Excited states of defect linear arrays in silicon: A first-principles study based on hydrogen cluster analogs
2018
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 full configuration-interaction, time-dependent Hartree-Fock 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 interdonor
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 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.
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