Large-Scale First-Principles Electronic Structure Calculations for Nano-Meter Size Si Quantum Dots

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We have studied the system size dependence of the density of states, band gap, and the charging energy of the large size Si quantum dots of 2.2 to 7.6 nm diameters by first-principles electronic structure calculations. The largest model examined in this study consists of over 10,000 Si atoms, and we performed such large calculations by using recently developed real-space density-functional theory code suitable for massively parallel computers. The density of states of 6 nm-diameter Si quantum dot is almost the same as that of the bulk Si. The band gaps of the Si quantum dots have been calculated by the ΔSCF method with local-density approximation, and we have found that the difference between the ΔSCF band gap and the Kohn-Sham eigenvalue gap is equal to the inverse of the dot radius. Consequently the ΔSCF band gap converges to the Kohn-Sham eigenvalue gap in the infinitely large size limit with the local-density approximation. [DOI: 10.1380/ejssnt.2010.48]

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