Curvature estimate for multilayer rolled-up nanostructures with cubic crystal anisotropy under initial strains

Abstract

The generalized plane strain solution for anisotropic multilayer nanostructures with cubic crystal symmetry under the influence of initial strains has been derived. This solution can be used to estimate equilibrium curvature radius and strains/stresses of rolled-up anisotropic multilayer nanostructures, whose deformations are induced by crystal lattice mismatch. The solution has been applied for calculation of curvature radii and strain components of a bilayer In0.2Ga0.8As/GaAs rolled-up nanostructure. The results are in agreement with those obtained by a finite element analysis.

Strain profiles and radii of semiconductor rolled‐up tubes made by a single material

“…The constant residual strain profile (C) is structurally equivalent to a bilayer fabricated from two different materials, with a constant value of the residual strain in each material depending on its lattice constant. In such tubes the simulated final strain profiles are almost linear, in good agreement with results from the literature 8, 21. The slope of the strain profile is the same in both parts of the layer with a discontinuity at the interface ( z = d s ); the radial component of the strain decreases and the azimuthal strain increases with increasing z .…”

“…This produces residual elastic strain consistent with isotropic relaxation of the lattice misfit strain 13. The advantage of this method is its simplicity, since it neglects the (unknown) atomic details of the plastic deformation but at the same time it incorporates the full strain anisotropy and is therefore more realistic than continuum methods assuming an isotropic crystal 20, 21. This allows us to study the macroscopic effect of a varying strain profile, which is not accessible even to advanced continuum models 21.…”

“…The advantage of this method is its simplicity, since it neglects the (unknown) atomic details of the plastic deformation but at the same time it incorporates the full strain anisotropy and is therefore more realistic than continuum methods assuming an isotropic crystal 20, 21. This allows us to study the macroscopic effect of a varying strain profile, which is not accessible even to advanced continuum models 21. A more complete treatment of the effects of plastic deformation could be obtained, e.g., by introducing a z ‐variation in the VFF parameters to account, e.g., for hardening of the material and possible Ge incorporation.…”

Strain-driven self-rolling mechanism for anomalous coiling of multilayer nanohelices

“…[18][19][20] Generally, the multilayer films persist rolling along the preferential winding direction determined by the orientation of the smallest Young's modulus, and form the helices with the helicity angles not less than 45°under the uniaxial bent torque induced by the initial stress partially relaxing along the rolled-up direction. 21 The existed closed-form theories, [22][23][24][25] however, failed in presenting an accurate description of the strain-driven self-rolling mechanism of nanobelts under the biaxial torque and therefore the geometry of the formed nanohelices, though they can estimate the curvature radius and strain components of the rolled nanohelices in the uniaxial stress relaxation condition. This desirable concept has been materialized in the SiGe/Si and SiGe/Si/Cr nanohelices due to the additional torque coming from the edge effects of stress relaxation at the sides of the nanobelts.…”

Microassembly based on hands free origami with bidirectional curvature

“…The addition of programable hinge stops 18 will allow for reconfiguration of specific hinges in order and enable the folding and unfolding of more complex origami models. We also believe that the incorporation of nanoscale patterning and larger driving forces generated by epitaxial stresses 10,22 can be used to create hinges with tighter nanoscale radii of curvature. FIG.…”