Symmetry in strain engineering of nanomembranes: making new strained materials.

Strain in a material changes the lattice constant and thereby creates a material with new properties relative to the unstrained, but chemically identical, material. The ability to alter the strain (its magnitude, direction, extent, periodicity, symmetry, and nature) allows tunability of these new properties. A recent development, crystalline nanomembranes, offers a powerful platform for using and tuning strain to create materials that have unique properties, not achievable in bulk materials or with conventional processes. Nanomembranes, because of their thinness, enable elastic strain sharing, a process that introduces large amounts of strain and unique strain distributions in single-crystal materials, without exposing the material to the formation of extended defects. We provide here prescriptions for making new strained materials using crystal symmetry as the driver: we calculate the strain distributions in flat nanomembranes for two-fold and four-fold elastically symmetric materials. We show that we can controllably tune the amount of strain and the asymmetry of the strain distribution in elastically isotropic and anisotropic materials uniformly over large areas. We perform the experimental demonstration with a trilayer Si(110)/Si((1-x))Ge(x)(110)/Si(110) nanomembrane: an elastically two-fold symmetric system in which we can transfer strain that is biaxially isotropic. We are thus able to make uniformly strained materials that cannot be made any other way.