Theoretical study of electromechanical property in a p-type silicon nanoplate for mechanical sensors

Electromechanical property of a p-type single-crystal silicon nanoplate is modelled by a microscopic approach where the hole quantization effect and the spin--orbit coupling effect are taken into account. The visible anisotropic subband structures are calculated by solving self-consistently the stress-dependent 6$\times $6 ${\bm k} \cdot {\bm p} $ Schr\"{o}dinger equation with the Poisson equation. The strong mixing among heavy, light, and split-off holes is quantitatively assessed. The influences of the thickness and the temperature on the piezoresistive coefficient are quantitatively investigated by using the hole concentrations and the effective masses from the complex dispersion structure of the valence band with and without stresses. Our results show that the stress determines the extent to which the band is mixed. The hole quantization effect increases as the thickness decreases, and therefore the valence band is strongly reshaped, resulting in the size-dependent piezoresistivity of the silicon nanoplate. The piezoresistive coefficient increases almost 4 times as the thickness reduces from the bulk to 3\,nm, exhibiting a promising application in mechanical sensors.