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Excited states of a single donor in bulk silicon have previously been studiedextensively based on effective mass theory. However, a proper theoreticaldescription of the excited states of a donor cluster is still scarce. Here westudy the excitations of lines of defects within a single-valley spherical bandapproximation, thus mapping the problem to a scaled hydrogen atom array. Aseries of detailed full configuration-interaction and time-dependent hybriddensity-functional theory calculations have been performed to understand linearclusters of up to 10 donors. Our studies illustrate the generic features oftheir excited states, addressing the competition between formation ofinter-donor ionic states and intra-donor atomic excited states. At shortinter-donor distances, excited states of donor molecules are dominant, atintermediate distances ionic states play an important role, and at longdistances the intra-donor excitations are predominant as expected. Thecalculations presented here emphasise the importance of correlations betweendonor electrons, and are thus complementary to other recent approaches thatinclude effective mass anisotropy and multi-valley effects. The exchangesplittings between relevant excited states have also been estimated for a donorpair and for a three-donor arrays; the splittings are much larger than those inthe ground state in the range of donor separations between 10 and 20 nm. Thisestablishes a solid theoretical basis for the use of excited-state exchangeinteractions for controllable quantum gate operations in silicon.

Excited states of defect lines in silicon: A first-principles study based on hydrogen cluster analogues