Melih Papila, Piezoresistive microphone design Pareto optimization: Tradeoff between sensitivity and noise floor Melih PapilaMark Sheplak Raphael T. Haftka Toshikazu Nishida Multidisciplinary&Structural Optimization Group Interdisciplinary Microsystems Group

Melih Papila, 2 Outline  Design problem  Objective and methodology  Design variables and objective functions  Single and multi-objective optimization results  Parameter uncertainty  Concluding Remarks

Melih Papila, 3 Design Problem: Piezoresistive Microphone dB (2000 Pa) Aeroacoustic Measurements 130 dB (200 Pa) 60 dB (20x10 -3 Pa) 0 dB (20x10 -6 Pa) Threshold of normal hearing Jet noise Taper Resistor Arc Resistor

Melih Papila, 4 Design Problem: Piezoresistive Microphone 0dB=20x10 -6 Pa Tradeoff!!! Actual device performance designed for Aeroacoustic Measurements 60 – 160 dB

Melih Papila, 5 Optimized Performance Objective Piezoresistors Diaphragm Optimized Design parameters Find the optimum dimensions of the diaphragm and the optimum piezoresistor geometry and location in order to achieve optimum performance Investigate trade off between sensitivity and noise floor via Pareto Optimization

Melih Papila, 6 Methodology: Pareto Optimization  In multi-objective optimization problem with conflicting objectives  Pareto optimal points: one objective cannot be improved without deterioration in one of the other objectives,  Construct a Pareto hypersurface minimized maximized

Melih Papila, 7 Outline  Design problem  Objective and methodology  Design variables and objective functions  Single and multi-objective optimization results  Parameter uncertainty  Concluding Remarks

Melih Papila, 8 Design Variables I: Diaphragm/Structural z p 0 r = a h/2 Sheplak and Dugundji, 1998 a : radius of the diaphragm h : thickness of the diaphragm Structural responses of the diaphragm directly determine performance of the MEMS microphone measured by its sensitivity, bandwidth and linearity

Melih Papila, 9 Design Variables II: Piezoresistor Shape The geometry and location of the piezoresistors affect sensitivity and noise characteristics of the device Arc resistor Tapered resistor Taper  Arc 

Melih Papila, 10 Piezoresistive microphone: Design Variables  Structural Variables : Radius and thickness  Piezoresistor Variables : Resistor Shape Parameters (3)  Operation Variable : Bias voltage  Material variable : Doping concentration

Melih Papila, 11 Objective Function I Maximum sensitivity Pressure Diaphragm Deflection Resistance Modulation Output Voltage Modulation Large a/h Small resistor area High bias voltage Low doping concentration

Melih Papila, 12 Objective Function II: Minimum noise floor Thermal noise voltage fluctuations due to scattered electrons by thermal energy + 1/f noise random conductance fluctuations Large a Large resistor volume Low bias voltage High doping concentration

Melih Papila, 13 Piezoresistive Pressure Sensor Optimization Problem  Objective function(s)  Maximum sensitivity  Minimum noise floor  Design variables  Diaphragm/Structural Variables : Radius and thickness  Piezoresistor Variables : Resistor Shape Parameters (3)  Operation Variable : Bias voltage  Material variable : Doping concentration  Constraints  Linearity  Power consumption  Bounds on variables

Melih Papila, 14 Outline  Design problem  Objective and methodology  Design variables and objective functions  Single and multi-objective optimization results  Parameter uncertainty  Concluding Remarks

Melih Papila, 15 Results: Single objective function  Large a/h, but linear  Small resistor area  High bias voltage  Low doping concentration  Large a  Large resistor area and thickness  Low bias voltage  High doping concentration

Melih Papila, 16 Results: Pareto optimization Many ways to trade off S EM and V N

Melih Papila, 17 Relative loss criteria on Pareto curve Different criterion, different best design

Melih Papila, 18 Physical Trade-off Objective: Minimum Detectable Pressure Large a/h Small resistor area High bias voltage Low doping concentration Large a Large resistor volume Low bias voltage High doping concentration ?

Melih Papila, 19 Results  Large a, but linear  Intermediate resistor area  Intermediate bias voltage  High doping concentration  Large a/h, but linear  Small resistor area  High bias voltage  Low doping concentration  Large a  Large resistor area and thickness  Low bias voltage  High doping concentration

Melih Papila, 20 Results: Pareto curve Minimum MDP is a Pareto optimal design and a compromise between sensitivity and noise floor

Melih Papila, 21 Selection based on practical use… Pareto optimal design equivalent to 2 nd generation design in terms of dynamic range 160 dB (2000 Pa) Aeroacoustic Measurements 130 dB (200 Pa) 60 dB (20x10 -3 Pa) 0 dB (20x10 -6 Pa) Threshold of normal hearing Jet noise

Melih Papila, 22 Results

Melih Papila, 23 Outline  Design problem  Objective and methodology  Design variables and objective functions  Single and multi-objective optimization results  Parameter uncertainty  Concluding Remarks

Melih Papila, 24 Parameter uncertainty  Material properties, design variables and process parameters as random parameters, N(μ param,σ param )  1000 Monte Carlo simulations at each Pareto point Process and material parameters fixed in optimization

Melih Papila, 25 Parameter uncertainty  Noise floor least sensitive at min V N design  Sensitivity and minimum detectable pressure at min MDP design

Melih Papila, 26  Tradeoff between sensitivity and noise floor  Increased sensitivity by a factor of more than 10, but dramatic increase in noise…  Decreased noise, but also decrease in sensitivity  Compromise: Minimization of minimum detectable pressure Concluding Remarks  Pareto optimization helps to understand tradeoffs  Optimum design by Minimization of minimum detectable pressure is the least sensitive to parameter uncertainty

Melih Papila, 27 THANK YOU…

Melih Papila, 28 Structural Problem Assumptions…  Isotropic material properties  Clamped end conditions  Known in-plane residual stress due to thermal mismatch in the manufacturing process  Small deformation accompanied by a linearity check such that large deflection solution is different not more than 5%.

Melih Papila, 29 Piezoresistors Assumptions…  Doping concentration is constant through the thickness of the piezoresistors  Stresses are constant through the thickness of the piezoresistors and equal to stresses at the diaphragm surface multiplied by the ratio of the Young’s modulus  Dependence of piezoresistance coefficients to doping concentration is characterized by experimental data (Harley and Kenny 2000)  Dependence of mobility of holes to the doping concentration is given by Nishida and Sah (1987)

Melih Papila, 30 Formulation & Implementation Solved by MATLAB Optimization Toolbox

Melih Papila, 31 Design Constraints Linearity maximum non-dimensional loading that will produce a 5% departure from linearity in the center deflection as a function of tension parameter k and the relation can be approximated p (Pa) linear non-linear Sheplak and Dugundji, 1998