Phonons in Stabilized B or N doped graphene

Based on \textit{Ab-initio} density functional perturbation theory, we have investigated various doped B and N based graphene sheets by raising their concentrations upto 50{\%} of the host carbon. Although the doped structures seem to stabilize in 2-D configurations, but the resulting Phonon frequencies do not confirm the stability as the transverse modes above critical concentrations of B and N tend to result in negative eigenvalues. This essentially requires strained 2-D sheets when doped above such critical concentrations. We find the results of phonons and thermodynamics very interesting and attempt to report these in strained lattices. The motivation to do such a calculation results from our primary goal to address the issue of heat dissipation rate in the devices based on designable electronic and optical properties of such doped graphene reported already.