  Excited states of a single donor in bulk silicon have previously been studied
extensively based on effective mass theory. However, a proper theoretical
description of the excited states of a donor cluster is 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 full configuration-interaction and time-dependent hybrid
density-functional theory 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
inter-donor ionic states and intra-donor atomic excited states. At short
inter-donor distances, excited states of donor molecules are dominant, at
intermediate distances ionic states play an important role, and at long
distances the intra-donor excitations are predominant as expected. The
calculations presented here emphasise the importance of correlations between
donor electrons, and are thus complementary to other recent approaches that
include effective mass anisotropy and multi-valley effects. The exchange
splittings between relevant excited states have also been estimated for a donor
pair and for a 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.
