Hydrostatic Response of Piezoresistive Stress Sensors

The (111) surface of silicon offers unique advantages for fabrication of piezoresistive stress sensors. Resistive sensor elements fabricated on this particular surface respond to all six components comprising the state of stress. Hence, a multi-element rosette has the capability of measuring the complete stress state at a point in the material. To extract the stress state at points on the die from the resistance changes measured with the sensor rosettes, it is necessary to have accurately calibrated values of six piezoresistive coefficients. Four-point bending and wafer-level calibration methods can measure four out of six piezoresistive coefficients for both p- and n-type resistors. To measure the other two coefficients, a hydrostatic test method has been developed where a high capacity pressure vessel is used to apply triaxial load on a single die. During the test procedure, resistance changes of resistors on the die are monitored. The slopes of the adjusted resistance change versus pressure plots are then used to calculate the desired last two coefficients. A step-by-step hydrostatic test procedure is demonstrated and sample data are presented.