Simulation of thermal-field directed self-assembly of epitaxial quantum dots

Thermal-field directed self-assembly (TDSA) of epitaxial self-assembled quantum dots (SAQDs) is the method of using spatially varying temperature patterns to influence SAQD growth kinetics and ultimately the order and positions of SAQDs. The effectiveness of TDSA in enhancing the size and spatial order or precision placement of single dot or dot cluster is investigated via a two dimensional (one dimensional surface) finite element based model of Ge dots grown on Si. Three different cases of heating are studied, namely, spatially constant heating, spatially periodic heating, and a Gaussian shaped hot spot. Statistical measures are used to study the evolution of quantum dot heights and spacings between the quantum dots for different temperatures and heating cases. Spatially periodic heating is investigated for a wavelength of about 185 nm corresponding to the wavelength of an excimer laser. In order to investigate the effectiveness of spatially periodic heating in enhancing the spatial and size order of the SAQD array, the results are compared with those obtained from spatially uniform heating. Simulations using Gaussian shaped hot spot are performed to demonstrate its effectiveness in placing a distinct dot at a desired location. Results from the simulations indicate that spatially periodic heating proves to be an effective means for producing an array of uniformly sized and spaced quantum dots for a broad range of temperatures. Also, the results from the simulations using Gaussian shaped hot spots show that such a form of heating can effectively place a distinct quantum dot near a desired location for a broad range of temperature values. (C) 2007 American Institute of Physics.