  The structure of the ground state exciton of Cd(Se,Te) quantum dots embedded
in ZnTe matrix is studied experimentally using photoluminescence spectroscopy
and theoretically using ${\bf k}\cdot{\bf p}$ and configuration interaction
methods. The experiments reveal a considerable reduction of fine-structure
splitting energy of the exciton with increase of Se content in the dots. That
effect is interpreted by theoretical calculations to originate due to the
transition from spatially direct (type-I) to indirect (type-II) transition
between electrons and holes in the dot induced by increase of Se. The trends
predicted by the theory match those of the experimental results very well.The
theory identifies that the main mechanism causing elevated fine-structure
energy in particular in type-I dots is due to the multipole expansion of the
exchange interaction. Moreover, the theory reveals that for Se contents in the
dot $>0.3$, there exist also a {\bf peculiar type of confinement showing
signatures of both type~I and type~II} and which exhibits extraordinary
properties, such as almost purely light hole character of exciton and toroidal
shape of hole states.
