Insights into Electron Transport in a Ferroelectric Tunnel Junction

Abstract

The success of a ferroelectric tunnel junction (FTJ) depends on the asymmetry of electron tunneling as given by the tunneling electroresistance (TER) effect. This characteristic is mainly assessed considering three transport mechanisms: direct tunneling, thermionic emission, and Fowler-Nordheim tunneling. Here, by analyzing the effect of temperature on TER, we show that taking into account only these mechanisms may not be enough in order to fully characterize the performance of FTJ devices. We approach the electron tunneling in FTJ with the non-equilibrium Green function (NEGF) method, which is able to overcome the limitations affecting the three mechanisms mentioned above. We bring evidence that the performance of FTJs is also affected by temperature–in a non-trivial way–via resonance (Gamow-Siegert) states, which are present in the electron transmission probability and are usually situated above the barrier. Although the NEGF technique does not provide direct access to the wavefunctions, we show that, for single-band transport, one can find the wavefunction at any given energy and in particular at resonant energies in the system.

Parametric FEM simulation of composite barrier FTJs under external bias at room temperature

“…Both j ON and j OFF increase by about two orders of magnitude when U c increases, whereas TER varies only between ∼ 1.5×10 3 -2×10 3 . However, the most important result of the simulations at 50 K is the disappearance of the features in j ON an TER curves, which supports their assignment to the presence of resonant states at higher temperature, in fair agreement with the findings in 17 .…”

“…The observed oscillations are indicative of the fact that resonances play a significant role in the transport process at high temperatures. However, the oscillations disappear at lower temperature of the system, such as T = 50 K (Figures 13(a) and (b)), in support of a resonant mechanism of electron transport at high temperature 17 . We also note that increasing the dielectric thickness determines large increases in j ON and TER values at 300 K, (Figures 14(a) and (b)), an effect that we ascribe to a large thermionic contribution to j ON via resonance states.…”

“…Maybe the most used method for calculating the transmission coefficient across energy barriers of FTJs is the WKB (Wentzel-Kramers-Brillouin) approximation, which is a semiclassical approach to compute the stationary solution of the Schrödinger equation, with the barrier approximated by its average value 4,15,16 . However, the WKB approximation cannot explain the resonance phenomena appearing in some systems 17 and is inaccurate for barrier profiles which vary abruptly. Therefore, alternative methods were proposed for calculating the transmission current across arbitrary potential barriers 18 .…”