Quantifying Spin Defect Density in hBN via Raman and Photoluminescence Analysis

TL;DR

The paper addresses the challenge of quantifying absolute spin-defect density for $V_B^-$ centers in ultrathin hBN. It develops an all-optical method that correlates defect-related Raman features (D1 and D2) and photoluminescence with irradiation fluence, supported by polarization-resolved measurements and DFT calculations. A graphene-inspired phenomenological model connects Raman and PL intensities to a defect-spacings parameter $L_D$, yielding a quantitative spin density $n_D$ that follows a power law with fluence and remains broadly universal across irradiation types. This approach provides a direct, non-destructive readout of spin-defect density in thin hBN, enabling robust benchmarking and optimization of hBN-based quantum photonic devices.

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.

Figures (16)

• Figure 1: (a) Optical (b) SEM and (c) integrated PL images of irradiated hBN. The areas are labeled as Tiles 1-12, irradiated with decreasing ion fluence. Tile-1 (yellow) was irradiated with the highest fluence and Tile-12 (violet) with the lowest. For PL maps, spectra have been recorded point-by-point and the spectra have been integrated from 1.37eV to 1.65eV. (d) Simulated boron vacancy density created by a focused ion beam using the software SRIM. The depiction represents a cross section in the x-z plane where the x-y plane is parallel to the sample surface. The density is shown on a logarithmic color scale. (e) Vertical line profiles for the red line shown in (d), while the green line is averaged over the x-dimension (green box around (d)). (f) Depth distribution of the vacancy yield per ion distinguished by target atom. The data is the sum of every vacancy created at a certain depth regardless of the x or y position. (g) Characteristic spectra of the Raman modes D2, D1, $E_\mathrm{2g}$ and PL for Tiles 1 and 12 with a laser excitation energy of $E_L=2.33eV$ (532 nm).
• Figure 2: Linear polarization-dependent Raman modes: (a) Spectra corresponding to $Z(XX)\Bar{Z}$ and $Z(YX)\Bar{Z}$, are shown in red and blue, respectively. The color contour plots present the variation of Raman (b) and PL signals (c) with respect to incident light polarization direction. (d) Lorentzian fitting of the D2 mode for two polarization configurations. For $\parallel$ polarization, the D2 peak is resolved into two sub-modes, D2a and D2b, appearing at $\approx$ 459 and 352 cm$^{-1}$ with width $\Gamma \approx$ 138 and 191 cm$^{-1}$, respectively. In contrast, for $\perp$-polarization, D2b is not detected, and D2a appears with reduced intensity at 465 cm$^{-1}$ with $\Gamma$$\approx$ 120 cm$^{-1}$. (e,f) Polar plots of all Raman modes and the PL signal, normalized to their $Z(XX)\Bar{Z}$ values. (e) Representing the isotropic behaviour of PL, $E_\mathrm{2g}$ , and D$_1$. (f) $\cos^2{\theta}$ dependence of D2a and D2b.
• Figure 3: (a) Characteristic Raman and PL spectra recorded at different tiles, as shown in \ref{['fig:optical-image']} (a) and (b). (b) Calculated Raman spectrum and (c) Schematic diagram of atomic vibrations responsible for different Raman modes. (d)-(f) Schematic illustrations of defect densities for each irradiation fluence are presented in panels, adapted from lucchese2010quantifying. As the defect density increases, the overlap becomes more pronounced, adversely affecting both the Raman and PL signals. (g) The red region represents the area directly impacted by ion collisions, while the light blue region indicates the extent to which the ion impacts remain visible.
• Figure 4: (a) Dependence of integrated area $A$ under curve for D1, $E_\mathrm{2g}$ Raman modes and PL at $E_\mathrm{L} = 2.33eV$ on the irradiation fluence. Dotted traces are guides to the eye. (b) Data points represent $(A_\mathrm{D1}+A_\mathrm{PL})/A_{E_\mathrm{2g}}$, and the solid traces are calculated following \ref{['eq:eqn-2']} for three $E_\mathrm{L}$ values. (c) The calculated spin density using \ref{['eq:eqn-2']}. The shaded area represents the error associated with the fitting. The solid line is a fit of $C\cdot D^{\gamma}$ with $\gamma=1.8\pm0.01$, representing the power law dependence of the spin-defect density on the irradiation fluence. The colored boxes mark the values for the corresponding tiles in Fig. 1. (d) The plot illustrates the direct estimation of spin defect density from the ratio $(A_\mathrm{D1}+A_\mathrm{PL})/A_{E_\mathrm{2g}}$ in uncharacterized systems based on spectral response. The dashed line is a guide to the eye. The values $(A_\mathrm{D1}+A_\mathrm{PL})/A_{E_\mathrm{2g}}$$\approx 191$gottscholl2021spin,$\approx 165$venturi2024selective and $\approx 20$ren2023creation, calculated from spectral response data in these references, following the described method are marked by different asterisks.
• Figure S1: Raman spectra of irradiatd hBN on Au/Cu (a) and SiO$_2$/Si substrates (b).