Design space for stabilized negative capacitance in HfO2 ferroelectric-dielectric stacks based on phase field simulation

Polarization evolution with space and time in HfO2 based metal-ferroelectric-insulator-metal (MFIM) structure is studied based on the phase field model by self-consistently solving the two-dimensional time-dependent Ginzburg-Landau and Poisson equations. Through examining the domain wall and electrostatic (depolarization) energies compared with the negative ferroelectric (FE) anisotropy energy, the correlation between the domain pattern (phase transition) and negative capacitance (NC) effect is revealed for different structure parameters and material properties, including FE thickness and gradient coefficient, dielectric permittivity and thickness, and operation frequency of applied voltage. The design space for stabilized NC with (near) hysteresis-free operation accompanied with voltage amplification is limited by phase transition, implying the potentials and limitations of FE HfO2 for energy-efficient steep-slope devices.