In the context of condensed matter physics, the Sommerfeld parameter describes the enhancement or suppression of free-carrier charge density in the vicinity of a charged center. The Sommerfeld parameter is known for three-dimensional systems and is integral to the description of trap-assisted recombination in solids. Here we derive the Sommerfeld parameter in one and two dimensions and compare with the results in three dimensions. We provide an approximate analytical expression for the Sommerfeld parameter in two dimensions. Our results indicate that the effect of the Sommerfeld parameter is to suppress trap-assisted recombination in decreased dimensionality.

Hexagonal boron nitride has been found to host color centers that exhibit single-photon emission, but the microscopic origin of these emitters is unknown. We propose boron dangling bonds as the likely source of the observed single-photon emission around 2 eV. An optical transition where an electron is excited from a doubly occupied boron dangling bond to a localized B p_{z} state gives rise to a zero-phonon line of 2.06 eV and emission with a Huang-Rhys factor of 2.3. This transition is linearly polarized with the absorptive and emissive dipole aligned. Because of the energetic position of the states within the band gap, indirect excitation through the conduction band will occur for sufficiently large excitation energies, leading to the misalignment of the absorptive and emissive dipoles seen in experiment. Our calculations predict a singlet ground state and the existence of a metastable triplet state, in agreement with experiment.

Trap-assisted nonradiative recombination is known to limit the efficiency of optoelectronic devices, but the conventional multiphonon emission (MPE) process fails to explain the observed loss in wide-band-gap materials. Here, we highlight the role of trap-assisted Auger-Meitner (TAAM) recombination and present a first-principles methodology to determine TAAM rates due to defects or impurities in semiconductors or insulators. We assess the impact on efficiency of light emitters in a recombination cycle that may include both TAAM and carrier capture via MPE. We apply the formalism to the technologically relevant case study of a calcium impurity in InGaN, where a Shockley-Read-Hall recombination cycle involving MPE alone cannot explain the experimentally observed nonradiative loss. We find that, for band gaps larger than 2.5 eV, the inclusion of TAAM results in recombination rates that are orders of magnitude larger than recombination rates based on MPE alone, demonstrating that TAAM can be a dominant nonradiative process in wide-band-gap materials. Our computational formalism is general and can be applied to the calculation of TAAM rates in any semiconducting or insulating material.