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Photonic integrated circuits hold promise as miniaturized and scalable platforms for classical and quantum photonic information processing. Second-order nonlinearity (χ^(2)) is the basis of many important applications such as second-harmonic generation, spontaneous parametric down-conversion, and optical parametric oscillation. Here, we present systematical investigation and optimization of the second-harmonic generation in a dual-resonant aluminum nitride microring resonator. By optimizing the quality factor, independently engineering the coupling conditions for dual-band operation, and perfectly fulfilling phase-match conditions through thermal tuning, we demonstrate a second-harmonic generation efficiency of 2500%  W^−1 in the low-pump-power regime. To the best of our knowledge, this is a state-of-the-art value among all the integrated photonic platforms. We also study the high-power regime …