Excited states of a single donor in bulk silicon have previously been studied extensively based on effective mass theory. However, proper theoretical descriptions of the excited states of a donor cluster are still scarce. Here we study the excitations of lines of defects within a single-valley spherical band approximation, thus mapping the problem to a scaled hydrogen atom array. A series of detailed time-dependent Hartree-Fock, time-dependent hybrid density-functional theory and full configuration-interaction calculations have been performed to understand linear clusters of up to 10 donors. Our studies illustrate the generic features of their excited states, addressing the competition between formation of interdonor ionic states and intradonor atomic excited states. At short interdonor distances, excited states of donor molecules are dominant, at intermediate distances ionic states play an important role, and at long distances the intradonor excitations are predominant as expected. The calculations presented here emphasize the importance of correlations between donor electrons, and are thus complementary to other recent approaches that include effective mass anisotropy and multivalley effects. The exchange splittings between relevant excited states have also been estimated for a donor pair and for three-donor arrays; the splittings are much larger than those in the ground state in the range of donor separations between 10 and 20 nm. This establishes a solid theoretical basis for the use of excited-state exchange interactions for controllable quantum gate operations in silicon.

• Received 27 October 2017

DOI:https://doi.org/10.1103/PhysRevB.97.035205