Stress sensing test chips are widely utilized to investigate integrated circuit die stresses arising from assembly and packaging operations. The test chips incorporate resistor or transistor sensing elements that are able to measure stresses by observing the changes in their resistivity or carrier mobility. This piezoresistive behavior of such sensors is characterized by three piezoresistive coefficients, which are electro-mechanical material constants. We are interested in stress characterization over a very broad range of temperatures. However, the literature provides limited data over the desired range, and even the data at room temperature, exhibit wide discrepancies in magnitude as well as sign. This work focuses on an extensive experimental study of the temperature dependence of the piezoresistive coefficients, π11, π12, and π44, for both p- and n-type silicon. In order to minimize errors associated with misalignment with the crystallographic axes on (100) silicon wafers, anisotropic wet etching was used in this work to accurately locate the axes. A special four-point bending apparatus has been constructed and integrated into an environmental chamber capable of temperatures from −155 to +300°C. Experimental calibration results for the piezoresistive coefficients as a function of temperature from −150°C to +125°C are presented and compared and contrasted with existing values from literature. Measurements were performed using stress sensors fabricated on (100) silicon mounted on PCB material including both die-on-beam and strip-on-beam mounting techniques. Four-point bending (4PB) was used to generate the required stress, and finite element simulations have been used to determine the actual states of stress in the silicon material.
