The effects of thin film homogeneity on the performance of ferroelectric tunnel junctions

The compelling physical properties of the recently discovered ferroelectric phase in thin film Hf _x Zr_1-x O₂ have opened a window for applications such as non-volatile resistive switching memory devices with high retention known as ferroelectric tunnel junctions. In this article, we investigate the stability of these two-terminal, polarization induced resistance-switching devices with respect to the statistical reproducibility of constitutive electrical parameters based on surface thickness inhomogeneities. We provide a straightforward, quantitative model to estimate tunneling currents dependent on thickness variations, and the resulting tunneling electroresistance (TER) ratios and breakdown probability. An analytical expression for the probability distribution of tunneling currents for normally distributed thicknesses is given. Using material parameters of a TiN/HZO/Pt heterostructure, practical design requirements are deduced and an estimation with respect to the surface roughness is given for practical ferroelectric layer thicknesses and voltages below 4 nm and 1 V, respectively. In this regime, the simple model of a ballistic, direct tunneling mechanism can be used to adequately model the thickness and voltage dependence of the resistivity.