We investigated the size and temperature dependence of the energy gaps in H-terminated Si, SiC, and C quantum dots with diameters ranging from 1 to 10 nm, using tight-binding molecular dynamics (MDs) simulations. For the quantum dots with more than 1000 atoms, the order-N Krylov subspace method was employed. From our results, we formulated the energy gaps of the quantum dots as a function of their size and temperature. Our formula is applicable to the estimation of the energy gaps at any given temperature in the 0-600 K range, for a wide variety of quantum dot sizes (from a small quantum dot to bulk). The calculated energy gaps were in good agreement with the experimentally measured values. The thermal fluctuations of the band gap for a Si quantum dot were also analyzed in detail. We found that, unlike the case of bulk, the decrease in the energy gap at higher temperatures is predominantly caused by an increase in the splitting of the HOMO levels, with only a small contribution from the size expansion effect. For the temperature dependence of the energy gap of Si quantum dots, we also examined the effect of the media surrounding the quantum dots by performing tight-binding MDs simulations at finite temperatures with and without the restriction on the freedom of the motion of the surface H atoms. Our results have clarified that the temperature dependence of the energy gaps of quantum dots in a medium with weak restrictions on the freedom of the surface atomic motion (e.g., in gas or liquid) is larger than in a medium with strong restrictions (e.g., like SiO 2 ), especially in the case of small quantum dots.

We have performed first-principles total-energy electronic-structure calculations based on the densityfunctional theory to clarify energetics and electron states of the Ge vacancies in strained Ge layers on the Si͑001͒ surface. We find that pairing distortion is a principal relaxation pattern around the vacancies. The pairing of the two atoms located on either ͑110͒ or ͑110͒ plane is remarkably enhanced due to compressed strain in the lateral plane. It is found that the enhanced pairing causes reduction of formation energies, disappearance of deep levels in the monovacancy, deep-level crossing in the divacancy, and arrangement of the trivacancy on the ͑110͒ or the ͑110͒ plane. We have also found that the vacancy at the very interface layer facing the Si substrate is energetically unfavorable due to the larger energy cost to generate Si dangling bonds compared with Ge dangling bonds upon removal of atoms.

We have studied energetics and atomic and electronic structures of Ge mono-vacancies under biaxial and uniaxial strain. We have found that compressive strain drastically reduce the formation energy of Ge mono-vacancy, and strain induced Ge vacancy formation is expected. Further, our calculations show that energy levels of Ge mono-vacancies sensitively depend on the types of applied strain. In particular, direction of uniaxial strain greatly affects the position of Ge mono-vacancy levels. Our calculation indicates that acceptor levels are easily generated under [110] uniaxial compressive strain. Whereas, acceptor level generation is difficult under [100] uniaxial compressive strain.

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In this paper, we present a problem solving environment (PSE) for the large scale electronic structure calculations based on the O(N) tight binding method. We have developed a simulator named Fujitsu Tight binding Simulator (FuTiS). By implementing the O(N) method on parallel computers and introducing a common interface, we can perform the electronic structure simulations involving more than a few million atoms and expand the range of the application. We have performed the tight binding calculations to explore temperature dependencies of the energy gap in silicon quantum dots with several diameters using FuTiS.