A Gibbs energy view of double hysteresis in ZrO2 and Si-doped HfO2

The Gibbs energy can yield fundamental insight into the material properties of ferroelectrics such as energy barriers and phase transitions. Particularly for newly emerging classes of ferroelectric and antiferroelectric materials, such as fluorite-structured HfO2 and ZrO2, the Gibbs energy can bridge theoretical calculations with experimental observations. Experimentally observed dynamic double hysteresis loops in thin film ZrO2 and Si-doped HfO2 capacitors are used to obtain a solution to the Gibbs energy by calculating the internal electric field with depolarization. By accounting for dipole-field interaction energies and static energies in the solution of the Gibbs energy of double-hysteresis ZrO2 and Si-doped HfO2, a characteristic triple-well with two polar and one nonpolar energy minima emerges. Macroscopic metastable polar and nonpolar phases close in free energy are shown to be in agreement with first-order phase transitions underlying double hysteresis in ZrO2 and Si-doped HfO2. The application of an external field is demonstrated to lower the free energy minimum of the polar phase below the nonpolar phase, providing macroscopic support that a first-order phase transition driven by an electric field is responsible for antiferroelectric behavior in doped HfO2 and ZrO2. Energy barriers for the nonpolar -> polar phase transition from 0.75 to 4.3meV per formula unit are calculated for ZrO2 and Si-doped HfO2. The macroscopic Gibbs energy profiles obtained through experimental measurements and device modeling connect the fundamental phenomenology of ferroelectrics and antiferroelectrics to electronic devices.