Summary

We develop the density-functional calculation code based on the real-space approach. We also apply the code for the materials with nanometer-scale sizes. In particular, we elucidate that the electronic structure of Si10000 cluster is completely different from that of the bulk Si due to the nano-scale confinement effect.

Achievements

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First-principles electronic structure calculation based on the Density-Functional Theory (DFT) has become a reliable tool for quantitative prediction on the matterial properties of various kinds in physics, chemistry, biology, and industry. In order to cover such wide range of the fields and materials, DFT program code is often required to treat large-size systems, such as proteins and nano structures wihch are constructed from a few thousand to a few hundred thousand atoms, within a reasonable computational time.

In our group, we have developed a DFT program code suitable for massively parallel computer architecture, and have applied it to the systems of 10,000 Si atoms. The program code is based on the real-space finite-difference pseudopotential method, which is more suitable for parallel computation than the usual plane-wave basis method. The most demanding parts of the calculations, namely the Gram-Schmidt orthogonalization and the sub-space diagonalization, whose computational scaling are the cube of the system size, can be performed with the 80% of the theoretical peak performance due to the tunig for enhanced use of the level 3 BLAS.

Fig. 1 shows a Si quantum dot of 10,701 Si atoms and 1,996 H atoms. For this system, we perform the self-consistent electronic structure calculation with 1,024 nodes of the massively parallel cluster PACS-CS at CCS. The result of the density of states (DOS) is shown in Fig. 2. The DOS is almost the same as that of the bulk (which is also shown in Fig.2 for comparison). However, we found that the band gap is still higher than the bulk one by a few hundred meV, and therefore the quantum dot of 10,701 Si atoms can be regarded as a system combines the properties of a bulk and a finite system.

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Future plan

Nano-structures such as semiconductor clusters reveals bulk-like properties when the sizes of nano-structures becomes large. However, there are few systematic studies which aim to clarify how the properties of nano-structures reaches bulk-like as the system size increases. Our group focused on band gap as an example of material properties, and clarify the detailed behaviors of cluster size dependence of band gaps. Here, we investigate the electronic structures such as energy level structures of nano-structures and clarify their size dependence. In particulr, we plan to point out the difference between nano-structures with direct and indirect gaps based on the large scale first principles calculations, leading to the physics based guiding principles toward future nano-technologies.

Center for Computational Sciences, University of Tsukuba