Quantum dots (QDs) have discrete energy levels thus a well-defined band gap, which may be engineered by controlling their size and morphology. These unique features, plus dislocation-free obtainability via Stranski Krastanov growth, make QDs promising candidates for designing novel optoelectronic devices. We modeled the formation, spontaneous evolution and stability of quantum dots during heteroepitaxial growth under electric and stress fields, via irreversible thermodynamics treatment of surfaces and interfaces. The simulations demonstrated the interplay between the stable QDs and the material properties (e.g., crystallographic orientation and initial thickness of the film, diffusion and surface stiffness anisotropies, surface and interfacial energies, wetting contact angle and mismatch/external stresses). The investigation of stable QD morphologies enabled us to generate phase diagrams that show the stable QD configurations for a given set of material/process parameters. This information will provide design capability for QDs and hence desired QD-based device technologies. Supported by TUBITAK (grant no 315M222).