Photoluminescence lifetimes of Si quantum dots

Abstract

We present a continuum model for the calculation of the electron states in Si dots that accounts for the effects of size, shape, and crystallographic orientation of the dots. This formalism has been used to study the behavior of the photoluminescence (PL) lifetime in Si quantum dots. This is due to the anisotropy of the silicon band structure and the confinement in quantum dots, which result in a cluster of energy levels from the different valleys of Si. Although these levels are very close in energy, they have very different recombination rates. Hence, there are (relatively) fast and slow levels at approximately the same energy. This feature causes a temperature dependence of PL in Si nanostructures, hence it is suggested that dispersion in the magnitude of the PL lifetimes in Si dots is at the origin of the observed stretched exponential behavior of PL lifetime in porous Si. Both zero phonon and phonon-assisted recombinations have been included in the calculations. Zero phonon recombination dominates in small dots (∼2nm) and the lifetime is ∼10μs. In larger dots, of a size of ∼4nm and above, phonon-assisted transitions become dominant and PL lifetimes are of the order of 1–10ms.