Experimental characterization of the temperature dependence of the piezoresistive coefficients of silicon

Stress sensing test chips are used to investigate die stresses arising from assembly and packaging operations. The chips incorporate resistor or transistor sensing elements that are able to measure stresses via the observation of the changes in their resistivity/mobility. The piezoresistive behavior of such sensors is characterized by three piezoresistive (pi) coefficients, which are electro-mechanical material constants. In most prior investigations, calibration of the piezoresistive coefficients has been performed at room temperature. The limited data at other temperatures, and even the data at room temperature, exhibit wide discrepancies in magnitude as well as sign. Thus the literature data limits the accuracy of test chip stress measurements made at other temperatures. We are interested in stress measurements over a very broad range of temperatures, 77K - 450K or more, and this work focuses on an extensive experimental study of the temperature dependence of the piezoresistive coefficients of silicon. Calibration has been performed using four-point-bending of chip-on-beam specimens. A special four-point bending apparatus has been constructed and integrated into an environmental chamber capable of conditioning to temperatures from -185 to 300 C. Finite element analysis has been used to calculate the stress states applied to the calibration samples. Our first test results show that the piezoresistive coefficients for p- and n-type silicon decrease monotonically with increasing temperature over the temperature range -150 to 100 C. This work is currently being extended to higher temperature and performing temperature dependent hydrostatic pressure tests