  We propose here a model for the pair tunneling states observed by Ashoori and
co-workers (Phys. Rev. Lett. {\bf 68}, 3088 (1992)) in GaAs quantum dots. We
show that while GaAs is a weakly-polar semiconductor, coupling to optical
phonons is sufficiently strong to mediate a negative-U pairing state. The
physical potential in which the two electrons are bound can be composed of a Si
impurity and a parabolic well that originates from the potential created by the
$\delta-$dopants in the backing layer of the dot. Such a pair state breaks up
at moderate magnetic field strengths ($\approx$ 2 T), as is seen
experimentally, and is unstable when the confining radius of the dot is smaller
than $\approx 400$\AA.
