Critical cluster size of InAs quantum dots formed by Stranski–Krastanow mode

Abstract

The number of In atoms in a critical cluster, i*, in Stranski-Krastanow ͑S-K͒ mode of InAs islands was determined to be 1-10. The i* was determined using an activation energy E A of 2.0 eV determined from an Arrhenius plot of the saturated density of InAs islands formed on a GaAs ͑001͒ surface by S-K mode of molecular beam epitaxy ͓K. Shiramine et al., J. Cryst. Growth 242, 332 ͑2002͔͒, and an activation energy of 1.6 eV for migration ͑surface diffusion͒ of In adatoms, inferred from other references. The common value ϳ2.0 eV of E A in S-K mode was ascribed to the small i*.

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

“…In the literature, the above experimental observations [89,[123][124][125][126][127][128] have often been taken as strong experimental evidence to support the view that InAs QD formation should be a surface process remarkably similar to adatom aggregation in homoepitaxial growth in the submonolayer regime. However, it will be further demonstrated in Section 4 that the outcome of practical epitaxial growth of InAs QDs depends sensitively on the growth parameters, such as the flux rate F and temperature T ; although some experimental data in the literature obtained under certain growth conditions seem to be consistent with Eqs.…”

“…For example, as mentioned in Section 3.2.4, Leon et al [124] and Shiramine et al [125] successfully fitted their experimental data for InGaAs/GaAs(001) to Venables' theoretical expression for the saturated density of 2D epitaxial islands [93], which was established originally for 2D epitaxial islands in the submonolayer regime of homoepitaxial growth. Furthermore, in general, InAs QDs are experimentally observed to be uniform in both size and shape; i.e., the island size distribution is quite narrow.…”

“…(3.2.2.9). Moreover, by such a fitting, Shiramine et al [125] even obtained a critical island size of 1-10 atoms for InAs QD formation via adatom aggregation and a thermal activation energy of 2.0 eV for the corresponding Arrhenius behavior. Even further, some authors [127,128] have successfully fitted their experimental observations of the InAs QD size distribution with the scale invariance ansatz, Eq.…”

“…In contrast, from the experimental viewpoint, InAs QD formation is definitely a self-limited growth process, and the growth power law s av ∝ θ z for an aggregation process makes no sense for InAs QD growth behavior. Therefore, the apparent fitting of the experimental data reported in these references [89,[123][124][125][126][127][128] may only demonstrate that both the universal laws, Eqs. (3.2.2.9) and (3.2.3.6), are very versatile and flexible in fitting experimental data obtained in a large number of cases, and may provide little insight into the nature of the InAs QD formation process.…”

“…(3.2.2.9) and (3.2.3.6), respectively. In the literature, some authors [123][124][125][126] have claimed that their experimental data on InAs QD number density are fitted well by the Arrhenius law, Eq. (3.2.2.9).…”