Analysis of vibrational properties of C-doped hexagonal boron nitride (h-BN)

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We present a systematic theoretical investigation of the vibrational properties of C-doped single layer hexagonal boron nitride (h-BN). Our studies have been carried out by the forced vibrational method, which is based on the idea of mechanical resonance and efficient for very complex and large system. We have estimated the phonon density of states (PDOSs) of h-BCN network with random and regular distribution of C atoms. It is found that the PDOS greatly depends on the C distribution and coverage. For randomly distributed C atoms, we observe that the longitudinal and the transverse optical (LO) and (TO) phonon branches for in-plane motion are nondegenerate at the Γ-point of the Brillouin zone. We determine a critical value of C concentration for the onset of this C-induced vibrational transition. We have found that C concentrations of about 10% and higher, the E2g peak of h-BN has been reduced into a shoulder or it has completely disappeared. For h-BCN network with regular domains of C, the PDOSs changes more abruptly. With the increase of C concentration, the high frequency optical phonons peaks above the 1400cm−1 increase linearly while the h-BN peaks below the 1400cm−1 are broadened and distorted. The disorder causes the phonon modes to be localized in the real space. Phonon localization in the hybrid BCN network is studied and the extent of localization is quantified by the typical mode pattern and the localization length. Spatial analyses of the eigenvectors using typical mode patterns show that Γ-point of the LO and TO phonon modes is strongly localized and show random behavior within a region of several nanometers in the BCN structure. In particular at 1400cm−1, a typical localization length is on the order of ≈4nm for randomly distributed C atoms and ≈8.5nm for the regular domains of C of 20% concentration, while at 1590cm−1, these values are ≈2nm and ≈4nm for randomly distributed C atoms and regular domains of C, respectively. These results are expected to stimulate further studies aimed at better understanding of the phenomena allied with vibrational properties such as thermal conductivity, specific heat capacity, and electron–phonon interaction of h-BN and BCN networks.