Order, Randomness and Fluctuations in Heteroepitaxial Quantum Dot Growth

Lawrence Friedman

Department of Engineering Science and Mechanics
Penn State University

Abstract. Epitaxial self-assembled quantum dots (SAQDs) represent an important step in the advancement of semiconductor fabrication at the nanoscale that will allow breakthroughs in electronics and optoelectronics. SAQDs are a result of Stranski-Krastanow growth whereby a growing planar film becomes unstable after an initial wetting layer is formed. In the case of SAQDs, this instability is driven by lattice-mismatch strain energy, but also tempered by surface energy and wetting energies. Typical systems include Ge_{x} Si_{1-x} deposited on a Si substrate and In_{x}Ga_{1-x}As/GaAs. In applications, order of SAQD arrays is a key factor. There are two types of order, spatial and size order. Spatial order is needed for nanoelectronic applications, while size order is required for both nanoelectronic and optoelectronic applications.

The role of crystal anisotropy and random fluctuations in influencing SAQD order during early stages of SAQD formation is studied through a stochastic model of surface diffusion. Results are presented from the first stage of modeling, a linear analysis of surface diffusion with stochastic initial conditions. It is found that spatial and size order are related and characterized similarly in terms of correlation lengths. There are two relevant and predictable correlation lengths that grow as the square-root of time. One of them is present in both the isotropic and anisotropic cases, but the other one is due to crystal anisotropy. This second anisotropy related length plays a limiting role for SAQD order. Finally, it is also found that SAQD order is enhanced when the deposited film is allowed to evolve at heights near the critical wetting surface height that marks the onset of non-planar film growth. Later stages of modeling will include solving the appropriate linear and non-linear Langevin equation for surface diffusion. Experimental observations are related to the presented results and expected future modeling outcomes.