Piezoresistive Cantilever Performance—Part I: Analytical Model for Sensitivity

Abstract

An accurate analytical model for the change in resistance of a piezoresistor is necessary for the design of silicon piezoresistive transducers. Ion implantation requires a high-temperature oxidation or annealing process to activate the dopant atoms, and this treatment results in a distorted dopant profile due to diffusion. Existing analytical models do not account for the concentration dependence of piezoresistance and are not accurate for nonuniform dopant profiles. We extend previous analytical work by introducing two nondimensional factors, namely, the efficiency and geometry factors. A practical benefit of this efficiency factor is that it separates the process parameters from the design parameters; thus, designers may address requirements for cantilever geometry and fabrication process independently. To facilitate the design process, we provide a lookup table for the efficiency factor over an extensive range of process conditions. The model was validated by comparing simulation results with the experimentally determined sensitivities of piezoresistive cantilevers. We performed 9200 TSUPREM4 simulations and fabricated 50 devices from six unique process flows; we systematically explored the design space relating process parameters and cantilever sensitivity. Our treatment focuses on piezoresistive cantilevers, but the analytical sensitivity model is extensible to other piezoresistive transducers such as membrane pressure sensors.

The Tactile Receptive Fields of Freely Moving Caenorhabditis elegans Nematodes

“…For tracking and targeting, we built on systems reported by Leifer et al 8 and Stirman et al 26 , who implemented real-time tracking for delivering optical stimuli to user-defined body segments ( Figure 1). For mechanical stimulus delivery, we relied on our previous system consisting of a custom, self-sensing, cantilever force probe [18][19][20] integrated into a closed loop control system 16 . HAWK introduces the ability to automatically measure and classify behavioral responses.…”

“…Central to the function of HAWK are two key, custom innovations: 1) a custom-force sensing cantilever that acts as the stimulator [15][16][17] and 2) an optical system to track and target the animal. The detailed design, fabrication and signal conditioning of these silicon, piezeoresistive cantilevers were previously reported [18][19][20] . We present the design of the optical system here.…”

Transferable micromachined piezoresistive force sensor with integrated double-meander-spring system

“…2a. Theoretically, the longitudinal stress σ L in the [110] direction can be calculated using the following expression (Park et al, 2010):…”

“…(1) the geometrical factors of the beam are given by the beam length l, width w and thickness t (Park et al, 2010). Subject to material properties, the stress σ L can be described as a product of the elastic modulus E and the longitudinal strain ε L along the x axis.…”

Fast on-wafer electrical, mechanical, and electromechanical characterization of piezoresistive cantilever force sensors

“…For the more general case other models are available which include issues such as non-uniform doping of the piezoresistors. 20,21 A. Spring constant: cantilever mechanical model…”