Laser light can modulate the kinetic energy spectrum of free electrons and induce extremely high acceleration gradients, which are instrumental to electron microscopy and electron acceleration, respectively. We present a design scheme for a silicon photonic slot waveguide which hosts a supermode to interact with free electrons. The efficiency of this interaction relies on the coupling strength per photon along the interaction length. We predict an optimum value of 0.4266, resulting in the maximum energy gain of 28.27 keV for an optical pulse energy of only 0.22 nJ and duration 1 ps. The acceleration gradient is 1.05 GeV/m, which is lower than the maximum imposed by the damage threshold of Si waveguides. Our scheme shows how the coupling efficiency and energy gain can be maximized without maximizing the acceleration gradient. It highlights the potential of silicon photonics technology in hosting electron-photon interactions with direct applications in free-electron acceleration, radiation sources, and quantum information science.