ISSN 0005-1179, Automation and Remote Control, 2014, Vol. 75, No. 11, pp. 2034–2040.
© Pleiades Publishing, Ltd., 2014.
Original Russian Text © I.A. Averin, I.A. Pronin, N.D. Yakushova, M.V. Goryacheva, 2012, published in Datchiki i Sistemy, 2012, No. 12, pp. 12–16.
Penza State University, Penza, Russia e-mail: micro@pnzgu.ru, pronin i90@mail.ru, winter-kalt17@mail.ru
Received July 20, 2012
Abstract— This paper considers the major factors affecting the nonlinearity in the volt-ampere characteristics of resistive gas sensors. The authors establish that, under small gaps between sensor electrodes (particularly, in multisensor systems), the dominating contribution to the nonlinearity is made by three factors, namely, the drift of chemisorbed ions to an anode, the drift of protons on the surface to a cathode and the drift of intrinsic defects through the sublattice.
DOI: 10.1134/S0005117914110113
Design of multisensor gas identification systems represents a pressing problem in sensor industry
[1–5]. There exist several technologies of sensitive elements [6–10]. The primary task lies in eliminating the errors of each system element with a specific law of ageing. Therefore, engineers give preference to homogeneous-material sensors, since the symbate ageing of all elements minimizes the errors [11].
During construction of modern multisensor gas identification systems, a gas-sensitive film undergoes segmentation by a set of complanar metal electrodes. Here the size of a sensitive element constitutes tens of microns [12] (see Fig. 1).
Under small gaps between the electrodes, the volt-ampere characteristics (VACs) of even ohmic sensors may deviate from the linear law for a small potential difference applied.
It seems that the following processes have the main contribution to the deviation of the characteristic from the linearity:
—the drift of chemisorbed oxygen ions to an anode;
—the drift of protons on the surface to a cathode along the contracting percolation cluster of adsorbed water;
—the drift of intrinsic electrically active defects in the bulk through the sublattice.
Fig. 1.
The multisensor chip PGA-120 in the housing.
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THE VOLT-AMPERE CHARACTERISTICS OF RESISTIVE GAS SENSORS 2035
Fig. 2.
The typical volt-ampere characteristic of a sensitive element with a small gap between electrodes.
Consider the drift of negatively charged oxygen ions between electrodes towards an anode on the surface of a semiconducting gas sensitive film [13]. The hysteresis appears on the volt-ampere characteristic of the sensitive element, see Fig. 2.
The ion current j s on the surface of a sensitive element is defined by [14] j s = qμ s θN s EL D , (1) where q means ion charge; μ s stands for surface mobility; θ is the filling degree of adsorption centers;
N s specifies the surface concentration of surface centers; E denotes the field strength in a sample; and finally, L D represents the Debye screening length.
Therefore, the process of current transfer involves two types of charge, viz.
, electrons or holes in the bulk of semiconductor and ions on its surface.
Oxygen ions on the surface have smaller mobility than free carriers in the bulk; and so, they are accumulated in the anode region. According to the electrical neutrality principle of semiconductors, electrons from the bulk are accumulated in the cathode region. As a result, the depletion anode region restricts the cubic conductance.
Consequently, there appear two electrical circuits: a controlling one (associated with ion transfer processes on the surface) and a controlled one (determined by the bulk of semiconductor).
According to Eq. (1), the circuit with ion conductance starts dominating as the potential difference applied to the structure increases; almost all voltage in this circuit drops. Voltage decrease on the structure does not modifies the sizes of this region until the ion-transfer velocity on the surface appears smaller than the desorption rate of particles from the surface to the gaseous phase. This is the reason of hysteresis occurrence on the volt-ampere characteristic.
Write down Eq. (1) with due account of the partial pressure p of the reactant gas: j s = qμ s N s EL D
γp
γp + 1
.
(2)
Here γ represents some coefficient depending on the properties of the reactant gas and the semiconductor. Direct analysis of the obtained expression indicates of the following. The growing partial pressure of the reactant gas amplifies the contribution of the ion component to the surface current. Figure 3 illustrates the typical VACs of sensitive elements [15] under identifying different concentrations of carbon monoxide.
Clearly, for small applied voltages (i.e., the field strength between contacts is below 1000 V/cm), the VACs of sensitive elements possess the quasilinear character. This testifies to the negligibly
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2036 AVERIN et al.
Fig. 3.
The VACs of sensitive elements under different partial pressures of carbon monoxide: curve
1
—122 ppm; curve
2
—230 ppm; curve
3
—326 ppm.
small contribution of ion current on the surface. As the voltage goes up, the ion component in the current transfer increases gradually due to formula (2). Subsequently, the total VAC becomes nonlinear (see Fig. 3). In the general form, it can be approximated by the function
I = AU n
, (3) where A denotes an approximation constant; n is a certain coefficient which depends on gas grade and working temperature (and slightly on its concentration). Within the low voltage range, the coefficient n equals unity, whereas the constant A plays the role of bulk electrons conductance.
And so, there is the additional feasibility of selective gas identification in the analysis of sensors operation in high-strength fields.
The temperature effect in the VACs of sensitive elements [16] is shown by Fig. 4; here readers can observe the temperature dependencies of sensitive elements based on SnO
2
-CuO films in deoxidizing and oxidizing gaseous media.
According to Fig. 4, the exponent n is close to unity in the low-temperature range, and surface ions current has a small contribution to the conductance of the gas-sensitive structure. Probably, this is connected with the insufficient thermal energy of ions for breaking the drift barrier. Moreover, note that different forms of charged oxygen prevail on the semiconductor’s surface within different temperature ranges (see the table). They have different surface binding energies and different surface mobility μ s due to nonidentical desorption temperatures.
Oxygen forms on the semiconductor’s surface and their desorption temperatures
◦
C Oxygen form Desorption temperature,
O
O
O
−
−
2 −
85
150
560
Therefore, the contribution to the exponent n is made by two competing processes, namely, ion thermal energy growth (on the one hand) and ion-substrate binding energy increase (on the other hand). If these energies coincide, we observe the maximum deviation of the exponent n from unity
(see the minimum point in Fig. 4). For any temperatures below (above) this minimum, the main contribution belongs to the first (second, respectively) process.
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THE VOLT-AMPERE CHARACTERISTICS OF RESISTIVE GAS SENSORS 2037
Fig. 4.
The temperature dependence of the exponent n in the surface conductance
G of gas-sensitive films:
(a) oxidizing medium; (b) deoxidizing medium; curve
1
—
U <
5 V; curve
2
—
U >
5 V.
Consequently, by combining the temperature of the gas-sensitive layer with simultaneous variation of the working voltage in strong fields, one can extend the sensor response capabilities with respect to gaseous mixtures. By-turn, this guarantees an appreciable improvement in sensor selectivity without multisensor system construction.
The second process contributing to the deviation of VACs from the linearity consists in the drift of protons on the surface to a cathode. This process runs according to two possible mechanisms [17], i.e.,
—the Grotthuss mechanism;
—the transport mechanism.
During realization of the first mechanism, a proton moves along hydrogen bonds. In the case of the second mechanism, proton movement occurs owing to carrier movement (water). The Grotthuss mechanism is realized on the gas sensor surface and a proton moves in the form of a hydroxonium molecule or a hydronium molecule (H
2
O-H
+ or H
3
O
+
, respectively). Similarly to holes in semiconductors, the state H + is transferred to neighbor water atoms, moving to the cathode. This process contributes to the nonlinearity of VACs only if the contracting percolation cluster of water appears on the sensor’s surface. In this case, protons easily move towards the cathode along hydrogen bonds. A similar principle underlies porous ionized materials. Here the pioneering material is Nafion created by DuPont [18]; it represents a fluocarbon skeleton (which ensures the rigidity of the whole structure) with side branchings ended by the SO
−
3
H
+ sulfone group.
According to T. Gierke’s model [19] (see Fig. 5), sulfone groups tend to aggregation within a polymer matrix by forming almost spherical clusters of approximate diameter from 2 to 4 nm, whose inner surface is filled by SO
−
3
H
+ groups. These clusters are interconnected via channels; in the narrowest part (
∼
1 nm), the size of the channels is estimated using the conduction analysis data of hydrated Nafion. Exactly the spherical clusters accumulate water molecules during material hydrogenation due to the hydrophilic character of sulfone groups. The interconnection of all clusters via the channels guarantees the continuous flow of protons within the polymer membrane.
It was established [20] that proton conductance has a complicated dependence on the structural features of proton-conducting membranes, i.e., the structure of domains, the concentration
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2038 AVERIN et al.
Fig. 5.
T. Gierke’s model.
of sulfone groups in a membrane and the efficiency of proton mobility. However, the presented material prepares a reader to the development of independent theoretical beliefs about the proton conductance of sensor structures.
The third factor contributing to the nonlinearity of VACs and hysteresis occurrence concerns the drift of intrinsic electrically active defects in the bulk through the sublattice [21–23]. In this case, charged ions start drifting under voltage application to the sensor’s electrodes. Here the major role belongs to doubly ionized oxygen vacancies V
2+
O
[24]. And their distribution depends on the distance d between the electrodes and the total charge Q ( t ) passing through the sensor structure: grad( V 2+
O
)
∼
Q ( t ), d
−
2
.
This formula yields a couple of important conclusions.
First, the distribution of vacancies depends on the total charge Q passing through the structure. Second, concentration gradient increases dramatically as the sizes go down. For any material, gradient values in the nanoscale are by several orders higher than in the microscale. Therefore, the described effect becomes appreciable for the characteristics of the sensors under consideration as their sizes reach the nanometer range.
The equilibrium concentration gradient of the vacancies corresponds to the equality between the diffusion and drift components of ion currents: j dif
= j dr
. And the equilibrium distribution of the vacancies is the solution to the differential equation d (ln V 2+
O
) dx
=
−
U dϕ T
, where U denotes the applied voltage; ϕ T means the thermal potential ( k is the Boltzmann constant and T specifies temperature).
Consequently, a built-in electrical field appears in the sensor structure and exists even after removal of external voltage. The main charge carriers—electrons—repeat the distribution of oxygen vacancies in the sublattice. If we apply a fixed-frequency variable sinusoidal voltage to the structure, its volt-ampere characteristic takes the form resembling the Lissajous figure centered in the origin.
ACKNOWLEDGMENTS
This work was supported by the Ministry of Education and Science of the Russian Federation in the framework of the base part of governmental task no. 2014/151, project no. 117.
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THE VOLT-AMPERE CHARACTERISTICS OF RESISTIVE GAS SENSORS 2039
REFERENCES
1. Averin, I.A., Moshnikov, V.A., Nikulyn, A.S., et al., A Sensitive Element of Gas Sensor with a Nanostructured Surfaced Relief, Datch. Sist.
, 2011, no. 2, pp. 24–27.
2. Pronin, I.A., Controlled Synthesis of Gas-Sensitive Tin Dioxide Films Obtained by a Sol-Gel-Technology
Method, Molodoi Uchenyi , 2012, no. 5, pp. 57–60.
3. Pronin, I.A., Analysis of Intrinsic Defects Concentration in Gas-Sensitive Structures Design Based on
Tin Dioxide, Molodoi Uchenyi , 2012, no. 8, pp. 7–8.
4. Averin, I.A., Moshnikov, V.A., and Pronin, I.A., Effect of Type and Concentration of the Own Defects on the Properties of Structures of Tin Dioxide, Nano Mikrosist. Tekhn.
, 2013, no. 1, pp. 27–29.
5. Pronin, I.A., Dimitrov, D.Tz., et al., Theoretical and Experimental Investigations of Ethanol Vapour
Sensitive Properties of Junctions Composed from Produced by Sol-Gel Technology Pure and Fe Modified
Nanostructured ZnO Thin Films, Sensors Actuat. A: Phys.
, 2014, vol. 206, pp. 88–96.
6. Pronin, I.A. and Goryacheva, M.V., Principles of Structure Formation and Synthesis Models of Produced by the Sol-Gel Method SiO
2
-Me x
O y
Nanocomposites, Surf. Coat. Techn.
, 2013, vol. 235, pp. 835–840.
7. Averin, I.A., Pecherskaya, R.M., and Pronin, I.A., Features of Low Self-Organized Sols Based on Binary
Systems Based on SiO
2
-SnO
2
, Nano Mikrosist. Tekhn.
, 2011, no. 11, pp. 27–30.
8. Gracheva, I.E., Moshnikov, V.A., and Pronin, I.A., Analysis of Materials Based on Tin Dioxide under the Conditions of Self-Assembling Kinetics and Spinodal Decomposition of Two Types, Nanotechnics ,
2011, no. 2(9), pp. 46–54.
9. Kononova, I.E., Moshnikov, V.A., Krishtab, M.B., and Pronin, I.A., Fractally Aggregated Micro- and
Nanosystems Synthesized from Sols, Glass Phys. Chem.
, 2014, vol. 40, no. 2, pp. 190–202.
10. Averin, I.A., Karmanov, A.A., Moshnikov, V.A., et al., Distinctive Features of Synthesizing and Researching Nanocomposite Films Obtained by a Sol-Gel-Technology Method, Izv. Vyssh. Uchebn. Zaved.,
Povolzh. Region, Fiz.-Mat. Nauki , 2012, no. 2, pp. 155–163.
11. Pronin, I.A., Averin, I.A., Aleksandrova, O.A., and Mochnikov, V.A., Modifying the Selectivity and Gas
Sensitivity of Resistive Adsorption Sensors by Targeted Doping, Datch. Sist.
, 2013, no. 3, pp. 13–16.
12. Simakov, V.V. and Voroshilov, S.A., Surface Ionic Transport in Thin-Film Chemoresistors, Vestn. Saratov. Gos. Tekhn. Univ.
, 2006, vol. 4, no. 1, pp. 38–40.
13. Simakov, V.V., Yakusheva, O.V., Grebennikov, A.I., and Kisin, V.V., Current-Voltage Characteristics of Thin-Film Gas Sensor Structures Based on Tin Dioxide, Tech. Phys. Lett.
, 2005, vol. 31, no. 4, pp. 339–340.
14. Simakov, V.V., Yakusheva, O.V., Grebennikov, A.I., and Kisin, V.V., Temperature Variation of the
Current-Voltage Characteristics of Thin-Film Gas Sensors, Tech. Phys. Lett.
, 2006, vol. 32, no. 1, pp. 48–50.
15.
Osnovy vodorodnoi energetiki (Foundations of Hydrogen Power Engineering), Moshnikov, V.A. and
Terukov, E.I., Eds., St. Petersburg: S.-Peterburg. Gos. Elektrotekh. Univ. LETI, 2011.
16. Souzy, R. and Ameduri, B., Functional Fluoropolymers for Fuel Cell Membranes, Progr. Polym. Sci.
,
2005, vol. 30, no. 6, pp. 644–687.
17. Gierke, T.D., Munn, G.E., and Wilson, F.C., The Morphology in Nafion Perfluorinated Membrane
Products, as Determined by Wide- and Small-Angle X-Ray Studies, J. Polymer. Sci.
, 1981, vol. 19, no. 11, pp. 1687–1704.
18. Gursel, S.A., Gubler, L., and Gupta, B., Phase Transformation Characteristics of Barium Strontium Titanate Films on Anisotropic Substrates with (001) Epitaxy, Adv. Polym. Sci.
, 2008, vol. 215, pp. 157–217.
19. Eliseev, N., Memristors and Crossbars: Nanotechnology for Processors, Electronics: Science, Technology,
Business , 2010, no. 8, pp. 84–89.
AUTOMATION AND REMOTE CONTROL Vol. 75 No. 11 2014

2040 AVERIN et al.
20. Zyat’kov, I.I., Chirkin, L.K., and Yurchenko, E.P., Raschet MDP-priborov (Calculation of MIS Devices),
Leningrad: Leningr. Gos. Elektrotekh. Inst., 1991.
21. Dimitrov, D.Tz., Lutskaya, O.F., and Moshnikov, V.A., The Control of Defect in the Gas-Sensitive Tin
Dioxide Layers, Electron Techn.
, 2000, vol. 33, no. 1/2, pp. 61–65.
22. Ponomareva, A.A., Moshnikov, V.A., Delan, A., et al., Metal-Oxide-Based Nanocomposites Comprising
Advanced Gas Sensing Properties, J. Phys.: Conf. Ser.
, 2012, vol. 345, no. 1, article id. 012029.
23. Moshnikov, V.A., Gracheva, I.E., and Nalimova, S.S., Mixed Metal-Oxide Nanomaterials with Deviation from Stoichiometry and the Prospects of Their Application to Engineering, Vestn. Ryazan. Gos.
Radiotekh. Univ.
, 2012, no. 42-2, pp. 59–67.
24. Zyat’kov, I.I., Pichugin, I.G., Chernova, R.P., and Yurchenko, E.P., Tekhnologiya poluprovodnikovykh priborov i integral’nykh mikroskhem (Technology of Semiconductor Devices and Integrated Microcircuits), Leningrad: Leningr. Gos. Elektrotekh. Inst., 1986.
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