The mobility limiting scattering mechanisms for amorphous semiconductors and polar polycrystalline semiconductors are studied in the context of developing new high‐performance thin‐film transistor (TFT) channel layer materials for large‐area electronics. A physics‐based model for carrier transport in an amorphous semiconductor is developed to estimate the mobility limits of amorphous semiconductor TFTs. The model involves band tail state trapping of a diffusive mobility. Simulation reveals a strong dependence on the band tail density of states. This consideration makes it difficult to realize a high‐performance p‐type oxide TFT. A polar crystalline semiconductor may offer a higher mobility but is fundamentally limited by polar optical phonon scattering. Any crystalline TFT channel layer for practical large‐area applications will not be a single crystal but polycrystalline, and therefore, grain size and grain boundary‐dependent scattering will further degrade the transport properties.