Theory of strain relaxation in heteroepitaxial systems

Abstract

We introduce a general approach to calculating the morphological consequences of coherent strain relaxation in heteroepitaxial thin films based on lattice statics using linear elasticity. The substrate and film are described by a simple cubic lattice of atoms with localized interactions. The boundary conditions at concave and convex corners that appear as a result of this construction, those along straight interfacial segments, and the governing equations are obtained from a variational calculation applied to a discretized form of the total elastic energy. The continuum limit of the equations and the boundary conditions along straight boundaries reproduces standard results of elasticity theory, but the boundary conditions at corners have no such analog. Our method enables us to calculate quantities such as the local strain energy density for any surface morphology once the lattice misfit and the elastic constants of the constituent materials are specified. The methodology is illustrated by examining the strain, displacement, and energies of one-dimensional strained vicinal surfaces. We discuss the effects of epilayer thickness on the energy of various step configurations and suggest that coupling between surface and substrate steps should affect the equilibration of the surface toward the bunched state.

Direct imaging of quantum wires nucleated at diatomic steps

“…[1][2][3][4][5][6][7][8][9][10][11] In particular, these steps are thought to constitute a heterogeneous source of nucleation for the formation of nano-objects and structural defects at the initial stages of the growth of many semiconductor nanostructures. 12,13 It is critically important to identify the nucleation sources for individual nano-objects such as quantum dots and wires because they constitute the fundamental blocks of future nanoelectronics and nanophotonics devices. 14 The ability to control the nucleation of these nano-objects will contribute significantly to the development of reliable single-photon sources for applications in quantum information technology.…”

Simulation of self-assembled compositional core-shell structures in InxGa1−xN nanowires

“…The total elastic strain energy el E is calculated using an atomistic strain model 22,23 , which assumes harmonic potentials and includes nearest-neighbor (NN), next-NN (NNN), and bond-bending (BB) interactions ( ) ( ) ( ) valence force field results 25 .…”

Strain in layered nanocrystals

“…The strain field produced by a surface step, on an epitaxial surface, interacting with a buried step, on the interface between an epitaxial thin film and the substrate has been successfully studied in [7] using discrete harmonic potentials developed in [2]. We now try to understand step relaxation in core-shell layered nanocrystal system in a way that is analogous to that in [7].…”