Dimensional parameters are optimized comparing stoichiometric and Si-rich silicon nitride-based push-pull modulators using a slot waveguide structure, electro-optic polymer cladding, and in-plane ground-signal-ground electrode. An optical power confinement in slot spacing is examined for choosing the optimal device parameters for wavelength of 1550nm. The electrical simulations are set to calculate an asymmetric spatial distribution of poling efficiency and modulating refractive index change in polymer. The influence of carrier charge in Si-substrate is also considered. The voltage-length products as well as the poling efficiency of Si-rich SiN are calculated as 1.47 V•cm and 0.74 respectively for a polymer with a , of 100 pm/V. For the selected polymer the calculated efficiency comparable to standard silicon based plasma dispersion depletion modulators. The efficiency can be increased more than two times for demonstrated polymers with a , of ~230. Low metal absorption loss of ~ 1dB/cm can be achieved from the optimal designed device. Comparing to the conventional simulation method without Si-substrate effect, a more accurate simulation method is also presented in this work.