This paper investigates the subthreshold behavior of Fin Field Effect Transistor (FINFET) by solving 3D Laplace, and Poisson equations. Based on the potential distribution inside the fin, the appropriate band bending and the change in the band bending (∂ψ<sub>s</sub>) were calculated. Three-dimensional analysis of (∂ψ<sub>s</sub>) the change in the band bending indicates that (∂ψ<sub>s</sub>)is less (by ~ 20% for a channel width (T<sub>fin</sub>) of 20 <i>nm</i>) in the middle of the channel compared to that at the Si-Si<sub>O2</sub> interface. The decrease in (∂ψ<sub>s</sub>) towards the middle of the channel indicates that the control of the gate decreases towards the middle of the channel. Simulation results show that the S-factor of the device increases as T<sub>fin</sub> increases. It is observed that the S-factors calculated from the Laplace and the Poisson equations differ by ~7% for a device with a T<sub>fin</sub> = 50 <i>nm</i>. However this difference in S-factor gradually decreases and for smaller channel width devices, the S-factors calculated using Laplace and Poisson equations are the same. A comparison of S-factors obtained from Laplace and Poisson equation shows that the S-factor obtained from Poisson equation agrees very well with the reported experimental results. Thus, the systemic study of subthreshold behavior of FinFET shows that it is most appropriate to determine the S-factor of wider channel devices by solving 3D Poisson equation with appropriate doping concentration.