SaM - Collapsed Piezoresistive Coefficient Tensor for Silicon

NOTE: We use the Piezoresisitve Coefficient Tensor $\left(\overline{\overline{\Pi }}\right)$ to calculate the change in resisitivity when a material is deformed, more information in the “Piezoresistivity Effect” Lecture.

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Here’s the generic collapsed piezoresisitve coefficient tensor for Silicon (an isotropic material):
So ==for Silicon==, we can write the special $[3\times 3\times 3\times 3]$ $\overline{\overline{\Pi }}$ piezoresistive coefficients tensor with only $3$ indipendent constants: ${\Pi }_{11},{\Pi }_{12},{\Pi }_{44}$.
These inidipendent constants depend on the type and doping level.