Ab InitioCalculations for Large Dielectric Matrices of Confined Systems

Calculations for optical excitations in confined systems require knowledge of the inverse screening dielectric function ϵ^-1(r,r^'), which plays a crucial role in determining exciton binding energies. We present a new efficient real-space method of inverting and storing large ab initio dielectric matrices of confined systems, which relies on the separability of $ϵ$ matrix in r and r^'. The method has allowed, for the first time, full ab initio calculation of ϵ^-1(r,r^') of dimension N~270 000, and for quantum dots as large as Si₃₅H₃₆. The effective screening in Si quantum dots up to 1.1 nm in diameter is found to be very ineffective with average dielectric constants ranging from 1.1 to 1.4.