A numerical modeling approach to estimate the piezoresistance of diffused resistors with experimental validation

Silicon piezoresistive sensors have been widely used for many applications in recent decades. Monocrystalline silicon resistors are realized using an ion-implantation or a thermal diffusion process with a Gaussian or complementary error function profile. However, over the years, most researchers have neglected the doping concentration profile of the piezoresistor in the modeling stages resulting in erroneous responses that are far removed from experimental results of fabricated resistive sensors. In the present work, we propose a simulation approach to accurately estimate the piezoresistance of thermally diffused resistors with a non-uniform doping profile. We have modeled the diffused resistor as a parallel combination of several small slices, each having a unique piezoresistive coefficient. Three different slicing strategies were investigated to evaluate the impact of the piezoresistive coefficients, the electrical resistivity of the resistor slices, and the stress profile across the thickness of the resistor embedded in an accelerometer device. The cumulative impact of these parameters on the sensor’s overall sensitivity is evaluated. Further, we have also studied the influence of the accelerometer’s flexure thickness on the sensor’s sensitivity. It is observed from the simulation results that one of the slicing strategies with more slices at the surface of the resistor results in less than 1% error compared to the experimental results of an accelerometer device with a 60 µm flexure thickness.