Silicon Piezoresistive Transducer Carrier Density Fundamentals and Gauge Factors
P-type silicon piezoresistors doped with boron to 1e18 cm-3 achieve an optimal balance between gauge factor magnitude and thermal coefficient stability.
Ion Implantation Profile
Distribution Pattern
Depths and concentrations of added impurities follow specific mathematical curves determined by acceleration energy and target mass. The ion implantation profile shows exactly where dopants settle relative to the crystal surface. Precise control over this distribution enables the formation of thin conductive layers for sensing.
Energy Adjustment
Changes in the voltage of the accelerator shift the peak of the dopant concentration further into the substrate. An ion implantation profile is tailored to create high sensitivity regions while avoiding deep punch through into the bottom of the wafer. Engineers use monte carlo simulations to predict these outcomes before starting a batch.
Annealing Shift
Post implantation heat treatments cause the atoms to move slightly from their initial landing positions. The final ion implantation profile after thermal soaking is what determines the device resistance. Monitoring these shifts is necessary to prevent the doping from becoming too diluted over the sensor depth.
Metrology Interface
Verification of the depth uses secondary ion mass spectrometry to count atom numbers at every micron. If the ion implantation profile deviates from the design document, the sensitivity of the piezoresistor will not meet the expected tolerance. Deviations here typically trigger recalibration of the delivery system.