Modeling of Negative Capacitance in Ferroelectric Thin Films.

The negative capacitance (NC) effect in ferroelectric thin films has attracted a great deal of attention from the material and semiconductor device communities because it could be a possible solution to the impending problems related to field-effect transistor power consumption and dynamic random-access memory charge loss. A short discussion on the fundamental premise of the NC effect is presented. A phase-field model based on the time-dependent Ginzburg-Landau (TDGL) formalism in conjunction with the Chensky-Tarasenko (C-T) formalism for multidomain configuration is then developed to reveal the subtle correlation between the domain wall motion and NC effect for different thicknesses of ferroelectric and dielectric films. When a ferroelectric film becomes thin enough, a stripe domain structure can be achieved through competition between the electrostatic energy and domain wall energy. This stripe domain structure is quite resilient to transition to a homogeneous polarization state, making it very useful for (quasi-)static NC operation. Finally, the physical implications of the numerical results are explored with analytical modeling. It is identified that the domain wall motion in the stripe domain structure remains dominated by the external field, even when the entire film is in the (quasi-)static NC state.