Raman and Infrared Signatures of Layered Boron Nitride Polytypes: A First-Principles Study

We present a study based on first-principles calculations of the vibrational and spectroscopic properties of four types of layered boron nitride (BN) polymorphs: <i>e</i>-BN (AA), <i>h</i>-BN (AA'), <i>r</i>-BN (ABC), and <i>b</i>-BN (AB). By using density functional perturbation theory with van der Waals corrections, we calculate phonon frequencies and Raman/infrared (IR) activities at the Γ point and extract specific spectral fingerprints for each stack. In <i>e</i>-BN, we observe a sharp, isolated high-frequency E' mode at 1420.9cm-1 that is active in both Raman and IR. For <i>h</i>-BN, the characteristic Raman E2g line occurs at 1415.5cm-1. The out-of-plane IR-active A2u branch shows a mid-frequency TO/LO pair at 673.5/806.6cm-1, which closely matches experimental results. Rhombohedral <i>r</i>-BN has a strong, coincident Raman/IR high-frequency feature (<i>E</i>) at 1418.5cm-1, along with a large IR LO partner at 1647.3cm-1, consistent with observed Raman and IR signatures. Bernal <i>b</i>-BN displays the most complicated pattern. It combines a robust mid-frequency A2″ pair (TO/LO at 697.9/803.5cm-1) with multiple high-frequency E' modes (TO near 1416.9 and 1428.1cm-1, each with LO counterparts). These stack-dependent Raman and IR fingerprints match existing experimental data for <i>h</i>-BN and <i>r</i>-BN and provide clear predictions for <i>e</i>-BN and <i>b</i>-BN. The results offer a consistent framework for identifying and interpreting vibrational spectra in layered sp2 boron nitride and related materials.