Minimizing off-axis aberrations in multi-beam electron optical systems: An analytical approach

The multi-beam electron optical system (MBEOS) is critical for high-throughput electron microscopy and electron beam lithography. However, their performance is constrained by both on-axis and off-axis aberrations, which significantly degrade the final spot size. A systematic approach to control these aberrations and to optimize the overall system design has not yet been fully addressed. In this work, we extend the analytical model proposed by M. J. van Bruggen to develop a simplified method for rapidly determining the optimal operating conditions-specifically, the beam deflection angle at the field lens (an intermediate accelerating lens) and the corresponding field lens strength-that minimize off-axis aberrations in a two-lens demagnification system. Our results reveal that the minimum total aberration occurs when the beamlets pass very close to, rather than exactly through, the center of the second lens. Furthermore, we observe a non‑monotonic relationship between off‑axis aberration and the beamlet's radial distance to the optical axis at the field lens. As this radial distance increases, the aberration first decreases and then increases. After geometric aberrations are minimized, spherical and chromatic aberrations become the dominant contributors to the final spot size. Based on these insights, we propose a practical optimization routine applicable to MBEOS designs employing two-lens demagnification system. Using this method, we demonstrate that a total usable beamlet generation area of up to 480 µm × 480 µm can be achieved while maintaining a spot size near 10 nm. This work provides a practical analytical framework for designing high-performance MBEOS with minimized off-axis aberrations.