Doping-induced anisotropic lattice strain in homoepitaxial heavily boron-doped diamond

As a result of the larger covalent radius of boron (rB = 0.88 Å) when compared to that of carbon (rC = 0.77 Å), the introduction of substitutional boron into diamond leads to an expansion δa/a of the lattice parameter. This has been found previously to follow a linear interpolation (Vegard law) as long as the boron content is lower than about 0.5 at.% in MPCVD epilayers or 1.5 at.% in HPHT bulk crystals.Above those concentrations, the expansion is less pronounced than predicted by Vegard. In order to explain this effect, we have performed ab initio calculations on C:B substitutional alloys. The results show that the presence of interstitial boron and of boron clusters is not necessary to explain the experimental data available in the literature. Moreover, quantitative estimates are proposed for the deformation potential of the valence band maximum and for the steric effect associated to boron pairing. We then apply these conclusions to discuss the different variations of δa/a vs boron contents observed by high resolution XRD experiments performed on “insulating” and metallic (and superconducting) p++ diamond epilayers grown by MPCVD on (100)- and (111)-oriented type Ib substrates, for which boron concentration profiles have been determined by Secondary Ion Mass Spectroscopy.