We performed a rate equation analysis on the dynamics of exciton Mott transition (EMT) with assuming a detailed balance between excitons and unbound electron-hole (e-h) pairs. Based on the Saha equation with taking into account the empirical expression for the band-gap renormalization effect caused by the unbound e-h pairs, we show that the ionization ratio of excitons exhibits a bistability as a function of total e-h pair density at low temperatures. We demonstrate that an incubation time emerges in the dynamics of EMT from oversaturated exciton gas phase on the verge of the bistable region. The incubation time shows a slowing down behavior when the pair density approaches toward the saddle-node bifurcation of the hysteresis curve of the exciton ionization ratio.
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