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On Teaching the Operating Principles of Piezoresistive Sensors AC 2010-1626: ON TEACHING THE OPERATING PRINCIPLES OF PIEZORESISTIVE SENSORS Richard Layton, Rose-Hulman Institute of Technology Richard A. Layton is the Director of the Center for the Practice and Scholarship of Education (CPSE) and an Associate Professor of Mechanical Engineering at Rose-Hulman Institute of Technology. He earned a B.S. in Engineering from California State University, Northridge, and received his M.S. and Ph.D., both in Mechanical Engineering, from the University of Washington, Seattle. His areas of scholarship include student team management, assessment, education, and remediation, undergraduate engineering laboratory reform focused on student learning, data analysis and visualization, and engineering system dynamics. His work has been recognized with multiple best-paper awards. He conducts workshops in student team-building, team-formation and peer evaluation, in laboratory assessment, and in effective teaching. Prior to his academic career, Dr. Layton worked for twelve years in consulting engineering, culminating as a group head and a project manager. He is a guitarist and songwriter and a member of the rock band “Whisper Down”. Thomas Adams, Rose-Hulman Institute of Technology Thomas M. Adams is an Associate Professor of Mechanical Engineering at Rose-Hulman Institute of Technology. He earned a B.S. in Mechanical Engineering from Rose-Hulman Institute of Technology, and received his M.S. and Ph.D., both in Mechanical Engineering, from the Georgia Institute of Technology. His areas of expertise include heat transfer and energy systems, MEMS, and microfluidics. He has worked extensively to bring the field of MEMS and microscale technology to an undergraduate audience. He is the recipient of best paper awards for both educational and technical papers and has been awarded the Dean’s Outstanding Teaching Award at Rose-Hulman Institute of Technology. He is an avid fingerstyle/jazz guitarist, an amateur body-builder, and a yoga instructor. Page 15.923.1 Page © American Society for Engineering Education, 2010 On Teaching the Operating Principles of Piezoresistive Sensors Abstract We present an approach to teaching the operating principles of piezoresistive sensors that addresses many of the limitations of the treatments encountered in most instrumentation and MEMS textbooks. Namely, we direct the presentation to an undergraduate audience rather than a research-level audience and at the same time we avoid oversimplifying the development of the principles of operation. To this end, we make a discussion of bridge analysis central to the development, use a strain-formulation for gage factor and piezoresistor placement rather than the more common stress-formulation, and keep the associated physics and mathematics at an appropriate level for sophomore engineering undergraduates. In so doing, we maintain accessibility and coherence throughout. We present several sets of learning objectives and strategies for teaching the material that can be tailored to suit the needs of a particular course. Introduction Piezoresistive sensors are commonplace—the dominant commercial applications are piezoresistive accelerometers for automotive airbag deployment and piezoresistive pressure sensors for both automotive and medical applications1. Because of this widespread use, particularly in micro-electro-mechanical systems (MEMS) applications, undergraduate engineering programs whose learning outcomes include instrumentation technologies generally include an introduction to the basic operating principles of piezoresistive sensors. In our opinion, however, the exposition of these principles in popular textbooks for instrumentation systems and MEMS are generally inadequate—authors tend to either oversimplify, leaving a student unaware of operational details, or write for a research-oriented audience, making the material inaccessible to undergraduates. In this paper we present an approach to teaching the operating principles of piezoresistive sensors that addresses these issues. The distinguishing features of our approach are its accessibility and coherence. First, the technical content and mathematics are appropriate for sophomore-level engineering undergraduates. Second, the technical material is presented coherently and completely, that is, each step of the exposition is motivated by the results of the previous step. Third, since mechanical strain is the physical phenomenon relating input to output, a strain-formulation is used for gage factor and for the placement and orientation of the piezoresistors instead of the stress-formulation found in most textbooks. In this paper we share our approach with the instrumentation education community in the hope that its accessibility and coherence will help improve the teaching of the operating principles of this one important type of sensor. Limitation We have no student learning data to specifically support our assertion that the approach we present has greater coherence and accessibility for undergraduates than any other. However we do make the case in the following section that our work makes a contribution via a synthesis of 15.923.2 Page the strengths of widely-used texts. Also, in recent years we have seen a steady increase in our accreditation program-outcome measures supported by our measurement systems course, although this material on piezoresistive sensors would contribute at most two hours of content to the course. Based on these broad measures, we are satisfied that a presentation of sensor operating principles like the one developed here contributes to meeting our learning objectives. We plan to develop an approach for measuring success for the next offering of the course. Background In doing our literature survey for a chapter on piezoresistive sensors for our recently published book2 on introductory micro-electro-mechanical systems (MEMS), we sought a treatment suitable for a sophomore-level audience. Though several authors give excellent developments on particular aspects of the topic, none were quite what we wanted. In our opinion, the general problems are that authors of textbooks on measurement and instrumentation systems tend to give good coverage to metallic strain gages but only a passing or no reference to semiconductors. (In some indices, the term “piezoresistance” does not even appear.) In the case of MEMS textbooks, however, the authors tend to give good coverage to the piezoresistive effect, but write for an advanced audience. For example, measurement and instrumentation systems texts by Beckwith et al.3, Holman4, Northrop5, and Wheeler and Ganji6 all give good developments of metal strain gages and bridge analysis, but only passing reference to piezoresistance and semiconductors. Texts by Figliola and Beasley7 and Doebelin8 are similar, and though they include brief discussions of piezoresistive coefficients, they do so without a coherent connection to their strain-gage material. Among these texts, only Doebelin and Northrop use the Taylor series—the proper mathematical tool, in our opinion—for exploring small changes in variables such as sensor output voltage, electrical resistance, and area change. And while the texts by Holman and by Wheeler and Ganji pay some attention to the dimensional geometry associated with strain, none of these texts develops the geometry in detail. The text on sensors by Busch-Vishniac9 is an exception. The author provides a fairly complete development of the piezoresistive effect and of metal and semiconductor piezoresistors, though written for an advanced audience. The best-known MEMS texts have the same “deficiency” (for our purposes) of tending to be written for an advanced audience. All cover the piezoresistance principles of adequately, sometimes going deeper into molecular behavior than is needed by our audience. Standouts in this area include authors Maluf10 and Senturia11. Also because of their advanced audience, like Busch-Vishniac9, these books tend to omit or superficially treat bridge analysis—an important topic in our approach. We also find that MEMS texts tend to cover deformation mechanics in more detail than that needed by our audience, e.g., texts by Senturia and by Madou12. Nevertheless, some of these MEMS texts provide important material for our approach that is generally missing from conventional treatments on measurement and instrumentation systems3–8. Such attributes include deriving general mathematical models of piezoresistance to include both 9 metal and semiconductor piezoresistors , developing a strategy for placement of piezoresistors 15.923.3 Page on the mechanical system subjected to strain11,12, development of the geometry of piezoresistors under strain10,13, some details of the configuration of piezoresistive sensors (how they are put together)9,10,13, and numerical values for coefficients of piezoresistance and elastoresistance9,10,12. These developments tend to use a stress formulation (using the π piezoresistance coefficients) rather than the strain formulation we recommend here (using the γ elastoresistance coefficients). One last small but notable shortcoming of these texts, in common with the measurement and instrumentation systems previously described, is their tendency to neglect the application of the Taylor series for exploring small changes in variables. We draw on the individual strengths of these references to synthesize a complete, coherent, and balanced approach to teach the operating principles of piezoresistive sensors. We use a “system- level” perspective and attempt to develop each
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