We present the comprehensive analysis and the compact modeling methodology of fast electron detrapping from the bandgap engineered tunneling oxide (BE-TOX) in 3-D NAND flash memories. To this end, we develop a physics-based detrapping model considering the detailed electron dynamics in the BE-TOX and various emission paths of the detrapping mechanism. By the aid of the carrier density rates from the accurately calibrated model, we find that the major path of the charge loss can be direct tunneling (DT) or trap-to-band tunneling (TBT) depending on the temperature and the nitride layer position in the BE-TOX. In addition, we compare the model result and the fitted stretched exponential function. From those comparisons, we correlate several indicators (time constant and curve shape) of the retention characteristics with the major paths of the charge loss. Finally, our model facilitates the quantitative separation of the detrapping mechanism into different paths.