Analytical solution for elastic fields caused by eigenstrains in a half-space and numerical implementation based on FFT

The impact of shallow trench isolation effects on circuit performance

“…However, general STI geometries may be have arbitrary three-dimensional rectilinear shapes, as observed in Figure 1. It is common practice [13] in micromechanics to divide an arbitrary shaped inclusion into smaller substructures and use linear superposition to find the total stress. Here, a general STI geometry is as a union of smaller cuboidal shapes, whose stress and strain contributions are superposed.…”

“…The inclusion problem in micromechanics finds the stress state of such a system. There is a rich body of work on this class of problems in micromechanics [13], [15]- [17]. Shallow trench isolation (STI) is made up of SiO2 and is embedded in silicon at a high temperature of 1000…”

“…Using displacement potential theory, the elastic displacement can be expressed as a second partial derivative of a single vector function, the Galerkin vector function [13]. Elastic strains and stresses can be deduced from Equations (4) and (5).…”

“…Let (x1,x2,x3) denote a point in the source subdomain; the corresponding position vector is denoted byx. The elastic displacements ui and stress components σij due to eigenstrains eij, i, j ∈ {x1, x2, x3} in terms of a Galerkin vector function Φ(x) are given by [13]:…”

“…A general solution for a cuboidal inclusion has been presented in [13]. The work presents a detailed mathematical framework based on Galerkin vector formulation.…”