Pair Tunneling in Semiconductor Quantum Dots

We propose here a model for the pair tunneling states observed by Ashoori et al. [Phys. Rev. Lett. 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 $\approx 400$ Å.