We have developed a comprehensive modeling framework to explain the switching characteristics of BEOL-compatible FeFET with an amorphous IGZO channel. Our TCAD-based modeling framework, calibrated against measurement data, jointly incorporates a) the distributed channel, b) a physics- based nucleation-limited switching dynamics model for multi- domain ferroelectric polarization (PFE) and c) the domain-domain interaction. To our knowledge, this is the first demonstration of a physics-based comprehensive model of BEOL-compatible FeFET. Our model reproduces and explains the experimentally- observed abrupt current jumps in the reverse and forward DC sweeps. Further, our model is capable of processing arbitrary input waveforms such as quasi-DC and different kinds of pulse trains used in neuromorphic applications. This comprehensive modeling framework would enable researchers to explore the BEOL FeFET applications and guide device optimization and development.