JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 20, NO. 3, JUNE 2011 609 A Multilevel CMOS–MEMS Design Methodology Based on Response Surface Models Norio Sato, Member, IEEE, Yasuhiro Sato, Member, IEEE, Yuichi Kado, Member, IEEE, Mauro Ciappa, Senior Member, IEEE, Dölf Aemmer, Member, IEEE, Hubert Kaeslin, Senior Member, IEEE, and Wolfgang Fichtner, Fellow, IEEE Abstract—We have developed a novel methodology to design systems composed of complementary metal–oxide–semiconductor (CMOS) and microelectromechanical systems (MEMS) parts. This multiscale methodology combines bottom-up modeling and top-down design-space exploration through the following steps: 1) In bottom-up modeling, characteristics of CMOS circuits and MEMS structures are accurately simulated at the circuit and MEMS device level; 2) on the basis of the results of a statistical regression method, these characteristics are abstracted into indi- vidual response surface models (RSMs), each with a set of coef- ficients of design parameters; 3) the models are mathematically connected to describe an elemental unit comprising CMOS and MEMS components; 4) the characteristics of the whole system of elemental units are abstracted into another RSM to cover the system performance; and 5) in top-down design-space exploration, the system requirements are connected to a set of design param- eters for the CMOS circuits and MEMS structures by utilizing the RSMs in the reverse direction. To verify the concept, our design methodology was applied to a CMOS–MEMS fingerprint sensor. [2010-0084] Index Terms—Bottom-up and top-down design methodology, complementary metal–oxide–semiconductor (CMOS), fingerprint sensor, microelectromechanical systems (MEMS), multilevel, re- sponse surface model (RSM), system performance. I. I NTRODUCTION M ICROELECTROMECHANICAL systems (MEMS) devices have the potential to offer new and unique functions to modern electronic systems. For example, MEMS accelerometers have revolutionized applications such as air-bag systems and the motion-sensing units of game controllers. These MEMS devices are typically employed as sensor and/or actuator devices, and they are usually connected with Manuscript received March 25, 2010; revised January 22, 2011; accepted February 27, 2011. Date of publication May 11, 2011; date of current version June 2, 2011. Subject Editor N. Aluru. N. Sato was with the NTT Microsystem Integration Laboratories, NTT Corporation, Atsugi 243-0198, Japan. He is now with NTT Electronics Corporation, Yokohama 221-0031, Japan (e-mail: sato-norio@ntt-el.com). Y. Sato is with the NTT Microsystem Integration Laboratories, NTT Corporation, Atsugi 243-0198, Japan (e-mail: yasu@aecl.ntt.co.jp). Y. Kado was with the NTT Microsystem Integration Laboratories, NTT Corporation, Atsugi 243-0198, Japan. He is now with Kyoto Institute of Technology, Kyoto 606-8585, Japan (e-mail: kado@kit.ac.jp). M. Ciappa, D. Aemmer, H. Kaeslin, and W. Fichtner are with the Inte- grated Systems Laboratory, Swiss Federal Institute of Technology (ETH), 8092 Zurich, Switzerland (e-mail: ciappa@iis.ee.ethz.ch; aemmer@iis.ee.ethz.ch; kaeslin@ee.ethz.ch; www.iis.ee.ethz.ch/~fw). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2011.2140352 complementary metal–oxide–semiconductor (CMOS) analog- digital circuits for control, input–output, and further digital processing. The overall performance of a coupled CMOS–MEMS system is determined by the behavior of the combined MEMS and CMOS parts. This basic fact, however, is usually ignored in the design and development of such a system. As different fabrica- tion technologies and design tools are used to create “exotic” MEMS components, those components are typically developed first, possibly even by other engineering groups (or even other companies). CMOS analog circuits are subsequently employed to fulfill the requirements of MEMS outputs. After that, a unit of MEMS devices and CMOS analog circuits is connected with CMOS digital circuits. This approach easily leads to suboptimal solutions because of mismatches between MEMS and CMOS parts, resulting in low-performance systems, long development times, and high cost. To resolve this unacceptable situation, a comprehensive design methodology for coupled CMOS–MEMS systems is needed. This methodology should not be confined to either the MEMS or the CMOS world, but it should provide a platform common to both fields, with the power to handle different abstraction levels, ranging from the system to the individual devices and circuits. We propose a novel multilevel CMOS–MEMS design methodology for top-down design-space exploration. Input– output relationships at each level are reduced into compact models by using a response surface method. Since this method is not based on physics but statistics, it is general enough to characterize not only physical quantities of mechanical and electrical relationships but also nonphysical quantities of the system performance itself. Our methodology can connect dif- ferent fields of CMOS and MEMS and the hierarchical levels comprising the system, components, circuits, and structures. Therefore, our methodology is powerful in translating system performance requirements into the requirements for critical design parameters of MEMS and CMOS parts. II. CURRENT STATUS OF DESIGN AND MODELING Together with the astonishing advances in semiconductor technology, the success of electronic design automation has led to a flourishing microelectronics industry. Over the last two decades, CMOS digital design has become an established en- gineering field with standardized processes and methodologies 1057-7157/$26.00 © 2011 IEEE