Abstract:  The technology of photon counting has wide applications in physics and electrical engineering.Single photon detectors based on avalanche photodiodes are attractive，Considering their advantages including compact sizes，broad spectrum of responses，and high detection efficiencies.The semiconductor single photon detector normally works in the gated mode，where photons can only be detected when the gate is open.However，if any photon is detected by the photon counter during the gate，several gates after the detection will be forced to shut down so that no photon can be detected during this period.The timing duration that the gates are down is called the dead time.This article mainly focuses on the photon counting performance of the ID­201 semiconductor photon counter，which is produced by the ID Quantique company.The purpose is to derive a photon counting formula for ID­201 and verify it using experiments.Starting with a simple Poisson distribution，we first studied the relationship between the detection probability and the average numbers of the photons when the dead time effect was absent.Next，we examined the effect of the dead time by separating the general counting processes of ID­201 into two different types，for which the photon detection probabilities could be easily calculated.Finally，based on the above analysis methods，we successfully derived a mathematical formula that related the photon counts per second to several important parameters such as the optical power，the trigger frequency，the gate width，the detection efficiency and the dead time.To verify the derived formula，a series of experiments were performed using the ID­201 in together with a power­adjustable fiber­optic light source that operated at 1550 nm.It is found that under different conditions，the derived formula well agree with the experimental results.