Boron spectral density and disorder broadening in B-doped diamond

Abstract

Comparison of periodic B dopants with a random alloy of substitional boron in diamond is carried out using several supercells and the coherent potential approximation (CPA) for the random alloy case. The main peak in the B local density of states is shifted to lower binding energy compared to the corresponding C peak in intrinsic diamond. In supercells, this shows up as strongly B-character bands split from bulk C bands away from the zone center, in an energy region around $\ensuremath{-}1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Even for a $4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4$ supercell $({\mathrm{BC}}_{127})$, effects of the dopant order are evident in the form of primarily B-character bands just below the Fermi level at the supercell zone boundary. The bands resulting from the CPA are of continuous mixed C-B character. They resemble virtual crystal bands, but broadened somewhat reflecting the disorder-induced lifetime, and are consistent with angle-resolved photoemission band maps. The B character is 1.7 times larger than for C (per atom) near the top of the valence bands for CPA, and roughly the same for supercells. CPA results are particularly useful since they characterize the wave vector and energy dependence of disorder broadening.