  Confined states of a positronium (Ps) in the spherical and circular quantum
dots (QDs) are theoretically investigated in two size-quantization regimes:
strong and weak. Two-band approximation of Kane dispersion law and parabolic
dispersion law of charge carriers are considered. It is shown that the
electronpositron pair instability is a consequence of dimensionality reduction,
not of the size quantization (SQ). The binding energies for the Ps in circular
and spherical QDs are calculated. The Ps formation dependence on the QD radius
is studied.
