Quantitative prediction of critical size for the formation of semiconductor quantum dots

Semiconductor quantum dots (QDs) are often fabricated by epitaxial growth. Germanium QD formation on Si(001) is an important prototype model system for both fundamental research and practical application. Ge film grows on Si via the Stranski-Krastanov growth mode, first forming a smooth wetting layer several monolayers thick, followed by three-dimensional islanding. The originally formed 3D Ge islands are called “huts”, being coherent with the Si substrate and bounded by 105-faceted crystalline planes. By combining the first-principles calculation with continuum theoretical modeling, we prescribe a “sequential multi-scale approach” to quantitatively investigate the formation and stability of Ge QD on Si. We calculate from first-principles the surface energies, surface stresses and their strain dependence of Ge-covered Si (001) and (105) surfaces, as a function of deposited Ge layer thickness. Using these results as input parameters, we further perform continuum model calculations to quantitatively predict the critical size for Ge QD nucleation/formation and assess their thermodynamic stability. Our studies have not only elucidated the existing experimental results, but also provided new insights to understanding the physical mechanisms underlying the QD formation and self-assembly.