Modelling of Self-Positioning Micro-/Nanostructures

The finite element procedure is developed for the solution of three-dimensional geometrically nonlinear problems with small strains and large rotational and translational displacements. Updated Lagrangian formulation is used with controlling strains and stresses at local coordinate frames at element integration points. Equilibrium iterations at each step are performed according to the Newton-Raphson method. Hexahedral 20-node elements are used for discretization. The developed finite element procedure is applied to modelling of self-positioning microand nanostructures. A multilayer structure is formed with the molecular beam epitaxy method. Some layers have different lattice periods that leads to the structure self-positioning after etching out a sacrificial material layer. In computational modelling, etching of the sacrificial layer is simulated by release of displacement constraints or by specifying zero elasticity modulus in elements of the sacrificial layer. Results for a selfpositioning micromirror with a hinge of a variable width are compared to the closed-form solutions for limiting cases of narrow and wide hinges.