Available online at www.sciencedirect.com Physica E 17 (2003) 480–483 www.elsevier.com/locate/physe Coherent growth of InAs/GaAs self-assembled quantum dots S.N. Santalla * , C. Kanyinda-Malu, R.M. de la Cruz Departamento de F sica, Universidad Carlos III de Madrid. Av. de la Universidad 30, 28911 Legan es (Madrid), Spain Abstract An energetic balance between surface and elastic strain energies based in continuum elastic theory is applied to evaluate the transition thickness in InAs/GaAs (0 0 1) self-assembled quantum dots. The growth process follows a Stranski–Krastanov (S–K) pattern, where a two–three-dimensional transition is undertaken at the so-called transition thickness. The system under investigation is a pseudomorphological structure characterized by a coherent behavior at the substrate/lm interface. For the dependence of the lattice parameter with height, a sigmoidal-type function with appropriate constraints is considered. Non-rigid substrate approximation is used in the evaluation of the transition thickness and the obtained numerical values are compared with the experimental ones. From these results, it can be claimed that the non-rigid substrate approach is appropriate to explain the relaxation process in the S–K growth mode. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 68.66.Hb; 68.65.-k; 61.46.+w Keywords: Self-assembled quantum dots; Elastic continuum model; Non-rigid approximation; Transition thickness 1. Introduction Since the last years, there is an increasing interest to achieve self-assembled nanostructures which are homogeneous in their sizes and shapes. In this chal- lenge, strained and unstrained quantum dots (QDs) have been fabricated using dierent types of tech- niques. For instance, molecular beam epitaxy (MBE) technique used to grow mismatch materials based in III–V and II–VI semiconductors yields Stranski– Krastanov (S–K) structures, which are quasi-uniform in their sizes and shapes. Although the phenomenol- ogy of the S–K growth mode is well known [1], the origin of the island formation mechanism is still a subject of debate. Two models are reported in the * Corresponding author. Tel.: +34-91-624-9184; fax: +34-91- 624-8749. E-mail address: ssantall@s.uc3m.es (S.N. Santalla). literature which explain the islanding mechanism. One of them suggests a continuous evolution from a at lm to three-dimensional (3D) islands [2–4],whilethe second one proposes an island faceting [5] by means of an abrupt overcoming of energetic barrier. Within the framework of the rst model, many theories based on equilibrium considerations of the balance of strain, interface and surface energies have been developed. Some of them use atomistic calculations for the stress distribution inside the as-grown lm [6], while others use continuum description of the elastic strain energy [2,7,8]. Despite the large number of works on growth process, few have been devoted to prediction of the “transition thickness”, thickness at which the bi-dimensional (2D) to 3D growth transition takes place [7,9–11]. In our previous works [10,11] we applied the continuum model to estimate the transi- tion thickness in arbitrarily shaped InAs/GaAs (0 0 1) 1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00845-7