Vibration Analysis of Hexagonal Boron Nitride under Electric Field via Semiempirical Quantum Mechanical Method

The vibrational behavior of micronano structures is crucial for advancing micronano electromechanical systems (MEMS)-like resonators, oscillators, and sensors. Electric fields significantly influence these devices, but classical molecular dynamics (CMD) lacks a mechanism to account for the effects on electrons and first-principles simulations are constrained by their limited scale. In this study, we employ an extended tight-binding (xTB) semiempirical quantum mechanical method to model the impact of electric fields on a relatively large number of atoms. We specifically investigate the vibration of a 2D hexagonal boron nitride (h-BN) under an electric field. The piezoelectric constants of h-BN are calculated using xTB and compared with density functional theory results. Additionally, we compare the electric field forces between atoms derived from semiempirical quantum mechanical molecular dynamics (SQMD) and CMD simulations. The analysis focuses on the effect of the electric field on natural frequencies. Our findings reveal that CMD considers only the effect of electric field force. However, the electric field force alone cannot fully replicate the effects of an electric field on h-BN, as the field also influences the bond properties in SQMD. Notably, the change of initial strain does not affect the trend of frequency change under an electric field. This investigation into h-BN vibrations under electric fields holds significant importance for the development of MEMS.