Generalized plane strain deformation of multilayer structures with initial strains

Abstract

A closed-form solution for multilayer structures with initial strains under generalized plane strain conditions is presented. Such solutions can be useful for estimating the curvature radius and strains or stresses for self-positioning micro-and nano-structures with lattice mismatched layers. Comparison with finite element results shows that the developed solution predicts reasonable values of the curvature radius at the central part of the structure. Strains provided by the generalized plane strain solution are in agreement with those obtained by finite element analysis.

Atomic-Scale Analysis of Self-Positioning Nanostructures

“…For the self-positioning structure shown in Figure 1, the main structural parameter of interest is the local curvature radius in the equilibrium configuration. Analytical solutions have been derived based on continuum mechanics theory to predict the curvature radius [10][11][12]. Computational modeling has been also performed to understand characteristics of self-positioning nanostructures [13][14][15][16].…”

Effect of thickness on the self-positioning of nanostructures

“…One possible approach to nanofabrication is the use of self-positioning phenomenon of multilayer structures composed of materials with different lattice periods. [1][2][3] Various approaches have been applied to investigation of the self-positioning nanostructures including experimental research, [4][5][6][7][8] analytical studies, [9][10][11][12] and computational modeling. 13,14 Previous analytical studies and computational finite element modeling were based on continuous medium relations and were not able to account for atomic-scale effects of the selfpositioning.…”

Deviation from Regular Shape in the Early Stages of Formation of Strain-Driven 3D InGaAs/GaAs Micro/Nanotubes

“…In our study the strained structure consists of three layers of thicknesses 1 = 3.3 nm, 2 = 4 nm and 3 = 11.5 nm. The curvature of a trilayer can be calculated by setting = 3 in (13) of [26], where values are defined as 0 = 0, 1 = 1 , 2 = 1 + 2 , and 3 = 1 + 2 + 3 and 1 0 = ( 1 − GaAs )/ GaAs , 2 0 = ( 1 − 2 )/ GaAs , and 3 0 = 0, with 1 , 2 , and GaAs given by the lattice constants of In 0.2 Ga 0.8 As, In 0.1 Ga 0.9 As, and GaAs, respectively. Following this notation, 1 0 , 2 0 , and Figure 4(c).…”

“…In order to calculate the expected value of tube diameter by using the actual parameters of the structure, we followed the approach proposed by Nishidate and Nikishkov in [26] for the calculation of generalized plane strain deformation of multilayer structures. On the basis of plane strain elasticity theory, authors derive curvature estimation for strained multilayer structure with an initial strain due to lattice mismatch.…”