  In this paper, a numerical solution for a hybrid plasmonic modulator is
presented with a six-layer structure consisting of an air superstrate, a gold
layer, a barium titanate layer, a n type silicon layer, a gold layer and an
Al2O3 nanolattice substrate. Regarding the suggested structure, the parameters
related to the phase and the absorption modulation are investigated at
different thicknesses. Here, the Pockels effect and the free carrier dispersion
effect are considered simultaneously. The dispersion equation of this structure
is analytically obtained and numerically solved by the Nelder-Mead method. The
minimum {\pi} shift length is predicted to be equal to 6.91{\mu}m and the
maximum calculated figure of merit is 10.74. Furthermore, according to our
results, it is understood that this modulator has a high ability to be utilized
in optical communication systems. Also, it could be integrated to the
microelectronic systems and it is compatible with CMOS technology.
