Electronic Structure Pseudopotential Calculations of Large (.apprx.1000 Atoms) Si Quantum Dots

Abstract

The electronic structure of quantum dots containing N [ge] 1000 atoms is difficult to calculate by conventional molecular methods since the effort scales as N[sup 3]. Our newly developed method allows calculation of eigenstates within a desired [open quotes]energy window[close quotes] and thus has a linear-in-N scaling. This method is applied here to Si quantum dots using a plane wave basis expansion and an empirical pseudopotential Hamiltonian. Hydrogen atoms passivate the surface dangling bonds using a realistic surface relaxation geometry. We investigate the dependences of energy gaps and radiative recombination rates on the size, shape, and orientation of the Si quantum dots. We find that (1) a unified curve exists for band gap vs size of quantum spheres, cubes, and rectangular boxes; (2) the band edge states of Si quantum dots are bulklike, not surfacelike; (3) the band gap is insensitive to the surface orientation and to the overall shape of the quantum dot as long as it is not too prolate; (4) the radiative lifetime is sensitive to the shape and orientation; and (5) effective mass and single band truncated crystal models describe inadequately the electronic structure of Si quantum dots in the size range ([approx lt]40 [angstrom]) studiedmore » here. 52 refs., 8 figs., 2 tabs.« less