Field Emission at Grain Boundaries: Modeling the Conductivity in Highly Doped Polycrystalline Semiconductors

In this contribution, we elaborate a conductivity model for highly doped polycrystalline semiconductors. The prominent feature of the model is the description of grain-boundary scattering by field emission, i.e., quantum-mechanical tunneling of electrons through potential barriers at grain boundaries. For this purpose, we adapt a theory of Stratton [Theory of field emission from semiconductors, Phys. Rev. 125, 67 (1962)] to double Schottky barriers at grain boundaries. We provide strong evidence that field emission rather than the predominantly applied thermionic emission is the dominant transport path across grain boundaries in semiconductors with carrier concentrations exceeding approximately 10 19 cm −3 . We obtain a comprehensive conductivity model for highly doped polycrystalline semiconductors by combining field emission with two intragrain scattering mechanisms, that are ionizedimpurity and electron-phonon scattering. The model is applied to a wide range of literature data in order to show its applicability and explanatory power. The literature data comprise, in particular, transparent conductive oxides with a special emphasis on aluminum-doped ZnO.