Interband Coulomb coupling in narrow-gap semiconductor nanocrystals:k·ptheory

Abstract

We derive the matrix elements of Coulomb interaction between states with different numbers of electrons and holes in a semiconductor nanocrystal within the eight-band $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ theory. These matrix elements are responsible for multiple exciton generation which may contribute to the enhancement of the efficiency of solar cells. Our calculations are performed within the multiband envelope function formalism based on the states resulting from diagonalization of the eight-band $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ Hamiltonian. We study in detail and compare two contributions to the interband Coulomb coupling: the mesoscopic one, which involves only the envelope functions and relies on band mixing, and the microscopic one, which relies on the Bloch parts of the wave functions and is nonzero even between single-band states. We show that these two contributions are of a similar order of magnitude. We also study the statistical distribution of the magnitudes of the interband Coulomb matrix elements and show that the overall coupling to remote states decays according to a power law favorable for the convergence of numerical computations.