Browsing by Subject "crystal growth"

Now showing 1 - 4 of 4
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    Analysis of Droplets and Bubbles in Crystal Growth Processes: Migration and Engulfment
    (2024) Pawar, Swanand
    The crystal growth process for certain materials faces the problem of foreign particles, drops or bubbles getting lodged into the solid as it is grown. There can be significant risks associated with such impurities. In materials such as sapphire and silicon being grown from the melt, bubbles could enter the melt phase and make their way into the crystal by the process of engulfment. This is very commonly observed in sapphire crystals. There is also a chance for growth instabilities during certain solution growth processes, which could result in pockets of high solute concentration in certain places. This has been seen in scintillator crystals such as cadmium zinc telluride and even Arctic ice. This work is divided into two parts. In the first part, the engulfment of bubbles into a crystal is studied using detailed finite element modelling. The effect of various process parameters is studied and an effort is made to understand process conditions under which such engulfment can be avoided. In the second part, a simplified one-dimensional transport model is developed for the temperature gradient zone melting technique, in which a thermal gradient is applied across a solid to move any liquid drops stuck inside it to one end of the sample. Analytical expressions for drop size, speed and position as a function of time are derived for a drop undergoing such thermal migration. The derivation is also used to gain insight into process physics and some important time scales.
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    Mathematical modeling for assorted problems in crystal growth
    (2019-12) Wang, Kerry
    Crystal growth is a field that is ripe with opportunities for mathematical modeling to elucidate interesting phenomena. Important process parameters such as solute concentration, interface shape and location, and temperature field are uniquely difficult to observe \textit{in-situ} for many high temperature melt crystal growth systems. Additionally, the slow process of growing large, industrially-relevant single crystals can be prohibitive in time, material cost, and labor for tedious repeated experimental studies that are likely to be destructive. Modeling provides an efficient way for researchers to quickly gain an understanding of the physics underlying a crystal growth system. In this thesis, we examine three different cases where mathematical modeling can be utilized to interrogate crystal growth systems. First, we investigate the transport of oxygen in Czochralkski-grown silicon by posing a simple lumped-parameter model. The lumped-parameter model tracks transport of oxygen into and out of the melt without specifying its spatial distribution, relying only on estimated fluxes from various surfaces. The lumped-parameter model offers a near-instantaneous way to obtain a coarse estimate of oxygen given process parameters such as crystal/crucible rotation scheme, melt height, and melt overheating. Second, we examine a past experiment involving Europium-doped BaBrCl monitored \textit{in-situ} via Energy-Resolved Neutron Imaging. Europium acts as a strong neutron attentuator, allowing visualization of its migration in both the solid and melt phases. A prior experiment was conducted to perform \textit{in-situ} imaging of a melt crystal growth system, and we realized this presented an opportunity to use modeling to extract additional data from this past experiment. A 1D model of europium migration in both phases was formulated and solve via Finite Fourier Transforms and Finite Difference Method. The Finite Difference Method, being more flexible, allowed us to deduce the apparent solid and liquid diffusion coefficients of Eu as well as its segregation coefficient. This coupling of \textit{in-situ} imaging and modeling presents an exciting new way to measure physical properties and extract additional value from past experiments. Last, we analyze the curious phenomenon of Temperature Gradient Zone Melting (TGZM), whereby a solute-rich liquid particle migrates through a solid crystal under a thermal gradient. While this phenomenon has been studied in the past, prior models failed to give practical predictions in the time-evolution behavior of such migrating particles. We pose analytical and numerical models of 1-dimensional TGZM, which agree well with each other. The numerical model, solved via Finite Element Method, shows reasonable agreement with experimental data on Te-rich second-phase particles migrating in CdTe. It additionally shows excellent agreement with another physical system, NaCl brine particles in water ice, providing a far more accurate description of the particle's migration than previous theoretical models. Considerations are made for extending the model to higher dimensions in order to understand changes in particle morphology during migration. Different types of modeling using various analytical and numerical techniques are employed for each of these case studies. These three example cases show different scenarios in which mathematical modeling can be utilized to help researchers gain insight in crystal growth systems.
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    Processing of Copper Zinc Tin Sulfide Nanocrystal Dispersions for Thin Film Solar Cells
    (2016-06) Williams, Bryce
    A scalable and inexpensive renewable energy source is needed to meet the expected increase in electricity demand throughout the developed and developing world in the next 15 years without contributing further to global warming through CO2 emissions. Photovoltaics may meet this need but current technologies are less than ideal requiring complex manufacturing processes and/or use of toxic, rare-earth materials. Copper zinc tin sulfide (Cu2ZnSnS4, CZTS) solar cells offer a true "green" alternative based upon non-toxic and abundant elements. Solution-based processes utilizing CZTS nanocrystal dispersions followed by high temperature annealing have received significant research attention due to their compatibility with traditional roll-to-roll coating processes. In this work, CZTS nanocrystal (5 – 35 nm diameters) dispersions were utilized as a production pathway to form solar absorber layers. Aerosol-based coating methods (aerosol jet printing and ultrasonic spray coating) were optimized for formation of dense, crack-free CZTS nanocrystal coatings. The primary variables underlying determination of coating morphology within the aerosol-coating parameter space were investigated. It was found that the liquid content of the aerosol droplets at the time of substrate impingement play a critical role. Evaporation of the liquid from the aerosol droplets during coating was altered through changes to coating parameters as well as to the CZTS nanocrystal dispersions. In addition, factors influencing conversion of CZTS nanocrystal coatings into dense, large-grained polycrystalline films suitable for solar cell development during thermal annealing were studied. The roles nanocrystal size, carbon content, sodium uptake, and sulfur pressure were found to have pivotal roles in film microstructure evolution. The effects of these parameters on film morphology, grain growth rates, and chemical makeup were analyzed from electron microscopy images as well as compositional analysis techniques. From these results, a deeper understanding of the interplay between the numerous annealing variables was achieved and improved annealing processes were developed.
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    Understanding growth rate limitations in production of single-crystal cadmium zinc telluride (CZT) by the traveling heater method (THM)
    (2017-03) Peterson, Jeffrey
    Cadmium telluride (CdTe) and cadmium zinc telluride (CZT) are important optoelectronic materials with applications ranging from medical imaging to nuclear materials monitoring. However, CZT and CdTe have long been plagued by second-phase particles, inhomogeneity, and other defects. The traveling heater method (THM) is a promising approach for growing CZT and other compound semiconductors that has been shown to grow detector-grade crystals. In contrast to traditional directional solidification, the THM consists of a moving melt zone that simultaneously dissolves a polycrystalline feed while producing a single-crystal of material. Additionally, the melt is highly enriched in tellurium, which allows for growth at lower temperatures, limiting the presence of precipitated tellurium second-phase particles in the final crystal. Unfortunately, the THM growth of CZT is limited to millimeters per day when other growth techniques can grow an order of magnitude faster. To understand these growth limits, we employ a mathematical model of the THM system that is formulated to realistically represent the interactions of heat and species transport, fluid flow, and interfacial dissolution and growth under conditions of local thermodynamic equilibrium and steady-state growth. We examine the complicated interactions among zone geometry, continuum transport, phase change, and fluid flow driven by buoyancy. Of particular interest and importance is the formation of flow structures in the liquid zone of the THM that arise from the same physical mechanism as lee waves in atmospheric flows and demonstrate the same characteristic Brunt--V ais al a scaling. We show that flow stagnation and reversal associated with lee-wave formation are responsible for the accumulation of tellurium and supercooled liquid near the growth interface, even when the lee-wave vortex is not readily apparent in the overall flow structure. The supercooled fluid is posited to result in morphological instability at growth rates far below the limit predicted by the classical criterion by Tiller et al. for constitutional supercooling.