Quantifying the Full Damage Profile of Focused Ion Beams via 4D-STEM Precession Electron Diffraction and PSNR Metrics

TL;DR

This work tackles the challenge of quantifying the full damage footprint of focused ion beams (FIBs), not just the beam core, by employing 4D-STEM with precession electron diffraction and a PSNR-based analysis of CBED patterns. By calibrating CBED degradation against known Ga$^{+}$ fluences at $30$ keV and mapping PSNR-derived damage across regions around implanted sites, the method reveals extended damage tails and allows conversion to spatial ion-dose maps $(\text{ions nm$^{-2}$})$ with nanometer-scale localization. The approach yields a more complete, quantitative characterization of FIB-induced damage, offering a practical pathway to tailor FIB parameters for quantum devices and other precision nanofabrication tasks; EBSD is discussed as a complementary, higher-throughput, but lower-resolution cross-check. Overall, the study provides a robust framework to profile ion-matter interactions beyond the beam core, addressing a critical gap in FIB metrology and enabling more accurate performance benchmarking and device-level design.

Abstract

Focused ion beams (FIBs) are widely used in nanofabrication for applications such as circuit repair, ultra-thin lamella preparation, strain engineering, and quantum device prototyping. Although the lateral spread of the ion beam is often overlooked, it becomes critical in precision tasks such as impurity placement in host substrates, where accurate knowledge of the ion-matter interaction profile is essential. Existing techniques typically characterise only the beam core, where most ions land, thus underestimating the full extent of the point spread function (PSF). In this work, we use four-dimensional scanning transmission electron microscopy (4D-STEM) to resolve the ion beam tail at defect densities equivalent to $<$0.1 ions nm$^{-2}$. Convergent beam electron diffraction (CBED) patterns were collected in calibration regions with known ion fluence and compared to patterns acquired around static dwell spots exposed to a 30 keV Ga$^{+}$ beam for 1-10 s. Cross-correlation using peak signal-to-noise ratio (PSNR) revealed that 4D-STEM datasets are ultra-sensitive for defect quantification and more robust against scanning artefacts than conventional dark-field imaging. This approach is complementary to image resolution methods enabling a comprehensive profiling of ion-induced damage even at low-dose regimes, offering a more accurate representation of FIB performance and supporting application tailoring beyond the conventional resolution metrics focused solely on the beam core.

Figures (14)

• Figure 1: Conventional imaging resolution measurement using linear greyscale profile across a heterojunction. Inset: A $1024 \times 943$ pixel$^2$ secondary electrons micrograph obtained by scanning a 30 keV Ga$^+$ beam such as around 4200 electrons per pixel is used to produce the image. The red line on the top-middle part of the inset figure represents the region where a greyscale profile $S(x)$ was collected. The data was fitted using \ref{['Eq.Sx']} to give imaging resolution $2\sigma=11.9$ nm.
• Figure 2: Imaging resolution versus damage profile study using annular dark-field scanning transmission electron microscopy (ADF-STEM). a) ADF-STEM images around spots dwelled with a 7.5 pA 30 keV Ga$^+$ beam. The times on the bottom-right of each image is the dwell time for the far-right spot, with exponential increments between them. Scan field of view corresponds to 8µm. b) High-magnification high-angle annular dark-field (HAADF) STEM image of the initially drilled hole. The image shows a central darker region, corresponding to the hole or very thin areas, surrounded by a dark-grey annular region, indicative of damaged (likely amorphous) areas. The untouched crystal appears in light grey. The red dashed line marks the region where the greyscale profile was obtained, which is plotted in the red inset. The yellow curve represents a Gaussian fit with a full width at half maximum equivalent to the imaging resolution obtained in \ref{['fig:ImagingResolution']}. c) Evolution of hole size and the corresponding surrounding damage, demonstrating a progressively higher damage profile relative to the hole diameter.
• Figure 3: 10,000 integrated CBED patterns obtained by scanning the 0.8 mrad precessed 100 keV, 12 mrad convergence, 100 pA probe current with a 1 ms dwell time per pixel. The CBED patterns have dimensions of $512\times512$ pixels$^2$ and are plotted using a logarithmic intensity scale. The numbers at the top-left of each CBED pattern indicate the dose used in the corresponding calibration square, with 0.00 representing the pristine region.
• Figure 4: Calibration of peak signal-to-noise ratio (PSNR) as a function of ion dose. a) Low-angle Annular dark-field STEM (LAADF-STEM) image of the calibration region, where the numbers indicate the ion implantation dose in ions per nm². Red dashed squares mark the 4µm areas scanned to acquire the 4D-STEM data used for PSNR analysis. b) PSNR values plotted as a function of ion dose. Black dots represent individual PSNR values (100,000 per dose) calculated from the CBED patterns in each calibration region. Red dots show the mean PSNR for each dose, with vertical bars indicating the standard deviation. Reddish blurred regions underneath the plot corresponds to heat distribution of the PSNR values for each dose. The red curve is a fit of the data using a Gaussian error function.
• Figure 5: Focused ion beam-induced damage analysis quadrants with its bottom-left corner aligned at the centre of a milled hole. a–c) ADF-STEM images illustrating the damage across the quadrant with contrast defined by scattering events. d-f) Averaged PSNR values obtained by comparing each $100\times100$ scanned pixels from the 4D-STEM dataset to 10 randomly selected CBED patterns from a pristine reference region. g–i) 2D ion dosage maps derived by converting the PSNR values to ion dose (ions nm$^{-2}$) using parameters from the Gaussian error function fit. White regions indicate PSNR values outside the plateaus in \ref{['fig:Calibration']}, corresponding to either minimal or saturated damage levels. The left, middle, and right columns correspond to dwell times of 1 s, 5 s, and 10 s, respectively.