  Exchange interaction has been studied for electrons in coupled quantum dots
(QD's) by a configuration interaction method using confinement potentials with
different profiles. The confinement potential has been parametrized by a
two-centre power-exponential function, which allows us to investigate various
types of QD's described by either soft or hard potentials of different range.
For the soft (Gaussian) confinement potential the exchange energy decreases
with increasing interdot distance due to the decreasing interdot tunnelling.
For the hard (rectangular-like) confinement potential we have found a
non-monotonic behaviour of the exchange interaction as a function of distance
between the confinement potential centres. In this case, the exchange
interaction energy exhibits a pronounced maximum for the confinement potential
profile which corresponds to the nanostructure composed of the small inner QD
with a deep potential well embedded in the large outer QD with a shallow
potential well. This effect results from the strong localization of electrons
in the inner QD, which leads to the large singlet-triplet splitting.
Implications of this finding for quantum logic operations have been discussed.
