Trap-Limited Space-Charge Limited Current in 2D Thin Film Dielectric

Due to the lack of intrinsic charge in insulator or dielectric, significant charge injection from electrode into the solid is required and the transport is known as space charge limited current (SCLC) in solid. By measuring the current-voltage characteristics, one can estimate the mobility of the charge injection. For 1D model transport, it is a well-known technique for both trap-free [1] and trap-filled [2] solids. For a thin film setting, it is more complicated that requires numerical solution even for a trap-free solid [3] . Such thin film setting can even approach the limit of monolayer of 2D materials [4] . In this paper, we consider a trap-filled solid and formulate a SCLC model for different contact geometries relevant to 2D thin film. By solving the Cauchy-type singular integral equation, our results show that the calculated results are different from traditional models. Using our model, we can estimate the mobility for a given trap distribution and geometrical setting. The developed SCLC model developed here shall offer a practical tool for more accurate estimation of carrier mobility of ultrathin dielectric slab used in various applications of high current transport in nanodiodes [5] including electrical contact and dielectric breakdown.