Simulation and design of piezoelectric microcantilever chemical sensors

Transcription

1 Sensors and Actuators A 125 (2005) Simulation and design of piezoelectric microcantilever chemical sensors Wei Zhou a, Abdul Khaliq a, Yanjun Tang a, Haifeng Ji a,c, Rastko R. Selmic a,b, a Institute for Micromanufacturing, Louisiana Tech University, Ruston LA 71272, USA b Department of Electrical Engineering, Louisiana Tech University, Ruston LA 71272, USA c Department of Chemistry, Louisiana Tech University, Ruston LA 71272, USA Received 17 May 2004; accepted 21 July 2005 Available online 1 September 2005 Abstract This paper presents an analytical modeling of a piezoelectric multi-layer cantilever used as a micro-electro-mechanical-system (MEMS) chemical sensor. Selectively coated microcantilevers have been developed for highly sensitive chemical sensor applications. The proposed piezoelectric chemical sensor consists of an array of multi-layer piezoelectric cantilevers with voltage output in the millivolt range that replaces the conventional laser-based position-sensitive detection systems. The sensing principle is based upon changes in the deflection induced by environmental factors in the medium where a microcantilever is immersed. Bending of the cantilever induces the potential difference on opposite sides of the piezoelectric layer providing an information signal about the detected chemicals. To obtain an application specific optimum design parameters and predict the cantilever performance ahead of actual fabrication, finite element analysis (FEM) simulations using CoventorWare (a MEMS design and simulation program) were performed. Analytical models of multi-layer cantilevers as well as simulation concept are described. Both mechanical and piezoelectric simulation results are carried out. The cantilever structures are analyzed and fabrication process steps are proposed Elsevier B.V. All rights reserved. Keywords: Microcantilever; MEMS; Piezoelectric; Chemical sensor; Cantilever; MEMS simulation 1. Introduction There has been a growing interest in piezoelectric thin films applied in variety of MEMS devices. These piezoelectric MEMS devices may take a form of individual or distributed mini-actuators or sensors. Highly sensitive MEMS chemical sensors with position-sensitive detector (PSD) have been developed, as shown in Fig. 1. In order to replace traditional laser-based PSD devices and design sensors that can be used in the field, novel chemical sensors based on piezoelectric principle have been studied. The novel sensors offer many advantages including higher sensitivities, simplified sensing systems, lower costs, and do not require complex and bulky PSDs. Corresponding author. Tel.: ; fax: address: rselmic@latech.edu (R.R. Selmic). URL: rselmic/. Smits and Choi [1] presented electromechanical characteristics of a heterogeneous piezoelectric bender subjected to various electrical and mechanical boundary conditions: a mechanical moment at the end of the bender, a force applied perpendicular to the tip of the bender, and a uniform load applied over the entire length of the bender. Cheng et al. [2] developed a model of multilayer piezoelectric cantilever beam micro-mirror and micro-laser arrays and used them in the closed-loop control structure in order to improve the mirror effectiveness. Zhang and Sun [3] described the relation between minimum detectable force gradients and level dimensions in non contact scanning force microscopy using piezoelectric microcantilever. Meng et al. generalized analytical formulation of mechanical formation of the piezoelectric laminated micro actuators [4]. There is a need for highly accurate and efficient modeling of the piezoelectric devices that can be used in a design stage [9 11,14]. Finite element analysis simulations using CoventorWare have been carried out in this study to pre /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.sna

2 70 W. Zhou et al. / Sensors and Actuators A 125 (2005) Fig. 3. Side view of piezoelectric multi-layer cantilever. Fig. 1. Chemical sensing using laser-based position detection system. Fig. 2. Proposed piezoelectric sensing systems. dict the static and dynamic performance of the multi-layer cantilever models that are built based on the geometry of a previously developed SiO 2 -based cantilevers. Both mechanical and piezoelectric analyses have been conducted for the perfectly bonded case of the cantilever over the range of the differential surface stress values to which the devices will be exposed during the chemical detection process. The current design and operational principles are outlined in this paper. The simulation results demonstrate the output voltage characteristics of the piezoelectric sensor and the optimum design parameters for our application. As shown in Fig. 2, the output voltage signal of the piezoelectric cantilever will be processed by an application-specific integrated circuit, and then transmitted through wireless sensor network to the computer base station for the monitoring purpose [5,6]. 2. Theoretical considerations There is no standard procedure to determine the electromechanical parameters of piezoelectric structures. In this paper, two different approaches have been used to study the parameters of the multi-layer cantilevers and to predict their performance during the chemical detection process. The first approach uses theoretical relationship between differential surface stress and tip displacement during the chemical reaction at the top layer of the cantilever. The relationship between the piezoelectric tip displacement and the induced voltage level is provided. In the second approach, FEM simulations by CoventorWare have been performed on multi-layer cantilevers (structure shown in Fig. 3) with the cantilever beam consisting of the following layers from the bottom up: SiO 2, Pt, Si 3 N 4, piezoelectric material (ZnO), Pt, and chemical recognition agent deposited on the top of Pt. These layers have the same geometry and dimensions but different thicknesses. In a chemical detection process, a recognition agent on the top of the cantilever reacts with the targeted chemicals in the air, soil, or solution (examples include relative humidity, mercury vapor and antibody antigen interactions), which would induce surface stress on the top of cantilever, resulting in a tip deflection of the cantilever beam [7]. Sensitive detection of chemicals is achieved by measuring the deflection induced voltage generated in the piezoelectric layer. Table 1 shows the materials and their functions used in the microcantilever design. Piezoelectric materials strain when exposed to a voltage and, conversely, electrical charge accumulates on opposing surfaces and produces a voltage when strained by an external force [7]. This is due to the permanent dipole nature of these materials. When chemical interactions occur on the top of the cantilever, the tip displacement z caused by the differential surface stress s can be written as [8] 3(1 v)l2 z = T 2 s, (1) E where L is the length of the cantilever, T the overall cantilever thickness, v the Poisson ratio, s the differential surface stress, and E the Young s module. Assuming a thin piezoelectric layer on a thick elastic substrate and without the external force or moment [2], the relationship between the cantilever tip displacement and the corresponding voltage is given by 3L 2 E p z = d 31 T 2 V, (2) E e where V is the voltage generated or applied on the piezoelectric layer, d 31 the piezoelectric constant of the piezoelectric material, E p and E e are the Young s modules of elasticity for the piezoelectric and elastic materials, respectively. Note that the thin piezoelectric layer is assumed and that the thickness of the elastic material is approximated with the thickness of the whole cantilever beam. Table 1 Description of cantilever layers Material Function SiO 2 Flexible basic layer of the cantilever beam Platinum Electrodes of piezoelectric layer Si 3 N 4 Used to cancel the initial charges in the cantilever beam Piezoelectric Piezoelectric layer

3 From Eq. (2) one can express the induced voltage V in terms of the tip displacement z as W. Zhou et al. / Sensors and Actuators A 125 (2005) V = T 2 E e 3d 31 L 2 z. (3) E p Considering the Young s module E in Eq. (1) as the equivalent Young s module of the whole multilayer beam, we can combine (3) and (1) such as V = T 2 E e 3(1 v)l 2 3d 31 L 2 E p T 2 s (4) E E e (1 v) V = s. (5) d 31 E p E Using the microcantilever chemical sensor developed at Louisiana Tech University [13] with the laser-based PSD system, experimental data have shown that the range of the possible cantilever displacement values is from several nanometers to 1 m, depending on the level of the chemical reaction on the top of cantilever and the structure of the cantilever sensor. According to the experimental data and Eq. (1), for a cantilever with a length, width, and thickness of 180, 30, and 1 m, respectively, regular differential surface stress s on the cantilever during the chemical detection process is found to be and N/m for the tip displacement of 35 and 120 nm, respectively. The maximum displacement on such cantilever is smaller than 1 m [12,13]. 3. Finite element analysis using CoventorWare Finite element analysis program CoventorWare is chosen as the simulation tool in this study because of its unique capabilities in MEMS design, simulation, and modeling. CoventorWare is a fully integrated MEMS design environment. It allows users to bypass computationally intensive tools during the initial research and design stages, to efficiently explore designs, and to converge on a design that has the highest probability of success. The advanced functions offered by CoventorWare significantly increase the efficiency of our designing process and reduce the development cost. In this simulation, a few assumptions have been made. The clamped end of the cantilever is defined at the origin of the x-axis. (1) Interfaces between layers are continuous and do not slip with respect to one another. (2) Every layer of the cantilever is in the static equilibrium. (3) Every layer is defined as a rectangular solid with the same length L and width W. The thickness of each layer is different from the rest. (4) All stresses are in the X Y plane. The average surface stress in the X Y plane is defined as s. (5) One end of the cantilever is defined as the origin of the X-direction. This is also consistent with the boundary conditions. Fig. 4. Meshed model of multi-layer cantilever. (6) All piezoelectric layers have already been polarized and the driving voltage will not change the polarization. Shell elements were used to model the cantilever, while mechanical and piezoelectric properties were introduced through the CoventorWare material database. In the mechanical analysis pressure forces with values derived from theoretical results are applied on the top of the cantilever nodes. Fine meshing was chosen for all devices varying between 15,000 and 35,000 elements. For instance, to obtain a solution in the modal analysis with a meshed model of a cantilever with dimensions 200 m 50 m (L W) and 1 m thickness would take about 15 min on Pentium IV computer. A fine meshed model of the multi-layer cantilever used in this simulation is shown in Fig. 4. A simple silicon cantilever model corresponding to existing Louisiana Tech s microcantilever sensor has been developed to determine the range of induced stress values during the chemical reaction on the top of cantilever beam. During the chemical agent detection process chemicals on the cantilever surface react with the target components, resulting in a surface stress on the top of the cantilever. In this study, the simulated stress values are applied on multi-layer cantilever models while displacements and piezoelectric induced voltages are measured as the resulting output values in the simulation process. The parameter study analysis using CoventorWare is employed to determine the change of the displacement at the tip of a cantilever and the induced voltage in the piezoelectric layer under different conditions. The first analysis aims to study the cantilever behavior under different chemical interactions by applying a linearly changing stress in X Y plane on the top of the cantilever model. The second analysis considers a linearly changing thickness of the multi-layer cantilever to determine the optimal cantilever parameters for the future fabrication steps. 4. Results and discussions 4.1. Single-layer cantilever model As shown in Fig. 5, a simple single-layer SiO 2 cantilever model is built to estimate the induced differential surface

4 72 W. Zhou et al. / Sensors and Actuators A 125 (2005) Fig. 5. Single-layer cantilever. stress values during the chemical reaction on the top of a cantilever. The cantilever length, width, and thickness are 180, 30, and 1 m, respectively, which correspond to the dimensions of the laboratory-developed cantilevers used in the PSD-based sensing system. CoventorWare does not allow a surface stress to be specified as the system input physical value. Instead, we have used the stress at the surface in X and Y directions with the units of MPa. In the simulation this stress at the cantilever surface is specified as the input on the top layer of the cantilever. The input values of the stress in X and Y direction cannot be arbitrarily chosen. We chose them to match experimental data for the cantilever displacement. This process provides us with the stress at the surface that corresponds to the surface stress appearing on the real microcantilever during the chemical detection process. The tip displacement of the cantilever varies with applied stress at the surface during the chemical detection process. The possible tip displacement values are between several nanometers to one micrometer according to the experimental data and the commonly observed value is from 20 to 500 nm. In order to evaluate the input stress values, we apply this displacement condition in the FEM mechanical simulations on the simple cantilever model. Equivalent stress at the surface condition is obtained such that 3 MPa of the stress in both X and Y directions on the top surface causes cantilever deflection of about 200 nm, 30 MPa causes around 1 m deflection. Fig. 6 shows the displacement variations as the X Y stress changes in the range from 0 to 30 MPa. These stress values are applied in the following piezoelectric multilayer cantilever analysis to emulate the real experimental conditions. Fig. 6. Displacement analysis with linearly increasing surface stress for simple cantilever, structures 1 and 2. Table 2 Multi-layer cantilever profiles Unit ( m) Length Width SiO 2 Platinum Si 3 N 4 ZnO Structure Structure large piezoelectric coefficient. Two different microcantilever profiles are given in Table 2. The effects of the applied linearly changing stress (0 30 MPa) on the displacements in X, Y, and Z directions and their corresponding piezoelectric effect are shown in Fig. 6 for the cantilever beams, structures 1 and 2 (profiles given in Table 2). Fig. 7 shows the induced piezoelectric voltage are a result of the applied stress on structures 1 and 2. The voltage increases almost linearly with applied stress in the range of 0 30 MPa. Note that Eq. (5) also predicts that the voltage depends linearly with the surface stress on the cantilever Multi-layer cantilever model Piezoelectric multi-layer cantilever models are built using 3D solid elements and meshed by Manhattan Bricks method with feature size of two bricks units. The selected piezoelectric layer in this study is ZnO due to its relatively Fig. 7. Piezoelectric effect analysis for linearly increasing surface stress based on structures 1 and 2.

5 W. Zhou et al. / Sensors and Actuators A 125 (2005) Fig. 8. Displacement analysis for linearly increasing cantilever length. Fig. 10. Displacement analysis for linearly increasing ZnO layer thickness. The simulation results using two different cantilever models, structures 1 and 2, have been compared. One can see that applying the same stress on a 500 m long cantilever (structure 2) induces twice as much displacement in Z-direction and about one third of the voltage output comparing with a 200 m long cantilever with the same layer structure and materials (structure 1). The effects of a linearly increasing cantilever length on the displacement as well as the voltage output are described in Fig. 8 and Fig. 9. The simulation is based on a model with structure 1 and the stress of 15 MPa applied in both X and Y direction at the top of the cantilever. The length to width ratio of the cantilever is fixed to 4:1 in this simulation. The simulation results also show that the induced voltage on the piezoelectric layer decreases as the cantilever length increases (Fig. 9). As mentioned above, the piezoelectric effect depends on the dimension, thickness, and the piezoelectric layer material properties of the microcantilever. The voltage output at the piezoelectric layer is proportional to the tip displacement with the factor of (T/L) 2. This means that with the increase of the piezoelectric layer, the output voltage will also increase. In order to illustrate the effects of changing thickness of the cantilever on the displacement and voltage output, parametric piezoelectric simulation procedure is carried out. During this simulation the thickness of the cantilever layers are simultaneously and linearly increased allowing us to keep the proper elastic layer thickness for support of the cantilever. The simulation is based on the structure 1 model and the stress of 15 MPa is applied in both X and Y directions at the top of the cantilever. The results are shown in Figs. 10 and 11. One can see that the voltage increased slowly when the thickness of ZnO reached certain level. We believe that there exists certain threshold value of piezoelectric layer thickness for different structures, which is one micrometer in a scenario of this study, as shown in Fig. 11. The slight discrepancy between theoretical and simulation results are due to the lower and Fig. 9. Piezoelectric effect analysis for linearly increasing cantilever length. Fig. 11. Piezoelectric effect analysis for linearly increasing ZnO layer thickness.

6 74 W. Zhou et al. / Sensors and Actuators A 125 (2005) Fig. 12. Fabrication steps for piezoelectric microcantilever chemical sensor. upper electrodes whose dimensions and the elastic parameters have been neglected in the calculation. Results shown in Fig. 11 will be used in a fabrication of the cantilever. For the sensor, maximum voltage output of mv that is recommended for the electronics interface in our particular application, 0.5 m of ZnO is suggested thickness of the piezoelectric layer. The cantilever sensor with thicker piezoelectric layer would provide even higher output voltage signal. That is not recommended, unless required by the electronics interface, since it would cause decreased sensor sensitivity and would add cost and complexity in fabrication. 5. Proposed fabrication process The piezoelectric microcantilever can be fabricated using the procedure illustrated in Fig. 12. The process flow starts with a silicon wafer and a thin SiO 2 layer. The pattern of microcantilever beam is transferred to the layer on one side by a standard lithography process to form a primary elastic layer of the cantilever structure. A thin layer of Pt is then deposited as the bottom electrode contact. Next, Si 3 N 4 is deposited to isolate the SiO 2 layer and the piezoelectric layer. Then Z n O films are deposited and patterned on the surface of the microcantilever beam via RF sputtering followed by thermal annealing at T = 500 C to reduce the highly compressive residual stress of the Z n O layer. Pt is then sputtered on the structure as the top electrode. Finally, the structures can be released using a photoresist mask to form the cantilever structure. 6. Conclusion It has been shown that the mechanical and piezoelectric characterization of a five-layer microcantilever can be carried out using MEMS design and simulation program Coventor- Ware. An analytical model is developed for the thin-film multi-layer microcantilever chemical sensor. Mechanical and piezoelectric simulations are implemented and the simulation results are confirmed with theoretical study for the perfectly bonded cantilever case. It is found that the design is feasible and the piezoelectric sensor would have a mv level voltage output during the simulated chemical detection process: from 8to14mVfora200 m long cantilever and m thick Z n O piezoelectric layer. This output satisfies the requirement of the application-specific integrated circuit of the proposed sensing system. Increasing the piezoelectric layer thickness or using other piezoelectric materials can provide even higher output voltage. But increasing the piezoelectric layer thickness beyond of what is needed in terms of voltage output is not recommended as it will cause a cantilever loss of sensitivity, increase in cost and fabrication complexity. The study improves the fabrication process and performance of the final piezoelectric sensor by providing preliminary design parameters of the piezoelectric microcantilever chemical sensor. References [1] J.G. Smits, W. Choi, The constituent equations of piezoelectric heterogeneous bimorph, IEEE Trans. Ultrason. Ferroelectr. Frequency Control 38 (3) (1991)

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Kim, Topics in finite-element modeling of piezoelectric MEMS devices, in: Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems, 2000, pp [13] H.F. Ji, R. Dabestani, E. Finot, T. Thundat, G.M. Brown, P.F. Britt, A noval self-assembled monolayer coated microcantilever for low level cesium detection, Chem. Commun. (2000) [14] M. Brissaud, S. Ledren, P. Gonnard, Modeling of a cantilever non-symmetric piezoelectric bimorph, J. Micromech. Microeng. 13 (2003) Biographies Wei Zhou received the BS degree in Electrical Engineering from Northern Jiaotong University, China, in He is currently a MS candidate in the Institute for Micromanufacturing and Electrical Engineering Department at Louisiana Tech University, Louisiana, USA. His Master thesis research topic is on the integration of MEMS sensors with wireless sensor networks. Abdul Khaliq received the BS degree in Electrical (Communication) Engineering from University of Engineering and Technology, Lahore, Pakistan, in 1994 and the MS degree in Electrical Engineering from Louisiana Tech University, in He is a research engineer at Institute for Micromanufacturing in Louisiana Tech University. His research interests are Micro-electronic devices design/simulation, TCAD, MEMS CAD, design and simulation of microfluidic devices, semiconductor device fabrication and characterization. Yanjun Tang received his BS (1992) in mechanical engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China. He has been working as a mechanical engineer in Chengdu Aircraft Industrial Corporation, Chengdu, China during the period of time His is currently a PhD candidate under the guidance of Dr. Hai-Feng Ji at Institute for Micromanufacturing of Louisiana Tech University. He is scheduled to defend his PhD thesis in April, Haifeng Ji is Assistant Professor of Chemistry since 2000 at Department of Chemistry and Institute for Micromanufacturing (IfM), Louisiana Tech University. He received his PhD from the Chinese Academy of Sciences in Beijing, China in After one year of postdoctoral study in Department of Chemistry, University of Florida, he moved to Oak Ridge National laboratory for two-and-half-year postdoctoral stay. Since 1995, he has published over 40 scientific papers in peer-reviewed journals on optical and micromechanical sensors. Currently his main research interests are in the combination of chem/bio microelectromechanical system (MEMs) and nanoelectromechanical system (NEMs). His webpage is hji. His address is hji@chem.latech. edu. Rastko R. Selmic received his BS (1994) in Electrical Engineering from University of Belgrade. In 1997, he received his Master s degree in Electrical Engineering and in 2000 PhD degree in Electrical Engineering, both from The University of Texas at Arlington. Since 2002, he has been Assistant Professor at Department of Electrical Engineering and Institute for Micromanufacturing at Louisiana Tech University. From 2000 to 2002 he was a senior DSP systems engineer in Signalogic, Inc. From 1995 to 2000, he was a graduate research assistant at Automation and Robotics Research Institute. His research interests are in MEMS wireless sensor networks, wireless sensors, nonlinear systems, and neural networks. He is the author/co-author of 2 book chapters, 30 journal and conference papers, textbook Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities, and the first US patent in intelligent actuator control in 2003.