Size and temperature dependence of Young's modulus of a silicon nano-plate

A semi-continuum approach is developed for the mechanical analysis of a silicon nano-plate. The strain energy of the nano-plate required in the semi-continuum approach is obtained by using the Keating model. The calculated Young's modulus of the silicon (0 0 1) nano-plate along the [1 0 0] direction is size dependent and is different from its bulk counterpart. Based on the quasiharmonic approximation, the temperature dependence of the lattice parameter and the bond length of silicon has been coupled into the semi-continuum model. It shows that the temperature coefficient of Young's modulus for the nano-plate is negative and nonlinear.