Predicting the electronic properties of 3D, million-atom semiconductor nanostructure architectures

The past ~10 years have witnessed revolutionary breakthroughs both in synthesis of quantum dots (leading to nearly monodispersed, defect-free nanostructures) and in characterization of such systems, revealing ultra narrow spectroscopic lines of <1meV width, exposing new intriguing effects, such as multiple exciton generation, fine-structure splitting, quantum entanglement, multiexciton recombination and more. These discoveries have led to new technological applications including quantum computing and ultra-high efficiency solar cells. Our work in this project is based on two realizations/observations: First, that the dots exhibiting clean and rich spectroscopic and transport characteristics are rather big. Indeed, the phenomenology indicated above is exhibited only by the well-passivated defect-free quantum dots containing at least a few thousand atoms (colloidal) and even a few hundred thousand atoms (self assembled). Understanding the behavior of nanotechnology devices requires the study of even larger, million-atom systems composed of multiple components such as wires+dots+films. Second, first-principles many-body computational techniques based on current approaches (Quantum Monte-Carlo, GW, Bethe-Salpeter) are unlikely to be adaptable to such large structures and, at the same time, the effective mass-based techniques are too crude to provide insights on the many-body/atomistic phenomenology revealed by experiment. Thus, we have developed a set of methods that use an atomistic approach (unlike effective-mass based techniques) and utilize single-particle + many body techniques that are readily scalable to ~10-10 atom nanostructures. New mathematical and computational techniques have also been developed to accelerate our calculations and go beyond simple conjugate gradient based methods allowing us to study larger systems. In this short paper based on a poster presented at the DOE SciDAC06 conference we will present the overall structure as well as highlights of our computational nanoscience project. 1. New algorithms for calculating electronic properties of large nanostructures The infrastructure we have developed to perform atomistic pseudopotential calculations of large nanostructures is composed of a series of different steps as shown in Figure 1. The input geometry is determined from geometrical considerations and experimental data. The atomic positions are obtained by minimizing the strain field using the classical valence force field (VFF) method trained to reproduce LDA equilibrium geometries of prototype structures [1]. The potential of the system is then Institute of Physics Publishing Journal of Physics: Conference Series 46 (2006) 292–298 doi:10.1088/1742-6596/46/1/040 SciDAC 2006 292 © 2006 IOP Publishing Ltd calculated using a superposition of screened atomic potentials which are fitted to the experimental band structure and LDA wavefunctions. Once we have calculated the potential we need to define a basis set in which the single particle Schrödinger equation will be solved. We have developed two different methods, one that uses a simple planewave basis set up to a certain energy cut-off (ESCAN[2]) and the other which uses a linear combination of strained bulk bands (SLCBB[3]). The single-particle Schrödinger equation is then solved as an interior eigenvalue problem, i.e. only a few eigenstates near the band gap are computed using the folded spectrum method. Once the singleparticle energies and wave functions have been obtained the next step is to calculate the electronic excitations of the quantum dot. This task is accomplished using the configuration interaction (CI) method after first calculating the Coulomb and exchange integrals. Finally we calculate different properties of the system such as absorption and emission spectrum (see Figure 1 for a full list) based on post processing of the outputs of the other codes. This pioneering methodology was developed by Zunger, Wang, Franceschetti and collaborators in the period 1995 to 2003. Atomistic Pseudopotential Theory of Nanostructures Minimize Strain (vff) Input Geometry Solve the single-particle Schroedinger Equation The Many-Body problem: Coulomb and exchange Integrals Configuration Interaction Calculate the Crystal Potential 1: superposition of atomic pseudopotentials 2: charge patching 3: screening; 4: surface polarization; 5: piezoelectric potential Post Processors and Functionalities • Absorption and emission spectrum: exciton, multiexcition, trions