The piezoresistive effect describes the change in a material’s conductivity when a stress is applied to the material. Unlike the piezoelectric effect, piezoresistivity is not reversible, so an applied current does not induce a stress (unless other secondary effects are present, such as heating). Piezoresistance is usually associated with semiconductor materials. In semiconductors, piezoresistance results from the strain-induced alteration of the material’s band structure and the associated changes in carrier mobility and number density.
where ρ is the resistivity and
Δρ is the induced change in the resistivity. In the general case,
ρ and
Δρ are both rank-2 tensors (matrices). The change in resistance is related to the stress,
σ, (for the piezoresistance form of the equations) or the strain,
ε, (for the elastoresistance form of the equations) by the constitutive relationship:
where Π is the piezoresistance tensor (SI unit: Pa
−1Ω⋅m) and
M is the elastoresistance tensor (SI unit:
Ω⋅m). Note that both of these quantities are material properties.
Π and
M are in this case rank-4 tensors; however, they can be represented as matrices if the resistivity, stress, and strain are converted to vectors within a reduced subscript notation.
