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Summary form only given. We developed a highly efficient tunable cw single-frequency light source in the deep ultraviolet region for laser cooling of silicon atoms. In the system two-stage highly efficient frequency conversion with binary external cavities is employed. The first frequency conversion system consists of a bow-tie ring type cavity and the phase matched LBO crystal, producing the second harmonic power of 526 mW at 373 nm by frequency doubling of the fundamental (746 nm) of a Ti:sapphire laser with a power of 1.3 W. The conversion efficiency in the first cavity reaches 38.4%, which is in good agreement with our numerical calculation. In the second stage, the system consists of a doubly resonant bow-tie-type cavity and the phase matched BBO crystal, generating the 252-nm radiation successfully, by the sum frequency mixing between the obtained 373-nm radiation with a power of 480 mW and the 780-nm light from a tunable laser diode with a power of 380 mW. The frequency of the single-frequency-laser diode is locked to the cavity frequency stabilized to the frequency of the second harmonic of the single-frequency Ti:sapphire laser through the two-stage Hansch-Couillaud stabilization scheme. The performance characteristics of this system should be enough to achieve laser cooling of silicon atoms.