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Single-photon avalanche diodes (SPADs) are semiconductor photodetectors for next-generation scintillation detectors, which are highly beneficial for many biomedical applications such as fluorescence lifetime imaging microscopy (FLIM), X-ray imaging, and time-of-flight positron emission tomography (ToF-PET). Those applications generally require SPADs with high fill factors and strong sensitivities in the blue-green wavelength range, matching the emission spectrum of commonly used scintillators. While front-illuminated (FI) SPADs are advantageous for detecting blue-green wavelengths due to their shallow junction depth, they suffer from optical losses caused by stacked dielectric layers and low fill factors due to the peripheral region for the guard ring and anode/cathode. These can be addressed using back-illuminated (BI) SPADs, but those devices typically have deeper junctions and smaller pixel pitches, limiting blue-green sensitivity and suitability for biomedical applications. This study presents the optimized BI SPAD with aggressive backside thinning, active-area enlargement, and backside patterning. These structural optimizations reduce the epitaxial thickness, increase photon interaction volume, and enhance internal light scattering, leading to significantly improved photon detection probability (PDP) in the blue-green wavelength range. Experimental results exhibit a PDP increase rate of over 98.21 % at 3 V excess bias voltage with a low dark count rate of less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10 \text{cps} / \mu_{\mathrm{m}^{2}}$</tex>. This work demonstrates a viable BI SPAD for scintillation detectors, especially for biomedical imaging systems requiring large pixel pitches and high blue-green sensitivity.