Dynamics and Modeling of Multidomains in Ferroelectric Tunnel Junction-Part I: Mathematical Framework

• Published in: IEEE transactions on electron devices Vol. 69; no. 12; pp. 7147 - 7155
• Main Authors: Pandey, Nilesh, Chauhan, Yogesh Singh
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 2-D Poisson’s equation; Boundary conditions; Charge distribution; Dirichlet problem; Domains; Electric potential; Electrostatics; Ferroelectric materials; ferroelectric tunnel junction (FTJ); Ferroelectricity; Green's function methods; Green's functions; Green’s function; Impact analysis; Iron; Mathematical analysis; Mathematical models; multidomain; Poisson equation; Poisson equations; Polarization; polarization gradient; Transport properties; Tunnel junctions; Two dimensional analysis
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2022.3218259

Ferroelectric tunnel junction (FTJ) with the dead layer (DE) exhibits the multidomain texture. These multidomains in the ferroelectric (FE) cause the 2-D gradients in local polarization charge distribution. The impact of such local variations in the domain's polarization is modeled by solving 2-D Poisson's equation. Green's function approach is used to solve the 2-D Poisson's equation with the 2-D gradient in the polarization. First, Green's functions for the FE and DE regions are derived using the appropriate Dirichlet and Neumann boundary conditions. Subsequently, derived functions are plugged into Green's identity to obtain the 2-D potential distribution. The analysis of this study is divided into two parts; the first part derives an analytical model of the multidomain FTJ. In the second part, we analyze the impact of domain dynamics on FTJ's electrostatics and transport characteristics.