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We investigate silicon waveguides with subwavelength-scale modulation for applications in free-electron-photon interactions. The modulation enables velocity matching and efficient interactions between low-energy electrons and co-propagating photons. Specifically, we design a subwavelength-grating (SWG) waveguide for interactions between 23-keV free electrons and ≈1500-nm photons. The SWG waveguide and electron system exhibit a coupling coefficient of |g_Qu| = 0.23, and as we corroborate with time-domain, particle-in-cell simulations, the system operates as a backward-wave oscillator. Overall, our results show that modulated waveguides could open the door to strong, extended interactions between photons and low-energy (10-keV-scale) electrons, like those typically present in scanning electron microscopes. Additionally, our SWG waveguide design suggests that periodic waveguides could offer intriguing dispersion engineering opportunities for tailoring these interactions.