In the last years graphene membranes have been object of intense theoretical and experimental investigations due to its rich electronic [1,2] and mechanical properties [1-3]. They exhibit and combine remarkable properties, such as, high mechanical resistance with low weight . However, in its pristine form graphene is a gapless material, which prevents its applications in some transistor applications . One possible solution to this problem it is to create an electronic gap through chemical functionalizations and/or graphene chemical doping. Effective doping can be achieved for example by replacing C atoms with B or N ones .
Recently, Ci et al.  synthesised a hybrid material composed of BN domains embedded into graphene membranes. This composition resulted in a new material with properties complementary to those of graphene and hexagonal boron nitride (h-BN), enabling a rich variety of electronic and mechanical properties .
It is interesting to determine how the mechanical and electronic properties vary as a function of the number and size of the BN domains. In this work we have used ab initio DFT (Density Functional Theory) and DFTB (Density Functional Tight-Binding) methods to investigate the electronic and mechanical properties of graphene containing different BN domains. Due to the high computational cost ab initio calculations were carried out for small model systems in order to establish a benchmark for the DFTB calculations carried out for larger systems (up to thousands of atoms). Our results showed that the hybrid material stiffness increases with increasing the number of BN domains and when under stress most of mechanical failures (fractures) occur on the interface of the graphene-BN domains. We have also investigated how the electronic structure changes as a function of these BN domains.
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