Effect of ¹⁰B isotope and vacancy defects on the phonon modes of two-dimensional hexagonal boron nitride

We report the details of the effects of the ¹⁰B isotope and those of B and N vacancies combined with the isotope on the phonon modes of two-dimensional hexagonal boron nitride (h-BN). The phonon density of states and localization problems are solved using the forced vibrational method, which is suitable for an intricate and disordered system. We observe an upward shift of Raman-active E_2g-mode optical phonons (32 cm^-1) for a 100% ¹⁰B isotope, which matches well with the experiment and simple harmonic oscillator model. However, a downward shift of E_2g-mode phonons is observed for B or N vacancies and the combination of the isotope and vacancy-type disordered BN. Strong localized eigenmodes are found for all types of defects, and a typical localization length is on the order of ∼7 nm for naturally occurring BN samples. These results are very important for understanding the heat dissipation and electron transport properties of BN-based nanoelectronics.