The Organic Field-Effect Transistor (OFET) is recognized as a pivotal device in applications such as flexible circuits, sensors, and memory storage. However, its performance typically lags behind that of inorganic counterparts. Enhancing the performance of OFETs necessitates precise control over the characteristics of the organic semiconductor layer. Recent advancements in molecular-level simulation techniques, including kinetic Monte Carlo methods, have significantly enhanced the capability to replicate the microscopic behavior of charge carriers. Nevertheless, these approaches often depend on two-dimensional Poisson equations, which inadequately capture short-range electrostatic interactions. In this research, we successfully employed a three-dimensional partial differential equation solver to model OFET devices, fully accounting for the Coulomb interactions between charge carriers. Our findings reveal that at elevated gate voltages, the transfer characteristics derived from the three-dimensional Poisson equation exhibit a downward curvature and lower values compared to those predicted by two-dimensional Poisson equations, suggesting strong concordance with experimental observations.