Under the proper orientations and excitations, the transverse output of rotationally symmetric four-contact van der Pauw (VDP) stress sensors depends upon only the in-plane shear stress or the difference of the in-plane normal stresses on (100) silicon. In bridge-mode, each sensor requires only one four-wire measurement and produces an output voltage with a sensitivity that is 3.16 times that of the equivalent resistor rosettes or bridges, just as in the normal VDP sensor mode that requires two separate measurements. Both numerical and experimental results are presented to validate the conjectured behavior of the sensor. Similar results apply to sensors on (111) silicon. The output voltage results provide a simple mathematical expression for the offset voltage in Hall effect devices or the response of pseudo Hall-effect sensors. Bridge operation facilitates use of the VDP structure in embedded stress sensors in integrated circuits.
Multi-element resistor rosettes on silicon are widely utilized to measure integrated circuit die stress in electronic packages and other applications. Past studies of many sources of error have led to rosette optimization and demonstrated that temperaturecompensated stress extraction should be used whenever possible. In this work, we extend the error analysis to include the inherent uncertainty in the measured values of the sensor resistances and the temperature at time of the measurement. The stresses in an under-filled flip chip package are calculated using finite element simulation and utilized to evaluate the stress dependent sensitivities across the die surface. Monte Carlo simulation results confirm that temperature compensated rosette configurations should be utilized whenever possible.
INTRODUCTIONMulti-element resistor rosettes on silicon have been widely utilized by many groups to measure integrated circuit die stress in electronic packages and other applications [1][2][3][4][5][6][7][8]. This work utilizes resistor rosettes on the (111) surface that respond to all six components of the stress state and therefore can measure the complete three-dimensional state of stress at points on the surface of a die by using properly designed silicon sensors [9,10].
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