FEM Modeling of Sensitive Layer Swelling Effect on Microbalance Gas Sensor Based on TFBAR Resonator

Transcription

1 Journal of Materials Sciences and Applications 2015; 1(4): Published online July 30, 2015 ( FEM Modeling of Sensitive Layer Swelling Effect on Microbalance Gas Sensor Based on Rafik Serhane, Fayçal Had Larbi, Abderrazak Smatti Division Microélectronique et Nanotechnologie, Equipe MEMS & Sensors, Centre de Développement des Technologies Avancées, Baba Hassen, Algiers, Algeria addresses (R. Serhane), (R. Serhane) Keywords Gas Sensor, TFBAR, ZnO, FEM Simulation, Swelling Effect Received: June 16, 2015 Revised: July 13, 2015 Accepted: July 14, 2015 Citation Rafik Serhane, Fayçal Had Larbi, Abderrazak Smatti. FEM Modeling of Sensitive Layer Swelling Effect on Microbalance Gas Sensor Based on. Journal of Materials Sciences and Applications. Vol. 1, No. 4, 2015, pp Abstract The electromechanical response of a chemical gas sensor based on a TFBAR (Thin Film Bulk Acoustic Resonator) structure coated with a sensitive polymer layer was simulated with a FEM (Finite Elements Method) software (COMSOL Multiphysics ). The principle of sensing is based on the change of the mechanical properties of the polymer due to the gas adsorption. This will cause an additional mechanical load inducing a shift in the electrical input admittance curve of the resonator which decreases the resonance frequency of the fundamental thickness mode. This work presents a comparison between two adsorption models describing non swelling and swelling mechanisms by using FEM simulation. The presented structure is a piezoelectric capacitance Al/ZnO/Al with thicknesses of 0.2 µm /6 µm /0.2µm respectively above which a thin film (0.4 µm) of CH 2 Cl 2 -sensitive Polyisobutylene (PIB) polymer is coated. The structure vibrates at a resonance frequency of MHz with a maximum mechanical displacement of 2.3 nm in the fundamental thickness mode. The FEM simulation has shown a sensor sensitivity of 3 Hz/ppm. The comparison between the two models shows that the model which considerates the swelling effect is more appropriate for describing the real sensitivity of the device. 1. Introduction Multiphysics simulation for design purposes occupies today a very important part in the manufacturing industry of MEMS components and sensors. Based on physical and mathematical models, we can model all the physical phenomena occurring in the structure and reproduce all the responses (electrical, mechanical, thermal and so on) under different types of solicitations. These simulation tools lead to the prediction of the device performance before the fabrication of the component. The simulation allows for a considerable gain in time and materials cost involved in the entire development process. We propose a comparison between two mechanisms of the gas adsorption by a sensitive polymer layer. The models describe the non swelling [1] and the swelling [2] effects using TFBAR (Thin Film Bulk Acoustic Resonator) as Microbalance [3]. The detection is based on the resonance frequency shift of the electrical characteristic caused by the gas mass loading.

2 Journal of Materials Sciences and Applications 2015; 1(4): Electromechanical Response of a 2.1. Structure The base structure of a TFBAR resonator is a MIM (Metal/Insulator/Metal) capacitance. The resonator is composed of a piezoelectric material (the insulator) sandwiched between two thin thickness metal electrodes (Fig. 1). uirepresents the displacement of particles (polarization of the wave) and ρ the material density, t the time and x the spatial coordinates. Using the previous two equations (1) and (2), we obtain: ρ u u U (3) i E l = c + 2 ikl eki t x xk x xk The 2 nd equation of state for the piezoelectric solid material can be written as follows: D = e S + ε s E or kl kl k k ul s U D = e ε (4) x x kl k k k Fig. 1. Gas sensor structure based on a TFBAR resonator. The application of an electric potential on the top electrode (while the bottom one is grounded) creates an electric field in the piezoelectric material and leads to a mechanical deformation by the Lippman effect, also called the reverse piezoelectricity [4]. The generated acoustic wave is spreading throughout the material with a speed V depending on the elastic properties of the medium and on the wave propagation direction. The resonance appears as a result of a standing wave construction which depends on the characteristic dimensions, in such a way that the propagation length d (thickness of the piezoelectric film) of the acoustic wave is n times of half a wavelength λ, such as d = nλ / Propagation of an Acoustic Wave in a Piezoelectric Solid Material A piezoelectric solid is a material that connects the electrical effects to the mechanical effects. The direct piezoelectric effect can be recognized by the appearance of electrical charges under the effect of a mechanical deformation, while the opposite effect results in a mechanical deformation of the solid under the effect of an applied external electric field. These coupled effects can be described by two state equations [4]. The first one is: D is the electric displacement (induction) and s ε k the dielectric permittivity at a constant strain. The piezoelectric crystal is an insulator and thus obeys to the Gauss-Maxwell equation [4]: D x = 0 According to the relations (4) and (5), we have: e kl 2 2 l s k k x xk (5) u U ε = 0 (6) x x In the case of a one-dimensional approximation (Mason s model), the solution of the system constituted of two coupled equations ((3) and (6)) can be resolved analytically [4]. 3. Finite Elements Simulation Model 3.1. Two-Dimensional Model for a Gas Sensor T = c E S e E i ikl kl ki k (1) 1 u k ul U With: Skl = + and Ek =, Ti are the 2 xl xk xk components of the stress tensor, Sklthe elements of the strain E tensor, c ikl the elastic constants at a constant electric field, ekithe piezoelectric tensor elements, Ekthe components of the electric field and U the electric potential. The fundamental equation of the dynamics in an elastic solid material can be written as follows: 2 ρ u T i i = 2 t x (2) Fig. 2. Gas sensor geometry based on a TFBAR structure. In the case of a two-dimensional multi-layered structure, the solution of the system coupled with the two equations (3) and (6) becomes analytically very complex considering the embedding conditions at the boundaries of the structure and the electrical excitation. This makes necessary the use of a multiphysics simulator involving numerical methods (as the

3 163 Rafik Serhane et al.: FEM Modeling of Sensitive Layer Swelling Effect on Microbalance Gas Sensor Based on finite elements method, FEM) to solve the previous system [5]. We used the COMSOL Multiphysics tool to simulate the response of a gas sensor as a TFBAR having a sensitive polymer layer. The studied structure (200 µm long) is represented in Fig. 2. This shows a 6µm ZnO-layer sandwiched between two Al electrodes (200 nm of thickness). The considered sensitive polymer layer is the Polyisobutene (PIB) with a thickness of 400 nm. At the fixed ends of the structure, we use perfectly adaptive regions (PML, Perfectly Matched Layer) of L pml = 10 µm long in order to consider the absorption mechanism of mechanical waves which enables the minimization of reflections and mode conversions [6]. Table 1. Physical parameters used in the simulation [7, 8]. Density ρ (kg/m 3 ) Young modulus E (GPa) Poisson ratio ν PIB Al In Table (1) are given the polymer and Aluminum electrode parameters used in the simulation: The relative dielectric constant of the polymer is 2.2, and its electrical conductivity σ is of 3.55Ω.m. Losses in the form of attenuation coefficient η= 0.001, directly linked to the mechanical quality factor (η=1/(2.q)), are also introduced in the model. The electrical response curve (input admittance denoted by Y 11 ) of the sensor in absence of gas is presented in Fig. 3. This curve looks like that of the one-dimensional model [4] but here, we note the presence of some parasitic modes caused by the transverse waves propagation along the structure, which leads to the establishment of standing waves for specific frequencies. Viewing the mechanical displacement profile, high-order harmonics show further resonance peaks in the electrical admittance curve of the TFBAR resonator. Fig. 3. Electrical input admittance (Y 11) of the device in absence of gas. Due to the imposed embedding conditions, the mechanical displacement amplitude at the ends of the structure is zero at all frequencies. The structure vibrates in thickness mode, at the resonance frequency (f r =491.2 MHz, see Fig. 4), the maximum magnitude of the mechanical displacement (about 2.3 nm) is obtained at the center of the membrane.

4 Journal of Materials Sciences and Applications 2015; 1(4): The partition constant of the couple (/CH 2 Cl 2 and PIB) used in our simulation is given in terms of log(k p ) and is equal to When the polymer adsorbs the gas, its density changes according to two models, the first one considers only the polymer density change as follows [1]: ρ = ρ + ρ (8) polymer+gas polymer The second one considers the swelling effect of the polymer [9, 10], where the density and the thickness of the polymer change simultaneously according to the relations (9) and (10) respectively. ρ polymer+gas = ρ polymer + K C p 1 + K C / ρ p v v v (9) and, Fig. 4. The mechanical displacement field at the resonance frequency (fundamental thickness mode, f r=491.2 MHz) Principle of Gas Adsorption by a Polymer The principle of gas detection is based on the variation in the mechanical parameters of the resonator such as the polymer thickness and density (mass loading) and/or its elastic constants (Young modulus and Poisson ratio). The mechanical characteristics of the PIB are listed in Table (1) and its density ρ polymer is 918 kg/m 3. The reaction between the considered gas and the polymer is characterized by a constant denoted K p and known as the partition constant which is the ratio between the gas concentration in the polymer phase C p at a steady state and its concentration in the gas (vapor) phase C v (See Fig. 5), K p is given by the relation (7): K p =C p /C v (7) h = h (1 + K C / ρ ) (10) polymer+gas 0 p v v Where ρ v represents the density of the adsorbed gas and h0 the initial polymer thickness. In the model (1), the additional density due to the gas adsorption (relation 9) is given by: ρ = C M (11) Where M gas is the molar mass of the gas. Using the relation (7), the relation (11) becomes: p gas ρ = K pcvm gas (12) In a constant volume, the gas flow, expressed by the number of ppm N ppm (ppm: parts per million) is a normalized concentration of the gas given by the ratio between the volume concentration C v of gas and the concentration C as follows: N ppm = ngas( Vapor) Cv n = C (13) n gas and n represent the mole number of the gas and the, respectively. Using the ideal gas law PV = nrt, the concentration is: C n P = = V RT (14) Finally, using the two previous relations (13) and (14), the relation (12) becomes: P ρ = K pm gas N ppm (15) RT Fig. 5. Schematic representation of gas partioning in the sensitive polymer layer. According to the relation (15), the additional density due to the gas adsorption is a function of the partition constant of the couple (gas and polymer) as well as of the pressure and the ambient temperature.

5 165 Rafik Serhane et al.: FEM Modeling of Sensitive Layer Swelling Effect on Microbalance Gas Sensor Based on 4. Results and Discussion In the first model (equation 8), the polymer density increases with gas concentration as shown in figure (6). However, in the second model (equation 9), it decreases because of the swelling effect described by the equation (10). 14 x Model 2 Model 1 Y (Ω -1 ) Without polymer Polymer coated Polymer density (Kg/m 3 ) Gas concentration in the (ppm) Fig. 6. PIB density variations versus CH 2Cl 2 gas concentration. The inspection of mass loading variations given in Fig. 7 shows that the adsorbed mass of gas increases with the gas concentration in both models. Despite the fact that in the second model the mass loading (Fig. 7) rises with the gas concentration, the corresponding polymer density decreases (see Fig. 6) as a consequence of the increase of the polymer volume. Adsorbed mass (µg) Gas concentration in the (ppm) Model 2 Model 1 Fig. 7. Comparison of the swelling and non swelling mass loading models. We represent in Fig. 8 the electrical response (input admittance) of the sensor coated with a PIB polymer and that of the uncoated resonator. Fig. 8. Effect of the polymer coating on the electrical input admittance. Even in the absence of gas, the polymer exerts a mechanical load on the TFBAR resonator that shifts the electrical admittance curve towards the low frequencies. The frequency shift for 0.4 µm of polymer thickness is about 5.7 MHz The Sensor Response Y (Ω -1 ) Y (Ω -1 ) x f(hz) x f(hz) x x 10-5 (a) 10 ppm 10 2 ppm 10 3 ppm ppm 10 4 ppm ppm 10 5 ppm 10 ppm 10 2 ppm 10 3 ppm ppm 10 4 ppm ppm 10 5 ppm f(hz) x 10 8 (b) Fig. 9. Influence of the gas concentration on the electrical response of the sensor : (a) 1 st model, and (b) 2 nd model.

6 Journal of Materials Sciences and Applications 2015; 1(4): In the presence of the gas, the polymer mass will increase by adsorption and the admittance curve will shift more towards the low frequencies (Fig. 9). Here, the sensor is exposed to varying concentrations (N ppm ) of the CH 2 Cl 2 gas in the at ambient temperature and at atmospheric pressure. If we look at the electrical admittance curve near the anti-resonance frequency (f r =511.3MHz), it is easy to note the decrease of the resonance frequency with the gas concentration (number of inected ppms) for both models (see Fig. 9.a and 9.b). This trend is shown in Fig. 10, and the shift in frequency, for 10 4 ppm of the gas, is about 60 khz for model (1) and 300 khz for model (2) The Sensor Sensitivity The sensitivity is a parameter expressing the variation in the sensor response (resonance frequency in our case) in function of the variation in gas concentration. A sensor is said to be sensitive if a small change in the gas concentration leads to an important change in the output signal. Therefore, the sensitivity S is defined by [11]: f S = r (16) C Where S is the sensitivity, f r (Hz) is the resonance frequency of the sensor (output parameter) and C (ppm) the concentration of the gas (input parameter). The difference between each anti-resonance frequency and the reference anti-resonance frequency f 0 =511.3 MHz (determined at 0 ppm) is plotted in Fig.10 as function of the gas concentration in the. The curve presents a linear change and the slope represents the sensor sensitivity. It is about 0.64 Hz/ppm for the model (1) and 2.98 Hz/ppm for the model (2), this later is in the same order of magnitude of the experimental results presented by Zhao et al. [5] and Ho et al. [7]. Fig. 10. Sensitivity of the sensor to the CH 2Cl 2 gas. 5. Conclusion A micro-gravimetric sensor, based on the use of the Al/ZnO/Al TFBAR structure (with thicknesses of 0.2 µm /6 µm /0.2 µm respectively) coated with 0.4 µm sensitive polymer layer (PIB) is presented. The structure works as a CH 2 Cl 2 gas sensor in the normal conditions of pressure and temperature. The electrical response of the sensor presented by the electrical input admittance has shown a resonance frequency at MHz and an anti-resonance frequency at MHz. The maximum mechanical displacement of the fundamental thickness mode is evaluated at 2.3 nm. The comparison of the two adsorption models describing respectively the swelling and non swelling mechanisms shows that the first model is more appropriate for describing the real sensitivity of the device, which is about 3 Hz/ppm. Acknowledgments This work was supported by the Algeria Ministry of Higher Education and Scientific Research, under the National Funding of Research (FNR), contract number: AWR2P/MEMS/DMN/CDTA/2015. References [1] N.J.R. Munira and K. Sathesh, 3D Modeling of a surface acoustic wave based sensor, Elixir Adv. Engg. Info. 40 (2011) [2] J.W. Grate and E.T. Zellers, The Fractional Free Volume of the Sorbed Vapor in Modeling the Viscoelastic Contribution to Polymer-Coated Surface Acoustic Wave Vapor Sensor Responses, Anal. Chem, 72 (2000) [3] S.M. Chang, H. Muramatsu, C. Nakamura, and J. Miyake, The principle and applications of piezoelectric crystal sensors, Materials Science and Engineering C 12_ [4] D. Royer et E. Dieulesaint, Ondes Elastiques dans les Solides, tome 2 : Génération, interaction acousto-optique, applications, ed. Masson, Paris, [5] Y.G. Zhao, M. Liu, D.M. Li, J.J. Li, J.B. Niu, FEM modeling of SAW organic vapor sensors, Sensors and Actuators A, 154 (2009) [6] T. Makkonen, A. Holappa, J. Ella and, M.M. Salomea, Finite element simulations of thin-film composite BAW resonators, IEEE Trans. on Ultras. Ferro. and Freq. Cont., 48 5(2001) [7] C.K. Ho, E.R. Lindgren, K.S. Rawlinson, L.K. McGrath and J.L. Wright, Developement of a surface Acoustic Wave Sensor for In-Situ Monitoring of Volatile Organic Compounds, Sensors, 3(2003) [8] S. Ahmadi, F. Hassani, C. Korman, M. Rahaman and M. Zaghloul, Characterization of multi-and single-layer structure SAW sensor [gas sensor], Sensors 2004, Proceedings of IEEE, 3(2004) [9] S.J. Martin' and G.C. Frye, Dynamics and Response of Polymer-Coated Surface Acoustic Wave Devices: Effect of Viscoelastic Properties and Film Resonance, Anal. Chem., 66(1994) [10] J. Kondoh, S. Shiokawa, M. Rapp and S. Stier, Simulation of Viscoelastic Effects of Polymer Coatings on Surface Acoustic Wave Gas Sensor under Consideration of Film Thickness, Jpn. J. Appl. Phys., 37(1998)

7 167 Rafik Serhane et al.: FEM Modeling of Sensitive Layer Swelling Effect on Microbalance Gas Sensor Based on [11] S.M. Chang, E. Tamiya and I. Karube, Chemical Vapour Sensor using a SAW Resonator Biosensors 13 Bioelectmnics, 6(1991) 9-14.