 mm) with decreasing CO2 concentration steps ranging from about 9500 ppm down to 500 ppm. The measurement bench, which mixed CO2 and dry, synthetic air (80% N2 and 20 % O2 ±2 %), allowed for a consistent gas flow of 850 cm3 min−<sup>1</sup> through the sensor enclosure. Each concentration step was maintained for 10 min, followed by a flush step of 0 ppm, allowing to evaluate the sensor's baseline after each concentration step. The temperature in the sensor enclosure during all measurements ranged from 31.8 °C to 34.3 °C with a mean temperature of 33.2 °C.

Figure 5 shows the absolute sensor signal with an absorption distance of 15.5 mm over a complete characterization procedure. Over the course of the measurement, the sensor signal repeatedly dropped in response to the application of the different CO2 concentration steps. The figure also shows the output of the reference sensor, for which a lower noise level compared to our sensor could be observed. However, in this regard, it has to be noted, that despite our sensor being an early prototype aiming for low-cost production of an

integrated MEMS solution, it yields almost similar results compared to the well-established NDIR reference sensor, which is a larger, fully developed product.

**Figure 5.** Measurement with an absorption distance of d = 15.5 mm showing 10 min steps with decreasing CO2 concentration together with the output of a NDIR reference sensor (12-times moving mean filter applied).

The sensor prototype clearly responded with a lower signal to the increased number of CO2 molecules inside the absorption path, as a portion of the infrared light intensity already was absorbed there rather than inside the pressure transducer. The signal level at the lowest CO2 concentration applied (95 ppm) was found to be 2.37 V ± 0.70 mV. The signal response ranged from a decrease of about 197 mV (8.3%) at a concentration of 9400 ppm to a decrease of 18.8 mV (0.8%) at a concentration of 560 ppm. The sensitivity was calculated as signal response per decrease of 1000 ppm CO2 and thus ranged from −21.5 mV/1000 ppm for 9500 ppm to −41.7 mV/1000 ppm for 500 ppm. The first 2 min before and after each concentration change were ignored in the data processing in order to ensure a stabilized CO2 concentration.

We also characterized the same sensor prototype using six different absorption lengths. Figure 6 shows the relative signal response of all six sensor distances to seven different CO2 concentrations. The signal of the sample with the shortest absorption length dropped between 2.9% at a concentration of 9500 ppm to 0.2% at a concentration of 570 ppm. As expected from the Beer-Lambert law, the measurements with the longest absorption distances resulted in the highest signal response and those with the shortest absorption path in the smallest signal response. The signals of the other sensor lengths are laid in between those two configurations. As already done for the data of Figure 5, all values have been calculated from signal regions with stable CO2 concentrations and with a moving mean filter over 12 measurement periods applied. Although longer absorption paths provide higher sensitivity, they also result in larger setup sizes. For this reason, this study focused only on variants with an absorption path smaller or equal to 15.5 mm.

Figure 6 also indicates an increasing non-linearity in terms of the relative signal response with increasing sensor distance. We assume this is mostly based on the natural non-linearity of the Beer-Lambert law, if calculated with non-monochromatic light. With increasing absorption path length and CO2 concentration, an increasing number of absorption lines in the CO2 spectrum gets fully absorbed within the absorption path, leading to an amplification of the non-linear effect. A simulation with HITRAN for the given concentrations and sensor distances confirmed this theory [23,24]. However, the simulation did not take into account any reflections inside the aluminum tube, which multiply the effective path lengths. The results are shown in the Appendix A in Figure A3.

**Figure 6.** Signal response of six different absorption path distances ranging from 3.0 mm to 15.5 mm at different CO2 concentrations, relative to the the lowest reachable concentration. Error bars represent standard deviation.

In order to get a meaningful sensor output, which can be compared to other CO2 sensors, a basic quadratic regression curve was calculated from the measurements for the d = 15.5 mm sensor (Curve is depicted in the Appendix A, Figure A4). This calibration curve was then applied to the signal shown in Figure 5. The calibrated sensor response of this sample is depicted in Figure 7.

**Figure 7.** Calibrated sensor response absorption distance of d = 15.5 mm showing 10 min steps with decreasing CO2 concentration together with the output of an NDIR reference sensor (12-times moving mean applied).

When applying the sensor's sensitivity to a commonly occurring CO2 concentration of 1000 ppm (−39.8 mV/1000 ppm), the standard deviation of the 15.5 mm sample was found to be equivalent to 18 ppm.

#### **4. Conclusions**

We presented a novel approach for manufacturing wafer-level photoacoustic gas sensors and provided the first proof-of-concept measurement results. Basic characterization of the built sensor modules at various absorption distances showed promising sensitivity and noise levels even at short absorption path lengths.

The photoacoustic transducer can be manufactured using only materials and process steps, which are already standard in the semiconductor industry and are therefore reasonably priced in production. Moreover, as in this approach, the acoustic detector can be

manufactured, tested, and handled separately from the photoacoustic cell. As a result, the exposition to harsh environments or the need for non-standard manufacturing processes is limited to a minimum. Earlier studies with pressure or sound transducers directly encapsulated in the gas-filled cell, either needed to use non-standard low-temperature encapsulation processes in gas bias atmospheres individually manufactured samples or harsh process environments [25–29].

The concept could be adapted for a wide range of gasses with absorption bands that overlap with the high-transmissivity region of silicon, which was used for the IR entrance window. The only changes needed for such an adaption would be the substitution of the gas inside the absorbing cavity with another target gas and the exchange of the IR source or filter to form a matching pair of emitter and detector. Possible target gas candidates could include Methane or fluorine-based refrigerants [28,30]. Further experiments on the photoacoustic transducers themselves could benefit from a variation of the inner pressure, as this would allow a higher relative sensor response [30].

To our knowledge, this is the first successful approach that combines elements of photoacoustic and NDIR sensing enabling low-cost and well-performing IR detectors for CO2 sensors.

**Author Contributions:** Conceptualization, R.S., S.G. and M.E.; methodology, S.G. and M.E.; software, S.G. and S.E.; validation, S.G. and M.G.; formal analysis, S.G.; investigation, S.G., M.E. and R.S.; resources, S.G., C.v.K. and R.S.; data curation, S.G. and C.v.K.; writing—original draft preparation, S.G., R.S. and S.E.; writing—review and editing, S.G. and K.S.; visualization, S.G.; supervision, J.W.; project administration, R.S. and M.E.; funding acquisition, S.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** The article processing charge was funded by the Baden-Württemberg Ministry of Science, Research and Art and the University of Freiburg in the funding program Open Access Publishing.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Appendix A**

**Figure A1.** Background-compensated infrared transmission spectrum of the photoacoustic transducer. A characteristic dip at 4.26 μm indicates the presence of a high concentration of CO2 inside the cavity of the device.

**Figure A2.** Raw microphone output signal over 1 s of sampling (**left**) and two periods (74 ms) of the signal (**right**).

**Figure A3.** Additional absorption, simulated with HITRAN, for applied CO2 concentrations in the sensor path, normalized to the absorption of each absorption path at the measurements' lowest CO2 concentration. Only the direct distance was calculated. Reflections inside the reflector tube were neglected.

**Figure A4.** Absolute signal response and quadratic regression curve of d = 15.5 mm sample to applied CO2 concentrations. Error bars represent standard deviation.
