Anal Bioanal Chem DOI 10.1007/s00216-013-7502-0
RESEARCH PAPER
Grain shape influence on semiconducting metal oxide based gas sensor performance: modeling versus experiment Julia Rebholz & Peter Bonanati & Udo Weimar & Nicolae Barsan
Received: 13 September 2013 / Revised: 31 October 2013 / Accepted: 8 November 2013 # Springer-Verlag Berlin Heidelberg 2013
Abstract A model for sensing with semiconducting metal oxide (SMOX)-based gas sensors was developed which takes the effect of the shape of the grains in the sensing layers into account. Its validity is limited to materials in which the grains of the SMOX sensing layer are large enough to have an undepleted bulk region (large grains). This means that in all experimental conditions, the SMOX properties ensure that the influence of surface phenomena is not extended to the whole grain. The model takes the surface chemistry and its impact on the electrical properties of the sensing material into consideration. In this way, it relates the sensor signal—defined as the relative change of the sensor’s conductance—directly to the concentration of the target gas and also exhibits meaningful chemical parameters, such as the type of reactive oxygen species, the reaction constants, and the concentration of adsorption sites. The validity of the model is confirmed experimentally by applying it to data gathered by measuring homemade sensors in relevant conditions. Keywords Modeling of sensing . Semiconducting metal oxide gas sensors . Grain shape . Surface chemistry . Sensing performance
Introduction Because of their high sensitivity to many relevant toxic or flammable gases, superconducting metal oxide (SMOX)based gas sensors are widely used as sensing devices [1–3]. Published in the topical collection Chemosensors and Chemoreception with guest editors Jong-Heun Lee and Hyung-Gi Byun. J. Rebholz : P. Bonanati : U. Weimar : N. Barsan (*) University of Tübingen, Auf der Morgenstelle 15, 72076 Tübingen, Germany e-mail: [email protected]
Their performance is determined by many factors, such as the morphology of the sensing layer, the operation temperature, and the presence of dopants, which influence the reception and/or the transduction function of the sensing mechanism. To design more-specific real-world gas sensors, it is crucial to know how and on which factors the sensor response depends [4]. Surface reactions, charge transfer processes, and other factors that influence the reception as well as factors that mainly have an impact on the transduction—such as the layer’s morphology—are still not completely understood. A generally applicable model dealing with many contributions involved in conduction by a real-world sensor was reported in [4]. Considering the different morphologies of the sensing layers, grain sizes, and surface reactions, the model relates chemical reactions occurring at the surface of the SMOX (described by using the quasi chemical equations formalism) to their electrical effects (captured by using a combination of the Poisson and electroneutrality equations) and leads to relations linking the sensor signal to the concentration of the target gas which are in line with the experimental results. The limitations of the models are mainly related to the fact that not all relevant crystallite geometries were taken into consideration. Later, Rothschild and Komem [5] focused on the effect of grain size on the sensitivity of nanocrystalline metal oxide gas sensors; the dependence of the effective carrier concentration on the surface state density, which is largely controlled by ambient gases, was numerically calculated by using the electroneutrality equation and the approximated Poisson equations for defined Debye lengths (L D) and bulk donor concentrations (N D). The link to the surface chemistry was not taken into consideration. Yamazoe and Shimanoe [6, 7] attempted to derive a comprehensive theory on the role of the shape and size of grains in SMOX-based gas sensors which combines the surface chemistry with the electrical properties. However, very strong simplifications such as the absence of any limitation for oxygen
J. Rebholz et al.
adsorption at the surface were used. Those assumptions decreased the model’s relevance to describe sensing in real materials. The link to the surface chemistry is somehow obscured by the introduction of normalization factors, and especially the influence of the shape on the dependence of the sensor signal on the reducing gas concentration is not taken into consideration. Moreover, because there is no relation to real materials and sensing, the model’s applicability remains unclear. More recently, Fort et al. [8] presented a model for nanowire sensors based on a nonlinear dynamics description of both the chemical reaction kinetics and the conductance dependence on the density of adsorbed species and the temperature. They linked their modeling to experimental data in a “gray box” type of approach, which makes it very difficult to correlate parameters with chemical significance to their results; to cite from the paper “parameters lose their immediate physical and chemical meaning.” In summary, we can state that there is a need to derive models better than those currently available and it is very important to ensure that they take the important morphological and geometrical parameters into account (e.g., grain shape and size) [9]. Here, as a first step, we propose a refinement of the concepts proposed in [4] for the cases in which the grains of the SMOX sensing layer are large enough to have an undepleted bulk region (large grains). This means that their radius is much greater than the Debye length (L D), which is a measure of the screening of the surface effects [10]. We will examine the impact of the shape of the crystallites on the sensing properties and on the effect of surface charge on the bulk situation, namely, the extension of the space charge region. We will also derive equations that link the sensor signal to the concentration of the target gases and in which it will be possible to identify the relevant chemistry. Moreover, we will apply the model to real data in the case of sensing materials we have studied intensively in recent years and for which we have already been able to obtain relevant data concerning the bulk and surface properties [11]. The way in which we produce the homemade sensors is similar to the way in which state-of-the-art commercial sensors are fabricated; namely, we deposit thick, polycrystalline films—based on preprocessed powders—onto alumina substrates provided with electrodes and heaters. The model presented in this work is only valid for n-type SMOX and if full depletion can be excluded.
Extension of the sensing model For oxygen adsorption at the surface of an n-type semiconductor, a surface depletion layer is formed owing to the trapping of electrons from the conduction band in surface acceptor states [10]. With exposure to reducing gases, the concentration of preadsorbed negatively charged oxygen ions and the surface
depletion layer will decrease. The concentration of free charge carriers, which are able to pass the grain boundaries, will increase [4, 11, 12]. This sensor effect can be described by applying an approach similar to that presented in [4] which combines the information provided by the surface chemistry with the information provided by semiconductor physics. Surface chemistry The oxygen chemisorption equilibrium is given by [4]: β gas O þ αe− þ S ⇌ O−α βS : 2 2
ð1Þ
Following the approach presented in [4], O −β αS is a chemisorbed oxygen species, where α =1 for singly ionized oxygen species, α =2 for doubly ionized oxygen species, and β =1 for atomic ions, β =2 for molecular ions, S is a surface site onto which oxygen can be adsorbed, and e - represents an electron from the conduction band that is captured at the surface and provides the negative charge to the resulting oxygen ion. Depending on the operation temperature and the catalytic properties of the sensing material, α and β can be 1 or 2. CO was chosen as a representative for a reducing gas because its surface chemistry in the absence of water vapor is simple [12] and there is no impact from reaction products. CO is considered to react with preadsorbed oxygen [4]: gas − βCO þ O−α βS ↔ βCO2 þ αe þ S:
ð2Þ
Combining the two equations and introducing the surface coverage θ as the ratio between the concentration of occupied surface sites, [O −α βS ] , and the total concentration of available surface sites for oxygen adsorption, [S t], one obtains in the steady state k ads β=2 1 k react β −1 nαs ¼ 1 þ pO2 p : θ k des k des CO
ð3Þ
For more details, see [4]. In Eq. 3, k ads is the reaction constant for oxygen adsorption, n S is the concentration of electrons at the surface, p O2 is the partial pressure of O2, k des is the oxygen desorption reaction constant, k react is the reaction constant for the forward reaction in Eq. 2, and p CO is the partial pressure of CO. It is important to note that the surface coverage θ and n S are not independent, so we need to determine the relation between them in order to be able to express n S, which is the parameter relevant for the electrical properties of the sensor as a function of the target gas concentration p CO. The approach to obtain that relation is to examine what happens in the semiconductor
Grain shape influence on semiconducting metal oxide
as a result of surface chemistry, which is described in the following section:
potential function reaches the value of the bulk, and V 0 is the potential in the center of the grain, with V 0 =0):
Contribution of the electrical semiconducting properties
V ðr Þ ¼
enb ðr−rb Þ2 2εε0
V ðr Þ ¼
1 enb 2 2 r r −rb 1 þ 2ln 4 εε0 rb
Schematic representations of one grain for the different grain geometries we examined are shown in Fig. 1. We chose the middle of the grain as the origin and considered only the dependence on r. This is to be expected in the case of spherical grains and is a good approximation in the case of thin plates with large lateral dimensions and long cylinders (a good model for nanowires). The shape-dependent Poisson equations can be solved analytically under the assumption that the Schottky approximation is valid (separation into space charge layer and bulk region with no free charge carriers present in the former) [6, 10]: 2
d V ðrÞ enb ¼ dr2 εε0
ð4Þ
for plates;
1 d d2 enb þ 2 V ðr Þ ¼ r dr dr εε0
1 d r2 dV enb ¼ 2 r dr dr εε0
for cylinders;
for spheres:
dV ðrÞ dr
¼ 0;
V ðrÞjr¼rb ¼ V 0
for spheres:
V ðrÞjr¼R ¼ V S ;
ð12Þ
where R is the distance from the grain center to its surface (Fig. 1), the surface potential can be calculated (see [6, 10]): enb ðR−rb Þ2 2εε0
1 enb 2 2 R VS ¼ R −rb 1 þ 2ln 4 εε0 rb
ð7Þ
ð8Þ
ð11Þ
For details, see [4]. With
ð6Þ
yield the dependence of V on r (r is the position in the grain, r b is the position in the grain at which the band bending Fig. 1 Representation of one grain as a plate, a cylinder and a sphere. The light-brown area shows the bulk and yellow shows the space charge layer. r is the position in the grain, r b is the position in the grain at which the band bending potential function reaches the value of the bulk, and R is the distance from the grain center to its surface
enb rb 3 r2 rb 2 þ − V ðr Þ ¼ εε0 3r 6 2
VS ¼
r¼rb
for cylinders; ð10Þ
ð5Þ
In the above equations, V is the electrostatic potential, e is the elementary charge, and n b is the bulk concentration of electrons in the conduction band. The solutions of the Poisson equations under the boundary conditions
ð9Þ
for plates;
VS ¼
ð13Þ
for plates;
enb rb 3 R2 rb 2 þ − εε0 3R 6 2
for cylinders; ð14Þ
for spheres:
ð15Þ
As in the case of Eq. 3, we again face a situation in which in one equation we have two parameters—r b and V S—which are not independent. Thus, we need an additional equation to decouple them. Assuming the Schottky approximation, all electrons of the space charge layer are trapped at the surface. This allows us to write the electroneutrality equations as αθ½S t A ¼ nb ðR−rb ÞA
for plates;
ð16Þ
J. Rebholz et al.
αθ½S t 2πRL ¼ nb πL R2 −r2b for cylinders; αθ½S t 4πR2 ¼
4 nb π R3 −r3b 3
for spheres;
ð17Þ ð18Þ
and solving them provides the means to decouple θ from r b and the link to the surface chemistry because of the presence of θ. The sensor response: a combination of surface chemistry and semiconductor physics To combine semiconductor physics (Eqs. 13, 14, and 15) and the surface chemistry (Eqs. 16, 17, and 18) according to [4], Eqs. 13, 14, and 15 have to be solved for r b, which is very easy for plates. For cylinders and spheres this dependence was found by fitting the range of V S shown in Fig. 2 of the numerical solutions for n b =2.14×1024 m-3 and R =100 nm (polycrystalline thick film layers) with a power-law function (y = ax b ). n b was obtained by performing simultaneous work function and DC resistance change measurements in different backgrounds [13]. The particle sizes were determined by high-resolution transmission electron microscopy [14]. r b is described by the following equations:
0:5 rb ¼ R− 0:51 10−15 V S
for plates;
ð19Þ
0:515 rb ¼ R− 1:54 10−15 V S
for cylinders;
ð20Þ
0:532 rb ¼ R− 4:31 10−15 V S
for spheres:
ð21Þ
The equations were obtained by analytically solving Eq. 13 for plates and by fitting the numerically calculated values—from Eqs. 14 and 15—with the same type of function as the one corresponding to the plates. It is Fig. 2 Depletion width of a cylindrical grain (left) and a spherical grain (right) as a function of V S
interesting to observe that the values of the exponent are very similar. In the electroneutrality equations r b can be now replaced by the functions described by Eqs. 19, 20, and 21. Furthermore, V S can be replaced by n S, according to [4], eV S nS ¼ nb exp − ; ð22Þ kT to finally express or calculate θ as a function of n S [4]. As is obvious from Eq. 3, 1θ −1 as a function of nS is of main interest; it was already shown in [4] that in certain
conditions it is possible to express 1θ −1 as a power-law function of n S: 1 −1 ≈ mnδS : ð23Þ θ Such an approximation has the advantage of being able to keep a relatively simple functional dependency of n S on p CO. For the specific case of the material we are considering (n b =2.14×1024 m−3, R =100 nm), in a V S variation range that was indicated by our formal experimental findings (0.15– 0.5 V, see [10]), the results are shown in Fig. 3, where both the results of the numerical calculations and the results of the fit with the function described by Eq. 23 are depicted. The quality of the fit depends on the values of [St] and α. For the latter, the values that make sense are (1) those corresponding to singly ionized oxygen species and (2) those corresponding to doubly ionized oxygen species. For [St], the concentration of all tin atoms at the surface is the highest possible value. For the two possible values of α one obtains excellent fits for different values of [St]: 3.4×1016 m−3, meaning 0.246 % of all tin atoms for α =1, or 1.7×1016 m−3, meaning 0.123 % of all tin atoms for α =2. Those values lie in the range considered as reasonable because of the Weisz limitation [14]. The calculated δ values from the fit for the different shapes are shown in Table 1. δ can be interpreted as a correction factor that depends on the properties of the material, including the shape of the grains.
Grain shape influence on semiconducting metal oxide
Fig. 3 Fit of the dependence of (1/θ) - 1 on n S for the three shapes with α =1 or α =2. The corresponding scale for V S is shown ot the top. With the function y =ax b , the dependence of (1/θ) - 1 on n S is approximated for values of parameters which are relevant to the application
By replacing 1θ −1 with mn δS, one obtains the dependency of n S, which can be related to the dependence of the resistance/conductance of the sensor on the concentration of the target gas: k ads β=2 k react β pO2 m nδS nαS ¼ 1 þ p : k des k des CO |fflfflfflfflffl ffl{zfflfflfflfflfflffl}
It is possible to further simplify the equation by grouping some of the constants: ð25Þ
The dependence of the sensor signal on the concentration of CO can be calculated by observing that in the absence of CO, we have nS;0
1 1 ðαþδÞ ¼ : ω
nS ¼ S¼ nS;0
1 k react β ðαþδÞ 1þ p : k des CO
ð28Þ
ð24Þ
ω
1 ðαþδÞ 1 k react β 1þ nS ¼ pCO : ω k des
Using Eqs. 25, 26, and 27, we can calculate the sensor signal:
ð26Þ
The result we obtained is very useful because from the experimental results it was possible to extract important information about the sensing properties: & &
The values of α and β indicate which type of oxygen ions are involved in the reaction. The values of kkreact are a measure of the reactivity of the des material with the target gas.
It is also interesting to note that there is a dependence of sensor signal on the grain shape that is contained in the value of δ. A larger value indicates a weaker response, which means that the best results are to be expected for spherical grains. However, that kind of influence is not very large. Limitations of the model
Keeping in mind that the conductance is proportional to n S [4], we have that the sensor signal defined as the ratio between the conductance in presence of CO (G CO) and the baseline conductance (G 0) in the background gas is S¼
GCO nS ¼ : G0 nS;0
ð27Þ
Table 1 δ values calculated for the different shapes Sensing material
Shape
δ
Polycrystalline thick film layers
Plate Cylinder Sphere
0.35 0.32 0.28
The shape of the grains has an impact on the conditions in which the full depletion is reached and the model’s assumptions lose their validity; if this happens, then r b =0. Substitution of r b =0 into Eqs. 13, 14, and 15 for V S leads to pffiffiffi R ¼ 2 LD
rffiffiffiffiffiffiffiffi V se for plates; kT
ð29Þ
pffiffiffi R ¼ 4 LD
rffiffiffiffiffiffiffiffi V se for cylinders; kT
ð30Þ
pffiffiffi R ¼ 6 LD
rffiffiffiffiffiffiffiffi V se for spheres: kT
ð31Þ
J. Rebholz et al.
Experimental validation
Fig. 4 The ratio R/L D as a function of V S for different grain shapes
Equations 29, 30, and 31 link the geometrical parameters (R , which describes the grain size) with the electronic properties of the SMOX (L D, which is related to the concentration of the free charges in the bulk) and allow the minimal value of the surface potential to be calculated, which is needed to reach full depletion. Because R as well as L D are material constants, this new way of analysis opens up the possibility to estimate whether full depletion has to be taken into account in certain conditions considering different grain shapes. Figure 4 depicts R/L D as a function of V S for the three grain shapes. It shows that for a certain R /L D, the spherical grain is fully depleted at lower values of V S than the cylindrical grain and the plates. Consequently, a sphere needs a lower surface potential to be fully depleted than a cylinder with the same radius and needs a surface potential even lower than that for a plate with a thickness that is the same as the diameter of the sphere. The influence of the shape is indicated by the different factors, pffiffiffi pffiffiffi pffiffiffi which are 2 for the plate, 4 for the cylinder, and 6 for the sphere. For the material examined here (i.e., R/L D =28), in all relevant conditions—in terms of V S values—we are still in a non-fully depleted situation, so the boundary conditions of the model fully apply.
Figure 5 shows the experimentally derived dependence of the sensor signal on CO concentration. It was obtained for sensors based on undoped SnO2 polycrystalline thick film sensing layers, synthesized by wet chemistry and screen-printed on alumina substrates; these are the same materials as the ones previously studied (see [11, 14]; the information obtained there was used in all our numerical calculations). The determining factor in controlling the particle size is the calcination temperature. A full description of the preparation procedure is presented in [15, 16]. The devices, kept at an operation temperature of 300 °C, were repeatedly exposed to different concentrations of CO (in the range 0.2–500 ppm, 30 min for each concentration step) in dry synthetic air (water vapor contamination below 30 ppm); a stabilization time of 24 h in synthetic air before starting the measurement was used. The sensor signals, S , were calculated by dividing the resistance measured in the background (synthetic air), R 0, by the resistance measured at a certain CO concentration in synthetic air, R CO: The data, shown in Fig. 5, were fitted with the function described in Eq. 32: y ¼ ða þ bxÞc
ð32Þ
for β ¼ 1:
This equation has the same form as Eq. 28 if one takes β =1. That choice (β =1) is supported by the data presented in the literature and collected in [4], which indicate that above 150 °C atomic ionized oxygen species dominate. From Eq. 28, 1 ¼ c; αþδ
ð33Þ
and δ can be estimated; the results for both values of α are shown in Table 2. The experiment and the model are in good agreement for α =2, which indicates that doubly ionized atomic oxygen ions (O2-) are the dominating reactive oxygen species at the surface in these conditions. According to Eq. 28, the ratio of the two reaction constants is given by k react ¼ b: k des
Table 2 Fit values and calculated δ values Fig. 5 The sensor signal as a function of the CO concentration for polycrystalline thick film layers with the fitting function for β =1. The error bars represent the deviation from the average performed over a series of two consecutive measurements
ð34Þ
α
β
a
b
c
δ
1 2
1 1
1.0 1.0
30.90 30.90
0.43 0.43
1.3 0.3
Grain shape influence on semiconducting metal oxide
Comparison with the b values of the fit in Table 2 indicates that the reaction constant of CO conversion is much larger than the reaction constant of oxygen desorption, which is the condition for gas sensing.
Conclusion We were able to develop a model for the sensor signal of ntype SMOX-based gas sensors which takes the impact of the shape of the grains into account. On the basis of knowledge already acquired, such as the concentration of the free charge carriers and the variation range of band bending, the model was built in a step-by-step approach that used numerical calculations for deriving chemically meaningful analytical approximations. It leads to simple equations linking the sensor signal to the concentration of the target gas in which it is possible to identify relevant material-specific parameters. Besides the fact that it does not need oversimplified assumptions, the model’s main advantage is that it can be applied to experimental data and provides information related to the surface chemistry responsible for sensing. It completes the investigation toolbox that we have developed in recent years and will be used to unravel the effect of various changes in the fabrication strategy for gas-sensing materials. One very interesting aspect will be to study doped materials, for which we already have information from work function change measurements, with the aim of identifying how they change the sensing performance. The applicability of the model is limited to the so-called large grains. The next steps will be to extend it to materials showing full depletion with the aim of developing a comprehensive modeling of gas sensing with SMOX.
References 1. Williams DE (1999) Semiconducting oxides as gas-sensitive resistors. Sensors Actuators B Chem 57:1–16
2. Afzal A, Cioffi N, Sabbatini L, Torsi L (2012) NOx sensors based on semiconducting metal oxide nanostructures: progress and perspectives. Sensors Actuators B Chem 171–172:25–42 3. Fine GF, Cavanagh LM, Afonja A, Binions R (2010) Metal oxide semi-conductor gas sensors in environmental monitoring. Sensors (Basel) 10:5469–5502 4. Bârsan N, Weimar U (2001) Conduction model of metal oxide gas sensors. J Electroceram 7:143–167 5. Rothschild A, Komem Y (2004) The effect of grain size on the sensitivity of nanocrystalline metal-oxide gas sensors. J Appl Phys 95:6374 6. Yamazoe N, Shimanoe K (2008) Roles of shape and size of component crystals in semiconductor gas sensors I. Response to oxygen. J Electrochem Soc 155:85–91 7. Yamazoe N, Shimanoe K (2008) Roles of shape and size of component crystals in semiconductor gas sensors II. Response to NO2 and H2. J Electrochem Soc 155:93–98 8. Fort A, Mugnaini M, Rocchi S et al (2010) Metal-oxide nanowire sensors for CO detection: characterization and modeling. Sensors Actuators B Chem 148:283–291 9. Korotcenkov G (2005) Gas response control through structural and chemical modification of metal oxide films: state of the art and approaches. Sensors Actuators B Chem 107:209–232 10. Morrison SR (1977) The chemical physics of surfaces. Plenum, New York 11. Bârsan N, Hübner M, Weimar U (2011) Conduction mechanisms in SnO2 based polycrystalline thick film gas sensors exposed to CO and H2 in different oxygen backgrounds. Sensors Actuators B Chem 157: 510–517 12. Bârsan N, Schweizer-Berberich M, Göpel W (1999) Fundamental and practical aspects in the design of nanoscaled SnO2 gas sensors: a status report. Fresenius J Anal Chem 365:287–304 13. Hübner M, Bârsan N, Weimar U (2012) Influences of Al, Pd and Pt additives on the conduction mechanism as well as the surface and bulk properties of SnO2 based polycrystalline thick film gas sensors. Sensors Actuators B Chem 171–172:172–180 14. Hübner M, Pavelko RG, Bârsan N, Weimar U (2011) Influence of oxygen backgrounds on hydrogen sensing with SnO2 nanomaterials. Sensors Actuators B Chem 154:264–269 15. Diéguez A, Romano-Rodríguez A, Morante JR et al (1999) Nanoparticle engineering for gas sensor optimisation: improved sol–gel fabricated nanocrystalline SnO2 thick film gas sensor for NO2 detection by calcination, catalytic metal introduction and grinding treatments. Sensors Actuators B Chem 60:125–137 16. Diéguez A, Romano-Rodríguez A, Alay JL et al (2000) Parameter optimisation in SnO2 gas sensors for NO2 detection with low crosssensitivity to CO: sol–gel preparation, film preparation, powder calcination, doping and grinding. Sensors Actuators B Chem 65: 166–168
RESEARCH PAPER
Grain shape influence on semiconducting metal oxide based gas sensor performance: modeling versus experiment Julia Rebholz & Peter Bonanati & Udo Weimar & Nicolae Barsan
Received: 13 September 2013 / Revised: 31 October 2013 / Accepted: 8 November 2013 # Springer-Verlag Berlin Heidelberg 2013
Abstract A model for sensing with semiconducting metal oxide (SMOX)-based gas sensors was developed which takes the effect of the shape of the grains in the sensing layers into account. Its validity is limited to materials in which the grains of the SMOX sensing layer are large enough to have an undepleted bulk region (large grains). This means that in all experimental conditions, the SMOX properties ensure that the influence of surface phenomena is not extended to the whole grain. The model takes the surface chemistry and its impact on the electrical properties of the sensing material into consideration. In this way, it relates the sensor signal—defined as the relative change of the sensor’s conductance—directly to the concentration of the target gas and also exhibits meaningful chemical parameters, such as the type of reactive oxygen species, the reaction constants, and the concentration of adsorption sites. The validity of the model is confirmed experimentally by applying it to data gathered by measuring homemade sensors in relevant conditions. Keywords Modeling of sensing . Semiconducting metal oxide gas sensors . Grain shape . Surface chemistry . Sensing performance
Introduction Because of their high sensitivity to many relevant toxic or flammable gases, superconducting metal oxide (SMOX)based gas sensors are widely used as sensing devices [1–3]. Published in the topical collection Chemosensors and Chemoreception with guest editors Jong-Heun Lee and Hyung-Gi Byun. J. Rebholz : P. Bonanati : U. Weimar : N. Barsan (*) University of Tübingen, Auf der Morgenstelle 15, 72076 Tübingen, Germany e-mail: [email protected]
Their performance is determined by many factors, such as the morphology of the sensing layer, the operation temperature, and the presence of dopants, which influence the reception and/or the transduction function of the sensing mechanism. To design more-specific real-world gas sensors, it is crucial to know how and on which factors the sensor response depends [4]. Surface reactions, charge transfer processes, and other factors that influence the reception as well as factors that mainly have an impact on the transduction—such as the layer’s morphology—are still not completely understood. A generally applicable model dealing with many contributions involved in conduction by a real-world sensor was reported in [4]. Considering the different morphologies of the sensing layers, grain sizes, and surface reactions, the model relates chemical reactions occurring at the surface of the SMOX (described by using the quasi chemical equations formalism) to their electrical effects (captured by using a combination of the Poisson and electroneutrality equations) and leads to relations linking the sensor signal to the concentration of the target gas which are in line with the experimental results. The limitations of the models are mainly related to the fact that not all relevant crystallite geometries were taken into consideration. Later, Rothschild and Komem [5] focused on the effect of grain size on the sensitivity of nanocrystalline metal oxide gas sensors; the dependence of the effective carrier concentration on the surface state density, which is largely controlled by ambient gases, was numerically calculated by using the electroneutrality equation and the approximated Poisson equations for defined Debye lengths (L D) and bulk donor concentrations (N D). The link to the surface chemistry was not taken into consideration. Yamazoe and Shimanoe [6, 7] attempted to derive a comprehensive theory on the role of the shape and size of grains in SMOX-based gas sensors which combines the surface chemistry with the electrical properties. However, very strong simplifications such as the absence of any limitation for oxygen
J. Rebholz et al.
adsorption at the surface were used. Those assumptions decreased the model’s relevance to describe sensing in real materials. The link to the surface chemistry is somehow obscured by the introduction of normalization factors, and especially the influence of the shape on the dependence of the sensor signal on the reducing gas concentration is not taken into consideration. Moreover, because there is no relation to real materials and sensing, the model’s applicability remains unclear. More recently, Fort et al. [8] presented a model for nanowire sensors based on a nonlinear dynamics description of both the chemical reaction kinetics and the conductance dependence on the density of adsorbed species and the temperature. They linked their modeling to experimental data in a “gray box” type of approach, which makes it very difficult to correlate parameters with chemical significance to their results; to cite from the paper “parameters lose their immediate physical and chemical meaning.” In summary, we can state that there is a need to derive models better than those currently available and it is very important to ensure that they take the important morphological and geometrical parameters into account (e.g., grain shape and size) [9]. Here, as a first step, we propose a refinement of the concepts proposed in [4] for the cases in which the grains of the SMOX sensing layer are large enough to have an undepleted bulk region (large grains). This means that their radius is much greater than the Debye length (L D), which is a measure of the screening of the surface effects [10]. We will examine the impact of the shape of the crystallites on the sensing properties and on the effect of surface charge on the bulk situation, namely, the extension of the space charge region. We will also derive equations that link the sensor signal to the concentration of the target gases and in which it will be possible to identify the relevant chemistry. Moreover, we will apply the model to real data in the case of sensing materials we have studied intensively in recent years and for which we have already been able to obtain relevant data concerning the bulk and surface properties [11]. The way in which we produce the homemade sensors is similar to the way in which state-of-the-art commercial sensors are fabricated; namely, we deposit thick, polycrystalline films—based on preprocessed powders—onto alumina substrates provided with electrodes and heaters. The model presented in this work is only valid for n-type SMOX and if full depletion can be excluded.
Extension of the sensing model For oxygen adsorption at the surface of an n-type semiconductor, a surface depletion layer is formed owing to the trapping of electrons from the conduction band in surface acceptor states [10]. With exposure to reducing gases, the concentration of preadsorbed negatively charged oxygen ions and the surface
depletion layer will decrease. The concentration of free charge carriers, which are able to pass the grain boundaries, will increase [4, 11, 12]. This sensor effect can be described by applying an approach similar to that presented in [4] which combines the information provided by the surface chemistry with the information provided by semiconductor physics. Surface chemistry The oxygen chemisorption equilibrium is given by [4]: β gas O þ αe− þ S ⇌ O−α βS : 2 2
ð1Þ
Following the approach presented in [4], O −β αS is a chemisorbed oxygen species, where α =1 for singly ionized oxygen species, α =2 for doubly ionized oxygen species, and β =1 for atomic ions, β =2 for molecular ions, S is a surface site onto which oxygen can be adsorbed, and e - represents an electron from the conduction band that is captured at the surface and provides the negative charge to the resulting oxygen ion. Depending on the operation temperature and the catalytic properties of the sensing material, α and β can be 1 or 2. CO was chosen as a representative for a reducing gas because its surface chemistry in the absence of water vapor is simple [12] and there is no impact from reaction products. CO is considered to react with preadsorbed oxygen [4]: gas − βCO þ O−α βS ↔ βCO2 þ αe þ S:
ð2Þ
Combining the two equations and introducing the surface coverage θ as the ratio between the concentration of occupied surface sites, [O −α βS ] , and the total concentration of available surface sites for oxygen adsorption, [S t], one obtains in the steady state k ads β=2 1 k react β −1 nαs ¼ 1 þ pO2 p : θ k des k des CO
ð3Þ
For more details, see [4]. In Eq. 3, k ads is the reaction constant for oxygen adsorption, n S is the concentration of electrons at the surface, p O2 is the partial pressure of O2, k des is the oxygen desorption reaction constant, k react is the reaction constant for the forward reaction in Eq. 2, and p CO is the partial pressure of CO. It is important to note that the surface coverage θ and n S are not independent, so we need to determine the relation between them in order to be able to express n S, which is the parameter relevant for the electrical properties of the sensor as a function of the target gas concentration p CO. The approach to obtain that relation is to examine what happens in the semiconductor
Grain shape influence on semiconducting metal oxide
as a result of surface chemistry, which is described in the following section:
potential function reaches the value of the bulk, and V 0 is the potential in the center of the grain, with V 0 =0):
Contribution of the electrical semiconducting properties
V ðr Þ ¼
enb ðr−rb Þ2 2εε0
V ðr Þ ¼
1 enb 2 2 r r −rb 1 þ 2ln 4 εε0 rb
Schematic representations of one grain for the different grain geometries we examined are shown in Fig. 1. We chose the middle of the grain as the origin and considered only the dependence on r. This is to be expected in the case of spherical grains and is a good approximation in the case of thin plates with large lateral dimensions and long cylinders (a good model for nanowires). The shape-dependent Poisson equations can be solved analytically under the assumption that the Schottky approximation is valid (separation into space charge layer and bulk region with no free charge carriers present in the former) [6, 10]: 2
d V ðrÞ enb ¼ dr2 εε0
ð4Þ
for plates;
1 d d2 enb þ 2 V ðr Þ ¼ r dr dr εε0
1 d r2 dV enb ¼ 2 r dr dr εε0
for cylinders;
for spheres:
dV ðrÞ dr
¼ 0;
V ðrÞjr¼rb ¼ V 0
for spheres:
V ðrÞjr¼R ¼ V S ;
ð12Þ
where R is the distance from the grain center to its surface (Fig. 1), the surface potential can be calculated (see [6, 10]): enb ðR−rb Þ2 2εε0
1 enb 2 2 R VS ¼ R −rb 1 þ 2ln 4 εε0 rb
ð7Þ
ð8Þ
ð11Þ
For details, see [4]. With
ð6Þ
yield the dependence of V on r (r is the position in the grain, r b is the position in the grain at which the band bending Fig. 1 Representation of one grain as a plate, a cylinder and a sphere. The light-brown area shows the bulk and yellow shows the space charge layer. r is the position in the grain, r b is the position in the grain at which the band bending potential function reaches the value of the bulk, and R is the distance from the grain center to its surface
enb rb 3 r2 rb 2 þ − V ðr Þ ¼ εε0 3r 6 2
VS ¼
r¼rb
for cylinders; ð10Þ
ð5Þ
In the above equations, V is the electrostatic potential, e is the elementary charge, and n b is the bulk concentration of electrons in the conduction band. The solutions of the Poisson equations under the boundary conditions
ð9Þ
for plates;
VS ¼
ð13Þ
for plates;
enb rb 3 R2 rb 2 þ − εε0 3R 6 2
for cylinders; ð14Þ
for spheres:
ð15Þ
As in the case of Eq. 3, we again face a situation in which in one equation we have two parameters—r b and V S—which are not independent. Thus, we need an additional equation to decouple them. Assuming the Schottky approximation, all electrons of the space charge layer are trapped at the surface. This allows us to write the electroneutrality equations as αθ½S t A ¼ nb ðR−rb ÞA
for plates;
ð16Þ
J. Rebholz et al.
αθ½S t 2πRL ¼ nb πL R2 −r2b for cylinders; αθ½S t 4πR2 ¼
4 nb π R3 −r3b 3
for spheres;
ð17Þ ð18Þ
and solving them provides the means to decouple θ from r b and the link to the surface chemistry because of the presence of θ. The sensor response: a combination of surface chemistry and semiconductor physics To combine semiconductor physics (Eqs. 13, 14, and 15) and the surface chemistry (Eqs. 16, 17, and 18) according to [4], Eqs. 13, 14, and 15 have to be solved for r b, which is very easy for plates. For cylinders and spheres this dependence was found by fitting the range of V S shown in Fig. 2 of the numerical solutions for n b =2.14×1024 m-3 and R =100 nm (polycrystalline thick film layers) with a power-law function (y = ax b ). n b was obtained by performing simultaneous work function and DC resistance change measurements in different backgrounds [13]. The particle sizes were determined by high-resolution transmission electron microscopy [14]. r b is described by the following equations:
0:5 rb ¼ R− 0:51 10−15 V S
for plates;
ð19Þ
0:515 rb ¼ R− 1:54 10−15 V S
for cylinders;
ð20Þ
0:532 rb ¼ R− 4:31 10−15 V S
for spheres:
ð21Þ
The equations were obtained by analytically solving Eq. 13 for plates and by fitting the numerically calculated values—from Eqs. 14 and 15—with the same type of function as the one corresponding to the plates. It is Fig. 2 Depletion width of a cylindrical grain (left) and a spherical grain (right) as a function of V S
interesting to observe that the values of the exponent are very similar. In the electroneutrality equations r b can be now replaced by the functions described by Eqs. 19, 20, and 21. Furthermore, V S can be replaced by n S, according to [4], eV S nS ¼ nb exp − ; ð22Þ kT to finally express or calculate θ as a function of n S [4]. As is obvious from Eq. 3, 1θ −1 as a function of nS is of main interest; it was already shown in [4] that in certain
conditions it is possible to express 1θ −1 as a power-law function of n S: 1 −1 ≈ mnδS : ð23Þ θ Such an approximation has the advantage of being able to keep a relatively simple functional dependency of n S on p CO. For the specific case of the material we are considering (n b =2.14×1024 m−3, R =100 nm), in a V S variation range that was indicated by our formal experimental findings (0.15– 0.5 V, see [10]), the results are shown in Fig. 3, where both the results of the numerical calculations and the results of the fit with the function described by Eq. 23 are depicted. The quality of the fit depends on the values of [St] and α. For the latter, the values that make sense are (1) those corresponding to singly ionized oxygen species and (2) those corresponding to doubly ionized oxygen species. For [St], the concentration of all tin atoms at the surface is the highest possible value. For the two possible values of α one obtains excellent fits for different values of [St]: 3.4×1016 m−3, meaning 0.246 % of all tin atoms for α =1, or 1.7×1016 m−3, meaning 0.123 % of all tin atoms for α =2. Those values lie in the range considered as reasonable because of the Weisz limitation [14]. The calculated δ values from the fit for the different shapes are shown in Table 1. δ can be interpreted as a correction factor that depends on the properties of the material, including the shape of the grains.
Grain shape influence on semiconducting metal oxide
Fig. 3 Fit of the dependence of (1/θ) - 1 on n S for the three shapes with α =1 or α =2. The corresponding scale for V S is shown ot the top. With the function y =ax b , the dependence of (1/θ) - 1 on n S is approximated for values of parameters which are relevant to the application
By replacing 1θ −1 with mn δS, one obtains the dependency of n S, which can be related to the dependence of the resistance/conductance of the sensor on the concentration of the target gas: k ads β=2 k react β pO2 m nδS nαS ¼ 1 þ p : k des k des CO |fflfflfflfflffl ffl{zfflfflfflfflfflffl}
It is possible to further simplify the equation by grouping some of the constants: ð25Þ
The dependence of the sensor signal on the concentration of CO can be calculated by observing that in the absence of CO, we have nS;0
1 1 ðαþδÞ ¼ : ω
nS ¼ S¼ nS;0
1 k react β ðαþδÞ 1þ p : k des CO
ð28Þ
ð24Þ
ω
1 ðαþδÞ 1 k react β 1þ nS ¼ pCO : ω k des
Using Eqs. 25, 26, and 27, we can calculate the sensor signal:
ð26Þ
The result we obtained is very useful because from the experimental results it was possible to extract important information about the sensing properties: & &
The values of α and β indicate which type of oxygen ions are involved in the reaction. The values of kkreact are a measure of the reactivity of the des material with the target gas.
It is also interesting to note that there is a dependence of sensor signal on the grain shape that is contained in the value of δ. A larger value indicates a weaker response, which means that the best results are to be expected for spherical grains. However, that kind of influence is not very large. Limitations of the model
Keeping in mind that the conductance is proportional to n S [4], we have that the sensor signal defined as the ratio between the conductance in presence of CO (G CO) and the baseline conductance (G 0) in the background gas is S¼
GCO nS ¼ : G0 nS;0
ð27Þ
Table 1 δ values calculated for the different shapes Sensing material
Shape
δ
Polycrystalline thick film layers
Plate Cylinder Sphere
0.35 0.32 0.28
The shape of the grains has an impact on the conditions in which the full depletion is reached and the model’s assumptions lose their validity; if this happens, then r b =0. Substitution of r b =0 into Eqs. 13, 14, and 15 for V S leads to pffiffiffi R ¼ 2 LD
rffiffiffiffiffiffiffiffi V se for plates; kT
ð29Þ
pffiffiffi R ¼ 4 LD
rffiffiffiffiffiffiffiffi V se for cylinders; kT
ð30Þ
pffiffiffi R ¼ 6 LD
rffiffiffiffiffiffiffiffi V se for spheres: kT
ð31Þ
J. Rebholz et al.
Experimental validation
Fig. 4 The ratio R/L D as a function of V S for different grain shapes
Equations 29, 30, and 31 link the geometrical parameters (R , which describes the grain size) with the electronic properties of the SMOX (L D, which is related to the concentration of the free charges in the bulk) and allow the minimal value of the surface potential to be calculated, which is needed to reach full depletion. Because R as well as L D are material constants, this new way of analysis opens up the possibility to estimate whether full depletion has to be taken into account in certain conditions considering different grain shapes. Figure 4 depicts R/L D as a function of V S for the three grain shapes. It shows that for a certain R /L D, the spherical grain is fully depleted at lower values of V S than the cylindrical grain and the plates. Consequently, a sphere needs a lower surface potential to be fully depleted than a cylinder with the same radius and needs a surface potential even lower than that for a plate with a thickness that is the same as the diameter of the sphere. The influence of the shape is indicated by the different factors, pffiffiffi pffiffiffi pffiffiffi which are 2 for the plate, 4 for the cylinder, and 6 for the sphere. For the material examined here (i.e., R/L D =28), in all relevant conditions—in terms of V S values—we are still in a non-fully depleted situation, so the boundary conditions of the model fully apply.
Figure 5 shows the experimentally derived dependence of the sensor signal on CO concentration. It was obtained for sensors based on undoped SnO2 polycrystalline thick film sensing layers, synthesized by wet chemistry and screen-printed on alumina substrates; these are the same materials as the ones previously studied (see [11, 14]; the information obtained there was used in all our numerical calculations). The determining factor in controlling the particle size is the calcination temperature. A full description of the preparation procedure is presented in [15, 16]. The devices, kept at an operation temperature of 300 °C, were repeatedly exposed to different concentrations of CO (in the range 0.2–500 ppm, 30 min for each concentration step) in dry synthetic air (water vapor contamination below 30 ppm); a stabilization time of 24 h in synthetic air before starting the measurement was used. The sensor signals, S , were calculated by dividing the resistance measured in the background (synthetic air), R 0, by the resistance measured at a certain CO concentration in synthetic air, R CO: The data, shown in Fig. 5, were fitted with the function described in Eq. 32: y ¼ ða þ bxÞc
ð32Þ
for β ¼ 1:
This equation has the same form as Eq. 28 if one takes β =1. That choice (β =1) is supported by the data presented in the literature and collected in [4], which indicate that above 150 °C atomic ionized oxygen species dominate. From Eq. 28, 1 ¼ c; αþδ
ð33Þ
and δ can be estimated; the results for both values of α are shown in Table 2. The experiment and the model are in good agreement for α =2, which indicates that doubly ionized atomic oxygen ions (O2-) are the dominating reactive oxygen species at the surface in these conditions. According to Eq. 28, the ratio of the two reaction constants is given by k react ¼ b: k des
Table 2 Fit values and calculated δ values Fig. 5 The sensor signal as a function of the CO concentration for polycrystalline thick film layers with the fitting function for β =1. The error bars represent the deviation from the average performed over a series of two consecutive measurements
ð34Þ
α
β
a
b
c
δ
1 2
1 1
1.0 1.0
30.90 30.90
0.43 0.43
1.3 0.3
Grain shape influence on semiconducting metal oxide
Comparison with the b values of the fit in Table 2 indicates that the reaction constant of CO conversion is much larger than the reaction constant of oxygen desorption, which is the condition for gas sensing.
Conclusion We were able to develop a model for the sensor signal of ntype SMOX-based gas sensors which takes the impact of the shape of the grains into account. On the basis of knowledge already acquired, such as the concentration of the free charge carriers and the variation range of band bending, the model was built in a step-by-step approach that used numerical calculations for deriving chemically meaningful analytical approximations. It leads to simple equations linking the sensor signal to the concentration of the target gas in which it is possible to identify relevant material-specific parameters. Besides the fact that it does not need oversimplified assumptions, the model’s main advantage is that it can be applied to experimental data and provides information related to the surface chemistry responsible for sensing. It completes the investigation toolbox that we have developed in recent years and will be used to unravel the effect of various changes in the fabrication strategy for gas-sensing materials. One very interesting aspect will be to study doped materials, for which we already have information from work function change measurements, with the aim of identifying how they change the sensing performance. The applicability of the model is limited to the so-called large grains. The next steps will be to extend it to materials showing full depletion with the aim of developing a comprehensive modeling of gas sensing with SMOX.
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