We demonstrate highly transparent silicon–vanadium and silicon–aluminum tunnel junctions with relatively low sub-gap leakage current and discuss how a trade-off typically encountered between transparency and leakage affects their refrigeration performance. We theoretically investigate cascaded superconducting tunnel junction refrigerators with two or more refrigeration stages. In particular, we develop an approximate method that takes into account self-heating effects but still allows us to optimize the cascade a single stage at a time. We design a cascade consisting of energy-efficient refrigeration stages, which makes cooling of, e.g., quantum devices from above 1 K to below 100 mK a realistic experimental target.