  Addition energy spectra at 0 T of circular and ellipsoidally deformed
few-electron vertical quantum dots are measured and compared to results of
model calculations within spin-density functional theory. Because of the
rotational symmetry of the lateral harmonic confining potential, circular dots
show a pronounced shell structure. With the lifting of the single- particle
level degeneracies, even a small deformation is found to radically alter the
shell structure leading to significant modifications in the addition energy
spectra. Breaking the circular symmetry with deformation also induces changes
in the total spin. This "piezo-magnetic" behavior of quantum dots is discussed,
and the addition energies for a set of realistic deformation parameters are
provided. For the case of the four-electron ground state at 0 T, a spin-triplet
to spin-singlet transition is predicted, i.e. Hund's first rule no longer
applies. Application of a magnetic field parallel to the current confirms that
this is the case, and also suggests that the anisotropy of an elliptical dot,
in practice, may be higher than that suggested by the geometry of the device
mesa in which the dot is located.
