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

Abstract

The Poisson's ratio nu(ij) = epsilon(res)(j)/epsilon(app)(i), where epsilon(app)(i) and epsilon(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 nu(yz) remains close to the Poisson's ratio of the bulk, nu(zx) and nu(xy) exhibit an increase and a sharp decrease from the bulk value, respectively, as the volume fraction of pores (phi) becomes large. It is shown that the characteristic dependence of the Poisson's ratio on phi 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.