Electron exchange interaction in electronically confined Si quantum dots

Electron exchange interactions in electronically confined Si quantum dots are modeled with an sp/sup 3/d/sup 5/s* empirical tight-binding model. Previous work has shown that the exchange energies for electrons confined by P donors in bulk Si display a fast oscillatory behavior with respect to the inter-donor distance (Koiller et al., 2002). This result implies that P donors need to be positioned with atomic-scale precision in order to implement a Si:P based quantum computer architecture. In contrast to the Si:P architecture, electronically confined Si quantum dots show a simple exponential decay of the exchange energies with the increase of the inter-dot distance. The exponential behavior is attributed to tensile biaxial strain in the Si quantum well, which is epitaxially grown on top of a relaxed Si/sub x/Ge/sub 1-x/ layer. The tensile biaxial strain lifts the degeneracy of six valleys in the Si band structure, with the Z valley at lower than the X and Y valleys. The lowest electron wave function originates from the Z valley, and hence Bloch oscillations are present in the z direction only. As a result, when the inter-dot distance changes along the x and y directions, the exchange energy, which is determined by the overlap between the two electron wave functions, does not oscillate.