Dependence of photoluminescence efficiency on size in silicon nanostructures: phenomenological investigations

The discovery of efficient photoluminescence (PL) in porous and nanocrystalline silicon has generated considerable interest over the last decade. The present work makes the following simple proposition: the dependence of the PL efficiency on size is non-monotonic and hence there exists an optimum size for PL efficiency in nanocrystalline silicon. We present simple phenomenological formulae which delineate the dependence of the efficiency on size. Besides the existence of an optimum size they also indicate that there is a nanometer range over which the efficiency is substantial. This assertion is not made on the basis of a theoretical calculation but by a wide study and careful analyses of extant literature, largely experimental. We present two sets of compelling reasons for our assertion, one empirical, and the other semi-empirical. We indicate how the assertion of the optimum size may be verified by experimental studies.