Theory of Split Quantum Dot Formation in Strained-Layer Semiconductor Heteroepitaxy

Semiconductor quantum dots (QDs) are three-dimensional (3D) nanocrystalline structures with a broad range of applications in the fabrication of electronic, optoelectronic, and photovoltaic devices. Controlling the size of quantum dots is used to tailor their electronic structure and has direct impact on their optoelectronic properties. A common approach to QD growth is strained-layer heteroepitaxy through the Stranski-Krastanow (SK) instability of the epitaxial film surface morphology, where the competition between surface energy and elastic strain energy in the epitaxial film results in a growth transition, from layer-by-layer epitaxy to formation of 3D islands. Intriguing, complex QD morphologies have been observed experimentally, such as those known in the literature as “double quantum dots” or “quantum dot pairs” characterized by split tips of variable height. This interesting pattern forming phenomenon can be exploited to control the size of QDs grown by strained-layer heteroepitaxy; however, such QD splitting is not well understood.

Toward a fundamental understanding of the quantum dot tip-splitting phenomenon, in this presentation, we report the results of a weakly nonlinear surface morphological stability analysis of a coherently strained heteroepitaxial thin film on a crystalline substrate. The analysis is based on a fully nonlinear continuum model of film surface morphological evolution coupled with the elastostatic boundary-value problem to determine the stress state in the epitaxial film. The model also accounts for a wetting potential contribution to the free energy of the film as well as surface diffusional anisotropy. The weakly nonlinear theory predicts that, in addition to the SK instability, long-wavelength perturbations from the planar film surface morphology also can trigger nonlinear instabilities, resulting in the splitting of a single QD into multiple QDs of smaller sizes. The theory also predicts the critical wavelength of the film surface perturbation for the onset of the nonlinear tip-splitting instability. We have found that, although the tip-splitting instability is caused entirely by the competition between the surface energy and the elastic strain energy, the wetting potential has a stabilizing effect on the planar film surface morphology, increasing the critical wavelength for the onset of the nonlinear tip-splitting instability. This critical wavelength is not affected by surface diffusional anisotropy. Moreover, we have conducted a systematic protocol of self-consistent dynamical simulations of the epitaxial film surface morphological evolution to assess the validity of the theoretical results. We have simulated QD tip splitting as a perturbed film planar surface evolves morphologically and validated the predictions of the weakly nonlinear stability theory. We have found that surface diffusional anisotropy affects the morphology of the QD, resulting in an asymmetric splitting of the QD and leading to QD morphologies that resemble strongly the TEM and AFM images of double QDs or QD pairs reported in the literature. Our study sets the stage for exploiting nonlinear surface phenomena in strained-layer heteroepitaxy toward precise engineering of tunable-size nanoscale surface features for optimal optoelectronic function.