This work proposes a distance-dependent trap model to overcome the limitations of conventional Technology Computer-Aided Design (TCAD) models, which fail to accurately represent the non-uniform charge distribution resulting from electron energy relaxation under strong tunneling conditions in 3D NAND flash memories. By incorporating a spatially varying capture cross-section within the charge trap layer (CTL), the model effectively captures trap centroid shifts under realistic programming conditions. Implemented through the physical model interface (PMI) in Sentaurus TCAD, this model shows significantly improved alignment with experimental data for incremental step pulse programming (ISPP) characteristics when compared to the conventional Shockley-Read-Hall (SRH) model. Additionally, a systematic analysis of trap distribution effects on programming speed and Z-interference is conducted. The results indicate a clear trade-off: traps located near the tunneling oxide (TOX) enhance programming speed but increase Z-interference, whereas traps near the blocking oxide (BOX) reduce Z-interference, but with slower programming speeds. These findings demonstrate the importance of precise control over trap distribution to optimize the performance and reliability of 3D NAND Flash memories.