  The effect of external electric field on the exchange interaction has been
studied by an exact diagonalization method for two electrons in laterally
coupled quantum dots (QD's). We have performed a systematic study of several
nanodevices that contain two gate-defined QD's with different shapes and sizes
located between source and drain contacts. The confinement potential is
modelled by two potential wells with a variable range and softness. In all the
considered nanodevices, the overall dependence of exchange energy $J$ on
electric field $F$ is similar, i.e., for low fields $J$ increases with
increasing $F$, for intermediate fields $J$ reaches a maximum, and rapidly
falls down to zero if $F$ exceeds a certain critical value. However, the $J(F)$
dependence shows characteristic properties that depend on the nanodevice
geometry. We have found that the low- and intermediate-field behaviour can be
accurately parametrized by linear function $J(F) = \\alpha F + \\beta$, where $
alpha$ is independent of the nanodevice geometry and softness of the
confinement potential. We have shown that the linear $J(F)$ dependence appears
only if the tunnel coupling between the QD's is weak, i.e., the interdot
separation is sufficiently large. The $J(F)$ dependence becomes non-linear for
the strong interdot tunnel coupling. If the QD located near the contact, to
which the higher voltage is applied, possesses the elliptic shape and is larger
than the other QD, the $J(F)$ dependence shows a plateau in a broad
electric-field regime. The linearity and rapid jumps of $J(F)$ as well as the
existence of the plateau can be applied to tune the exchange interaction by
changing the external electric field.
