  Based on the observed absorption spectral band shifts, the growth process of
the semiconductor clusters was divided into two phenomenological regimes: The
"molecular regime" that is associated with the band blue shift as the size of
cluster increases and the "crystallite regime" that is associated with the band
red shift as the size of cluster increases. We show that in the molecular
regime, the band blue shift associated with cluster growth can be understood by
a model that assume electrons are confined to a spherical potential well and
the clusters are made of some basic units. A formula is given for the lowest
excited electronic state energy. This expression contains an electron-hole-pair
(EHP) delocalization constant as an adjustable parameter which, however, can be
anchored to a definite value through the known transition energy at the spectra
turn-around point. The stability of clusters is characterized by a function
that can be calculated by the eigenvalues of the Hamiltonian of the model.
