A near-zero Poisson's ratio of Si with ordered nanopores

Abstract

The Poisson's ratio ν_ij = −ε^res_j/ε^app_i, where ε^app_i and ε^res_j (i,j = x, y, z) are applied and resulting strain, respectively, are computed from first-principles for Si with an array of cylindrical, nanometer-sized pores aligned in the z direction (nanoporous Si, or np-Si). Through density functional theory calculations, it is demonstrated that the periodic arrangement of pores introduces strong anisotropy in the Poisson's ratio of np-Si: while ν_yz remains close to the Poisson's ratio of the bulk, ν_zx and ν_xy exhibit an increase and a sharp decrease from the bulk value, respectively, as the volume fraction of pores (ϕ) becomes large. It is shown that the characteristic dependence of the Poisson's ratio on ϕ originates from the difference in the actual stress on np-Si, which is caused by the dissimilar surface geometry. Unlike random porous materials, this finding signifies the importance of structural details in determining the mechanical response of ordered systems at a nanoscale.