Dynamics and Modeling of Multidomains in Ferroelectric Tunnel Junction-Part-II: Electrostatics and Transport

• Published in: IEEE transactions on electron devices Vol. 70; no. 1; pp. 1 - 8
• Main Authors: Pandey, Nilesh, Chauhan, Yogesh Singh
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-01-2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coercivity; Current density; Depolarization; Depolarizing fields; Domain walls; Electric fields; Electric potential; Electrostatics; Energy; ferroelectric energy density; Ferroelectric materials; ferroelectric tunnel junction (FTJ); Ferroelectricity; Formulas (mathematics); Free energy; Green’s function; Mathematical analysis; Mathematical models; multidomain; Nucleation; Optimization; Optimization techniques; Poisson equation; Poisson equations; tunnel electroresistance (TER); Tunnel junctions; Tunneling; tunneling transport; Two dimensional analysis
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2022.3220490

We have derived the 2-D analytical multidomain electrostatics model of the ferroelectric tunnel junction (FTJ) in part-I of this work. Here, we have used the 2-D potential functions from part-I to determine the depolarizing energy density of the ferroelectric layer. The coupled solution of the Landau Ginzburg-Devonshire (LGD) equation with Poisson's equation is obtained to capture the domain texture in the ferroelectric layer. The nucleation and movement of the domain wall are incorporated into the model by minimizing net ferroelectric energy (depolarization energy density <inline-formula> <tex-math notation="LaTeX">+</tex-math> </inline-formula> free energy density <inline-formula> <tex-math notation="LaTeX">+</tex-math> </inline-formula> gradient energy density). Due to the mathematical complexity, spontaneous polarization <inline-formula> <tex-math notation="LaTeX">\text{(}\textit{P}_\textit{s}\text{)}</tex-math> </inline-formula> and coercive electric field <inline-formula> <tex-math notation="LaTeX">\text{(}\textit{E}_\textit{c}\text{)}</tex-math> </inline-formula> are assumed to be fixed, and the net system energy is minimized only by domain wall nucleation and movement in the ferroelectric layer. The analysis of this article is twofold; first, we study the impact of domain dynamics on electrostatics in an FTJ. Subsequently, the obtained electrostatics is used to study the variations in tunneling current, and ON/OFF ratio tunnel electroresistance (TER) originated from multidomain dynamics. We show that ON/OFF tunneling current density and TER varies locally in the ferroelectric region, and approximately one-decade local variations in current density are observed. The optimization techniques to achieve a uniform and maximum TER are also discussed. Furthermore, the impact of the bottom insulator layer on ferroelectric's gradient energy is also studied.