Integrated Mach-Zehnder modulators are key components in silicon photonic devices, which rely on a reverse-biased p-n junction to modulate the optical signal via a change of the waveguide refractive index. Reducing their energy consumption is a crucial issue towards applications of silicon photonics to optical communication. In this presentation, we describe the design of slow light structures consisting of silicon grating waveguides, which have an increased group index close to the photonic band edge. Also, we discuss how the design of p-n junctions affects matching between the optical field mode and the depletion region, in order to improve the modulation efficiency and to reduce the energy dissipation per bit of the modulator.