of Materials Science
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Computational Aspects of Materials Science |
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Epitaxy is the growth of a thin film as a single crystal whose properties
are determined by those of the substrate. Because of the wide range of
length and time scales involved in epitaxial growth, no single model is
adequate for its description. This talk will describe a multi-scale
approach involving atomistic, continuum and bulk models. In particular,
this includes a new island dynamics model for epitaxial growth and a level
set method for its simulation. This model involves coarse graining in the
lateral directions, but retains atomistic discreteness in the growth
direction. It has been validated by comparison to results from kinetic
Monte Carlo simulations. Finally, we discuss application of feedback
control in molecular beam epitaxy (MBE), both in simulation and in
experiment.
Devices based on III-V semiconductor materials are currently the
workhorse for high performance, high-frequency electronic and
optoelectronic applications. While most telecommunication appliances
currently use GaAs-based materials, InAs, when used in conjunction with
AlSb or GaSb, is a promising material for next-generation high-speed,
low power devices. We have developed a model for the epitaxial growth of
InAs which includes microscopic details (i.e. surface reconstructions
and zincblende lattice) and different behavior of In and As
kinetics. The relevant parameters are determined mainly by ab
initio density functional calculations. For describing equilibrium
properties, the model contains essentially no free parameters and
correctly describes experimentally observed features of the growth
surface such as a phase transition from the thermodynamically stable
(2x4)-a2 to the (2x4)-b2 reconstruction. The model also
correctly describes all of the known experimental trends for InAs
growth, including the As pressure dependence. The simulation results are
supported by a detailed comparison at a microscopic level to
experimental STM data.
The phase-field method has emerged as a powerful alternative to
traditional front tracking methods for modeling a wide range of
microstructural evolution problems in materials
science. This talk will discuss the basic physics/thermodynamics of
this approach and illustrate its application in the context
of dendritic solidification.
We have recently succeeded in constructing the first atomic-level description
of any perovskite that can both describe the full phase diagram and can be used
for the simulation of ferroelectricity in interfacial and defected systems. This
model, which combines a Buckingham potential with an isotropic shell model,
provides a good description of the ferroelectric phase behavior of KNbO3,
reproducing the experimentally observed sequence of phases on heating: rhombohedral,
orthorhombic, tetragonal and finally cubic, with transition temperatures very close
to the experimental values. Furthermore, the lattice parameters in the four phases
agree with experimental values to better than 1%, and the calculated polarization
in the tetragonal phase is only about 20% larger than the experimental value.
We have also constructed a potential that describes the incipient ferroelectric
behavior of KTaO3; this has allowed us to simulate the ferroelectric
properties of KTaxNb1-xO3 solid solutions and
KNbO3/KTaO3 superlattices. In each case, the atomic-level
information provided by the simulations has allowed us to elucidate the intimate
coupling of the ferroelectric behavior of the KNbO3 and KTaO3
components and the coupling between ferroelectricity and elastic strain.
Microstructure can be modeled in some crystals by
energy densities with multiple symmetry-related minimizing
configurations. For martensitic crystals, the bulk
elastic energy is minimized only by the fine scale mixing
of the symmetry-related variants.
Several computational methodologies can be used to
compute martensitic microstructure, the most appropriate
and efficient depends on what information is desired.
Direct finite element computation has been successfully done
to study the detailed microstructure for several problems.
For the computation of macroscopic deformation or properties,
it may sometimes be more efficient to use effective or
relaxed energy densities that account for the energy
attainable by microstructure.
Phase separation in crystalline solids is almost always accompanied by
long ranged elastic stress. These stresses, which result from a difference in
lattice parameter between the particle and matrix can give rise to qualitatively
new phenomena as compared those in a stress-free system, such as changes
in particle shape with increasing particle size, particle migration and
alignment, and inverse coarsening wherein small particles grow at the expense of large
particles. At issue is the manner in which these local phenomena influence the dynamics of
ensemble-averaged quantities. We have investigated the dynamics of Ostwald ripening in
elastically stressed crystalline solids through large-scale numerical simulations that employ
many thousands of particles. Using the insight provided by the simulations, a theory for
the dynamics of late-stage phase separation in elastically anisotropic homogeneous solids is
developed. Both the theory and simulations show that for the systems considered elastic stress does
not alter the exponent of the temporal power law for the average particle size but does effect
the amplitude of the power law in a manner that is only a function of the symmetry of the
particle morphology. The effect of interparticle elastic interactions on particle morphology and
spatial correlations will also be discussed.
The insatiable need for communications bandwidth has fueled an
unprecedented growth in optical networking systems and components. Optical
components will play an increasingly important role as networks and
computers approach the inherent limitations of electrical systems. I will
present details on two areas of optical device design which rely heavily on
the use of computational methods, understanding microstructured photonic
crystals and optimizing high-speed, electro-optic modulators.
Photonic crystals are composite systems composed of a periodic arrangement
(often on the order of the wavelength light) of two or more materials with
different optical properties. By carefully designing the structure, we
create optical materials which exhibit optical properties controlled
primarily by the crystal structure. The most compelling example of such a
photonic crystal is the photonic bandgap crystal. Similar to its electronic
analogue, a bandgap crystal inhibits the propagation of light (photons)
which has a frequency falling within the bandgap. However, the utility of
photonic crystals reaches far beyond this specific example. With the help
of optical modeling tools, we can design microstructured materials which
exhibit optical properties difficult to find in single material or more
conventional composite materials. I will present results concerning the
modeling and fabrication of 3d photonic crystals and 2d microstructured
optical fibers.
The second area I will discuss will concentrate on the design and modeling
of electro-optic modulators. An electro-optic modulator is the primary
interface between electrical signals and the optical signals used for long
haul communications networks. A modulator relies upon a material (such as
lithium niobate) which changes effective refractive index when subjected to
an applied electric field. The design of high speed modulators (10 Gb and
above) thus requires the modeling of the interaction of an applied RF signal
and the optical signal to be modulated. The fabrication of these modulators
requires significant understanding of the processing tolerances, but also
requires an understanding of the material response to both RF and optical
excitation. I will discuss the development of an optical, vector beam
propagation code and coupled Poisson solver for the treatment of
electro-optic materials and devices.
Talk 2: "Large Connecting Ab Inito and Kinetic Models: Simulation of the Equilibrium and Growth Kinetics of III-V Semiconductor Surfaces"
Talk 3: "Multiscale Modeling of Microstructural Evolution using the Phase-Field Method: From Atoms to Dendrites"
Talk 4: "Ferroelectricity in Perovskite Solid Solutions and Thin-Film Heterostructures by Molecular-Dynamics Simulation"
Talk 5: "Computational Methods for Crystal Microstructure"
Talk 6: "The Dynamics of Late-Stage Phase Separation in Elastically Stressed Solids"
Talk 7: "The Design and Understanding of Microstructured Photonic Crystals and Electro-optic Devices"
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