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Effects of residual C impurities and Ga vacancies on the dynamic instabilities of AlN/AlGaN/GaN metal insulator semiconductor high electron mobility transistors are investigated. Secondary ion mass spectroscopy, positron annihilation spectroscopy, steady state and time-resolved photoluminescence (PL) measurements have been performed in conjunction with electrical characterization and current transient analyses. The correlation between yellow luminescence (YL), C- and Ga vacancy concentration is investigated. Time-resolved PL indicating the C$_{\mathrm{N}}$O$_{\mathrm{N}}$ complex as the main source of the YL, while Ga vacancies or related complexes with C seem not to play a major role. The device dynamic performance is found to be significantly dependent on the C concentration close to the channel of the transistor. Additionally, the magnitude of the YL is found to be in agreement with the threshold voltage shift and with the on-resistance degradation. Trap analysis of the GaN buffer shows an apparent activation energy of $\sim$0.8eV for all samples, pointing to a common dominating trapping process and that the growth parameters affect solely the density of trap centres. It is inferred that the trapping process is likely to be directly related to C based defects.