A study on cosmogenic activation in germanium was carried out to evaluate the cosmogenic background level of natural and $^{70}$Ge depleted germanium detectors. The production rates of long-lived radionuclides were calculated with Geant4 and CRY. Results were validated by comparing the simulated and experimental spectra of CDEX-1B detector. Based on the validated codes, the cosmogenic background level was predicted for further tonne-scale CDEX experiment. The suppression of cosmogenic background level could be achieved by underground germanium crystal growth and high-purity germanium detector fabrication to reach the sensitivity requirement for direct detection of dark matter. With the low cosmogenic background, new physics channels, such as solar neutrino research and neutrinoless double-beta decay experiments, were opened and the corresponding simulations and evaluations were carried out.
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