Silicon nitride has emerged as a prominent platform for building photonics integrated circuits. While its nonlinear properties based on third-order effects have been successfully exploited, an efficient second harmonic generation in standard stoichiometric silicon nitride (Si3N4) waveguides can also be achieved after all-optical poling, as was recently shown. The root of such a phenomenon has been attributed to the inscription of a self-organized periodic space-charge grating along the waveguide, allowing an effective χ(2) and automatic quasi-phase-matching of pump and second harmonic. However, the different parameters and their role in increasing the efficiency of the process are still not fully comprehended. In this work, we use optical means to identify the general conditions of mode matching occurring during all-optical poling. The overlap integral between pump and second harmonic optical modes is shown to be the governing parameter in determining the features of the χ(2) gratings. Two-photon microscopy measurements of the χ(2) gratings reveal the presence of a secondary periodicity in some of the waveguides used in the study. According to overlap integral simulations, such an effect can occur due to mode mixing in the waveguide bends. From a study of poling dynamics, we observe that poling efficiency and rate increase as a function of optical pump power and waveguide length. However, in order to initiate poling, a critical pump intensity, which is lower for longer waveguides, must be coupled into a waveguide. Temporal and thermal stability tests reveal the nature of charge traps responsible for grating inscription. After applying thermally activated hopping as a conductivity mechanism in our samples, we show that only shallow traps seem to be activated during the all-optical poling process.