A finite-element study of strain fields in vertically aligned InAs islands in GaAs

Abstract

Finite-element calculations are used to study strain fields in vertically aligned InAs islands in GaAs. Such strain fields are found to be quite different from those of uncovered islands and nearly insensitive to the position of the island in the stacking. The driving force for vertically self-organized growth is known to be the interacting strain fields induced by the islands. The calculation of strain fields by the finite-element method makes it possible to model the correlations between adjacent InAs layers. A kinetic approach based on the effect of strain on surface diffusion is first proposed. A thermodynamic model is then analyzed to predict local island nucleation probabilities. Pairing probabilities of correlation between stacked islands, first calculated in the case of the InAs/GaAs system, are extended to the case of III-V semiconductors with a cubic crystalline structure. They are shown to be essentially dependent both on the ratio between the spacer layer thickness and the island height and on the lattice mismatch between islands and spacer layers.

Buried stressors in nitride semiconductors: Influence on electronic properties

“…31,32 A complete solution of the elasticity problem in the most general case of stressors in closed analytical form is not possible. For problems related to QDs, three main methods have been applied to determine the elastic behavior of the stressor: ͑i͒ theory of elastic inclusions based on exact or approximate analytical solutions of elasticity equations ͑"Eshelby-like" or related approaches͒, 11,14,23,25,30 ͑ii͒ finite element methods ͑FEM͒, 27,30,33,34 and ͑iii͒ atomistic modeling. 35,36 Approaches ͑i͒ to ͑iii͒ all have their particular advantages and disadvantages.…”

“…For calculating P pz we employ ͓see Eq. ͑8͔͒ the piezoelectric tensor of wurtzite nitride semiconductors, which gives us where the piezoelectric constants of GaN e 31 , e 33 , and e 15 have the values given in Sec. III.…”

Pit nucleation in the presence of three-dimensional islands during heteroepitaxial growth

“…In general E is a function of the strain, and near islands the strain is enhanced 17,18 . However, as discussed in the introduction, the analysis presented here will focus on the effect of adatom concentrations.…”

“…It may also arise due to the fact that the stress inhomogeneities induced by the islands lead to a local increase in the strain at the island edge. In fact, finite element calculations show that the strain close to an island 17,18 can be twice as high as the nominal mismatch. This strain concentration at the island edge would increase E, pushing the system into regime IB.…”

Theoretical analysis of strain and strain decay in InAs∕GaAs(001) multilayer quantum dot growth

“…29,30 Recently, various groups have addressed not just aspects concerning the nucleation and growth of the QDs but also the effects of strain and strain interactions on the ͑opto͒electronic properties of mature, capped QDs. [31][32][33] The calculations presented in this work will also be utilized as the basis for calculations of the electronic band structure, the details of which will be presented separately.…”