Energetics of neutral interstitials in germanium
Significant obstacles remain for the fabrication of germanium n-MOSFETs, including enhanced diffusion of donor atoms which leads to electrical deactivation. The preferential generation of self-interstitials via proton irradiation reduces donor diffusion and offers a promising route for effective fabrication of n-type devices. Fairly little effort has been devoted to the theoretical study of germanium interstitials. In this work, neutral self-interstitial formation energies are calculated with the accurate Diffusion Monte Carlo (DMC) method. Taking care to minimize errors, calculations are performed for 216 atom systems. Formation energies for hexagonal, tetragonal, and split/dumbbell structures are found to be 5.3 eV, 6.1 eV, and 4.7 eV, respectively; a significant increase over predictions from Density Functional Theory (DFT). This indicates a large error on the part of DFT, DMC, or both. If the DMC energies are biased, the most likely source is the fixed node error. Further calculations should be performed with better wavefunctions to resolve this concern, perhaps using fast multideterminant expansions beginning to be applied to condensed systems. A novel form of the quantum energy density is also introduced to exclude statistical noise from irrelevant portions of defect systems to improve DMC efficiency. The best results for the hexagonal structure achieve a 3x speedup over standard total energy calculations. No speedup is obtained for the tetragonal and split interstitial systems, perhaps due to the increased pressure in the fixed volume cells or the presence of charge-energy fluctuations across the defect/bulk boundary. Applications to even larger systems or further refinements to the method may be required to routinely increase efficiency for DMC formation energy calculations. Also included in this work are two sub-studies in addition to the major effort regarding germanium. The first involves the calculation of the vibrational excitation spectrum of bcc helium-4, which was experimentally observed to contain unexpected optic-like branches. This is explained by the quantum vibrational properties of helium atoms where states with d or 2s symmetry form the optical branches. The second project studies in detail the bias due to walker population control in the DMC method and a possible way to increase parallel efficiency while reducing the bias.
quantum monte carlo, diffusion monte carlo, correlation function monte carlo, germanium, interstitial, defect, formation energy, energy density, helium, population control bias
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign