Piezoelectricity in Hafnia

Hafnia (HfO2) has emerged as a technologically important ferroelectric compatible with semiconductor processing, enabling applications such as ferroelectric FETs and negative-capacitance devices. Unlike classic soft-mode ferroelectrics (perovskites like PbTiO3 or BaTiO3), HfO2 exhibits unusual features including possibly improper-like ferroelectricity, ultranarrow domains and domain walls, and improved ferroelectric performance at reduced dimensions. Recent first-principles studies predicted that ferroelectric HfO2 in its orthorhombic Pca21 phase should exhibit a negative longitudinal piezoelectric coefficient (d33 < 0), in contrast to perovskites. However, some experimental reports suggest a positive longitudinal response, leaving the sign and origin of HfO2’s piezoresponse as an open question. This work aims to determine the sign of the longitudinal piezoresponse experimentally and theoretically, elucidate its atomistic origin, and propose routes to control and potentially reverse it.

Prior work established ferroelectricity in HfO2-based thin films and explored unique ferroelectric behaviors (e.g., domain scaling, non-proper character). First-principles predictions indicated negative longitudinal piezoresponse in HfO2 (refs. 13,14) and negative response is well known in organic PVDF. Conversely, many piezoresponse measurements on doped HfO2 films reported positive d33,eff. Perovskite ferroelectrics like PbTiO3 exhibit large positive d33. The discrepancy in HfO2’s reported sign and the lack of atomistic understanding motivated the present combined theory–experiment study.

First-principles simulations: Density functional theory (DFT) with DFPT for response properties. Primary code VASP with PBEsol exchange–correlation, PAW potentials; treated valence states: Pb (5d,6s,6p), Ti (3p,4s,3d), O (2s,2p), Hf (5s,5p,6s,5d). Plane-wave cutoff 600 eV. k-point meshes: PbTiO3 (6×6×6 for 5-atom cell), HfO2 (4×4×4 for 12-atom cell). Structures relaxed to forces < 0.01 eV Å−1 and stresses < 0.1 GPa. Piezoelectric tensors (e, ē) and elastic tensors computed via DFPT; d obtained via d = Se. Cross-checked with ABINIT using PBEsol, ONCV pseudopotentials; Hf (5s,5p,4f,5d,6s) and O (2s) in valence, 60 Hartree cutoff, 4×4×4 k-grid, force convergence 1e−6 Ha/bohr. Epitaxial-strain simulations: constrained in-plane lattice vectors with a = a0(1+εepi), b = b0(1+εepi), 90° in-plane angle; relaxed internal coordinates and out-of-plane lattice parameter across εepi ≈ −7% to +4%. Computed bond lengths, charge densities, A (force-response internal strain) and Z* tensors versus εepi. Experimental: Sample preparation—PZT (200 nm, (111)-oriented, Zr/Ti 40/60) by magnetron sputtering on Pt with IrO2 top electrodes; La:HfO2 (20 nm) by ALD on TiN with TiN top electrode, annealed at 800 °C for 20 s in N2; PVDF (12 monolayers, 21.6 nm) by Langmuir–Blodgett on Pt/Si. PFM characterization: Switching spectroscopy PFM in resonance tracking (DART) mode on Asylum MFP-3D; tips: single-crystal diamond (D80) and Pt-coated (HQ:DPER-XSC11). AC modulation frequencies ~350 kHz (D80) and ~650 kHz (Pt tip); PFM loops acquired ~3 kHz below resonance. For PVDF, conducting tip served as top electrode; for capacitors, external probe applied bias. Phase loop rotation direction used to infer sign of d33,eff; amplitude used to estimate magnitude (bias-off mode to minimize electrostatics).

• First-principles (HfO2, Pca21): e33 total negative due to lattice-mediated contribution; computed d33 = −2.51 pm V−1 (VASP; ABINIT −1.64 pm V−1). Effective polycrystalline average d33,eff ≈ −0.94 pm V−1 for randomly oriented, poled grains.
• PbTiO3 (P4mm) benchmark: large positive d33 ≈ 208 pm V−1; much larger e and d than HfO2; softness along polar axis (S33 ≈ 48.72 TPa−1) vs HfO2 stiffness (S33 ≈ 2.97 TPa−1) explains magnitude difference.
• Experimental PFM: PZT shows clockwise phase loop (positive d33,eff); PVDF shows anti-clockwise (negative d33,eff). La:HfO2 (10–20 nm) shows anti-clockwise phase loops analogous to PVDF, indicating negative d33,eff; estimated magnitude −2 to −5 pm V−1, consistent with theory.
• Atomistic origin: Negative e33 arises from strain-induced forces (A tensor) causing OI anions (those responsible for polarization) to move upward and Hf cations downward under tensile η3, reducing P3. The bonding environment of OI—one bond aligned with the polar axis (Hf(1)–OI(1)) and two largely in-plane (Hf(2)/Hf(3)–OI(1))—governs the response.
• Tunability via epitaxial strain: Under in-plane epitaxial strain εepi from −7% to +4%, Hf–OI bond lengths are controllably modified. e33’s frozen-ion part stays nearly constant (positive), while the lattice-mediated part varies strongly and monotonically, making total e33 more negative under tensile εepi and switching to positive under sufficient in-plane compression (predicted sign change for large compression, beyond roughly −5%). Polarization remains positive and increases under compression (>70 μC cm−2 for εepi < −5%), so sign reversal occurs without switching polarization.
• Sample dependence: Literature and some in-house films can show positive d33,eff; La:HfO2 films here consistently showed negative d33,eff, possibly related to texture/strain but likely intrinsic for these samples.

The study resolves the debated sign of HfO2’s longitudinal piezoresponse by demonstrating a negative d33 both theoretically and experimentally in La-doped HfO2 thin films, aligning with prior first-principles predictions. The atomistic mechanism is traced to the unique chemical coordination of the active OI anions and the system’s tendency to preserve dominant Hf–O bond lengths under axial strain, which drives oxygen and cation displacements that reduce polarization upon tensile strain. This mechanistic insight explains the contrast with perovskite ferroelectrics, where analogous strain enhances polarization (positive e33). Importantly, the mechanism implies strong tunability: by altering the relative strengths of the vertical vs in-plane Hf–O bonds (e.g., via epitaxial strain), the lattice-mediated contribution can be modulated to enhance, weaken, or even reverse the sign of the longitudinal response without changing the polarization state. The findings suggest that observed sample-to-sample variability in the sign of d33,eff may stem from differing strain states, textures, compositions, or boundary conditions that alter the local OI bonding environment. This opens avenues to engineer piezoelectric responses in hafnia beyond the constraints seen in classic perovskites.

This work confirms that ferroelectric HfO2 exhibits a negative longitudinal piezoelectric response (d33 < 0), supported by DFPT calculations and PFM measurements on La:HfO2 films. It identifies the atomistic origin in the bonding environment of the active oxygen sublattice and demonstrates that epitaxial strain can continuously tune and even reverse the sign of the longitudinal piezoresponse without switching polarization—an unprecedented capability among ferroelectrics. Future research should systematically map how processing, texture, mechanical boundary conditions, dopant chemistry, thickness, and electrical cycling influence d33,eff and its sign, correlating electromechanical measurements with structural descriptors (e.g., texture-induced strain, bond metrics) to distinguish intrinsic vs extrinsic contributions and guide optimization for applications.

• The epitaxial-strain route predicted to reverse the sign of e33 requires large in-plane compressive strains (beyond approximately −5%), which may be challenging to realize and maintain in practical devices.
• Experimental d33,eff appears sample- and history-dependent; polycrystallinity, texture, and extrinsic factors (e.g., local strain, defects, interfaces) can influence the effective response, complicating direct comparison with single-crystal theoretical values.
• The atomistic bonding picture, while consistent with calculations and trends, is inferred from DFPT tensors and charge-density analyses; unambiguous experimental validation of local bonding changes under strain remains to be demonstrated.