Optimal Temperature Compensated Piezoresistive Stress Sensor Rosettes

Test chip stress sensors have been widely used for experimental structural analysis of electronic packages. Successful application of the integral piezoresistive sensors for stress measurement, however, requires accurately calibrated values of the piezoresistive coefficients of the sensing resistors as well as recognition of many potential sources of error during sensor application. Because of the high sensitivity of the sensor resistances to changes in temperature, temperature compensated measurements are almost always required to achieve accurate stress measurements. In this work, an analysis has been performed to identify sensor rosettes which can measure the maximum number of stress components in a temperature compensated manner. A general dual-polarity six element rosette with arbitrary sensor orientations has been considered on an general (uvw) silicon wafer surface. Theoretical relations have been established for the normalized resistance changes of the sensing elements in terms of the applied stress components and temperature change. A general inversion of the equations has then been performed to yield the expressions relating the stress components to the observed resistance and temperature changes. Analysis of the results has indicated that rosettes on the (111) surface have the ability to measure the highest number of temperature compensated stress components. Quantities which can be potentially measured in a temperature compensated manner using rosettes fabricated on this crystal plane include the three (in-plane and out-of-plane) shear stress components, and the difference in the in-plane normal stress components. In addition, it has been shown that the individual normal stress components (in-plane and out-of-plane) cannot be measured using a temperature compensated approach. An explicit rosette design on (111) silicon capable of such measurements has also been presented.