Slow light is a very important concept in nanophotonics, especially in the context of photonic crystals. In this work, we apply our previous design of band-edge slow light in silicon waveguide gratings [M. Passoni et al, Opt. Express 26, 8470 (2018)] to Mach-Zehnder modulators based on the plasma dispersion effect. The key idea is to employ an interleaved p-n junction with the same periodicity as the grating, in order to achieve optimal matching between the electromagnetic field profile and the depletion regions of the p-n junction. The resulting modulation efficiency is strongly improved as compared to common modulators based on normal rib waveguides, even in a bandwidth of 20-30 nm near the band edge, while the total insertion loss due to free carriers is not increased. The present concept is promising in view of realizing slow-light modulators for silicon photonics with reduced energy dissipation.