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

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.