MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Today ’ s Presentation Contents MEMS Comb Drive Actuator to Vary Tension & Compression of a Resonating Nano-Doubly Clamped Beam for High-Resolution & High Sensitivity Mass Detection Theory & Design GROUP D Fabrication Adam Hurst 1 John Regis 1 Chou Ying-Chi 1 Packaging Andrew Lie 2 Adrian Podpirka 3 1. Graduate Student in Mechanical Engineering, Columbia University 2. Undergraduate in Mechanical Engineering, Columbia University 3. Undergraduate in Material Science and Engineering, Columbia University
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Overview Contents Today ’ s presentation will cover the following : • Application & Functionality Theory & Design • Types of Actuators • Theory behind selected Actuator Fabrication • Thermal Time Constant Packaging • Fabrication • Packaging • Questions
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D NEMS Resonating Beam Contents • Applications - Hyper-sensitive mass detector (hydrogen sensor) Theory & Design - Anti bio-terrorism (organic compound sensor) - Mechanical signal processing - Parametric Amplification Fabrication • Functionality Packaging - NEMS Doubly-clamped Au/Pd beam (10 microns x 80nm x 100nm) - Resonant frequency shifts as a result of mass loading - Detection of frequency shift through magneto-motive technique - Frequency shift corresponds to loading or beam dimension changes
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D MEMS Device for Adjusting Tension of NEMS Resonators • Motivation Contents - Residual tensile stresses in beam due to fabrication - Increased sensitivity under compressive loading Theory & Design - Desired loading +/- 200Mpa • MEMS Actuators Fabrication - Capacitance-driven electrostatic actuator - Advantage: Easy fabrication Packaging - Disadvantage: Non-linear relationship between input voltage and resultant force/displacement - Magneto-motive actuator - Disadvantage: Semi-linear relationship between input voltage and resultant force/displacement - Comb drive electrostatic actuator - Advantage: Linear relationship between input voltage and resultant force/displacement, simple fabrication
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Proposed Comb Drive Design Contents Theory & Design Fabrication Packaging
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Comb Drive Design Contents Theory & Design Fabrication Packaging
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents Resonating Beam Equations: Required Force on beam is given by: (P = +/- 200MPa) Theory & Design F P = F = 1.6 micro N A Au / Pd Fabrication Beam axial deflection under +/- 200 MPa: Packaging E A E A + E Au Au Pd Pd = eAu / Pd A A + Au Pd σ L L Δ = L = 25.6nm 0 E Au / Pd
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents Comb Drive Equations: Energy in charged parallel plates: Theory & Design 2 1 AV ε ε r 0 U = 2 d Fabrication Differentiating with respect to x (lateral direction): Packaging 2 wV ε ε r 0 F = x d
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents Comb Drive Equations: Side Instability Voltage: Theory & Design d 2 k y y o 2 y o k x + d 2 V SI = 2 f o bn 2 k y - d d n Fabrication Packaging Beams supporting suspended comb drive resonator structure: 3 4 E bh F F k x k e = ⋅ 2 3 v ( x ) ( 3 x L x ) x = = − x eff 3 L 6 E I eAu / Pd (Assumed to be cantilever beams)
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents Critical Dimensions Based on Governing Equations: Comb Drive (50 Fingers): 2 µm x 5 µ m x 8 µ m Theory & Design Cantilevered Support Beams: 2 µm x 5 µ m x 50 µ m Fabrication Vertical Displacement due Packaging gravity (into page): 96.7pico-m Side instability voltage: 1320V
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents Voltage Input vs. Force: Voltage Input vs. Comb Drive Lateral Force Theory & Design Force Dependence on Voltage 200MPa on Beam 1.60E-05 1.40E-05 Fabrication 1.20E-05 Comb Drive Lateral Force (N) 1.00E-05 Packaging 8.00E-06 6.00E-06 4.00E-06 2.00E-06 0.00E+00 0 20 40 60 80 100 120 140 160 Voltage (V)
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents Voltage Input vs. Lateral Displacement: Voltage vs. Lateral Displacement Theory & Design Lateral Displacement Dependence on Voltage Lateral Displacement at 200MPa 40 35 Fabrication 30 Lateral Displacement (nm) 25 Packaging 20 15 10 5 0 0 20 40 60 80 100 120 140 160 Voltage (V)
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design: Thermal Time Constant Contents Thermal Time Constant: • Thermal time constant of an actuator is the measure of time required for Theory & Design actuator to cool to ambient temperature following actuation. • Speed at which frequency of the beam can be tuned is highly dependant Fabrication on time constant. Q ( x , t ) 2 u - k dx 2 2 2 u = • Heat Flow Equation: 2 t C p Packaging • Applied DC Current: I = (Io)*(t); I 2 = (Io) 2 *(t) Thus, Q(x,t) = ((Io) 2 *(t)*(R))/(h*w*L) • Boundary conditions (1-D): u(0,t)=T w ; u(L,t)=T w Initial condition: u(x,0)=T w
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design: Thermal Time Constant Contents • New function: v(x,t)=u(x,t)-T w v(0,t)=T w -T w =0; v(L,t)=T w -T w =0; Theory & Design v(x,0)=T w -T w =0 2 v - k dx 2 2 2 v = Q ( x , t ) • New Heat Flow Equation: Fabrication 2 t B . C .(1): v (0, t ) = 0 B . C .(2): v ( L , t ) = 0 Packaging I . C .: v ( x ,0) = 0 • Eigen-function Expansion: 3 / a n ( t ) z n ( x ) v ( x , t ) = n =1 n r x ) where z n ( x ) = sin( L
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Theory & Design of Comb Drive Electrostatic Actuator Contents • Sturm-Liouville • Eigenfunction Expansion<->Heat Flow equation Generalized Fourier Series for Q(x,t). Theory & Design • Rules of orthogonally (to solve for Fourier coefficients): L # Q ( x , t ) z n ( x ) dx Fabrication da n + m n ka n = 0 / q n ( t ) dt L # Q n 2 ( x ) dx 0 Packaging 3 / q n ( t ) z n ( x ) where Q ( x , t ) = n =1 • Orthogonally equation continuous. To make it integratable, use the Integrating Factor: e _ nkt Fourier Coefficient solved Longest time to reach steady state (n=1 eigenmode) Thermal time constant = 0.169 micro-seconds
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Fabrication Contents Mask #1: Au/Pd Contacts and Beam Mask #2: RIE Comb Drives Theory & Design Fabrication Packaging Close-Up View
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Fabrication Contents Process Flow Step Description Starting Material SOI (5 µ m-1 µ m-125 µ m) Clean Standard RCA clean Theory & Design Photo Resist Spin on photoresist PhotolithographyMask #1 (contacts) develop Remove area for contact and beam placement clean Standard RCA clean E-beam evap. Au/Pd e-beam evaporation to a depth of 80nm Fabrication strip Remove photoresist clean Stardard RCA clean Photo Resist Spin on photoresist PhotolithographyMask #2 (basic structure) develop Develop and remove used photoresist Packaging etch RIE to Silicon Dioxide surface strip Remove photoresist clean Standard RCA clean Optional - if by using SEM we notice the the underside of the beam is not cut, we will purge Etch (optional) the system with XeF2 clean Standard RCA clean Etch 5:1 BOE etch Drying Supercritical CO2 drying Clean Standard RCA clean Contacts Place contacts. Wire bond to package. Test Test structure Mount Pryrex mount Test Test structure
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Proposed Comb Drive Design Contents Theory & Design Fabrication Packaging
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Fabrication to Packaging Contents Theory & Design Fabrication Packaging
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Packaging Solution Contents Theory & Design Fabrication Packaging
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Packaging Contents Theory & Design Fabrication Packaging
MECE E4212 FALL ‘05 MEMS DESIGN PROJECT GROUP D Conclusion Contents • For this application, comb-drive actuator is superior to other mechanisms Theory & Design • Design will allow accurate and feasible application Fabrication • Design will be relatively easy to fabricate using Columbia University resources Packaging • Future Improvements: Feed back loop to determine distance traveled by block structure
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