MODELING AND CONTROLLING NANAOSCALE SELF-ASSEMBLY OF EPITAXIAL QUANTUM DOTS
Open Access
- Author:
- Kumar, Chandan
- Graduate Program:
- Engineering Science and Mechanics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 28, 2009
- Committee Members:
- Lawrence H Friedman, Dissertation Advisor/Co-Advisor
Lawrence H Friedman, Committee Chair/Co-Chair
Francesco Costanzo, Committee Member
Joseph Paul Cusumano, Committee Member
Kristen Ann Fichthorn, Committee Member - Keywords:
- Thermal Field Directed Self-Assembly
Multilayer
Spectral Analysis
Surface Diffusion
Stochastic
Self-assembly
Quantum Dot
Elastic Heterogeneity - Abstract:
- Semiconductor quantum dots offer possibilities of novel electronic, optoelectronic and computing devices. Epitaxial self-assembled quantum dots (SAQDs) are 3D nanostructures or nanocrystals formed as a result of growth of single crystal film on a single crystal substrate, such that there is a lattice mismatch between the film and the substrate. The growing film acquires the lattice structure and orientation of the substrate. After an initial layer-by-layer growth, a transition from 2D growth to 3D growth takes place. The growth mode resulting in the formation of SAQDs is referred to as the Stranski-Krastanow (SK) growth mode. This growth begins with morphological perturbations on the surface of the strained film, where the strain results from the lattice mismatch between the film and the substrate. Typical, among others, semiconductor quantum dots grown on semiconductor substrates include SiGe on Si, InAs on GaAs and PbSe on PbEuTe. The self-assembly of quantum dots poses a major challenge of controlling the fluctuations in size and shape of the quantum dots, and spacings between the quantum dots. Many potential devices either need a periodic array of quantum dots with uniform sizes or require quantum dots to be placed at precise locations. Self-assembly of quantum dots is the most preferable method to produce large number of quantum dots in an easy way. However, self-assembly is a stochastic process and results in an array of quantum dots with somewhat non-uniform sizes and spatial distribution. Better control of self-assembly is desirable for potential device applications of SAQDs. Techniques, such as substrate patterning or growing multiple layers of quantum dots have been used to control the size and spatial distribution of SAQDs. In an endeavor to better understand the basic mechanism of formation and ordering of SAQDs, this work is aimed at improving existing continuum models and using various statistical tools to probe the morphology of quantum dots and their ordering phenomenon in self-assembly, and to evaluate and understand a case of directed self-assembly. As a consequence it is necessary to develop tools that can be used to predict and quantify the morphology and order of SAQDs with greater accuracy. Various parameters that characterize the formation, morphology and order of SAQDs are identified and results are presented to depict the effect of these parameters on SAQD formation and ordering. Additionally, the results of this work are meant to inform future experiments and numerical models, and aid in developing more advanced and accurate models that can both help understand and predict the trends in SAQD formation. In particular, in this work, the formation, morphology and ordering of quantum dots formed as a result of self-assembly and thermal-field directed self-assembly have been studied in detail, and models have been developed for quantitative assessment using parameters that can control order and morphology in SAQDs. All calculations are performed for Ge dots grown on a Si substrate. The presented work addresses three aspects of SAQD formation and order. First, thermal field directed self-assembly is studied as a potential technique for controlling the position and uniformity in size and spacings of the quantum dots by applying a spatial temperature distribution on the surface of the film. Three cases of spatial heating are studied, namely, uniform heating, periodic heating and a Gaussian shaped focused heating. A finite element model for the growth of Ge dots on Si is used. It is shown that periodic heating is an effective means for producing a periodic array of quantum dots with uniform size. It is also shown that a gaussian heating can effectively place a distinct quantum dot at a desired location. It is thus shown that thermal-field directed self-assembly may be an effective means for controlling the order of SAQDs. Results have been reported in the Journal of Applied Physics. Next, self-assembly of quantum dots is studied using a linear elastic stochastic model with focus on the effects of elastic heterogeneity on the formation, morphology and ordering of SAQDs. A procedure is laid out to include both elastic heterogeneity and elastic anisotropy in the continuum model for SAQD growth. It is shown that models that ignore elastic heterogeneity between the film and the substrate can introduce significant errors in the calculations relating to instability of a strained epitaxial film layer and also in the calculations relating to order of SAQDs formed as a result of this instability. Average film height is identified as a parameter influencing the formation, morphology and order of SAQDs. Various parameters characterizing the formation, morphology and order of SAQDs are identified and their trends with respect to the average film height is studied. These calculations also lay down the premise for the development of advanced models, for example, spectral model for quantum dot multilayers. Results have been reported in the Journal of Applied Physics. Finally, the ordering phenomenon in quantum dot multilayers is studied by developing a 3D dynamic linear stochastic spectral model for multilayers. Multilayering of quantum dots can lead to more uniformly sized and spatially ordered array of quantum dots. Several continuum models based only on energetics already exist which mostly focus on qualitative assessment of the arrangement of SAQDs. Here, a continuum model is developed that takes into account both the energetics and the dynamics to quantitatively assess the enhancement in vertical and lateral order of the quantum dots and to study the effect of various SAQD multilayer parameters like, layer to layer thickness, elastic anisotropy, growth time and number of deposited layers on the order of SAQDs. Linear elastic calculations are performed to find the elastic energy density distribution in a multilayered quantum dot structure. A stochastic model is developed to calculate the power spectrum and correlation functions corresponding to film height in different layers. The power spectrum and correlation functions are then used to characterize the morphology and order of SAQDs in quantum dot multilayers. It is shown that it is possible to tune the parameters to achieve a highly ordered array of SAQDs. The multilayer model predictions are compared with analogous experimental observations. Few other predictions on pattern formation and order enhancement are made that have to be corroborated by future experiments and similar non-linear calculations.