Kevin P. Driver

Nanometer-scale composition measurements of Ge/Si(100) islands

Quantitative, nanometer-scale spatial resolution electron energy-loss spectroscopy (EELS) was used to map the composition of coherent islands grown by molecular-beam epitaxy of pure Ge onto Si(100). The Ge concentration XGe decreased, and the Ge/Si interface became more diffuse as the growth temperature increased from 400 to 700 °C. Integrated island volumes measured by atomic force microscopy (AFM) increased linearly with Ge coverage θGe, with slopes greater than 1. This result confirmed that island growth is faster than the Ge deposition rate due to Si interdiffusion. The linearity of the island volume versus θGe curves implied that XGe was independent of island size. XGe measured by EELS and AFM agree well with each other and correctly predicted the minimum dome size observed at each growth temperature.

All-electron path integral Monte Carlo simulations of warm dense matter: application to water and carbon plasmas.

We develop an all-electron path integral Monte Carlo method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend path integral Monte Carlo studies beyond hydrogen and helium to elements with core electrons. Path integral Monte Carlo results for pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics calculations at temperatures of (2.5-7.5)×10(5) K, and both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cm(3) and 10(4)-10(9) K.

Multiphase equation of state for carbon addressing high pressures and temperatures

We present a 5-phase equation of state for elemental carbon which addresses a wide range of density and temperature conditions: 3g/cc 100000K(bothfor ρ between3and12g/cc,withselecthigher-ρ DFTcalculationsas well). The liquid free energy model includes an atom-in-jellium approach to account for the effects of ionization due to temperature and pressure in the plasma state, and an ion-thermal model which includes the approach to the ideal gas limit. The precise manner in which the ideal gas limit is reached is greatly constrained by both the highest-temperature DFT data and the path integral data, forcing us to discard an ion-thermal model we had used previously in favor of a new one. Predictions are made for the principal Hugoniot and the room-temperature isotherm, and comparisons are made to recent experimental results.

Quantum Monte Carlo computations of phase stability, equations of state, and elasticity of high-pressure silica

Silica (SiO2) is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates, but fundamental failures occur. Such failures occur even in silica, the simplest silicate, and understanding pure silica is a prerequisite to understanding the rocky part of the Earth. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrödinger’s equation. Using ground-state QMC plus phonons within the quasiharmonic approximation of density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth’s core–mantle boundary. Our results provide the best constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the dense α-PbO2 structure above the core-insulating D” layer, but the absence of a seismic signature suggests the transition does not contribute significantly to global seismic discontinuities in the lower mantle. However, the transition could still provide seismic signals from deeply subducted oceanic crust. We also find an accurate shear elastic constant for stishovite and its geophysically important softening with pressure.

Phase transformation in Si from semiconducting diamond to metallic β-Sn phase in QMC and DFT under hydrostatic and anisotropic stress

Silicon undergoes a phase transition from the semiconducting diamond phase to the metallic -Sn phase under pressure. We use quantum Monte Carlo calculations to predict the transformation pressure and compare the results to density-functional calculations employing the local-density approximation, the generalizedgradient approximations PBE, PW91, WC, AM05, PBEsol, and the hybrid functional HSE06 for the exchangecorrelation functional. Diffusion Monte Carlo predicts a transition pressure of 14.0 1.0 GPa slightly above the experimentally observed transition pressure range of 11.3–12.6 GPa. The HSE06 hybrid functional predicts a transition pressure of 12.4 GPa in excellent agreement with experiments. Exchange-correlation functionals using the local-density approximation and generalized-gradient approximations result in transition pressures ranging from 3.5 to 10.0 GPa, well below the experimental values. The transition pressure is sensitive to stress anisotropy. Anisotropy in the stress along any of the cubic axes of the diamond phase of silicon lowers the equilibrium transition pressure and may explain the discrepancy between the various experimental values as well as the small overestimate of the quantum Monte Carlo transition pressure.

Evolution of Ge/Si(100) island morphology at high temperature

Atomic force microscopy, transmission electron microscopy, and electron energy-loss spectroscopy have been used to study the size, structure, and composition of Ge/Si(100) islands grown by molecular beam epitaxy at 700 °C. It is found that the island evolution is qualitatively different than for growth at lower substrate temperatures. For growth at 1.4 ML/min, the composition is determined to be Si0.56Ge0.44 and appears to be independent of island size. A higher growth rate, 4.8 ML/min, kinetically stabilizes pure Ge pyramids prior to Si interdiffusion taking place. These pure Ge clusters are absent at the lower growth rate, demonstrating the influence of deposition rate on island evolution. This result indicates that deposition kinetics can control island composition and morphology without varying growth temperature and associated thermally activated processes.

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy, which we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3-18.6  g cm(-3), 5.0×10(5)-1.3×10(8)  K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

First-principles equation of state calculations of warm dense nitrogen

Using path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD) simulation methods, we compute a coherent equation of state (EOS) of nitrogen that spans the liquid, warm dense matter (WDM), and plasma regimes. Simulations cover a wide range of density-temperature space,

First-principles equation of state and electronic properties of warm dense oxygen

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Equation of state and shock compression of warm dense sodium—A first-principles study

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