Nonlinear piezoresistance of silicon

We report on the piezoresistive characterization of various silicon materials, including low-doped (n = 10¹⁶ cm^-3) crystalline (c-Si), polycrystalline (poly-Si), and nanocrystalline (nc-Si) specimens. The employed wafer-scale microtensile technique enables the acquisition of linear and nonlinear piezoresistance coefficients. In contrast to previous studies where nonlinear coefficients were obtained for strains up to only 0.2%, the data presented here are extracted up to the fracture strain of about 1%, leading to more reliable higher-order piezoresistive parameters. Longitudinal and transverse resistance measurements of the specimen regions under uniform stress are realized during sample mechanical loading. Relative resistivity changes Δρ/ρ of up to -12.6, -36, and -40% are found for longitudinal resistance measurements at specimen fracture stresses of 1.4, 1.4, and 2.1 GPa for poly-Si and c-Si aligned with 〈100〉and 〈110〉 directions, respectively. Non-monotonic characteristics with maximal resistivity changes of -16% and 11.5% are found for transverse resistance measurements on c-Si along the 〈100〉and 〈110〉-directions, respectively. The nonlinear behaviour of c-Si is modeled by a fourth order polynomial, while a second order polynomial sufficiently fits the poly-Si data. Such findings are particularly relevant for the application of these materials in piezoresistive sensing devices subjected to relatively large stress levels.