Piezoresistive Coefficient
Material property matrices describe the directional dependence of stress-induced electrical resistivity changes in semiconductor lattices. Engineers use the crystalline silicon tensor to calculate how a specific orientation of a silicon wafer reacts to mechanical force. This relationship is not uniform, because the atomic arrangement of the crystal provides different resistance shifts along the different axes.
Directional Sensitivity
Orientation of the sensor on the wafer determines the gain of the signal produced by the bridge circuit. Designers align a crystalline silicon tensor with the primary axes of the silicon to maximize the output for pressure or force sensors. If the alignment shifts by even a few degrees, the output voltage drops and the sensor loses its ability to distinguish between different types of stress.
Doping Influence
Concentration of boron or phosphorus atoms inside the silicon lattice alters the coefficients within the mathematical matrix. High doping levels reduce the temperature sensitivity of the crystalline silicon tensor but also lower the total signal strength available to the amplifier. Low doping creates a more sensitive sensor that requires better temperature compensation to remain stable.
Advanced fabrication techniques allow for the fine adjustment of these coefficients to meet the needs of specific industrial applications.
Structural Bound
Physical limits of the silicon crystal define the range where these linear tensor models remain accurate. Once the applied stress exceeds the elastic limit of the material, the lattice deforms permanently and the tensor values no longer describe the electrical behavior.
