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In this paper, a numerical solution for a hybrid plasmonic modulator ispresented with a six-layer structure consisting of an air superstrate, a goldlayer, a barium titanate layer, a n type silicon layer, a gold layer and anAl2O3 nanolattice substrate. Regarding the suggested structure, the parametersrelated to the phase and the absorption modulation are investigated atdifferent thicknesses. Here, the Pockels effect and the free carrier dispersioneffect are considered simultaneously. The dispersion equation of this structureis analytically obtained and numerically solved by the Nelder-Mead method. Theminimum {\pi} shift length is predicted to be equal to 6.91{\mu}m and themaximum calculated figure of merit is 10.74. Furthermore, according to ourresults, it is understood that this modulator has a high ability to be utilizedin optical communication systems. Also, it could be integrated to themicroelectronic systems and it is compatible with CMOS technology.

Design of a hybrid plasmonic electro-optical modulator based on n doped silicon and barium titanate