Avalanche photodiodes (APDs) based on AlAs0.56Sb0.44, a material with a low ionization coefficient ratio (k), are promising for low-noise, high-speed optical detection. This work develops a Simplified Monte Carlo (SMC) model incorporating carrier drift, scattering, and impact ionization under a single parabolic valley approximation. Model parameters are calibrated with experimental data to extract effective ionization and dead-zone coefficients, enabling gain–noise analysis in low-doping regimes. Results indicate that moderate p-type doping minimizes excess noise, and an empirical relation between optimal doping and multiplication layer thickness is established, providing guidance for low-noise AlAs0.56Sb0.44 APD design.