Theoretical analysis and computational simulation of self-forming micro-lens arrays on silicon photomultipliers

Abstract Silicon photomultipliers (SiPMs) have emerged as pivotal devices in low-level light detection applications; however, the photon detection efficiency (PDE) of SiPMs incorporating small Geiger avalanche photodiode (G-APD) cells remains constrained by inherent structural limitations. The mandatory spacing between G-APD cells—essential for electrical isolation and optical crosstalk suppression—creates ‘dead zones’ that restrict the geometric fill factor (GFF), thereby impeding PDE enhancement. To address this challenge, this study proposes a novel approach for fabricating self-forming and self-aligning micro-lens arrays on SiPM surfaces, leveraging the synergistic effects of surface tension, gravitational force, and air pressure of liquid packaging media. Theoretical modeling confirms the feasibility of forming convex micro-lenses within metal meshes in dead zones, while computational simulations (Zemax simulation employs a single wavelength of 450 nm for GFF measurement, Comsol simulation covers a wavelength range of 200–1100 nm for photoresponsivity analysis, and incident conditions are 25 °C room temperature with wide-angle incidence) demonstrate that these lenses effectively focus incident light, redirecting photons that would otherwise be lost in non-sensitive areas to the photosensitive regions of G-APD cells. For SiPMs with 10 μ m and 25 μ m G-APD cells, the effective gain of this mechanism is mainly concentrated in the small-angle incidence range of 0°–15°, with the optimal enhancement of effective GFF achieved under normal incidence, reaching up to 30.8 ± 2.8 (10 μ m cell + 4 μ m metal step height) and 14.6 ± 2.0 (25 μ m cell + 4 μ m metal step height), respectively. The micro-lens arrays can be reliably solidified via thermal curing or UV irradiation, offering a scalable and cost-effective strategy for integration with existing SiPM manufacturing processes. The findings provide important references for designing high-performance SiPMs with surface-integrated micro-optics in small-angle high-precision low-light detection scenarios, as well as a feasible technical path for PDE optimization targeting collimated/quasi-collimated incident light.