We report on the design of Silicon Mach-Zehnder carrier depletion modulators relying on epitaxially grown vertical junction diodes. Unprecedented spatial control over doping profiles resulting from combining local ion implantation with epitaxial overgrowth enables highly linear phase shifters with high modulation efficiency and comparatively low insertion losses. A high average phase shifter efficiency of VπL = 0.74 V⋅cm is reached between 0 V and 2 V reverse bias, while maintaining optical losses at 4.2 dB/mm and the intrinsic RC cutoff frequency at 48 GHz (both at 1 V reverse bias). The fabrication process, the sensitivity to fabrication tolerances, the phase shifter performance and examples of lumped element and travelling wave modulators are modeled in detail. Device linearity is shown to be sufficient to support complex modulation formats such as 16-QAM.