Origin and photoluminescence of a shallow hydrogen-related donor in silicon

Paramagnetic color centers in silicon are being investigated recently for use in quantum technologies. While the origin of most of the prominent photoluminescence (PL) lines are well understood, that is not the case for those connected to hydrogen, even though it is almost always present in silicon, e.g., shallow hydrogen-related donors (SHDs), but their atomic structure remains elusive. Recent experiments suggested connection between the SHDs and the so-called X and the B$_i$ (or X$_i$) PL-lines. An SHD, termed the MT2 center, was tentatively assigned to a bistable, negative-U defect, arising due to the interaction of hydrogen with the self-interstitial complex I$_4$. Using high-level density functional theory calculations, we investigate the interaction of hydrogen with self-interstitial complexes In. A shallow effective-mass-theory donor arises when hydrogen attacks a Si-Si bond in I$_n$, inserting itself as a bond-center interstitial (I$_n$H$_{BC}$) in an exothermic reaction. We demonstrate this in the case of a single self-interstitial and of a complex of four. The latter I$_\mathrm{4}$H$_\mathrm{BC}$ complex shows electronic, spin and PL properties remarkably close to MT2. We find that hydrogen in the presence of I$_4$ follows the same behavior as in pristine silicon, i.e., it is a negative-U bistable defect, only detectable under illumination. In the I$_4$H$_{BC}$ complex, H can hop via photo-assisted mechanism between equivalent BC sites of the I$_4$ complex, leading to a motional averaged tetragonal symmetry as experimentally observed for MT2. The zero-phonon line is distinct from the X-line (attributed to the bare I$_4$ complex), and falls well into the range of the X$_i$ lines. Our results identify the I$_4$H complex as a prototype for a class of SHDs, inferring that similar SHDs may arise, with the X$_i$ lines as their PL fingerprints, when H attacks I$_n$ clusters.