Piezoresistive Cantilever Optimization and Applications
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1222-DD03-06
Piezoresistive Cantilever Optimization and Applications Joseph C. Doll, Sung-Jin Park, Nahid Harjee, Ali J. Rastegar, Joseph R. Mallon Jr., Bryan C. Petzold, Ginel C. Hill, A. Alvin Barlian and Beth L. Pruitt Stanford University, Stanford, CA
ABSTRACT Piezoresistors are commonly used in microsystems for transducing force, displacement, pressure and acceleration. Silicon piezoresistors can be fabricated using ion implantation, diffusion or epitaxy and are widely used for their low cost and electronic readout. However, the design of piezoresistive cantilevers is complicated by coupling between design parameters as well as fabrication and application constraints. Here we discuss analytical models and design optimization for piezoresistive cantilevers, and describe several applications ranging from studying electron movement using scanning gate microscopy to measuring the biomechanics of whole organisms. INTRODUCTION Piezoresistivity, the change in resistivity of a material under stress [1], is commonly used in microelectro-mechanical systems (MEMS) for transducing force [2, 3, 4], pressure [5, 6, 7] and acceleration [8]. The optimal sensor geometry depends upon the type of mechanical loading, but a simple cantilever beam implementation is ideal for many applications. Microfabricated silicon cantilevers are widely used in force [9, 10], topography [11], and biochemical sensing [12] applications by transducing a signal via cantilever deflection. There are numerous techniques to detect cantilever bending, but the most common approaches are off-chip optical sensing [11] and on-chip electronic sensing using piezoresistive strain gauges [13]. Electronic sensing scales well to large arrays [14], high frequencies [15], and situations where optics are inconvenient [16]. Piezoresistive sensors have several desirable characteristics including straightforward fabrication, simple signalconditioning circuitry, compact size, and large dynamic range. With proper design, the resolution of piezoresistive cantilevers is comparable to optical detection [3, 17, 18]. Here, we provide a brief review of silicon piezoresistors with an emphasis on force sensing, discuss some aspects of design modeling and optimization, and describe several example applications from our lab. This is a survey and not a complete review of the extensive work to date by research labs spread across the globe on piezoresistors.
MODELING AND DESIGN Principles of Piezoresistance The electrical resistance (R) of a homogenous electrical conductor with constant cross-section can be calculated from its dimensions and resistivity according to ρl (1) a where ρ is the resistivity, l is the length and a is the cross-sectional area. The resistance of the conductor changes with geometry (length and area) and resistivity (carrier mobility and density). Semiconductor resistance change is dominated by the stress-induced change in mobility and can be simplified as R=
∆ρ = πl σl + πt σt ρ
(2)
where πl and πt are the longitudinal and transverse piezoresistive coeffi
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