Tunneling injection to trap-limited space-charge conduction for metal-insulator junction

For a biased trap-filled insulator, the current transport is governed by the physics of charge injection from the metallic electrode and also the trap-limited space-charge conduction in the insulator. With a Schottky barrier at the interface of the metal-insulator junction, charge tunneling injection from a metal into the trap-filled insulator is different from an Ohmic contact. At sufficiently large amount of charge injection at high voltages, the charge transport becomes the trap-limited space-charge conduction. In this paper, we develop a consistent model to calculate the correct IV characteristics up to a breakdown field strength of 1 V/nm. Using this model, we analyze the transport characteristic of three different metal-insulator junctions (ITO/PPV, Al/h-BN, and Al/ZrO2) and identify the conduction mechanisms over a wide range of the applied voltage, insulator's thickness, and properties of the traps. Our findings report the interplay between various transport mechanisms, which is useful to characterize the correct current transport for novel insulators such as organic semiconductors, 2D insulators, and metal-oxide electronics.