Antiferroelectric negative capacitance from a structural phase transition in zirconia

Abstract

Crystalline materials with broken inversion symmetry can exhibit a spontaneous electric polarization, which originates from a microscopic electric dipole moment. Long-range polar or anti-polar order of such permanent dipoles gives rise to ferroelectricity or antiferroelectricity, respectively. However, the recently discovered antiferroelectrics of fluorite structure (HfO₂ and ZrO₂) are different: A non-polar phase transforms into a polar phase by spontaneous inversion symmetry breaking upon the application of an electric field. Here, we show that this structural transition in antiferroelectric ZrO₂ gives rise to a negative capacitance, which is promising for overcoming the fundamental limits of energy efficiency in electronics. Our findings provide insight into the thermodynamically forbidden region of the antiferroelectric transition in ZrO₂ and extend the concept of negative capacitance beyond ferroelectricity. This shows that negative capacitance is a more general phenomenon than previously thought and can be expected in a much broader range of materials exhibiting structural phase transitions.

Fig. 1. Origin of antiferroelectric negative capacitance.

a The polarization P-electric field E_a characteristics of an antiferroelectric material. The segment BAB’ corresponds to the non-polar, antiferroelectric ground state, and segments CD and C’D’ correspond to the polar phase. Segments BC and B’C’ represent the unstable negative capacitance (C < 0) regions. At Ea = E₁, the antiferroelectric has two stable states: M and N. b–d The antiferroelectric free energy landscape at E_a = 0 (b), E₁ (c) and −E₁ (d). d²G/dP² < 0 in the P-range corresponding to BC and B’C ‘forbidden’ regions.

Fig. 2. Standard characterization of antiferroelectric ZrO₂ thin film and heterostructure.

a Polarization P vs. electric field E_a characteristics of a TiN/ZrO₂(10 nm)/TiN capacitor measured using a standard ferroelectric tester at 1 kHz. b Low magnification high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image of the cross-section of a representative TiN/HfO₂/Al₂O₃/ZrO₂/TiN heterostructure grown on Si showing all the layers distinguishable with clear interfaces. Fast Fourier transforms of high magnification HAADF-STEM images of the same sample show amorphous rings in the HfO₂ layer and discrete diffraction spots in the ZrO₂ layer consistent with the tetragonal <010> zone axis.

Fig. 3. Demonstration of antiferroelectric negative capacitance.

a Experimental setup of the pulsed charge-voltage measurements on the dielectric-antiferroelectric heterostructure. V_in, V_DE-AFE, R and I are the applied voltage pulse, the voltage across the DE-AFE capacitor, the series resistor (5.6 kΩ) and the current through R, respectively. The waveforms of V_in and V_DE-AFE were measured using an oscilloscope at different amplitudes of the V_in pulse. b Transient waveforms of V_in, V_DE-AFE, I and integrated charge for a HfO₂(8 nm)/Al₂O₃(~ 1 nm)/ZrO₂(10 nm) capacitor. c Maximum charge Q_max, residual charge Q_res, and reversibly stored charge ΔQ as functions of maximum voltage across the DE-AFE capacitor V_a measured from the waveforms shown in b. d Polarization P as a function of extracted electric field E_a across the ZrO₂ layer in a HfO₂(8 nm)/Al₂O₃(~ 1 nm)/ZrO₂ (10 nm) heterostructure capacitor. The P–E_a characteristics of an equivalent stand-alone ZrO₂ capacitor measured on a conventional ferroelectric tester is also shown for comparison in the background. The negative capacitance regions (C_AFE < 0) in the P–E_a curve correspond to the capacitance enhancement regions in the ΔQ-V_a curve shown in c. e Extracted energy landscape of ZrO₂. Second derivative of the free energy G with respect to P based on a polynomial fit is shown below.

Fig. 4. Capacitance matching in antiferroelectric-dielectric heterostructure capacitors.

a The capacitance enhancement factor r = C_DE-AFE/C_DE in dielectric-antiferroelectric heterostructures with varying HfO₂ thickness as functions of the constituent dielectric capacitance C_DE. C_DE-AFE is the heterostructure capacitance. The best fit to the capacitance matching law: C_DE-AFE/C_DE = | C°_AFE | /( | C°_AFE | - C_DE) is obtained for C°_AFE = −4.75 µF cm⁻² at P = 16 µC cm^-2 with R² = 0.9986, which is plotted as the red line in a and b. b 1/C_DE-AFE is shown as a function of 1/C_DE. The intercept gives the inverse antiferroelectric capacitance 1/C°_AFE, which is negative. Note that the negative capacitance of ZrO₂ reported here is independent of C_DE.