Atomistic theory of nanostructures: beyond 10-million atoms in simulation*

Optical and electronic properties of novel nanostructures arise from atomic scale contributions related to alloy randomness, substrate orientation or thin monolayer-thick interfaces. All these effects must be accounted for by an accurate, atomistic approach. However, computations for realistic size nanostructures involve number of atoms going above 1-million atoms for nanowire quantum dots, exceeding 10-million atoms for crystal phase quantum dots and may reach 100-millon for future silicon nanodevices doped with chains of individual phosphorus atoms. In this presentation I present a step-by-step solution to this problem: empirical tight-binding and exact diagonalization scheme that unites linearly scaling computational time with the essentials of the atomistic modelling. I illustrate our method on the example of self-assembled quantum dot, with the emphasis on the dark exciton spectra. Next, I show that alloy randomness alone is sufficient to trigger substantial excitonic fine structure even in cylindrical nanowire quantum dots.
Finally, I show results of our approach applied to crystal phase quantum dots and phosphorous dopants in silicon involving up to 10 million atoms in the computation.