The single particle electronic level structure of semiconductor quantu
m dots (QDs) with a zinc-blende structure, and with size smaller than
the bulk exciton Bohr radius, is discussed. Using an empirical tight-b
inding theory, the energy levels and wave functions of GaAs crystallit
es containing upto approximate to 4000 atoms are obtained. The tight-b
inding (TB) results for the size-dependence of the near-band-edge ener
gy levels and the exciton energy are compared with those obtained usin
g the multiband effective mass approximation (EMA). We find that a sim
ple EMA picture is not even qualitatively correct for the conduction b
and levels in GaAs QDs, in the size range considered, and particularly
in smaller QDs. This is in contrast to CdS and CdSe QDs, for which ea
rlier TB calculations by our group showed that the EMA gives the corre
ct qualitative picture, so that a correspondence between the TB energy
levels and those calculated within a spherical multiband EMA could be
set up. The reasons for the differences in these materials are discus
sed.