Tsu-Esaki modeling of tunneling currents in ferroelectric tunnel junctions

We model tunneling currents through step barrier structures representative of ferroelectric tunnel junctions wherein one of the electrodes contributes to the barrier potential profile or an extra layer is grown between the ferroelectric barrier and one of the electrodes. We study current density-voltage (J-V) and tunneling electroresistance (TER) curves using the Tsu-Esaki formula with numerically calculated transmission. This method is computationally robust, and the same results cannot be obtained with the standard methods usually applied for interpreting experimental I-V curves. Our results predict that the effect of resonant tunneling produces asymmetry in the J-V curves and negative differential resistance characteristics. We show that the asymmetry of the J-V curves can be tuned by adjusting the barrier heights and widths and that changing the extra barrier width affects the asymmetry the most. The barrier widths and the main barrier height affect the magnitude of the tunneling current the most. The change in the tilt of the main barrier is suggested to produce a significant TER of the order of 10². Our numerical method provides a systematic way to study trends in tunneling currents through step barrier structures across a wide range of barrier parameters and bias voltages, in contrast to the necessity of employing several different approximations when using analytical formulae. Therefore, our method provides the means for interpreting existing and future experiments and can be used as a tool for designing new devices with desired functionalities.