Origin of pair-tunneling states in semiconductor quantum dots

We analyze the role optical and acoustic phonons and physical confinement play in stabilizing bound bipolarons in a GaAs quantum dot. We find that while acoustic phonons play a significant role in polaron formation, they play virtually no role in the stability of a bipolaron. In the weak-coupling limit, we find that the bipolaron is stable only when a local potential is present to physically confine the two electrons. Our results are then applied to the problem of pair electron tunneling [Phys. Rev. Lett. 68, 3088 (1992)] in GaAs quantum dots. We find that although GaAs is a weakly polar semiconductor, optical phonons and the physical confinement of the quantum dot can conspire to create a barrier to single-electron tunneling. Such a barrier to single-electron tunneling signifies the formation of -U pairing centers. 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 image potential created by the δ dopants in the backing layer of the dot. We find that pair binding is unfavorable at small separations between the two wells where the Coulomb repulsion obviates pair binding. A minimal separation of ≈800 Å is found for pair binding to occur. Hence, we argue that when the confining radius of the dot is smaller than ≈800 Å, pair tunneling states should not be observed. In addition, we find that the pair state is unstable at moderate magnetic field strengths (≈2 T), as is seen experimentally.