Silicon Photomultipliers (SiPMs) are attractive candidates for light detectors for next generation liquid xenon double-beta decay experiments, like nEXO. In this paper we discuss the requirements that the SiPMs must satisfy in order to be suitable for nEXO and similar experiments, describe the two test setups operated by the nEXO collaboration, and present the results of characterization of SiPMs from several vendors. In particular, we find that the photon detection efficiency at the peak of xenon scintillation light emission (175-178 nm) approaches the nEXO requirements for tested FBK and Hamamatsu devices. Additionally, the nEXO collaboration performed radioassay of several grams of bare FBK devices using neutron activation analysis, indicating levels of 40K, 232Th, and 238U of the order of <0.15, (6.9e10-4 - 1.3e10-2), and <0.11 mBq/kg, respectively.
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