Trap filled limit voltage (VTFL) and V2 law in space charge limited currents

There is no signature of the trap filled limit voltage (VTFL) in the J-V characteristics of a sample containing exponentially distributed traps. We show that VTFL and the voltage at which V2 dependence sets in (VMott) can be determined accurately. These voltages are independent of the energy distributions of the traps and depend strongly on the trap density Hb. Contrary to the literature results, it turns out that VTFL is significantly smaller than the VMott. In a specific case with Hb=1.6×1018cm−3 and for a 5% accuracy in the current the value of VMott is about 400V whereas VTFL is 13.5V. Universal J-V curves in reduced units are derived and plotted. The reduced value of VTFL is 0.5. These curves are valid for all organics and inorganic semiconductors and for all energy distributions of traps. It is shown mathematically that all J-V curves approached Mott’s V2 law asymptotically as V increases to infinity. To validate the theory, the experimental J-V curves in polycrystalline undoped and Al doped ZnO thin films are made. The experimental results show good agreement with the theory. In the undoped ZnO films the traps are exponentially distributed and the trap concentration is calculated to be 1.7×1017cm−3. The trap distribution in Al doped ZnO films is found to be discrete at a single level with trap concentration of 8×1016cm−3.