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Material selection for microcantilever.

S
Shubham Jain

This report analyzes different materials for coating micro cantilevers using Ashby's material selection approach. It determines that the optimal cantilever shape is tapered V or trapezoidal. Key performance indices like resonant frequency, deflection, and sensitivity are defined. Material properties like density, Young's modulus, and Poisson's ratio are plotted against each other for various materials. The plots show that SU8, aluminum, and silicon oxide satisfy the constraints of high frequency and sensitivity due to their lower modulus and density. Between these, aluminum provides the highest Poisson's ratio and is therefore concluded to be the best coating material, followed by SU8 and silicon oxide.

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Study Project Final Report Material Selection for Micro Cantilevers Using Ashbys Approach Submitted to: Dr. Navneet Gupta Submitted by: Shubham Jain 2013A3PS261P f2013261@pilani.bits-pilani.ac.in shubhamjainxi@gmail.com BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI CAMPUS
Abstract: Conventionally, most of the materials incorporated in MEMS devices belong to the silicon material system, which is the basis of the integrated circuit industry. However, new techniques are being explored and developed, and the opportunities for MEMS materials selection are getting broader. This report determines the optimum geometry of micro cantilever and presents the study of micro cantilevers coated with different materials, and analyze their performances in terms of deflection and shift in resonance frequency due to additional mass of analyte. The results of these studies can be used to increase the sensitivity of these devices. The present report tries to determine optimum material for micro cantilever sensors using Ashbys approach. 1. Introduction Micro cantilever beams are being used for fabricating high performance chemical and biological sensors. These sensors have a wide range of applicability in defense and medical fields. Micromechanical cantilever based sensors are reported to be used in varied applications ranging from physical, chemical to even biological fields. They operate on the basis of changes in the magnitude of surface-stresses when substance to be sensed (analyte) is adsorbed over the surface of cantilever. Consequently, it is important to find out ways of enhancing the sensitivity of the micro cantilever. This can be accomplished by optimizing combination of various parameters like choice of the materials, surface properties and geometric parameters. It is desirable to have sensitive micro cantilevers made of commonly and commercially available material. A well-established method of material selection is Ashbys Approach proposed by Ashby which is used in this report. The report is organized as follows: Section 2: Device Geometry. Section 3: Performance indices. Section 4: Material indices. Section 5: Ashbys Approach Section 6: Results and Discussion Section 7: Conclusion
2. Device Geometry Out of the various shapes reported in literature, the most popularly used shapes are: Rectangular shaped, T-shaped and V-shaped. These geometries were studied for variation in deflection and resonant frequency for different values of cantilever thickness. Shape-T was giving the maximum deflection for the same thickness and is more suitable for sensor operation in static mode as compared to other structures. For operation in the dynamic mode conventional rectangular shape gives the smallest mass sensitivity whereas V-shaped geometry gives almost eight times more mass sensitivity than the conventional rectangular shaped micro cantilever. But in case of V-shaped micro cantilever, it is difficult to fabricate sharp tip at the end, also narrow tip of V shape reduces the surface area available for sensor. So tapered V-shape (Trapezium) has been considered for the analysis, which shows sensitivity more than four times as compared to conventional rectangular micro cantilever. Hence by considering all the parameters optimum shape of cantilever beam for Bio-medical sensing application is tapered V shape or trapezoidal shape.
3. Performance Indices: Resonant frequency: Frequency of vibrations when analyte gets adsorbed on cantilever surface. = 巨 22 Here, E is youngs modulus of material. B is geometry factor d is thickness of cantilever. is density of material. l is length of cantilever. Also = 2 ; m is mass & k is spring constant, Hence change in frequency from f0 to f1 when there is change in mass of analyte adsorbed can be described by the equation: 1 1 2 1 0 2 = 42 From above equation It can be concluded that high fundamental frequencies are required for micro cantilever to achieve appreciable mass sensitivity. Frequency is inversely proportional to density of the material. Deflection: Amplitude of vibration of cantilever beam. = 4(1 )2 乞2 Here, is Poissons ratio is surface stress Higher value of deflection is desirable as it will be easier to detect and measure them. Amount of deflection is inversely proportional to Youngs modulus of the material. Also by Hookes Law F = -Kx, where F is the force applied and x is the deflection produced by that force.
Hence, deflection produced is inversely related to spring constant and in order to produce higher deflection a lower value of spring constant is desired. Sensitivity: It is the deflection produced per unit of stress induced. = ( 1 ＄ )( 1 ) Here C is constant; therefore, for higher value of sensitivity, density of material should be lower. Spring constant: = 乞ゐ3 43 Here, t is thickness of cantilever. Material with large value of Youngs modulus have higher value of spring constant. 4. Material Indices: Youngs modulus / elastic modulus. Density. Poissons ratio.
Material performance indices for several micromechanical elements Table 1: Silicon oxide Silicon nitride Si Ni Al Al2O3 SiC SU8 E(GPa) 70 250 168 207 69 393 430 3 (Kg/m3) 2200 3100 2330 8900 2710 3970 3300 1200 Poissons ratio 0.17 0.23 0.28 0.31 0.33 0.21 0.14 0.22 5. Ashbys Approach This approach involves comparing simultaneously the competing properties of various materials and choosing the material with optimum performance under given constraints. The four steps involved in this approach are: (i) Translation of design requirement (ii) Screening using constraints (iii) Ranking using objectives (iv) Seek supporting information and compare with experimental results. Here Ashbys Approach is used to find out the coating material with optimum Deflection and sensitivity.
Translation of Design Requirements as per Ashbys Approach Plot between density and youngs modulus (graph 1): Silicon oxide Silicon Nitride Si Ni Al Aluminium Oxide Silicon Carbide SU8 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 50 100 150 200 250 300 350 400 450 500 Density(Kg/m3) Young's Modulus (GPa) FUNCTION COATING MATERIAL Objective Minimize density. Minimize Youngs Modulus. Maximize Poissons ratio Constraints High resonant frequency. High deflection. High sensitivity. Free Variables Choice of materials.
Plot between Poissons ratio and youngs modulus (graph 2): 6. Results and Discussion: Based on the data given in Table 1, the interrelationship between material indices are plotted and shown in Graph 1 and Graph 2. Graph 1 shows the variation of density with Youngs modulus and Graph 2 shows the variation of Poissons ratio with Youngs modulus. It can be observed from the plots that SU8, silicon oxide and aluminum have a lower value of youngs modulus (0-70 GPa) and smaller density. Hence we found that SU8, silicon oxide and aluminum are the possible candidates that satisfy the constraints of high resonant frequency and high sensitivity. From graph 2 we observe that while silicon oxide and aluminum have nearly same value of Youngs modulus, aluminum has highest value of Poissons ratio among SU8, Silicon oxide and Aluminum. Hence between Silicon oxide and Aluminum, Aluminum is better material for micro cantilever coating. Also, while SU8 has lower value of Poissons ratio (0.22) than Aluminum (0.33), SU8 has much lesser value of Youngs modulus (3 GPa) than Silicon oxide Silicon Nitride Si Ni Al Aluminium Oxide Silicon Carbide SU8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 50 100 150 200 250 300 350 400 450 500 Poisson'sRatio Young's Modulus (GPa)
Aluminum (69 GPa). Therefore, based on above plots, it may be concluded that SU8 and Aluminum possess better performance indices as compared to others. 7.Conclusion: The key motivation for this study was to find out the coating material that provide best performance in micro cantilever based sensors. In this paper, certain performance indices and material indices were considered as the selection criteria for optimum geometry and material for micro cantilever. Optimum geometry for micro cantilever turned out to be trapezoidal shape. A methodology known as Ashbys Approach was adopted to find out the best coating material and based on this methodology various charts were plotted to compare different properties of competing materials. Using these charts, we conclude that we can arrange the coating materials in the ranking given below: 1. SU8. 2. Aluminum. 3. Silicon Oxide.
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Material selection for microcantilever.

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Material selection for microcantilever.

  • 1. Study Project Final Report Material Selection for Micro Cantilevers Using Ashbys Approach Submitted to: Dr. Navneet Gupta Submitted by: Shubham Jain 2013A3PS261P f2013261@pilani.bits-pilani.ac.in shubhamjainxi@gmail.com BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI CAMPUS
  • 2. Abstract: Conventionally, most of the materials incorporated in MEMS devices belong to the silicon material system, which is the basis of the integrated circuit industry. However, new techniques are being explored and developed, and the opportunities for MEMS materials selection are getting broader. This report determines the optimum geometry of micro cantilever and presents the study of micro cantilevers coated with different materials, and analyze their performances in terms of deflection and shift in resonance frequency due to additional mass of analyte. The results of these studies can be used to increase the sensitivity of these devices. The present report tries to determine optimum material for micro cantilever sensors using Ashbys approach. 1. Introduction Micro cantilever beams are being used for fabricating high performance chemical and biological sensors. These sensors have a wide range of applicability in defense and medical fields. Micromechanical cantilever based sensors are reported to be used in varied applications ranging from physical, chemical to even biological fields. They operate on the basis of changes in the magnitude of surface-stresses when substance to be sensed (analyte) is adsorbed over the surface of cantilever. Consequently, it is important to find out ways of enhancing the sensitivity of the micro cantilever. This can be accomplished by optimizing combination of various parameters like choice of the materials, surface properties and geometric parameters. It is desirable to have sensitive micro cantilevers made of commonly and commercially available material. A well-established method of material selection is Ashbys Approach proposed by Ashby which is used in this report. The report is organized as follows: Section 2: Device Geometry. Section 3: Performance indices. Section 4: Material indices. Section 5: Ashbys Approach Section 6: Results and Discussion Section 7: Conclusion
  • 3. 2. Device Geometry Out of the various shapes reported in literature, the most popularly used shapes are: Rectangular shaped, T-shaped and V-shaped. These geometries were studied for variation in deflection and resonant frequency for different values of cantilever thickness. Shape-T was giving the maximum deflection for the same thickness and is more suitable for sensor operation in static mode as compared to other structures. For operation in the dynamic mode conventional rectangular shape gives the smallest mass sensitivity whereas V-shaped geometry gives almost eight times more mass sensitivity than the conventional rectangular shaped micro cantilever. But in case of V-shaped micro cantilever, it is difficult to fabricate sharp tip at the end, also narrow tip of V shape reduces the surface area available for sensor. So tapered V-shape (Trapezium) has been considered for the analysis, which shows sensitivity more than four times as compared to conventional rectangular micro cantilever. Hence by considering all the parameters optimum shape of cantilever beam for Bio-medical sensing application is tapered V shape or trapezoidal shape.
  • 4. 3. Performance Indices: Resonant frequency: Frequency of vibrations when analyte gets adsorbed on cantilever surface. = 巨 22 Here, E is youngs modulus of material. B is geometry factor d is thickness of cantilever. is density of material. l is length of cantilever. Also = 2 ; m is mass & k is spring constant, Hence change in frequency from f0 to f1 when there is change in mass of analyte adsorbed can be described by the equation: 1 1 2 1 0 2 = 42 From above equation It can be concluded that high fundamental frequencies are required for micro cantilever to achieve appreciable mass sensitivity. Frequency is inversely proportional to density of the material. Deflection: Amplitude of vibration of cantilever beam. = 4(1 )2 乞2 Here, is Poissons ratio is surface stress Higher value of deflection is desirable as it will be easier to detect and measure them. Amount of deflection is inversely proportional to Youngs modulus of the material. Also by Hookes Law F = -Kx, where F is the force applied and x is the deflection produced by that force.
  • 5. Hence, deflection produced is inversely related to spring constant and in order to produce higher deflection a lower value of spring constant is desired. Sensitivity: It is the deflection produced per unit of stress induced. = ( 1 ＄ )( 1 ) Here C is constant; therefore, for higher value of sensitivity, density of material should be lower. Spring constant: = 乞ゐ3 43 Here, t is thickness of cantilever. Material with large value of Youngs modulus have higher value of spring constant. 4. Material Indices: Youngs modulus / elastic modulus. Density. Poissons ratio.
  • 6. Material performance indices for several micromechanical elements Table 1: Silicon oxide Silicon nitride Si Ni Al Al2O3 SiC SU8 E(GPa) 70 250 168 207 69 393 430 3 (Kg/m3) 2200 3100 2330 8900 2710 3970 3300 1200 Poissons ratio 0.17 0.23 0.28 0.31 0.33 0.21 0.14 0.22 5. Ashbys Approach This approach involves comparing simultaneously the competing properties of various materials and choosing the material with optimum performance under given constraints. The four steps involved in this approach are: (i) Translation of design requirement (ii) Screening using constraints (iii) Ranking using objectives (iv) Seek supporting information and compare with experimental results. Here Ashbys Approach is used to find out the coating material with optimum Deflection and sensitivity.
  • 7. Translation of Design Requirements as per Ashbys Approach Plot between density and youngs modulus (graph 1): Silicon oxide Silicon Nitride Si Ni Al Aluminium Oxide Silicon Carbide SU8 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 50 100 150 200 250 300 350 400 450 500 Density(Kg/m3) Young's Modulus (GPa) FUNCTION COATING MATERIAL Objective Minimize density. Minimize Youngs Modulus. Maximize Poissons ratio Constraints High resonant frequency. High deflection. High sensitivity. Free Variables Choice of materials.
  • 8. Plot between Poissons ratio and youngs modulus (graph 2): 6. Results and Discussion: Based on the data given in Table 1, the interrelationship between material indices are plotted and shown in Graph 1 and Graph 2. Graph 1 shows the variation of density with Youngs modulus and Graph 2 shows the variation of Poissons ratio with Youngs modulus. It can be observed from the plots that SU8, silicon oxide and aluminum have a lower value of youngs modulus (0-70 GPa) and smaller density. Hence we found that SU8, silicon oxide and aluminum are the possible candidates that satisfy the constraints of high resonant frequency and high sensitivity. From graph 2 we observe that while silicon oxide and aluminum have nearly same value of Youngs modulus, aluminum has highest value of Poissons ratio among SU8, Silicon oxide and Aluminum. Hence between Silicon oxide and Aluminum, Aluminum is better material for micro cantilever coating. Also, while SU8 has lower value of Poissons ratio (0.22) than Aluminum (0.33), SU8 has much lesser value of Youngs modulus (3 GPa) than Silicon oxide Silicon Nitride Si Ni Al Aluminium Oxide Silicon Carbide SU8 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 50 100 150 200 250 300 350 400 450 500 Poisson'sRatio Young's Modulus (GPa)
  • 9. Aluminum (69 GPa). Therefore, based on above plots, it may be concluded that SU8 and Aluminum possess better performance indices as compared to others. 7.Conclusion: The key motivation for this study was to find out the coating material that provide best performance in micro cantilever based sensors. In this paper, certain performance indices and material indices were considered as the selection criteria for optimum geometry and material for micro cantilever. Optimum geometry for micro cantilever turned out to be trapezoidal shape. A methodology known as Ashbys Approach was adopted to find out the best coating material and based on this methodology various charts were plotted to compare different properties of competing materials. Using these charts, we conclude that we can arrange the coating materials in the ranking given below: 1. SU8. 2. Aluminum. 3. Silicon Oxide.