Pair Tunneling in Semiconductor Quantum Dots

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.