The fabrication of complex low-dimensional quantum devices requires the control of the heteroepitaxial growth at the subnanometer scale. This is particularly challenging when the total thickness of stacked layers of device-active material becomes extremely large and exceeds the multi-µm limit, as in the case of quantum cascade structures. Here, we use the ultrahigh-vacuum chemical vapor deposition technique for the growth of multi-µm-thick stacks of high Ge content strain-balanced Ge/SiGe tunneling heterostructures on Si substrates, designed to serve as the active material in a THz quantum cascade laser. By combining thorough structural investigation with THz spectroscopy absorption experiments and numerical simulations we show that the optimized deposition process can produce state-of-the-art threading dislocation density, ultrasharp interfaces, control of dopant atom position at the nanoscale, and reproducibility within 1% of the layer thickness and composition within the whole multilayer. We show that by using ultrahigh-vacuum chemical vapor deposition one achieves simultaneously a control of the epitaxy down to the sub-nm scale typical of the molecular beam epitaxy, and the high growth rate and technological relevance of chemical vapor deposition. Thus, this technique is a key enabler for the deposition of integrated THz devices and other complex quantum structures based on the Ge/SiGe material system.