  We studied a vertical ``quantum dot molecule'', where one of the dots is
occupied with electrons and the other with holes. We find that different phases
occur in the ground state, depending on the carrier density and the interdot
distance. When the system is dominated by shell structure, orbital degeneracies
can be removed either by Hund's rule, or by Jahn-Teller deformation. Both
mechanisms can lead to a maximum of the addition energy at mid-shell. At low
densities and large interdot distances, bound electron-hole pairs are formed.
