  Accurate energy-size dependence of excitonic transitions in semiconductor
nanocrystals in the strong confinement regime using classical theoretical
approaches such as effective mass approximation, tight binding, or empirical
pseudo-potential is difficult. We propose a simple empirical expression with
three fitting parameters that accurately relates the size dependence of most
known excitonic transitions in CdSe and in InAs nanocrystals. We show that this
empirical expression can be deduced from a phase jump approach if the charge
carriers are considered to travel on the atomic lattice of the nanocrystal and
gain energy upon bouncing at the nanoparticle boundaries. This empirical
expression is also tested on the atomically flat CdSe nanoplatelets without any
adjustment of the parameters obtained with the CdSe spherical nanocrystals, and
provides an estimation of the CdSe nanoplatelets thickness that matches exactly
the experimental observations. These results suggest that a phase shift
approach could be useful to describe the electronic transitions in
semiconductor nanocrystals.

Materials Science