Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

Cryogenic on-chip multiplexer for the study of quantum transport in 256 split-gate devices

We present a multiplexing scheme for the measurement of large numbers of mesoscopic devices in cryogenic systems. The multiplexer is used to contact an array of 256 split gates on a GaAs/AlGaAs heterostructure, in which each split gate can be measured individually. The low-temperature conductance of split-gate devices is governed by quantum mechanics, leading to the appearance of conductance plateaux at intervals of 2e^2/h. A fabrication-limited yield of 94% is achieved for the array, and a "quantum yield" is also defined, to account for disorder affecting the quantum behaviour of the devices. The quantum yield rose from 55% to 86% after illuminating the sample, explained by the corresponding increase in carrier density and mobility of the two-dimensional electron gas. The multiplexer is a scalable architecture, and can be extended to other forms of mesoscopic devices. It overcomes previous limits on the number of devices that can be fabricated on a single chip due to the number of electrical contacts available, without the need to alter existing experimental set ups.

Evaluating boundary dependent errors in QM/MM simulations.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations provide a powerful tool for studying chemical reactions, especially in complex biochemical systems. In most works to date, the quantum region is kept fixed throughout the simulation and is defined in an ad hoc way based on chemical intuition and available computational resources. The simulation errors associated with a given choice of the quantum region are, however, rarely assessed in a systematic manner. Here we study the dependence of two relevant quantities on the QM region size: the force error at the center of the QM region and the free energy of a proton transfer reaction. Taking lysozyme as our model system, we find that in an apolar region the average force error rapidly decreases with increasing QM region size. In contrast, the average force error at the polar active site is considerably higher, exhibits large oscillations and decreases more slowly, and may not fall below acceptable limits even for a quantum region radius of 9.0 A. Although computation of free energies could only be afforded until 6.0 A, results were found to change considerably within these limits. These errors demonstrate that the results of QM/MM calculations are heavily affected by the definition of the QM region (not only its size), and a convergence test is proposed to be a part of setting up QM/MM simulations.

Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution.

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Polarisation dependent all-optical nonlinearity far from the bandedge in active GaAs/AlGaAs quantum well waveguides

This paper describes a measurement on a GaAs quantum well waveguide with a high built in field across the quantum wells at a wavelength far from the bandedge. The device structure used for the measurement has been fabricated at STC Technology Ltd and is that of a standard laser ridge structure. In fabrication double heterostructure layers are grown on a [001] n + GaAs substrate, with the active region containing two intrinsic GaAs quantum wells of 10nm thickness separated by 10nm. A 4μm wide ridge is etched to provide transverse optical guiding. The experimental work has involved the use of 1.06μm wavelength light from a Q-switched Nd:YAG laser. Any induced change in refractive index is determined by measuring the change in transmission of the quantum well waveguide Fabry-Perot cavity. The waveguide is placed on a Peltier temperature controller to allow thermal tuning.

Growth, structural and optical properties of GaAs/AlGaAs Core/shell nanowires with and without quantum well shells

We have investigated the growth, structural properties and photoluminescence of novel GaAs/AlGaAs radial heterostructure nanowires, fabricated by metalorganic chemical vapour deposition. The effect of growth temperature on nanowire morphology is discussed. Strong photoluminescence is observed from GaAs nanowires with AlGaAs shells. Core/multishell nanowires, of GaAs cores clad in several alternating layers of thick AlGaAs barrier shells and thin GaAs quantum well shells, exhibit a blue-shifted photoluminescence peak believed to arise from quantum confinement effects. A novel two-temperature growth procedure for obtaining GaAs cores is introduced, and other nanowire heterostructures are addressed. © 2006 IEEE.

Quantum dots and nanowires for optoelectronic device applications

InGaAs quantum dots (QDs) and nanowires have been grown on GaAs by metal-organic chemical vapour deposition on GaAs (100) and (111)B substrates, respectively. InGaAs QD lasers were fabricated and characterised. Results show ground-state lasing at about 1150 nm in devices with lengths greater than 2.5 mm. We also observed a strong influence of nanowire density on nanowire height specific to nanowires with high indium composition. This dependency was attributed to the large difference of diffusion length on (111)B surfaces between In and Ga reaction species, with In being the more mobile species. Selective area epitaxy for applications in quantum-dot optoelectronic device integration is also discussed in this paper. ©2006 IEEE.

Quantum dots and nanowires for photonics applications

We review our results on integrated photonic devices fabricated using InGaAs quantum-dots. Selective-area metal organic chemical vapor deposition (MOCVD) is used to grow the active region with quantum dots emitting at different wavelengths for fabrication of the integrated devices. We will also review the structural and optical properties of III-V nanowires, and axial and radial nanowire heterostructures grown by MOCVD. In addition to binary nanowires, such as GaAs, InAs, and InP, we have demonstrated ternary InGaAs and AlGaAs nanowires. Core-shell nanowires consisting of GaAs cores with AlGaAs shells, and core-multishell nanowires with several alternating shells of AlGaAs and GaAs, exhibit strong photoluminescence. Axial segments of InGaAs have been incorporated within GaAs nanowires to form GaAs/InGaAs nanowire superlattices.