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Two-dimensional materials are of current great interest for their promising applications to postsilicon microelectronics. Here we study, using first-principles calculations and a Monte Carlo simulation, the electronic structure and magnetism of CrI 3 monolayer, whose bulk material is an interesting layered ferromagnetic (FM) semiconductor. Our results show that CrI 3 monolayer remains FM with $ T_ {\text {C}}\sim 75\\text {K} $, and the FM order is due to a superexchange in the near-90 Cr-I-Cr bonds. Moreover, we find that an itinerant magnetism could be introduced by carriers doping. Both electron doping and hole doping would render CrI 3 monolayer half-metallic, and steadily enhance the FM stability. In particular, hole doping is three times as fast as electron doping in increasing T C, and a room temperature FM half-metallicity could be achieved in CrI 3 monolayer via a half-hole doping. Therefore, CrI 3 monolayer …