Greatly enhanced tunneling electroresistance in ferroelectric tunnel junctions with a double barrier design

Ferroelectric tunnel junctions (FTJs), typically metal/ferroelectric/metal (MFM) structures, are promising candidates for non-volatile memory due to their tunneling electroresistance (TER) effect—the conductance difference between ferroelectric polarization states. Research focuses on maximizing TER for better resistance state distinction. Existing methods mainly involve modifying barrier width or height in single-barrier FTJs. This paper explores an alternative approach using a double barrier design. Double-barrier structures, known for phenomena like resonant tunneling, offer a potential for significantly enhancing TER. The paper hypothesizes that a double-barrier FTJ (DB-FTJ) would exhibit a much larger TER than its single-barrier counterpart (SB-FTJ). This is based on the principle that the overall transmission probability in a double barrier is a function of the individual transmission probabilities of each barrier (T' = f(Ta, Tb)). In an idealized sequential tunneling model, where T' = TaTb, the ON/OFF ratio of a DB-FTJ consisting of two identical SB-FTJs would be the square of the ON/OFF ratio of the SB-FTJ (n = na*nb). Even with more accurate models considering incoherent and coherent resonant tunneling, the ON/OFF ratio for DB-FTJs is significantly increased. To validate this hypothesis, the paper designs a specific DB-FTJ structure and utilizes density functional theory calculations to investigate its TER and other properties.

Extensive research has been conducted on FTJs since the demonstration of nanoscale ferroelectricity in thin films. Various mechanisms for achieving large TER have been proposed, including the utilization of domain wall states, the screening effect of electrodes, defects, phase transitions, polar interfaces, and interfacial large polarizations. Almost all methods proposed for enhancing TER in SB-FTJs focus on modulating the effective barrier width and/or height. In contrast, double-barrier structures are well-studied in mesoscopic transport theory, exhibiting unique transport behaviors absent in single-barrier structures. The paper leverages this existing understanding to motivate the proposed DB-FTJ design.

The study employs density functional theory (DFT) calculations to investigate the transport properties of a designed DB-FTJ structure and compare it with SB-FTJs. The DB-FTJ model consists of Pt/BaTiO3/LaAlO3/Pt/BaTiO3/LaAlO3/Pt, where each BaTiO3/LaAlO3 (BTO/LAO) barrier consists of 5.5 unit cells (u.c.) of BTO and 1 u.c. of LAO. This structure is considered as two identical SB-FTJs connected in series. The SB-FTJs used for comparison have BTO thicknesses of 5.5 u.c. and 11.5 u.c. (the latter obtained by removing the central Pt layer from the DB-FTJ). The SIESTA package is used for structural relaxation, fixing the xy-plane lattice constant to the experimental value of tetragonal BTO. The atomic coordinates and z-direction lattice constant are fully optimized. The Perdew-Burke-Ernzerhof (PBE) form of the exchange-correlation potential under generalized gradient approximation (GGA) and double zeta basis sets are employed. The polarization direction of each BTO barrier is controlled by pre-setting Ti-O displacement. The Nanodcal package, combining DFT and non-equilibrium Green's functions (NEGF) method, is used for transport property calculations, using a 15x15x1 k-point grid for self-consistent calculations and a 300x300 k-point grid for transmission coefficient calculations. The equilibrium conductance G is calculated using equation (1), and the TER ratio is determined using equation (2). Real-space charge density distribution is obtained by integrating local density of states. The k-resolved transmissions, electrostatic potential energy distributions, projected density of states (PDOS), and real-space charge density distributions are analyzed to understand the observed TER.

The DB-FTJ exhibits a remarkable TER ratio of 2.210 × 10⁸%, at least three orders of magnitude larger than the SB-FTJs. The high conductance state of the DB-FTJ shows an ultra-low resistance area product (RA) of 0.093 kΩµm². The SB-FTJ with 5.5 u.c. BTO shows a TER ratio of 5.306 × 10³ and RA of 0.028 kΩµm² for the high conductance state, while the SB-FTJ with 11.5 u.c. BTO shows a TER ratio of 8.496 × 10⁵% and a significantly higher RA of 16.002 MΩµm². Analysis of the electrostatic potential energy and PDOS reveals that in the DB-FTJ's high conductance state, the conduction band minimum drops below the Fermi energy, effectively reducing barrier width and increasing transmission. In the low conductance state, the Fermi energy lies largely in the band gap. Orbital-resolved analysis shows the d_yz and d_xz orbitals contribute significantly to the high conductance state. Finally, a multiple resistance states DB-FTJ design is proposed, which, by independently controlling the polarization of each barrier, achieves four distinct resistance states with significantly different RAs, demonstrating the potential for multi-state memory applications.

The results strongly support the hypothesis that a double barrier design significantly enhances TER in FTJs. The observed giant TER ratio and ultra-low RA in the DB-FTJ are attributed to the double barrier effect, which amplifies the conductance difference between the two polarization states far beyond what is achievable with a single barrier of even double the thickness. The independent polarization control capability demonstrated in the multi-state DB-FTJ design expands the potential applications beyond simple binary memory to multi-state memory devices. While quantum well states formed by the middle metallic layer might contribute to the overall transmission, they are not the primary cause of the large TER difference. The significant enhancement seen is primarily a result of the double-barrier effect.

This study demonstrates the feasibility of significantly enhancing TER in FTJs through a double barrier design. The DB-FTJ achieves a giant TER ratio and ultra-low RA, outperforming SB-FTJs by at least three orders of magnitude. The ability to independently control the polarization of each barrier enables the realization of a multi-state memory device. Future research could explore optimized material choices, further investigation of defect and disorder effects, and integration of DB-FTJs into actual memory devices.

The study relies on DFT calculations, which have inherent limitations, such as the underestimation of band gaps. While DFT+U calculations were performed to address this, further experimental validation is needed. The model assumes ideal interfaces and does not account for possible defects or imperfections, which could affect the actual performance of the devices. The study focuses on a specific DB-FTJ design; further investigations are needed to explore other material combinations and structural parameters for further optimization.