Empirical Pseudopotential Calculation of Self-Assembled Quantum Dots

L.-W. Wang, J. Kim, A. Williamson, A. Zunger, National Renewable Energy Laboratory

Research Objective

Self-assembled, pyramidal semiconductor quantum dots can be formed during the Stranski-Krastanow growth mode in molecular beam epitaxy. Such systems have technological potentials for laser, LED (light-emitting diode), memory, and single-electron devices. Their electronic structures are fundamentally different from bulk systems. New physics emerge because the electron and hole are confined inside the small regions of the quantum dots. We performed state-of-the-art pseudopotential calculations of the quantum dot electronic structures to study this new physics. The systems calculated contain about one million atoms.

Computational Approach

The empirical pseudopotentials, and their changes with pressure, are fitted to the bulk band structures. The atomic positions are relaxed from the ideal zinc blende positions using the classical valence force-field model. The single-particle Schršdinger's equation is constructed from the relaxed atomic positions, and the empirical pseudopotentials. Schršdinger's equation for the million-atom system is solved using the folded spectrum method, making it an O(N) scheme. Parallel fast Fourier transformation on the Cray T3E is used to accelerate this process. The number of computational Flops scales linearly with the number of nodes on the T3E machine up to 256 nodes. Once the single-particle states are obtained, electron-hole coulomb and exchange integrals are computed. This gives the excitonic levels.

Accomplishments

The parallel code ESCAN has been tested and used extensively for many nanostructure calculations. InAs/GaAs pyramidal quantum dot has been studied for different dot sizes and shapes. Comparing with experimental data, our calculated results help to resolve the shape of the quantum dot, the anisotropy of the polarization, the number of bound electron states, and the level splittings of the electronic structures.

Significance

Nanoscale heterostructure is the future of semiconductor engineering. The ability to accurately calculate the electronic structure of such a million-atom system is crucial for the understanding of its new physics and for the possible design of such a system. The current approach represents a way to replace the old kp type calculations, which are inadequate for describing many aspects of the system.

Publications

L. W. Wang and A. Zunger, "Solving Schrodinger's equation around a desired energy: application to silicon quantum dots," J. Chem. Phys. 100, 2394 (1994).

Conduction states (CBM to CBM+3) and valence states (VBM to VBM-3) for different pyramidal quantum dot sizes: "b" is the length of the square of the pyramid base, and "a" is the zinc blende lattice constant.

A. J. Williamson, A. Zunger, and A. Canning, "Prediction of a strain-induced conduction-band minimum in embedded quantum dots," Phys. Rev. B, Rapid Commun. 57, R4253 (1998).