Size dependent electronic properties of silicon quantum dots - an analysis with hybrid, screened hybrid and local density functional theory

We use an efficient projection scheme for the Fock operator to analyze the size dependence of silicon quantum dots (QDs) electronic properties. We compare the behavior of hybrid, screened hybrid and local density functionals as a function of the dot size up to $\sim$800 silicon atoms and volume of up to $\sim$20nm$^3$. This allows comparing the calculations of hybrid and screened hybrid functionals to experimental results over a wide range of QD sizes. We demonstrate the size dependent behavior of the band gap, density of states, ionization potential and HOMO level shift after ionization. Those results are compared to experiment and to other theoretical approaches, such as tight-binding, empirical pseudopotentials, TDDFT and GW.