Vertical self-alignment of quantum dots in superlattice

Abstract

Self-alignment of quantum dots separated by spacer layers is investigated by using a three-dimensional finite element method. We find that the morphology of the top islands is not just simply a reproduction of the buried islands. It is dependent on the arrangement of the buried islands, the interruption time, and the spacer layer thickness. If the buried islands are uniform and regular, with appropriate choice of their spacing and aspect ratio and with a thin spacer layer, there exists a regime in which the steady-state top islands are always uniform and regular, vertically aligned, and stable against small perturbations. For a thicker spacer layer, due to the change of the strain energy density distribution on top of the spacer layer, the top islands are misaligned with the buried islands. If the buried islands are not uniform and regular, our simulations demonstrate the top islands may self-assemble into more uniform and regular arrangements.

Role of elastic anisotropy in the vertical alignment of In(Ga)As quantum dot superlattices

“…3,5,14 To explain this behavior, some authors have proposed that it is possible to obtain near equilibrium VAS QD structures only for highly elastic anisotropic materials. 3,12,15,16 In this sense, In͑Ga͒As islands on GaAs ͑001͒ have been observed to show surface alignment effects, 13,17,18 which give a clear indication of the anisotropy of the intrinsic surface stress tensor and the anisotropy of the bulk elastic modulus tensor. However, the molecular beam epitaxy ͑MBE͒ growth is governed by growth kinetics and this fact explains the lack of observations of anticorrelated behavior despite numerous studies of InGaAs multilayers.…”

“…Following this reasoning, several authors have proposed that both VCS and VAS in self-assembled QD structures can be explained, taking into account the elastic anisotropy of the strain energy profile above a predeposited QD layer. 3,5,12,[14][15][16]20 The elastic anisotropy would change both the depth and the position of the energy minima with respect to elastically isotropic spacer layers where the energy minimum is always on the top of the buried QDs. Specifically, for GaAs͑001͒, there are four energy minima above a quantum dot which occur at ±23°from the vertical in the ͗110͘ directions, assuming the calculations of Holy et al 14 So, for the ϳ40 nm QD width observed in the bottom layer of sample A, four strain minima shifted ±10.5 nm from the vertical along the ͗110͘ directions would occur above these islands.…”

“…Theoretical treatments have been successfully applied to explain VCS based on accounting the strain induced migration of atoms of the growing layer to positions above underlying QDs. 4,6,12,13 However, the detailed mechanism is still the subject of considerable debate, depending on the relative importance of nucleation and postnucleation effects.…”

High-Resolution Electron Microscopy of Semiconductor Heterostructures and Nanostructures

“…(2) Calculating the strain field by solving the anisotropic elastic theory equations by FEA using a compositional model of the studied nano-objects. This method has been proven to be one of the most efficient procedures to model the strain associated with these buried nanostructures [63][64][65][66]. Inputs for this compositional model are given by both spatially resolved EELS and aberration-corrected high-resolution Z-contrast images.…”

Effect of dissimilar anion annealing on structures of InAs/GaAs quantum dots

“…It has been shown that the dot size distribution and a vertical alignment need to be optimized among the growth conditions, including spacer thickness [17], material coverage [18], growth interruption [19], the number of periods of the multilayer [20,21], growth rate [22], post-growth annealing [23], and substrate miscut angle [24]. The physics behind them is the mechanical or elastic interaction of the islands via their strain fields.…”