An Explicit Analytical Solution to the Grain Boundary Barrier Height in Undoped Polycrystalline Semiconductor Thin-Film Transistors

Based on discrete grain analysis and U-shaped distribution of density of states (DOS) for grain boundary (GB) traps, a physical-based explicit analytical solution to the GB potential barrier height (ψ_B) is developed for undoped polycrystalline semiconductor thin-film transistors (TFTs). The explicit solution is derived using the Lambert W function, without additional approximations introduced. The validity and accuracy of the solution is demonstrated comparing the model with both numerical calculations and experimental ψ_B data of polycrystalline Si TFTs. Furthermore, it is found that a previous widely used Seto´s model could be consistent to the proposed model in the above-threshold region, in this case deep states DOS dominates ψ_B, where the monoenergetic trap density of Seto´s model roughly corresponds to the deep states DOS multiplying by 3-4 units of the thermal energy kT. Finally, the analytical model is applied in ZnO TFTs.