Stability of two-dimensional BN-Si structures

We have used \textit{ab initio} modeling to examine stability factors in two-dimensional (2D) CSi, BNC$_{\mathrm{2}}$, and recently proposed BNSi$_{\mathrm{2}}$ honeycomb structures. We have found that the lack of miscibility in the last two systems is due to limited involvement of nitrogen electronic states in the covalent bonding. Our evolutionary ground state searches uncovered that in the (BN)$_{\mathrm{x}}$Si$_{\mathrm{1-x\thinspace }}$pseudobinary system non-honeycomb flat structures have lower energy than the graphene-like configurations. Nevertheless, none of these or previously proposed polymorphs have been found to be stable with respect to phase separation into 2D Si and BN.