Fabrication uncertainties and yield optimization in MEMS tunable capacitors

Intrinsic uncertainties of MEMS fabrication processes can severely affect the performance of devices because the tolerance ranges of these processes are relatively large and improvement of process accuracy is very expensive. Therefore, the analysis of fabrication uncertainties and their outcome on a device performance is a vital task before finalizing the design. In this paper, the effects of process inaccuracy on the performance of MEMS tunable capacitors are studied. Design parameters such as dimensions of electrodes and the initial gap between them and the stiffness of supporting beams are considered as random variables. The variation of these parameters within tolerance ranges drastically alters the capacitor's actual response from the desired one and results in low yield. Hence, design optimization with the objective of maximizing yield in early steps becomes very important. An effective method for yield optimization of MEMS capacitors under given fabrication uncertainties is introduced. The method utilizes aspects of the advanced first-order second-moment (AFOSM) reliability method to find a linearized feasible region to estimate the yield. The yield is calculated directly using the joint cumulative distribution function (CDF) over the tolerance box requiring no numerical integration and avoiding computational complexity. The optimal design verified by Monte-Carlo (M-C) simulation exhibits a significant increase in the yield. The main advantage of this method comparing to other design optimization methods is that the proposed method does not change the design topology or fabrication accuracy. It increases the yield by finding the optimum design variables as demonstrated in this paper.

[1]  K. R. Farmer,et al.  Micromachined variable capacitors with wide tuning range , 2003 .

[2]  Alessandro Trifiletti,et al.  A novel yield optimization technique for digital CMOS circuits design by means of process parameters run-time estimation and body bias active control , 2005, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[3]  Erik D. Goodman,et al.  An evolutionary approach for robust layout synthesis of MEMS , 2005, AIM 2005.

[4]  Kumaraswamy Ponnambalam,et al.  Maximization of Manufacturing Yield of Systems with Arbitrary Distributions of Component Values , 2000, Ann. Oper. Res..

[5]  Kumaraswamy Ponnambalam,et al.  Probabilistic design of systems with general distributions of parameters , 2001, Int. J. Circuit Theory Appl..

[6]  Charles T. Sullivan,et al.  MEMS high-Q tunable capacitor for reconfigurable microwave circuits , 2003, SPIE MOEMS-MEMS.

[7]  Hiroo Masuda,et al.  A New Design-Centering Methodology for VLSI Device Development , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[8]  Nii O. Attoh-Okine.  UNCERTAINTY ANALYSIS IN SURFACE MICROMACHINED FORCE GAUGES: CONVEX MODEL APPROACH , 2004 .

[9]  P. E. Allen,et al.  Introduction to the theory and design of active filters , 1980 .

[10]  David Wood,et al.  The modelling and fabrication of widely tunable capacitors , 2003 .

[11]  Mohammad Shavezipur,et al.  Design and Modelling of Novel Linearly Tunable Capacitors , 2006 .

[12]  Robert L. Borwick,et al.  A high Q, large tuning range MEMS capacitor for RF filter systems , 2003 .

[13]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[14]  Yong-Kweon Kim,et al.  Measurement of the mechanical properties of electroplated gold thin films using micromachined beam structures , 2005 .

[15]  T. Yanagawa,et al.  Yield optimization of integrated circuits , 1973 .

[16]  Carlo Guardiani,et al.  Yield optimization of analog ICs using 2-step analytic modeling methods , 1992 .

[17]  C. Paoloni,et al.  Nonlinear yield analysis and optimization of monolithic microwave integrated circuits , 1995 .

[18]  Yuh-Chung Hu,et al.  A method for mechanical characterization of capacitive devices at wafer level via detecting the pull-in voltages of two test bridges with different lengths , 2007 .

[19]  Mohammad Shavezipur,et al.  Development of novel segmented-plate linearly tunable MEMS capacitors , 2008 .

[20]  P. Kumaraswamy.  A generalized probability density function for double-bounded random processes , 1980 .

[21]  A. Dewey,et al.  Behavioral modeling of microelectromechanical systems (MEMS) with statistical performance-variability reduction and sensitivity analysis , 2000 .

[22]  Stephen Ekwaro-Osire,et al.  Sensitivity Based Optimum Design Process for MEMS devices , 2004 .

[23]  T. Harnisch,et al.  Design centering methods for yield optimization of cryoelectronic circuits , 1997, IEEE Transactions on Applied Superconductivity.

[24]  Paul A. Kohl,et al.  Electrostatic actuators and tunable micro capacitors/switches with expanded tuning range due to intrinsic stress gradients , 2003, SPIE MOEMS-MEMS.

[25]  Charles T. Sullivan,et al.  A MEMS high-Q tunable capacitor for reconfigurable microwave integrated circuits , 2003 .

[26]  G. C. Johnson,et al.  MEMS process error characterization using lateral resonant structures , 2004, SPIE MOEMS-MEMS.

[27]  Carlo Guardiani,et al.  Yield optimization of analog ICs using 2-step analytic modeling methods , 1992, ESSCIRC '92: Eighteenth European Solid-State Circuits conference.

[28]  Chang Liu,et al.  Design and modeling of a micromachined high-Q tunable capacitor with large tuning range and a vertical planar spiral inductor , 2003 .