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This paper investigates the optimization of PECVD α-SiN-passivated AlGaN/GaN heterostructures to achieve higher 2-D electron gas (2DEG) densities and lower the electric fields residing in the AlGaN barrier layer. A model is developed to calculate the 2DEG density of passivated AlGaN/GaN heterostructures taking into account the piezoelectric and spontaneous polarization effects together with strain relaxation. The model is validated with 2DEG measurements and data from the literature. The optimized passivation layer thickness is calculated for different Al mole fractions and AlGaN thicknesses to achieve targeted 2DEG densities and polarization electric field. Fabrication of samples with different α-SiN thicknesses and effects of postannealing on 2DEG density are reported. The model accurately predicts the experimental results.