Substitutional clusters of multiple light element dopants are a promising route to the elusive shallow donor in diamond. To understand the behaviour of co-dopants, this report presents an extensive first principles study of possible clusters of boron and nitrogen. We use periodic hybrid density functional calculations to predict the geometry, stability and electronic excitation energies of a range of clusters containing up to five N and/or B atoms. Excitation energies from hybrid calculations are compared to those from the empirical marker method, and are in good agreement.
When a boron-rich or nitrogen-rich cluster consists of 3 - 5 atoms, the minority dopant element - a nitrogen or boron atom respectively - can be in either a central or peripheral position. We find B-rich clusters are most stable when N sits centrally, whereas N-rich clusters are most stable with B in a peripheral position. In the former case, excitation energies mimic those of the single boron acceptor, while the latter produce deep levels in the band-gap. Implications for probable clusters that would arise in high-pressure high-temperature (HPHT) co-doped diamond and their properties are discussed.