Quantifying Spin Defect Density in hBN via Raman and Photoluminescence Analysis

Abstract: Negatively charged boron vacancies ($\mathrm{V_B^-}$) in hexagonal boron nitride (hBN) are emerging as promising solid-state spin qubits due to their optical accessibility, structural simplicity, and compatibility with photonic platforms. However, quantifying the density of such defects in thin hBN flakes has remained elusive, limiting progress in device integration and reproducibility. Here, we present an all-optical method to quantify $\mathrm{V_B^-}$ defect density in hBN by correlating Raman and photoluminescence (PL) signatures with irradiation fluence. We identify two defect-induced Raman modes, D1 and D2, and assign them to vibrational modes of $\mathrm{V_B^-}$ using polarization-resolved Raman measurements and density functional theory (DFT) calculations. By adapting a numerical model originally developed for graphene, we establish an empirical relationship linking Raman (D1, $E_\mathrm{2g}$) and PL intensities to absolute defect densities. This method is universally applicable across various irradiation types and uniquely suited for thin flakes, where conventional techniques fail. Our approach enables accurate, direct, and non-destructive quantification of spin defect densities down to $10^{15}$ defects/ cm${}^3$, offering a powerful tool for optimizing and benchmarking hBN for quantum optical applications.