Hexagonal boron nitride (h-BN) finds widespread application, including gate dielectrics, passivation layers, and tunneling layers, owing to its outstanding properties. 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. Precisely ascertain the physical parameters of the Fowler-Nordheim tunneling model in the context of electron tunneling in h-BN 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 was 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.