The Optimal Design of Piezoresistive Sensor

• Main Authors: Lin, Rong-Sheng, 林容生
• Other Authors: Yuan-Fang Chou
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/61817995465505291904

博士 === 國立臺灣大學 === 機械工程學系研究所 === 86 === The piezoresistor has been admired for the large effect of stresses on the resistivity since 1954. Traditionally, the size of piezoresistor with regular shape has to be kept small enough to preserve the assumption of uniform stress distribution. In general, the electric potential of a piezoresistor subject to a non-uniform stress field can not be determined algebraically. Moreover, the assumption of uniform stress distribution may be questionable due to the miniaturization of transducer. The electric potential of a piezoresistor is dependent on the geometric shape, boundary conditions and stress distribution. The governing equation of electric potential with coefficients of electric conductivity and its derivatives is developed in this thesis. The electric conductivity is also formulated as an explicit form of specific resistivity, piezoresistity and temperature coefficients of resistivity. In order to investigate the electric potential numerically, a piezoresistive finite element is developed by variational scheme. Then the finite-element method can be employed to calculate the distribution of electric potential for the determination of output electrodes location. Since the distribution of impurity concentration is not uniform along the thickness of a piezoresistor as a consequence of doping method, the concept of equivalent conductivity is presented. The equivalent conductivity is expressed as an integral combination of electric conductivity developed previously. Based on the equivalent conductivity, the complex 3-dimensional analysis can be simplified to 2-dimensional analysis under the proper assumptions. The sensitivity of pressure sensors similar to Motorola X-ducer is investigated as an example. It is found that the algebraic solutions overestimate the sensitivity up to 49% under uniform low-doped concentration. The case of different impurity distributions is also studied. Finally, the method of shape optimization is applied to increase the sensitivity by fully taking the advantage of stress distribution in the available location of microsensors. The result of analysis indicated that the optimal shape of the four-terminal p-type piezoresistor would follow the maximum shear stress contour with extrusive output electrodes.