Graphene is renowned for its extraordinary mechanical, electronic, optical, and thermal properties. However, the absence of a band-gap limits its usefulness in practical applications. If it were possible to engineer graphene to exhibit a band gap, this would open the doors to a wide range of applications for the material, such as use in sensors, solar cells, and energy storage devices. This thesis attempts to definitively state the possibility of opening a band gap through in-plane strain engineering of graphene. This is inspired by the fact that the electronic properties of a number of materials have already been shown to be influenced by deformations. In this work, electronic structure calculations based on Density Functional Theory (DFT) in conjunction with nite deformation theory are employed to determine the effect of in-plane strains on the band gap of graphene. It can be affirmed that a band gap does not appear in graphene under uniaxial or biaxial strains, while moderate gaps do appear under large shear strains (20%). Notably, significant band gaps have been found to open under asymmetrical biaxial strain, particularly in the range of -15% to -20% (compression) in the armchair direction. The highest gap obtained was approximately 1 eV, identified at 11% strain in the zigzag direction and -20% in the armchair direction.
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