Origin of Baseline Drift in Metal Oxide Gas Sensors: Effects of Bulk Equilibration

Abstract

Metal oxide (MOX) gas sensors and gas sensor arrays are widely used to detect toxic, combustible, and corrosive gases and gas mixtures inside ambient air. Important but poorly researched effects counteracting reliable detection are the phenomena of sensor baseline drift and changes in gas response upon long-term operation of MOX gas sensors. In this paper, it is shown that baseline drift is not limited to materials with poor crystallinity, but that this phenomenon principally also occurs in materials with almost perfect crystalline order. Building on this result, a theoretical framework for the analysis of such phenomena is developed. This analysis indicates that sensor drift is caused by the slow annealing of quenched-in non-equilibrium oxygen-vacancy donors as MOX gas sensors are operated at moderate temperatures for prolonged periods of time. Most interestingly, our analysis predicts that sensor drift in n-type MOX materials can potentially be mitigated or even suppressed by doping with metal impurities with chemical valences higher than those of the core metal constituents of the host crystals.

1. Introduction

Metal oxide (MOX) gas sensors sensitively respond to oxidizing and reducing gases in the ambient air. Although such sensors exhibit a broad-range response to a wide variety of different gases, their cross-sensitivity spectra can nevertheless be tuned to respond preferably to target gases of major interest in certain application scenarios and also to interfering gases which are likely to turn up in these scenarios [1]. With this capability of cross-sensitivity shaping at hand, arrays of sensors with different and well-chosen cross sensitivity profiles can be constructed to address different target applications. Examples of E-Nose gas sensors that address a number of target scenarios of recent interest are described in contributions presented at the latest GOSPEL conference [2,3,4,5,6,7,8,9,10,11]. A recent application of sensing biohazards in the International Space Station (ISS) is described in references [12,13].

An effect that can negatively impact the performance of E-Nose-type gas sensors is sensor drift. Sensor drift arises from slow changes in the sensor baseline resistance and in the gas response, thus mimicking apparent changes in target and interfering gas concentrations over time [14,15,16,17]. In case such changes impact different sensors inside an array with different intensity, sensor drift can also negatively affect the discrimination power of gas sensor arrays rather than simply mimicking gas concentration changes [18]. Taking an overall view over the available literature, it becomes apparent that the phenomena of sensor baseline drift and ensuing changes in gas response are receiving increasing attention, but that almost all of those approaches aim at mitigating and correcting drift effects by algorithmic means [19,20,21,22,23,24,25,26,27,28,29].

In this paper, a different approach to the problem of sensor drift is presented which is more hardware-related and which aims at identifying and controlling those physical processes that drive the processes of sensor drift and sensor degradation. In the following, it is shown that MOX gas sensors feature an intrinsic tendency of drifting to increasingly higher baseline resistances $R$ and of lessening gas-induced resistance changes $\mathsf{\Delta }R$ in the course of time, however, with the ratios $\mathsf{\Delta }R/R$ remaining approximately constant over time. It is argued that these changes originate from the fact that n-type metal oxides are not normally doped with foreign impurities with chemical valences different than those of the core metal ions inside the MOX lattices, but rather by thermally generated oxygen vacancies. Such vacancies are normally generated during high-temperature materials preparation and become quenched in during cool-down after preparation. Representing non-equilibrium entities, such thermal donors tend to slowly relax towards lower densities, causing MOX materials to slowly drift towards lower baseline conductivities and lessening capabilities of accumulating negative oxygen ion adsorbates at their surfaces, which limits their reducing gas response. Perhaps, the most interesting conclusion is that sensor drift effects might be mitigated or even suppressed by doping the MOX materials with metal impurities with higher chemical valences than the constituent metals of the core crystals.

2. Experimental Evidence for Sensor Drift

The effects of long-term sensor drift in MOX materials were investigated by the Brescia group in the course of the S3 project [15]. There, the drift effects in SnO₂ nanowire materials were investigated which had been deposited at very high temperatures using the solid–liquid–vapor (SLV) condensation technique [30,31]. The nanowires were deposited on ceramic substrates with pre-deposited platinum (Pt) interdigital electrodes on the front side and Pt heater meanders on the backside. During SLV deposition very long nanowires with almost monocrystalline internal order formed on the interdigital electrodes, forming networks of randomly interconnected nanowires, as shown in Figure 1a,b.

In order to assess the effects of long-term sensor drift, the nanowires were continually heated to temperatures of 400 °C while being exposed to humidified synthetic air with a relative humidity of $r.h.=50\%$ at 20 °C. Eventual changes in baseline resistance and gas response were assessed by repeatedly performing CO gas sensing tests as detailed in Appendix A1. As shown in Figure 2a, the conductance of the nanowire networks showed a definite trend towards lower conductance both in humidified synthetic air ($G_{air}$), as well as under CO exposure ($G_{CO}$). Another interesting observation was that the relative change in conductance under gas exposure, $\mathsf{\Delta }G/G=\left(G_{CO}-G_{air}\right)/G_{air}$, remained relatively constant throughout the entire experiment (Figure 2b).

Upon closing this section, we note that the SLV growth superseded the earlier methods of RGTO (rheotaxial growth and thermal oxidation) growth in the Brescia laboratory [32,33], which consistently produced granular nanocrystalline materials with huge numbers of inter-grain contacts. A surprising result of our investigations was that RGTO materials exhibit very similar degradation characteristics as almost monocrystalline nanowire materials. In order to keep our arguments in this paper reasonably straight and simple, a thorough discussion of RGTO materials, inter-grain contacts and surface band bending regions is deferred to a forthcoming publication [34].

In view of the presently available experimental evidence that similar degradation characteristics can be observed both in fully monocrystalline and in nanogranular materials, we present below an explanation of the phenomenon of sensor baseline drift that focusses entirely on the bulk properties of SnO₂ crystals with nanometric dimensions and with the possibility of efficiently exchanging oxygen between bulk and surface regions.

3. Oxygen Vacancy Donors and Electrical Conductivity in n-Type Metal Oxides

In order to explain the above observations, it is necessary to take a closer look at the intrinsic thermal disorder in the SnO₂ lattice. As is well known, the regular lattice sites in SnO₂ crystals consist of $S{n}^{4+}$ and $O^{2-}$ ions, arranged in rutile or cassiterite lattice structures which ensure overall charge neutrality [35,36,37,38,39,40,41,42,43,44]. In Kröger–Vink notation [45], the regular lattice sites in SnO₂ crystals are denoted by $S{n}_{Sn}$ and $O_O$, both of which are attributed with zero formal charge. Charge states of more energetic lattice sites, which become possible at higher temperature, are always measured relative to the zero-formal charge of the $S{n}_{Sn}$ and $O_O$ lattice sites.

In SnO₂, the most important bulk defect sites are oxygen vacancies $V_O$ which are generated by removing oxygen atoms from regular $O_O$ sites and by injecting the liberated O atoms into the interstitial lattice, thus forming oxygen interstitials $O_i$. In this process of forming vacancy-interstitial pairs, the two electrons, formerly associated with the $O^{2-}$ lattice ions, remain with the newly formed vacancies. As this negative charge is compensated by the positive ionic charges of the nearest-neighbor Sn ions, both the $V_O$ and the $O_i$ sites maintain zero formal charge. Due to the high mobility of the $O_i$ interstitials, these are able to move towards the free surfaces where they can recombine with other oxygen atoms to form $O_2$ molecules, which can desorb into the ambient air. $O_2$ molecules, on the other hand, coming from the air ambient and re-adsorbing on the SnO₂ surface, can break up into individual oxygen atoms and diffuse through the interstitial lattice again until they eventually drop into empty vacancy sites in the interior. Through this exchange of oxygen across the air–solid interface, an equilibrium concentration of oxygen vacancies will develop inside the crystal, which depends on the temperature $T$ of the crystal lattice and the oxygen partial pressure $p_{O_2}$ in the ambient air. As described in Appendix A2, a volume density of oxygen vacancies $N_{VO}\left(T\right)$ will then develop, which depends on the volume densities of occupied oxygen ion sites $N_O$, interstitial vacancy sites $N_i$, and the vacancy formation energy $E_{VO}$ inside the crystal:

$$N_{VO}\left(T\right)=\sqrt{N_O{N}_i}exp\left[-\frac{E_{VO}}{2k_{B}T}\right].$$

(1)

Here, $E_{VO}$ is the vacancy formation energy, $T$—the absolute temperature and $k_B$—Boltzmann’s constant.

The key interest in these vacancy-type defects stems from the fact that these can act as shallow double donors with ionization energies of 30 and 150 meV below the conduction band edge $E_C$ [35,36,37,38,39,40,41,42,43,44]. This energetic situation is illustrated in Figure 3a. Shown in Figure 3b is a situation in which the two donor electrons are transferred to a Fermi level $E_F$ lying deeper in the bandgap, from where the two electrons can be re-excited into the conduction band, thus forming mobile charge carriers and enabling electrical conductivity.

With the donor levels transferring their electrons to a deeper-lying Fermi energy, the vacancies change their formal charge states from zero to positive and double-positive and they also refund a fraction of their formation energy to the thermal reservoir of lattice vibrations inside the SnO₂ crystal. With these lowered formation energies, the volume densities of singly and doubly ionized vacancy sites are significantly enhanced over the volume density of neutral donor sites and, in particular, the volume densities of these charged vacancies become Fermi-energy-dependent:

$$N_{VO}^{+}\left(E_F,T\right)=2N_{VO}\left(T\right)exp\left[\frac{E_{O_1}-E_F}{k_{B}T}\right],\mathrm{and}\text{:}$$

(2)

$$N_{VO}^{2+}\left(E_F,T\right)=N_{VO}\left(T\right)exp\left[\frac{E_{O_1}-E_F}{k_{B}T}\right]exp\left[\frac{E_{O_2}-E_F}{k_{B}T}\right].$$

(3)

In these latter equations $E_{O_1}$ and $E_{O_2}$ stand for the two ionization energies of the double donors. The factor of two in the first equation accounts for the possibility of two different spin orientations inside a singly ionized vacancy. In Appendix A2, attention is further drawn to the fact that enhanced densities of oxygen vacancy donors are expected in regions with upward band bending, i.e., near surfaces, at inter-grain contacts and around catalytic metal clusters. These latter effects will be discussed in a follow-on publication [34].

Returning to bulk regions with essentially flat bands, the volume densities of neutral, i.e., fully occupied, singly ionized, and doubly ionized vacancies are plotted in Figure 4a as a function of the Fermi energy position inside the gap, assuming a lattice temperature of $T\approx 1200\mathrm{K}$, typical of SLV growth conditions and a defect formation energy $E_{VO}$ of $4\mathrm{eV}$ [46]. Figure 4b, for comparison, shows this same situation, but as evaluated for a much lower temperature of 673 K, which had been chosen as the sensor operation temperature in the long-term tests described in Section 2. Comparing both graphs, it is seen that temperature has a huge influence on the concentration of neutral vacancies but a much more moderate influence on the much larger concentrations of positively charged vacancies with concomitantly lower formation energies. Also shown in Figure 4a,b are the volume densities of mobile electrons that are expected to be re-excited from the respective Fermi energies to the conduction band edge:

$$n\left(E_F,T\right)=N_{C}exp\left[-\frac{E_C-E_F\left(T\right)}{k_{B}T}\right].$$

(4)

Comparing both graphs, it becomes evident that the Fermi energy position that ensures overall charge neutrality is mainly determined by the volume densities of electrons and doubly ionized vacancies, i.e.:

$$n\left(E_F,T\right)\approx N_{VO}^{2+}\left(E_F,T\right).$$

(5)

Solving for $E_F\left(T\right)$, one then obtains:

$$E_C-E_F\left(T\right)=\frac{1}{3}\left\{\frac{E_{VO\_eff}}{2}-k_B T ln\left[\frac{N_O}{N_C}\right]\right\},$$

(6)

and for the equilibrium charge carrier density:

$$n_{eq}\left(E_F,T\right)=N_C^{2/3}{N}_O^{1/3} exp\left[-\frac{E_{VO\_eff}}{6 k_{B}T}\right],$$

(7)

with

$$E_{V0\_eff}=E_{V0}+2\left(E_C-E_{O_1}\right)+2\left(E_C-E_{O_2}\right)$$

(8)

standing for the effective vacancy formation energy of neutral oxygen vacancies.

Overall, the above equations indicate that in monocrystalline MOX materials an Arrhenius-type temperature-dependence of the electrical conductivity should arise under thermal equilibrium conditions. Additionally, a fractional power dependence on the volume density of occupied oxygen lattice sites, $N_O$, should be observed, which depends on the availability of O₂ molecules in the ambient air, i.e., on the oxygen partial pressure $p_{O_2}$ there [35,36,37,38,39,40,41,42,43,44,45]. This dependence on $p_{O_2}$ is widely employed in λ-probes where Ytterbium-doped ZrO₂ crystals are used to measure the difference in oxygen partial pressures in the outside air and exhaust gas streams of automobiles [47]. Due to larger oxygen vacancy formation energies and less mobile oxygen interstitials, these latter effects are less dominant in the electron conductors that are conventionally employed in MOX gas sensors and sensor arrays.

4. Thermal Quenching of Electrical Conductivity and Conductivity Relaxation

So far, our arguments have followed the general background of metal oxide materials widely described and disseminated in the published literature [35,36,37,38,39,40,41,42,43,44,45]. The ideas presented in the following with regard to equilibration, thermal quenching, metastability and sensor drift, in contrast, largely build on ideas previously developed in the field of amorphous semiconductors, and in particular of hydrogenated amorphous silicon (a-Si:H). In order to ease understanding of these issues, some of those ideas are briefly described in Appendix A3, where some of the key background literature is also cited.

Considering the fact that the key intrinsic donor defects in MOX materials are oxygen vacancies that can only be formed by simultaneously generating oxygen interstitials, it is clear that adaptations of the donor defect densities to different Fermi energy positions will be kinetically controlled by the rates with which oxygen interstitials are able to diffuse through the interstitial lattices of MOX materials. Upon arriving at one of the free surfaces, pairs of interstitials can recombine into O₂ molecules which are then free to interchange with O₂ molecules in the ambient air, thus allowing the bulk electrical conductivity to equilibrate with the O₂ concentration in the ambient air.

With oxygen diffusion constants $D\left(T\right)$ following Arrhenius laws [48,49,50,51],

$$D\left(T\right)=D_0 exp\left[-\frac{E_D}{k_{B}T}\right],$$

(9)

equilibration requires that at each temperature $T$, the crystal be maintained for a time ${\tau }_{eq}\left(T\right)$ long enough to make the oxygen diffusion length $L_D=\sqrt{D\left(T\right){\tau }_{eq}\left(T\right)}$ comparable to the crystal size $L_{Sn{O}_2}$:

$$L_{Sn{O}_2}=\sqrt{D\left(T\right){\tau }_{eq}\left(T\right)}.$$

(10)

Combining the latter two equations, ${\tau }_{eq}\left(T\right)$ emerges as:

$${\tau }_{eq}\left(T\right)=\frac{L_{Sn{O}_2}{}^2}{D_0 }exp\left[\frac{E_D}{k_{B}T}\right].$$

(11)

Considering a situation in which a piece of monocrystalline MOX material is allowed to cool down from the initially very high preparation temperatures to increasingly lower temperatures and that sufficient time is allotted at each temperature to allow equilibration of the oxygen vacancy densities with the outside air, Equation (11) can be inserted in Equation (7) to obtain the equilibrated density of mobile electrons in the conduction band as a function of time:

$$n_{eq}\left( {\tau }_{eq}\right)=N_C^{2/3}{N}_O^{1/3} exp\left\{-\frac{1}{6}\frac{E_{VO\_eff}}{E_D} ln\left[\frac{D_0 {\tau }_{eq}}{L_{Sn{O}_2}{}^2}\right]\right\}$$

(12)

In Figure 5, the equilibration temperature $T_{eq}$ reached after a time ${\tau }_{eq}$ is plotted as a function of ${\tau }_{eq}$. The red line in this plot shows that the SnO₂ lattice will have thermalized to the chosen sensor operation temperature of $T_{MOX}\approx 673 \mathrm{K}$after a time ${\tau }_{eq}\approx 4\times {10}^7$s, corresponding to about 400 days of continuous sensor operation. In this estimate, published oxygen diffusion parameters [48,49,50,51] have been used. The blue line in Figure 5 shows the corresponding drop in the equilibrated charge carrier density after times ${\tau }_{eq}$. The equilibrium charge carrier density in the conduction band at the chosen sensor operation temperature is then estimated to be about $2\times {10}^{15}{\mathrm{cm}}^{-3}$, corresponding to an equilibrium bulk conductivity of about ${10}^{-3}{\mathsf{\Omega }}^{-1}{\mathrm{cm}}^{-1}.$ As shown in Appendix A1, such bulk conductivity values are in an order-of-magnitude agreement with the macroscopically determined conductances of (${10}^{-7}-{10}^{-6}$)${\mathsf{\Omega }}^{-1}$ reported in Figure 2.

From both lines in Figure 5, it becomes evident that a considerable part of the equilibration does take place in the initial phases after high-temperature materials preparation and cool-down to storage conditions. During these initial phases of cooldown, the volume density of oxygen vacancy donors rapidly equilibrates to the increasingly lower temperatures until equilibration rates become too slow to allow for further equilibration to continuously lower temperatures. This condition is met after a time ${\tau }_{qe}$, after which the oxygen vacancy donor density has dropped to an equilibrium value corresponding to a temperature.

$$T_{qe}\left({\tau }_{qe}\right)=\frac{E_D}{k_B ln\left[\frac{D_0 {\tau }_{qe}}{L_{Sn{O}_2}^2}\right]}.$$

(13)

Below this temperature, the different kinds of oxygen vacancy densities become frozen in metastable non-equilibrium states whose volume densities do no longer change as temperatures further drop. These latter conditions of initial equilibration and following quench-in are illustrated in Figure 6a,b, with the first figure representing freeze-in of neutral oxygen vacancy donors at different temperatures $T_{qe}$and the second freeze-in of twofold positively charged oxygen vacancy donors at these same temperatures $T_{qe}$.

The two bottom pictures of Figure 6 show the consequences that arise for the quenched-in non-equilibrium states with regard to the temperature-dependent Fermi level positions (Figure 6c) and mobile electron densities in the conduction band (Figure 6d). Both pictures show that MOX materials in their quenched-in states behave like “normal” semiconductors doped with substitutional n-type donor impurities. In these quenched-in states, Fermi energies are very close to the conduction band at very low temperatures and shift down deeper into the forbidden gap due to the effects of statistical Fermi energy shift as temperatures are increased [40]. In these states, the concomitant effects of increasingly larger activation energies for mobile charge carrier excitation are counteracted by the exponentially increasing probabilities of mobile charge carrier generation as temperatures increase. In this way, temperature-independent densities of mobile charge carriers arise in these quenched-in metastable states. When temperatures are increased towards and beyond the initial quench-in temperature $T_{qe\_1}$, the quenched-in metastable states again become unstable and start to rapidly equilibrate again. While equilibration is relatively fast at and around the originally employed quench-in temperature $T_{qe\_1}$, the quenched-in metastable states are also unstable at much lower temperatures. At temperatures $T<T_{eq\_1},$ however, the rates of relaxation towards equilibrium are much longer than usually employed changes in gas concentration, sensor operation or biasing conditions [52,53]. Equilibration in these latter cases usually goes undetected and only shines up when specifically designed long-term tests are carried out, as described in Section 2.

Returning to the problem of analyzing experimental sensor drift data, one problem is that in such analyses, neither times nor temperatures of freeze-in are known. In this situation, the best approach is returning to Equation (12) and evaluating the ratio of conductivities at the beginning and at all intermediate times during the long-term stability tests. In this way, the loss in sensor conductivity ${\sigma }_{loss}\left(\tau ,{\tau }_{ref}\right)$ at time $\tau$ can be related to the unknown reference time ${\tau }_{ref}$ at which the metastable state of concern had been quenched-in:

$${\sigma }_{loss}\left(\tau ,{\tau }_{ref}\right)=\frac{n_{eq}\left(\tau \right)}{n_{eq}\left({\tau }_{ref}\right)}=exp\left\{-\frac{1}{6}\frac{E_{VO\_eff}}{ E_D} ln\left[\frac{\tau }{{\tau }_{ref}}\right]\right\}.$$

(14)

With the bulk values of the vacancy formation energy $E_{VO\_eff}\approx 4 \mathrm{eV}$[46], and an oxygen diffusion energy $E_D\approx 1.83 \mathrm{eV}$, well within the range of published oxygen diffusion data [48,49,50,51], the data in Figure 7 were obtained. The only free parameter in this equation is the reference time ${\tau }_{ref}\approx {10}^{6 }\mathrm{s} \approx 6 \mathrm{d}$. This latter figure indicates that some uncontrolled equilibration may have taken place either during cool-down from preparation or during some initial gas-sensing tests prior to initiating the very long-term tests.

The other interesting piece of experimental evidence presented in Section 2 is the parallel variation of the relative gas response upon prolonged sensor operation. Such parallel variations in sensor baseline conductance and relative gas response had already been observed in earlier experiments and explained in references [41,42]. This subject will also be taken up again in our forthcoming publication dealing with surface band bending regions [34].

5. Impurity Doping, Mitigation and Suppression of Sensor Drift

So far, we have been dealing with the intrinsic oxygen vacancy donors which turn many MOX materials naturally n-type. As a culmination point, we have arrived at the conclusion that the experimentally observed effects of sensor drift arise from the slow annealing of quenched-in oxygen vacancy donors. In this final section, we turn to n-type and p-type doping by adding metal impurities with chemical valences different from those of the core metal constituents of the host crystals. These latter considerations reveal that the formation of positively ionized oxygen vacancy donors can be largely suppressed, and sensor drift effects be mitigated by adding n-type impurities whose densities are permanently fixed during materials preparation. P-type doping, in contrast, appears less attractive as it enhances the formation of oxygen vacancy donors which are responsible for the sensor drift.

Dissimilar to crystalline silicon (c-Si), for instance, where both heavy n- and p-type impurity doping is possible, a large asymmetry between n- and p-type doping exists in n-type metal oxides. This asymmetry is illustrated in Figure 8. Figure 8a shows that incorporating increasing densities of donor impurities successfully moves the Fermi energy from its intrinsic position in the upper half of the forbidden gap to positions increasingly closer to the conduction band. As in c-Si and other crystalline semiconductors, largely enhanced and temperature-independent mobile electron densities are then observed (Figure 8b). Similar to conventional semiconductors, the introduction of increasing densities of acceptor impurities does move the Fermi energy deeper into the forbidden gap, a conversion towards p-type conductivity, however, cannot be observed in this case. This latter fact is vividly demonstrated by Figure 8b, where it is shown that Arrhenius-type temperature dependencies, similar to the undoped case, are retained. Any signs of an extrinsic and temperature-independent p-type conductivity, however, clearly do not show up.

The observed asymmetry of n- and p-type doping is a direct consequence of Equations (2) and (3), which predict that oxygen vacancy concentrations are Fermi-energy-dependent. While the introduction of shallow n-type donors prevents neutral oxygen vacancies from discharging towards singly and doubly ionized positive charge states, Figure 9a shows that in this case, the densities of positively charged oxygen vacancies are hardly able to equilibrate to densities much higher than the neutral donor density. Similar to conventional semiconductors, the electroneutrality condition in n-type doped MOX materials is then dominated by the equation $n_{E\_n}\approx N_D^{+}$, where $N_D$ is the donor impurity density and $n_{E\_n}$ the mobile electron density in n-type doped material. Considering the fact that the concentration of donor impurities $N_D$ is permanently fixed during materials preparation, the baseline conductivity and its ensuing gas response become independent of the lattice temperature. Sensor drift thus can be mitigated or even suppressed. In this context, it is relevant to note that n-type doping of SnO₂, for instance, is possible by substituting antimony ions on $S{n}_{Sn}$ lattice sites in SnO₂ [52].

The situation of p-type doping with shallow acceptor impurities is a very different one. In this case, empty acceptors with energy levels close to the valence band edge, actively drive neutral oxygen vacancies towards their positively charged states and densities of $N_{VO}^{++}$ donor sites towards high and acceptor-controlled densities satisfying $N_{VO}^{++}\approx N_A^{-}$. Figure 9b shows that in this case, the Fermi energy is pinned between equal densities of positively charged vacancy donor levels close to the conduction band edge and negatively charged acceptor impurity levels close to the valence band edge. The small remaining mobile electron densities $n_{E\_p}$ in this case are counterbalanced by similarly small and very strongly temperature-dependent densities of singly charged $N_{VO}^{+}$ vacancies, i.e., $n_{E\_p}\approx N_{VO}^{+}.$ As the densities of $N_{VO}^{+}$ sites remain sensitive to the lattice temperature, doping with p-type impurities does not appear to be an equally interesting option, as n-type impurity doping for mitigating or suppressing sensor drift.

In concluding this section, we note that similar effects of sensor baseline drift and ensuing changes in gas response as in Section 2 have also been observed in p-type NiO [31]. It therefore appears that our arguments can—mutatis mutandis—also be extended to p-type materials. In brief, it appears possible that intrinsically p-type materials can be stabilized by p-type impurity doping thus overwhelming the effects of intrinsic metal vacancies.

6. Conclusions

In this paper, we have provided experimental evidence for the effect of sensor baseline resistance drift in metal oxides, and we have developed a framework for the theoretical explanation of this effect.

Concerning experimental evidence, we have concentrated on SnO₂ as the most extensively used MOX material for resistive gas sensors. Performing tests on SLV-deposited nanowire materials, we have provided evidence that sensor drift is not an artifact arising from poor crystallinity, but that the phenomenon of sensor drift principally also occurs in materials with almost ideal crystalline order.

Building on the fact that the nanowire materials had not been intentionally doped with metal impurities with chemical valences different than the core Sn ions, a theoretical framework has been developed which focuses on shallow oxygen-vacancy donors as the key reason for the occurrence of sensor baseline drift.

With shallow oxygen vacancy donors being key components of the thermal lattice disorder, their number densities are principally dependent on the sensor operation temperatures that are being employed. As oxygen vacancy donors can exist in three different charge states, i.e., neutral, singly and doubly positively charged, their charge states and number densities are also sensitively dependent on Fermi-level positions in the sensor´s bulk and at band-bending regions at the nanowire surfaces. Whereas annealing of quenched-in bulk vacancy donors cause the sensor baseline conductivity to drop, the annealing of vacancy donors also lowers the capability of the nanowires to adsorb surface oxygen ions. In this way, concomitant changes towards lower reducing gas responses are initiated. These latter conclusions about adsorption are still of a preliminary nature and more detailed results will be reported in a follow-on publication which will deal in an exhaustive manner with the effects of adsorption, band bending, and equilibration processes in nanowires and granular materials with large numbers of inter-grain contacts [34].

As equilibration rates of oxygen vacancy donors are limited by the slow rates of diffusion of lattice oxygen ions, equilibration processes normally do not become visible at the relatively fast rates at which gas exposure conditions and sensor operation parameters are being changed [53,54]. Due to the low speed of defect equilibration processes, the effects of long-term sensor drift often take the form of apparently random and hardly reproducible dirt effects. With the approaches taken in this paper, a framework has been established that allows such seemingly irreproducible effects to be turned into reproducible effects that are amenable to physical analysis.

As authors, we regard our experiments and theoretical treatments as a first step towards more systematic investigations of sensor drift effects and their impacts on gas sensitivity changes and gas discrimination capabilities of metal oxide materials. The potential reward of baseline resistance suppression discussed in Section 5 appears to be a good motivation to progress towards this direction.