Hexagonal boron nitride （h-BN） is found to have widespread application， owing to its outstanding properties， including gate dielectrics， passivation layers， and tunneling layers. The current studies on the fundamental physical properties of these ultrathin h-BN films and the electron tunneling effect among them are inadequate. In this work， the effective mass in h-BN was successfully determined through a combined approach of experimental and theoretical research methods by fitting the current-voltage curves of metal/insulator/metal structures. It was observed that within a range of 4-22 layers， the effective mass of h-BN exhibits a monotonic decrease with an increase in the number of layers. The physical parameters of the Fowler-Nordheim tunneling model in the context of electron tunneling in h-BN are precisely ascertained by utilizing the extracted effective mass. Additionally， the impact of fixed charges at the metal/h-BN interface and various metal electrode types on Fowler-Nordheim tunneling within this structure is investigated utilizing this physical parameter in Sentaurus TCAD software. This work is informative and instructive in promoting applications in the fields of h-BN related infrared physics and technology.