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Using a Second Order Sigma-Delta Control to Improve the Performance of Metal-Oxide Gas Sensors Lukasz Kowalski 1 , Joan Pons-Nin 1 Manuel Domínguez-Pumar 1, * ID 1

2

*

ID

, Eric Navarrete 2 , Eduard Llobet 2

ID

and

Micro and Nano Technologies Group, Electronic Engineering Department, Universitat Politècnica de Catalunya—BarcelonaTech, 08034 Barcelona, Spain; [email protected] (L.K.); [email protected] (J.P.-N.) MINOS-EMaS Group, Electronic Engineering Department, Universitat Rovira i Virgili, 43003 Tarragona, Spain; [email protected] (E.N.); [email protected] (E.L.) Correspondence: [email protected]; Tel.: +34-93-401-5679

Received: 31 January 2018; Accepted: 19 February 2018; Published: 23 February 2018

Abstract: Controls of surface potential have been proposed to accelerate the time response of MOX gas sensors. These controls use temperature modulations and a feedback loop based on first-order sigma-delta modulators to keep constant the surface potential. Changes in the surrounding gases, therefore, must be compensated by average temperature produced by the control loop, which is the new output signal. The purpose of this paper is to present a second order sigma-delta control of the surface potential for gas sensors. With this new control strategy, it is possible to obtain a second order zero of the quantization noise in the output signal. This provides a less noisy control of the surface potential, while at the same time some undesired effects of first order modulators, such as the presence of plateaus, are avoided. Experiments proving these performance improvements are presented using a gas sensor made of tungsten oxide nanowires. Plateau avoidance and second order noise shaping is shown with ethanol measurements. Keywords: sigma-delta modulation; metal-oxide sensors; gas sensors; electrochemical impedance

1. Introduction Interest in metal-oxide (MOX) gas sensors has grown significantly during the recent years. Different materials, such as SnO2 , WO3 , or ZnO, and specific fabrication techniques have been developed to form the sensing layers of such sensors, often structured as nanoneedles, nanotubes, nanorods, etc. The high surface-to-volume ratios of these nanostructures allow high levels of interaction with the environment, thus providing high sensitivities. Good stability, reduced cost, low power consumption, and compatibility with semiconductor fabrication processes are other advantages of this type of sensors [1–5]. All this makes them excellent candidates in applications such as detection of hazardous gases, pollution observation, or detection of gas leaks [6–8]. The mode of operation of the MOX gas sensors usually consists of monitoring the conductivity of the sensing layer. Since this layer is a semiconductor, its conductance strongly depends not only on the temperature but also on the chemical reactions involved in the gas adsorption and ionization processes [9]. Moreover, the conductivity of the sensor layer can be seen as the result of two simultaneous competing mechanisms that have different time scales. The first mechanism is due to the temperature applied, which produces redistribution in the energies of the charge carriers and causes fast changes in the conductivity of the layer; the second mechanism consists in changes in the chemical reaction rates with the gas species, which generate slow changes in the conductivity of the sensing layer. MOX sensors are usually operated in open-loop at constant-high temperature, of 100 ◦ C

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and above, depending on the specific materials of the sensing layer. To reach and maintain constant operating temperature, heaters are usually embedded in the sensors. However, the performance of MOX-based gas sensors becomes limited by their slow time response to changes in gas concentration and, in some cases, by unwanted long term drifts. As a first step towards studying these issues, dynamic models of the sensors have been proposed [10,11], and it is widely accepted that nonlinear models must be used to describe the evolution with time of the chemical reactions in the layer. As a consequence, complex digital-processing tools, such as neural networks [12], probabilistic state estimation [13], reservoir computing [14], and support vector machines [15] are used to improve sensor performance. Temperature modulations have also been used in works reported in the literature with MOX gas sensors to reduce measurement uncertainty [13], to improve feature extraction [16–19], or to reduce power consumption [20,21]. Additionally, single walled carbon nanotubes have been used in conjunction with MOX modulated in temperature to reduce power consumption [22]. A new approach for smart operation of MOX gas sensors has been proposed recently by the authors [23]. There, a closed-loop technique, inspired in first order sigma-delta modulation, is applied to enforce a sliding mode control on the state variables of the sensor [24]. In particular, the feedback loop produces the temperature modulations necessary to operate the sensor under constant surface potential. In this case, the output of the sensor is the average temperature applied to the sensing layer. This strategy allows the time dynamics of the system to be changed: since the control variable (the surface potential) is constant, the excursion of one or several state variables is reduced and the time response of the system no longer depends on its own free (and slow) dynamics, but on the marginal dynamics obtained within the control surface. This way, fast time responses with a MOX gas sensor have been demonstrated [23]. However, some known issues of first-order sigma-delta modulators can limit the effectiveness of the technique proposed in [23]. One is the presence of a Devil’s Staircase fractal, a typical effect when leaky integrators are used [25]; a fractal plateau is in practice a “dead zone” that cannot be observed or controlled, thus hindering the possibility of having a good control in certain cases. Another issue is poor quantization noise shaping, which can pose a problem for retrieving real-time information about the sensing layer. According to this, this paper introduces a new second-order sigma-delta strategy to control the chemical resistance of MOX gas sensors. This method improves the one previously proposed, providing second order quantization noise shaping, smoother sensor responses, and allows for the avoidance of the plateaus observed in the first-order approach. The feasibility and the features of the new method are demonstrated experimentally through extensive comparisons of both control methods in gas sensing applications with tungsten oxide nanowires. 2. Materials and Methods 2.1. First and Second Order Sigma-Delta Loops for Gas Sensing As it has been mentioned in the Introduction, the typical operation of chemical gas sensors based in semiconductor metallic oxide (MOX) layers consists in keeping such sensing layers at constant temperature and monitor changes in its resistivity. Under this approach, the time response of the sensor is completely determined by the dynamics of the surface adsorption and ionization reactions, which can be generally very slow. In order to improve the time response of the sensors, the control proposed in [23] operates the sensor under a new condition: Constant Surface Potential Operation. This is done by implementing a sliding mode controller [26] using the scheme of a first order sigma-delta modulator [24]. Sliding mode controllers confine the dynamics of the dynamical system to a predetermined control surface. By doing this, the dynamics of the whole system can be completely changed under some conditions. This control can be performed using the sigma-delta approach, in which the topology of these analog-to-digital

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converters is used to obtain the desired sliding motion on the control surface. In our case, then the control surface is constant Surface Potential. the conductivity of the chemical sensing layer follows this general expression [23]: 3 of 13 SensorsNow, 2018, 18, x FOR PEER REVIEW   qVs G= G T exp − ( ) = 0 ( ) exp − kT , ,

(1) (1)

in inwhich which G0(( T)) isis aa factor factor depending depending on on temperature, temperature,T, T,qqisis the the electron-elementary electron-elementarycharge, charge, Vs isis the surface potential, and k is the Boltzmann constant. From this expression it is clear that in order to the surface potential, and k is the Boltzmann constant. From this expression it is clear that in order keep constant, the conductivity of the sensing layer must be kept constant and measured to keep Vs constant, the conductivity of the sensing layer must be kept constant and measuredat at constant temperature. constant temperature. The Thecontrol controlproposed proposedin in [23] [23] isis shown shown in in Figure Figure 1a. 1a. ItItachieved achievedthe theconstant constantSP SPoperation operationby by applying an adequate sequence of temperature waveforms to the sensor. These waveforms, applying an adequate sequence of temperature waveforms to the sensor. These waveforms,called called BIT0 can be beseen seenininFigure Figure1b.1b. periodically sampling conductivity ofsensing the sensing BIT0 and and BIT1, BIT1, can ByBy periodically sampling the the conductivity of the layer, layer, at the end of each sampling period, it is possible to monitor changes in Vs, since both at the end of each sampling period, it is possible to monitor changes in Vs, since both waveforms end waveforms endtemperature with the same temperature value T . The control is designed to apply,sampling for the with the same value Thigh . The control ishigh designed to apply, for the following following period [ , ( + 1) )] , a BIT1 waveform if [ ] > or a BIT0 if period [nTsampling s , ( n + 1) Ts )], a BIT1 waveform if G [ nTs ] > Gtarget or a BIT0 if G [ nTs ] < Gtarget . This way, [ ] < . This way, it is possible to change the average temperature in the sensor, while it is possible to change the average temperature in the sensor, while making decisions based on the making decisions based on the conductivity of the sensing layer, measured at the same temperature. conductivity of the sensing layer, measured at the same temperature.

Ionized surface states leak

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Figure Figure 1.1. (a) (a)First-order First-ordersigma-delta sigma-deltamodulator modulatortopology topologytotocontrol controlthe thechemical chemicalresistance resistanceof ofthe the metal-oxide metal-oxidesensing sensinglayer. layer.At Ateach eachsampling samplingtime timeTTSS, ,depending dependingon onwhether whetherthe thechemical chemicalresistance resistance RRchem, measured at the reference temperature Thigh, is below (or above) the desired value Rth, a BIT1 (or chem , measured at the reference temperature Thigh , is below (or above) the desired value Rth , a BIT1 (or BIT0) temperature BIT0) temperaturewaveform waveformisisapplied appliedto tothe thesensor sensorduring duringthe thenext nextsampling samplingperiod; period;(b) (b)parameters parameters of the BIT0 and BIT1 waveforms. of the BIT0 and BIT1 waveforms.

This control replicates the usual circuit topology of a 1st order sigma-delta modulator. The This control replicates the usual circuit topology of a 1st order sigma-delta modulator. The sensing sensing layer can be seen as a reservoir of ionized surface states, which can be negatively or positively layer can be seen as a reservoir of ionized surface states, which can be negatively or positively charged. charged. In an oxidizing atmosphere, increasing (decreasing) the average temperature will increase In an oxidizing atmosphere, increasing (decreasing) the average temperature will increase (decrease) (decrease) the adsorption of gas molecules that, when ionized, will increase (decrease) the total the adsorption of gas molecules that, when ionized, will increase (decrease) the total negative ionized negative ionized surface states. In this case, the average temperature generated by the control must surface states. In this case, the average temperature generated by the control must be able to keep be able to keep constant the interchange of ionized surface states with the surrounding atmosphere constant the interchange of ionized surface states with the surrounding atmosphere by applying a by applying a suitable sequence of temperature waveforms. Changes in the atmosphere are therefore suitable sequence of temperature waveforms. Changes in the atmosphere are therefore compensated compensated for by changes in the average temperature generated by the control. for by changes in the average temperature generated by the control. As it has been mentioned before, this paper presents a second order sigma-delta topology for As it has been mentioned before, this paper presents a second order sigma-delta topology for surface potential control in MOX-based gas sensors. By adding an integrator to the control loop, it is surface potential control in MOX-based gas sensors. By adding an integrator to the control loop, it is possible to obtain a second order zero in the quantization noise at zero frequency [27]. This integrator possible to obtain a second order zero in the quantization noise at zero frequency [27]. This integrator is implemented numerically, see Figure 2, and good values of the α parameter are empirically found. is implemented numerically, see Figure 2, and good values of the α parameter are empirically found. Besides the improvement in the quantization noise, second order modulators do not present plateaus Besides the improvement in the quantization noise, second order modulators do not present plateaus in in the case of leaky integrators. On the other hand, they can become unstable under some conditions the case of leaky integrators. On the other hand, they can become unstable under some conditions [27]. [27].

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Figure 2. Block diagram (Top) and equivalent sampled circuit (Bottom) of the 2nd order sigma-delta Figure 2. Block diagram (Top) and equivalent sampled circuit (Bottom) of the 2nd order sigma-delta topology designed to control the chemical resistance of the MOX sensing layer. topology designed to control the chemical resistance of the MOX sensing layer.

Figure 2 presents the qualitative translation of the 2nd order control loop to the standard sigma2 presents the qualitative translation of the the continuous 2nd order leak control loop tosurface the standard delta Figure idealized representation. Parameter β represents of ionized states, sigma-delta idealized representation. Parameter β represents the continuous leak of ionized surface ∆ represents the differences at the sampling times between the resistivity of the layer and the states, ∆R represents the differences at the sampling times nT between the resistivity of the layer n s target value set ( )− , and are the values of the second numerical integrator. The and the target set Rchem (are nTsperformed the values the seen second integrator. ) − Rth , and n are functions of thevalue first integrator byvthe sensing layerof itself, as anumerical reservoir of ionized The functions of the first integrator are performed by the sensing layer itself, seen as a reservoir of surface states. The purpose of the control circuit is therefore to cancel the value at the output of this ionizedintegrator surface states. The purpose of the control circuit is therefore to cancel the value at the output second by applying an adequate sequence of BIT0/BIT1 waveforms to the sensor. of this second integrator by applying an adequate sequence of BIT0/BIT1 waveforms to the sensor. 2.2. Description of the Gas Sensors 2.2. Description of the Gas Sensors 2.2.1. 2.2.1. Sensing SensingLayer Layer Synthesis Synthesis The The sensing sensing layers layers consist consist of of pristine pristine tungsten tungsten oxide oxide nanowires nanowires directly directly grown grown on on top top of of the the membranes of a 4-element micro-machined silicon transducer employing an Aerosol Assisted membranes of a 4-element micro-machined silicon transducer employing an Aerosol Assisted Chemical Chemical Vapor Deposition (AACVD) process. Eachwithin membrane within the 4-element Vapor Deposition (AACVD) process. Each membrane the 4-element chip containschip POClcontains 3 -doped −4/°C) and platinum POCl 3-doped polysilicon heaters (16 Ω/sq, 0.47 μm thickness, and TCR = 6.79 × 10 − 4 ◦ polysilicon heaters (16 Ω/sq, 0.47 µm thickness, and TCR = 6.79 × 10 / C) and platinum electrodes electrodes (0.2 μm thickness, electrode μm). To electrically insulate the electrodes on top (0.2 µm thickness, electrode gap = 100 gap µm).= 100 To electrically insulate the electrodes on top from the from the heater, 800-nm-thick silicon oxide layers were deposited by Low Pressure Chemical Vapor heater, 800-nm-thick silicon oxide layers were deposited by Low Pressure Chemical Vapor Deposition Deposition (LPCVD). In the AACVD growth of tungsten oxide nanowires, tungsten hexacarbonyl (50 (LPCVD). In the AACVD growth of tungsten oxide nanowires, tungsten hexacarbonyl (50 mg, mg, Sigma-Aldrich, Saint Louis, MO, USA, ≥97%) dissolved in a mixture of acetone and methanol Sigma-Aldrich, Saint Louis, MO, USA, ≥97%) dissolved in a mixture of acetone and methanol (15 (15 mL mL of acetone mLmethanol, of methanol, Sigma-Aldrich, ≥99.6%) used. solution in a of acetone and and 5 mL5 of Sigma-Aldrich, ≥99.6%) was was used. The The solution was was kept kept in a flask flask and placed an ultrasonic humidifier. and placed in anin ultrasonic humidifier. The resulting aerosol was transported thethe reactor by by a 500 mL/min flow flow of nitrogen. The The resulting aerosol was transportedto to reactor a 500 mL/min of nitrogen. substrates were placed inside the reactor and the whole system was heated up to 370 °C (see Figure The substrates were placed inside the reactor and the whole system was heated up to 370 ◦ C (see 3). A mask was placed top ofon thetop substrate protect to theprotect contactthe pads of thepads heater Figure 3). A mask wasonplaced of the to substrate contact ofand the electrodes, heater and leaving exposed the electrode areas only. The reactor outlet was vented directly into the extraction electrodes, leaving exposed the electrode areas only. The reactor outlet was vented directly into the system of a fume cupboard. The deposition time ranged between 30 to 40 min, until all of the extraction system of a fume cupboard. The deposition time ranged between 30 to 40 min, until all precursor had passed through the reactor. At the end of the growth, the flow of nitrogen of the precursor had passed through the reactor. At the end of the growth, the flow of nitrogen was was interrupted, ◦ C for interrupted, and and the the substrates substrates were were kept kept in in the the reactor reactor at at 370 370 °C for another another 60 60 min. min. This This helps helps the the removal of the precursor residues and further oxidizes nanowires. Films have a pale-yellow color, removal of the precursor residues and further oxidizes nanowires. Films have a pale-yellow color, which which indicates indicates that that aa close close to to stoichiometry stoichiometry tungsten tungsten oxide oxide is is obtained. obtained. Finally, Finally, the the sensors sensors were were wire-bonded to standard TO-8 packages. wire-bonded to standard TO-8 packages.

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Figure 3. Artistic view inside of the hot wall reactor during the AACVD process. A nitrogen flow Figure 3. Artistic view inside of the hot wall reactor during the AACVD process. A nitrogen flow carries the aerosol droplets of solvent containing the organic precursor. carries the aerosol droplets of solvent the organic Figure 3. Artistic view inside of thecontaining hot wall reactor during precursor. the AACVD process. A nitrogen flow carries the aerosol droplets of solvent containing the organic precursor.

2.2.2. Material Characterization 2.2.2. Material Characterization 2.2.2. Material Characterization The morphology and crystalline phase of the gas sensitive films were analyzed using an The morphology and crystalline phase of the gas sensitive films were analyzed using an The morphology and crystalline phase(ESEM) of the gas films were(XRD). analyzed using4aan Environmental Scanning Electron Microscope andsensitive X-Ray Diffraction Figure shows Environmental Scanning Electron Microscope (ESEM) andX-Ray X-RayDiffraction Diffraction (XRD). Figure 4a shows Environmental Scanning Electron Microscope (ESEM) and (XRD). Figure 4a shows typical XRD results for the films grown. These results indicate that a slightly oxygen-defective typical XRDXRD results for for the films grown. resultsindicate indicatethat that a slightly oxygen-defective typical films grown. These These a slightly tungsten oxide isresults obtained, the which corresponds to results WO2.72 nanowires that have aoxygen-defective P2/m belonging to tungsten oxide is obtained, which corresponds nanowires that have a P2/m belonging tungsten oxide is obtained, which correspondsto toWO WO2.72 2.72 nanowires that have a P2/m belonging to to the monoclinic system, in accordance to the JPCD card no. 73-2177. Figure 4b shows ESEM results. the monoclinic system, in in accordance card no. no.73-2177. 73-2177. Figure 4b shows ESEM results. the monoclinic system, accordancetotothe the JPCD JPCD card Figure 4b shows ESEM results. The lower magnification micrograph shows one membrane with interdigitated electrodes and, in The lower magnification micrograph shows membrane with interdigitatedelectrodes electrodes and, and, in in light The lower magnification micrograph shows oneone membrane with interdigitated light light grey,grey, the the sensing layer composed of WO 3 nanowires. The higher magnification micrograph sensing layer composed of WO3 nanowires. The higher magnification micrograph grey, the sensing layer composed of WO3 nanowires. The higher magnification micrograph shows a shows a closer view of the nanowire film. shows a closer view of the nanowire film. closer view of the nanowire film.

(a)

(a)

(b) Figure 4. (a) XRD results obtained for typical tungsten oxide nanowire films. Tungsten oxide is single

Figure 4. (a) XRD results obtained for typical tungsten nanowire films. Tungsten oxide is (b)(b) lowoxide crystalline and belongs to the monoclinic phase; magnification micrograph showing the single crystalline and belongs to the monoclinic phase; (b) low magnification micrograph showing the AACVD grown film on top of the electrode area of a sensor within the 4-element transducer (Left). Figure 4. grown (a) XRDfilm results obtained typical area tungsten oxide nanowire films. Tungsten oxide is single AACVD on top of thefor electrode of a microstructure sensor withinofthe transducer Higher magnification micrograph showing the typical the4-element AACVD grown tungsten(Left). crystalline and belongs to the monoclinic phase; (b) low magnification micrograph showing the Higher magnification micrograph showing the typical microstructure of the AACVD grown tungsten nanowire films (Right). AACVD grown film on top of the electrode area of a sensor within the 4-element transducer (Left). nanowire films (Right). Higher magnification micrograph showing the typical microstructure of the AACVD grown tungsten nanowire films (Right).

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2.3.Experimental ExperimentalSetup Setup 2.3. The experiments designed for thiswork workaimed aimedtotocompare comparethe theeffectiveness effectiveness andperformance performance The experiments designed for this and ofof thefirst first and second order control methods discussed above; they included measurementswith withthe the the and second order control methods discussed above; they included measurements tungsten oxide nanowire sensors that are presented, both in controlled atmospheres of synthetic tungsten oxide nanowire sensors that are presented, both in controlled atmospheres of synthetic airair and synthetic with small concentrations ethanol. and ofof synthetic airair with small concentrations ofof ethanol. Accordingly, measurement setup described Figure 5 has been used. The sensor was placed Accordingly, thethe measurement setup described in in Figure 5 has been used. The sensor was placed inside a gas chamber. To set different target gas concentrations, a calibrated ethanol cylinder with inside a gas chamber. To set different target gas concentrations, a calibrated ethanol cylinder withair balance gasgas waswas used. This This was further diluted by employing a cylinder of dry air computerairasas balance used. was further diluted by employing a cylinder ofand dryaair and a controlled mass flowmass meter system. The total flow the chamber waschamber kept constant at 100 mL/min computer-controlled flow meter system. Theinto total flow into the was kept constant thethroughout experiments. dead volume the gaswithin chamber mL. Thewas periodical atthroughout 100 mL/min theThe experiments. The within dead volume thewas gas 4chamber 4 mL. measurements of the chemicalofresistance of the sensing layer the application the BIT0 and BIT1 The periodical measurements the chemical resistance of theand sensing layer andof the application of temperature waveforms are implemented using a standard FPGA-based National Instruments the BIT0 and BIT1 temperature waveforms are implemented using a standard FPGA-based National PXIe-1073 acquisition equipmentequipment controlledcontrolled from the same computer. The experimental data was Instruments PXIe-1073 acquisition from the same computer. The experimental post-processed using standard MatLabMatLab software. data was post-processed using standard software. In each experiment reported in this paper, a previous characterization ofsensor the sensor with In each experiment reported in this paper, a previous characterization of the layer layer with the the temperature was performed to choose the appropriate values of the and of the temperature was performed to choose the appropriate values of the BIT0 andBIT0 BIT1and andBIT1 of the control control parameters: , T low, Concretely, R th, etc. Concretely, the same procedure as in [23] was used, e.g., see parameters: Thigh , Tlow ,TRhigh , etc. the same procedure as in [23] was used, e.g., see details in th details in Figure 6 and related text of this reference. Figure 6 and related text of this reference.

Figure Description the experimental setup. Figure 5. 5. Description ofof the experimental setup.

Resultsand andDiscussion Discussion 3.3.Results accordance with theoretical expectations discussed above, objective of this section InIn accordance with thethe theoretical expectations discussed above, the the objective of this section is to is to demonstrate experimentally that, under certain conditions, the 1st order loop control may suffer demonstrate experimentally that, under certain conditions, the 1st order loop control may suffer from from "plateau-related" phenomena, in practice leads to transient losses of control of the “plateau-related” phenomena, which inwhich practice leads to transient losses of control of the chemical chemical resistance, and that using a 2nd order loop allows for the avoidance this problem. This resistance, and that using a 2nd order loop allows for the avoidance this problem. This section also section also intends to verify the improvement of the quantization noise shaping when higher-order intends to verify the improvement of the quantization noise shaping when higher-order loops are used. loops used.are Allfurther these effects are further using an ethanol gas-sensing application as All theseare effects investigated usinginvestigated an ethanol gas-sensing application as reference. reference. 3.1. Experiment Set 1—Chemical Resistance Control with First and Second Order Sigma-Delta Loops 3.1. Experiment Set 1—Chemical Resistance Control with First and Second Order Sigma-Delta Loops The first set of experiments aimed to investigate the feasibility of both control loops to obtain The first set of experiments aimed to investigate feasibility of control loops to obtain a sequence of arbitrary values of chemical resistance. the Accordingly, in both the experiment reported in a sequence of arbitrary values of chemical resistance. Accordingly, in control the experiment reported Figure 6a, the sensor was placed in synthetic air, and the 1st order loop (see Figure in 1) Figure with 6a, the sensor was placed in synthetic air, and the 1st order control loop (see Figure 1) with a sampling a sampling time TS = 1 s was used to set seven different values of Rth in 15 min intervals. It is seen TS =6a1 sthat wasthe used set seven different values of Rth since in 15 the mintarget intervals. It is seen in Figure intime Figure 1st to order control works mostly fine, chemical resistances are6a that the 1stachieved order control works mostlyaverage, fine, since thetemperature target chemical resistances successfully successfully and the bit stream or the average appliedare to the sensor, achieved and the biteach stream average, or the temperature applied to the sensor, tends to tends to stabilize after Rth step. For example, at t = 10 minaverage Rchem must be increased, and therefore stabilize after each Rth step. For example, at t = 10 min Rchem must be increased, and therefore the control loop applies more BIT1s (Thigh dominant), increasing the oxygen adsorption in the sensing

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the control loop applies more BIT1s (Thigh dominant), increasing the oxygen adsorption in the sensing layer, until R Rchem is reached; from then thestream/temperature bit stream/temperature average RthRis from then on, on, the bit average slowlyslowly tends tends to the chem= = th reached; to the necessary value necessary toRkeep Rchem constant. However, two “plateau and II in value to keep chem constant. However, two “plateau events”,events”, labeledlabeled as I andasIII in Figure Figure 6a, are also observed. these the events, the average temperature injected into the sensor 6a, are also observed. During During these events, average temperature injected into the sensor becomes becomes 240 ◦ C (which corresponds to average the samenumber averageofnumber of BIT1s locked tolocked 240 °C to (which corresponds to the same BIT1s and BIT0s,and i.e.,BIT0s, bn = 0.5i.e., or bthe 0.5 or the temperature (Thighand, + Tlow and,the in practice, the system behaves as inthus open-loop, value (Thighvalue + Tlow)/2), in )/2), practice, system behaves as in open-loop, losing n =temperature thus losing control value of Rchem . control on the valueonofthe Rchem .

I

II I

II

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(b) Figure 6. 6. Experimental are used used to to obtain Figure Experimental results results in in which which 1st 1st and and 2nd 2nd order order controls controls are obtain aa given given sequence sequence th. (a) Time evolution of the chemical resistance (Left) and of the of target chemical resistances R of target chemical resistances Rth . (a) Time evolution of the chemical resistance (Left) and of the average average temperature byorder the 1stloop order loop (Right); th was set to 376, 385, 375, 381, 377, 382, temperature providedprovided by the 1st (Right); Rth wasRset to 376, 385, 375, 381, 377, 382, and ◦ ◦ high = 280 ° C, T low = 200 ° C, δ = 25%, andTTS== 11 s; s; (b) (b) same same results results when when and 380 kΩ in 15 min intervals; T 380 kΩ in 15 min intervals; Thigh = 280 C, Tlow = 200 C, δ = 25%, and S 341, 348, 335, 346, 337, 344, and 339 kΩ in 60 min intervals; 2nd order order control controlwas wasapplied appliedto toset setRRchem to 2nd chem to 341, 348, 335, 346, 337, 344, and 339 kΩ in 60 min intervals; ◦ C,TT ◦ C, high ==280 low = 200 ° C, α = 2 kΩ, δ = 20% and T S = 2Ts. = In2left plots, grey lines the are rawthe signals Thigh T 280°C, = 200 α = 2 kΩ, δ = 20% and s. In left the plots, the greyare lines raw S low at the sampling frequency, while the green one is the moving average obtained with 200 samples. signals at the sampling frequency, while the green one is the moving average obtained with 200 samples.

On the other hand, Figure 6b shows the result of an experiment similar to that of Figure 6a, using On the other hand, Figure 6b shows the result of an experiment similar to that of Figure 6a, using the 2nd order controller (see Figure 2) with TS = 2 s. The curves of Figure 6b demonstrate that the 2nd the 2nd order controller (see Figure 2) with TS = 2 s. The curves of Figure 6b demonstrate that the 2nd order loop allows for the successful achievement of all target values of Rchem and that plateau-related order loop allows for the successful achievement of all target values of Rchem and that plateau-related events are no longer seen, even using a slower sampling rate. events are no longer seen, even using a slower sampling rate. In the experiment reported in Figure 7, the sensor is again placed in synthetic air and both control In the experiment reported in Figure 7, the sensor is again placed in synthetic air and both control loops are used to obtain the same sequence of target chemical resistances, with TS = 0.5 s. According loops are used to obtain the same sequence of target chemical resistances, with TS = 0.5 s. According to to sigma-delta theory, in 1st order loops with leaky integrators the presence of plateaus becomes less sigma-delta theory, in 1st order loops with leaky integrators the presence of plateaus becomes less evident for increasing values of the sampling frequency 1/TS [25]. Note that, although the sampling evident for increasing values of the sampling frequency 1/TS [25]. Note that, although the sampling frequency doubles that of Figure 6a, plateau-related events are still observed with 1st order control, frequency doubles that of Figure 6a, plateau-related events are still observed with 1st order control, see Figure 7a. On the other hand, no plateaus are seen in the 2nd order case, see Figure 7b. see Figure 7a. On the other hand, no plateaus are seen in the 2nd order case, see Figure 7b. This means that even by doubling the sampling frequency of the experiment in Figure 6, first order controls may still produce plateaus (Figure 7). However, using the 2nd order control method allows for the avoidance of these plateau-related events, thereby improving the performance of the sensor as a system.

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This means that even by doubling the sampling frequency of the experiment in Figure 6, first order controls may still produce plateaus (Figure 7). However, using the 2nd order control method allows for the avoidance of these plateau-related events, thereby improving the performance of the sensor as a system. Sensors 2018, 18, x FOR PEER REVIEW 8 of 13

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(b) Figure 7. Experimental results in which 1st and 2nd order controls are used to obtain the same

Figure 7. Experimental results in which 1st and 2nd order controls are used to obtain the same sequence sequence of target chemical resistances Rth = 370, 382, 372, 358, 368, 388, 372, and 352 kΩ in 60 min of target chemical resistances Rth = 370, 382, 372, 358, 368, 388, 372, and 352 kΩ in 60 min intervals. intervals. In both cases, Thigh = 280 °C, Tlow = 200 °C, δ = 20%, and TS = 2 s; α = 2 kΩ in the 2nd order In both cases, Thighevolution = 280 ◦ C,ofTthe = 200 ◦ C,resistance δ = 20%, (Left) and Tand α =average 2 kΩ in the 2nd order case; (a) time S = 2ofs;the low chemical case; (a) time temperature provided by evolution of the chemical resistance (Left) and of the average temperature provided byplots, the 1st the 1st order loop (Right); (b) same results when 2nd order control was applied. In left theorder grey loop (Right); same results when order control was applied. left plots, linesaverage are the raw lines(b) are the raw signals at 2nd the sampling frequency, while theIngreen one isthe thegrey moving signals at the sampling frequency, while the green one is the moving average obtained with 50 samples. obtained with 50 samples.

The last experiment reported in this section aims to compare the behavior of the two control

The last experiment reported in this section aims to compare the behavior of the two control loops in terms of quantization noise in the output bit stream. As it has been said before, a first order loops in terms of quantization noise in the output bit stream. As it has been said before, a first order sigma-delta topology produces a zero of first order. This means a slope of approximately 20 sigma-delta topology produces a zero firstzero order. This means slope of approximately dB/decade dB/decade in the quantization noiseofnear frequency. Withathe second order control, a20slope of in theapproximately quantization40 noise near zero frequency. With the second order control, a slope of approximately dB/decade should be obtained. To observe this effect, the sensor was placed again 40 dB/decade obtained. To observe effect, sensor placed againchemical in synthetic in syntheticshould air andbe each type of control with Tthis S = 0.5 s wasthe applied for was 3 h to set a target resistance of 340 kΩ. As shown 8a,b, applied constant for chemical andchemical constant resistance average of air and each type of control with Tin 0.5 s was 3 h toresistance set a target S =Figure temperature areinsuccessfully achieved with both control methods. 340 kΩ. As shown Figure 8a,b, constant chemical resistance and constant average temperature are The spectral power density corresponding to 16,384 samples of stabilized bit stream was successfully achieved with both control methods. calculated in each case. Figure 8c compares the obtained spectra. It is seen therebit how the presence of The spectral power density corresponding to 16,384 samples of stabilized stream was calculated the additional integrator in the 2nd order controller produces noticeable differences. With the 2nd in each case. Figure 8c compares the obtained spectra. It is seen there how the presence of the additional order control, the response at low frequencies becomes improved, and the quantization noise is rolled integrator in the 2nd order controller produces noticeable differences. With the 2nd order control, the out of the band of interest with a slope of 40 dB/decade, being this figure 20 dB/decade in the 1st response at lowLet frequencies becomes improved, the quantization noise is rolled outinof the band order case. us note that these results stronglyand resemble those obtained in other works, which of interest slope of 40 dB/decade, being this figure 20 dB/decade in the 1st order case. Let us 1st andwith 2nd a order sigma-delta loops are applied to thermal modulators for flow sensing applications note [28] thatand these resultsdielectric stronglycharging resemble obtained in [29] other works, which 1st and 2nd order to control in those electrostatic MEMS and CMOSincapacitors [30]. sigma-delta loops are applied to thermal modulators for flow sensing applications [28] and to control dielectric charging in electrostatic MEMS [29] and CMOS capacitors [30].

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Figure order controls areare applied to to setset Rchem to 340 kΩ for Figure8.8.Experimental Experimentalresults resultsininwhich which1st 1stand and2nd 2nd order controls applied Rchem to 340 kΩ C, T◦low =T200 =°C, δ ◦=C, 25%, and Tand S = 0.5 s; α = 1.4 kΩ in the 2nd order case. 3for h. 3Inh.both cases, ThighT= 290=°290 In both cases, C, 200 δ = 25%, T = 0.5 s; α = 1.4 kΩ in the 2nd order S high low (a) Chemical resistance of the sensing layer (Top) averaged temperature provided by the by 1stthe order case. (a) Chemical resistance of the sensing layer and (Top) and averaged temperature provided 1st loop (Bottom); (b) same results as provided by the 2nd order loop; (c) power spectrum densities after order loop (Bottom); (b) same results as provided by the 2nd order loop; (c) power spectrum densities 16,384 samples of theofbit obtained with standard P-Welch MatLab after 16,384 samples thestreams, bit streams, obtained with standard P-Welch MatLabestimation. estimation.InIntop top(a,b) (a,b) plots, plots, the thegrey grey lines linesare are the the raw rawsignals signalsat atthe thesampling samplingfrequency, frequency, while while the the green green one one is is the the moving moving average average obtained obtained with with 200 200 samples. samples.

3.2. 3.2. Experiment ExperimentSet Set2—Gas 2—GasSensing Sensingwith with First First and and Second Second Order Order Sigma-Delta Sigma-Delta Loops Loops This sectioninvestigates investigates improvements introduced 2nd order control in the This section thethe improvements introduced by the by 2ndthe order control in the performance performance of the sensor. To this effect, different ethanol concentrations have been applied, while a of the sensor. To this effect, different ethanol concentrations have been applied, while a control loop is control looptoissetbeing used to “constant set the condition resistance Rchem measured at being used the condition chemical “constant resistance chemical Rchem measured at constant temperature constant temperature T high” in the sensing layer. Thigh ” in the sensing layer. In In the the first first two two experiments, experiments, the the sensor sensor was was initially initially under under synthetic synthetic air air for for 20 20 min, min, then then aa concentration of 125 ppb of ethanol was applied for another 20 min, and finally synthetic air concentration of 125 ppb of ethanol was applied for another 20 min, and finally synthetic air was was applied applied again again for for 20 20 min. min. Either Eitheraa1st 1stor oraa2nd 2ndorder ordercontrol controlloop loopwas wasapplied appliedon oneach eachexperiment, experiment, with with the the same same BIT BIT parameters, parameters, to to set set the the chemical chemical resistance resistance to to 300 300 kΩ. kΩ. AAresult resultcomparison comparison of of these these experiments is available in Figure 9. It is seen there that, with both controls, the ethanol step produces experiments is available in Figure 9. It is seen there that, with both controls, the ethanol step produces a apositive positivestep stepofofthe theaverage average temperature applied, which is the sensor output. This is consistent with temperature applied, which is the sensor output. This is consistent with the the ethanol is a reducing gas,itsbut its mixing with air makes the environment still factfact thatthat ethanol is a reducing gas, but mixing with air makes the environment remain remain still oxidant, oxidant, and therefore it is necessary increase ratio(Tof BIT1s (Thigh dominant or temperature and therefore it is necessary to increasetothe ratio ofthe BIT1s high dominant or temperature increase) to increase) to constant keep almost constantresistance. the chemical Thesethat results indicate that the sensor keep almost the chemical Theseresistance. results indicate the sensor response under both response under both controls is rather similar and, in particular, that the 2nd order controller controls is rather similar and, in particular, that the 2nd order controller does not reduce its speed, does a key not reduce its speed, key feature of this kinddue of sensors. Additionally, due against to the improved response feature of this kind ofa sensors. Additionally, to the improved response quantization noise against quantization noise provided by the integrator, a noticeably smoother control of the chemical provided by the integrator, a noticeably smoother control of the chemical resistance is achieved when resistance is achieved when using the 2nd order loop. using the 2nd order loop.

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Figure 9. 9. Experimental a 1st 1st or or aa 2nd 2nd order order control control loop loop isis used usedto toset setRRchem to to Figure Experimental results results in in which which either either a chem ◦ δ = 290 °◦C, Tlow = 160 °C, 300 kΩ kΩ while 300 while aa step step of of ethanol ethanol concentration concentration was was applied applied to to the the sensor. sensor. T Thigh high = 290 C, Tlow = 160 C, = 25%, and T S = 1 s in both cases; α = 3 kΩ in the 2nd order case. (a) Evolution with time of the ethanol δ = 25%, and TS = 1 s in both cases; α = 3 kΩ in the 2nd order case. (a) Evolution with time of the ethanol concentration (Top), (Top),the the average temperature provided bycontrol the control loop (Middle), and the concentration average temperature provided by the loop (Middle), and the chemical chemical resistance (Bottom) when 1st order control was used; (b) same results for 2nd order resistance (Bottom) when 1st order control was used; (b) same results for 2nd order control. In control. bottom In bottom plots the are grey the raw signals at thefrequency, samplingwhile frequency, while theisgreen one is plots the grey lines thelines raware signals at the sampling the green one the moving the moving average obtained with 60 samples. average obtained with 60 samples.

The last two experiments reported consist in applying a sequence of small-increasing steps of The last two experiments reported consist in applying a sequence of small-increasing steps of ethanol concentration to the sensor, while either a 1st or a 2nd order control loop is configured to set ethanol concentration to the sensor, while either a 1st or a 2nd order control loop is configured to set the chemical resistance of the sensing layer to 155 kΩ. Each step increases the ethanol concentration the chemical resistance of the sensing layer to 155 kΩ. Each step increases the ethanol concentration in in 25 ppb and lasts for 10 min. The same set of BIT0 and BIT1 parameters was used in both controls, 25 ppb and lasts for 10 min. The same set of BIT0 and BIT1 parameters was used in both controls, and and the results are shown in Figure 10. The unwanted effect of a plateau is clearly seen in the case of the results are shown in Figure 10. The unwanted effect of a plateau is clearly seen in the case of the the 1st order control, Figure 10a. Specifically, the sensor becomes locked to a constant average 1st order control, Figure 10a. Specifically, the sensor becomes locked to a constant average temperature temperature (again corresponding to (Thigh + Tlow)/2, bn = 0.5), thus producing the same output value, (again corresponding to (Thigh + Tlow )/2, bn = 0.5), thus producing the same output value, for two for two different steps of gas concentration. different steps of gas concentration. This insensitivity to changes in gas concentration does not exist in the case of the 2nd order This insensitivity to changes in gas concentration does not exist in the case of the 2nd order control, which provides an output behavior that clearly follows the increasing-step shape of ethanol control, which provides an output behavior that clearly follows the increasing-step shape of ethanol concentration applied, see Figure 10b. We can conclude that the 2nd order controller ensures a 1-toconcentration applied, see Figure 10b. We can conclude that the 2nd order controller ensures a 1-to-1 1 relationship between gas excitation and sensor response. relationship between gas excitation and sensor response.

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Figure 10. 10. Experimental Experimental results control loop loop has has been been used used to to set set Figure results in in which which either either aa 1st 1st or or aa 2nd 2nd order order control chem to 155 kΩ when a sequence of small steps of ethanol of 25 ppb concentration was applied to the R Rchem to 155 kΩ when a sequence of small steps of ethanol of 25 ppb concentration was applied to the 290 ◦°C, C, TTlow == 160 °◦C, δ = 25%, and TS = 1 s in both cases; α = 3 kΩ in sensor in in 10 10 min minintervals. intervals.TThigh == 290 sensor high low 160 C, δ = 25%, and TS = 1 s in both cases; α = 3 kΩ in the 2nd 2nd order case. (a) the averaged bit stream the order case. (a) Evolution Evolution with with time time of of the the ethanol ethanol concentration concentration (Top), (Top), the averaged bit stream provided by by the the control control loop loop (Middle), (Middle), and and the the chemical chemical resistance resistance (Bottom) (Bottom) when when 1st 1st order order control control provided was used; used; (b) (b)same sameresults resultswhen when2nd 2ndorder order control was used. In bottom plots areraw the was control was used. In bottom plots the the greygrey lineslines are the raw signals at the sampling frequency, while the green one is the moving average obtained with 200 signals at the sampling frequency, while the green one is the moving average obtained with 200 samples. samples.

4. Conclusions 4. Conclusions A new second-order delta sigma method that is used to control the chemical resistance of A new second-order delta sigma method that is method used to control the one chemical resistance of MOXMOX-based gas sensors has been introduced. This improves previously proposed by based gas sensors has been introduced. This method improves one previously proposed by and the the authors, providing second-order quantization noise shaping, providing smoother responses, authors, providing second-order quantization noise shaping, providing smoother responses, and allowing for the avoidance of the unwanted plateau-related phenomena that are typical of first-order allowing for the avoidance of the unwanted plateau-related phenomena that are typical of first-order strategies. The feasibility and the features of the new method have been demonstrated experimentally. strategies. the optimizing features of the new method and have been demonstrated Future workThe will feasibility be orientedand towards controller parameters architecture, improving experimentally. Future work will be oriented towards optimizing controller parameters and the electronic readout of the sensor, and optimizing the sensor physical structure. architecture, improving the electronic readout of the sensor, and optimizing the sensor physical Acknowledgments: This work was supported, including the funds for covering the costs to publish in open structure. access, by the Spanish Ministry MINECO under Project grant no. ESP2016-79612-C3-2R. The development of the Acknowledgments: This was supported, including funds covering the costs open gas sensor was funded in work part by MINECO and FEDER viathe grant no. for TEC2015-71663-R and to bypublish AGAURinunder grant 418. E.N. gratefully acknowledges a doctoral fellowship from MINECO grant BES-2016-076582. access,2017SGR by the Spanish Ministry MINECO under Project grant no. ESP2016-79612-C3-2R. Theno. development of the E.L. is supported by the in Catalan institution Research Studies via the 2012 Edition of the ICREA gas sensor was funded part by MINECOfor and FEDERand viaAdvanced grant no. TEC2015-71663-R and by AGAUR under Academia Award. grant 2017SGR 418. E. Navarrete gratefully acknowledges a doctoral fellowship from MINECO grant no. BESAuthor Contributions: L.K.by and conceived andfor designed experiments; L.K. performed the 2016-076582. E. Llobet isM.D.-P., supported theJ.P.-N. Catalan institution Researchthe and Advanced Studies via the 2012 experiments; and Award. L.K. analyzed the data; E.N. and E.L. fabricated the sensors; J.P.-N., M.D.-P. and Edition of theM.D.-P., ICREA J.P.-N. Academia E.L. wrote the paper. Author Contributions: M. Domínguez, L. Kowalski, and J. Pons conceived and designed the experiments; L. Kowalski performed the experiments; M. Domínguez, J. Pons, and L. Kowalski analyzed the data; E. Navarrete and E. Llobet fabricated the sensors; J. Pons, M. Domínguez, and E. Llobet wrote the paper.

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Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

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