On the structural origins of ferroelectricity in HfO₂ thin films

Recent studies have demonstrated the emergence of ferroelectricity in HfO₂ thin films doped with elements including Si,¹ Y,¹ and Al,² among others.³ Combined with controlled doping, the response is further influenced by dimensional confinement introduced through capping layers including TiN,¹ TaN,⁴ RuO₂,⁵ Pt,^5,6 or Ir.^7–9 While these HfO₂ thin film structures show promise as candidates for non-volatile memory applications,¹⁰ direct identification of the phase responsible for spontaneous polarization has remained experimentally elusive.

At atmospheric temperature and pressure, bulk HfO₂ adopts a monoclinic structure with space group P2₁/c. The structure is centrosymmetric and hence does not support spontaneous polarization necessary for a true ferroelectric response. When doped and confined, however, HfO₂ thin films have been proposed to undergo a transition to a non-centrosymmetric orthorhombic structure.^10,11 This has been claimed based on a comparison of HfO₂ to the related ZrO₂, which shares many phase similarities with HfO₂ including the transition from cubic to tetragonal to monoclinic as temperature decreases.¹² Specifically, there are four proposed orthorhombic HfO₂ phases adopting the space groups Pmn2₁, Pca2₁, Pbca, and Pbcm.^4,13–17 Of these phases, only Pca2₁ and Pmn2₁ are non-centrosymmetric.¹⁵ 

For comparison, Figure 1(a) shows each of the aforementioned phases projected along the four major zone axes $[ 100 ], [ 010 ], [ 001 ]$⁠, and $[ 110 ]$⁠. The four Hf atoms form a distorted face centered lattice with the eight O atoms occupying the pseudo-tetrahedral interstitial sites. Close inspection of Pca2₁ and Pmn2₁ phases reveals that oxygen atoms shift along the c axis thereby allowing spontaneous polarization. Here, we focus on the lower symmetry phases of HfO₂, i.e., monoclinic and orthorhombic, as the two higher symmetry phases $Fm3¯m$ and P4₂nmc are paraelectric.^1,18,19

Due to consistencies with the related ZrO₂ system, the Pca2₁ orthorhombic structure is primarily thought to be the cause of ferroelectricity in HfO₂, but this has not been unambiguously confirmed by experiment.¹⁰ While grazing incidence x-ray diffraction (GIXRD) experiments point to the existence of an orthorhombic phase, the analysis of the patterns is complicated due to the mixture of different phases in the film, similarities between the respective reference patterns of the potential HfO₂ phases, and severe peak broadening of polycrystalline thin films, as shown in Figure 1(b). Moreover, the Pmn2₁ phase has also been proposed as a candidate following a search for low-energy phases using density functional theory (DFT).¹⁵ 

In this letter, we explore the structural origins of ferroelectricity in HfO₂ films using aberration corrected scanning transmission electron microscopy (STEM). We apply high-angle annular dark-field (HAADF) STEM imaging to directly observe and quantify the film structure along a variety of crystallographic directions. Complementing imaging, we use position averaged convergent beam electron diffraction (PACBED) to determine the projected symmetry and polarity at the nanoscale.²⁰ Through the combination of these techniques, we report direct experimental evidence for the presence of the polar orthorhombic Pca2₁ phase in Gd doped HfO₂ thin films.

Metal-insulator-metal capacitor structures were fabricated as described in Ref. 4. In the present work, the Gd doped HfO₂ thin film with a thickness of 27 nm was annealed at 650 °C for 20 s. Polarization (triangular field sweep, 10 kHz) and small-signal capacitance (triangular bias field sweep, 10 Hz; 150 mV small-signal amplitude, 10 kHz) were measured using a TF Analyzer 3000 by aixACCT Systems. TEM samples were prepared from Gd:HfO₂ capacitors using focused ion beam (FEI Helios nanolab 600i dual beam system). HAADF-STEM and PACBED were acquired using a probe-corrected FEI Titan G2 60–300 kV operated at 200 kV with a beam current of approximately 70 to 100 pA. The collection inner semi-angle and probe semi-convergence angle were approximately 77 mrad and 14 mrad or 20 mrad, respectively. Images were acquired and processed with the revolving STEM (RevSTEM) method (details provided in Ref. 21). Each RevSTEM dataset contained 20 image frames of size 1024 × 1024 pixels with a 90° rotation between each successive frame. Atom column positions in each RevSTEM image were then determined by fitting each atom column to a two-dimensional Gaussian function and then mapped into a matrix representation.²² Lattice constants were measured directly from the distance between atom column locations in real-space.²³ PACBED diffraction patterns were simulated with the dynamical diffraction simulator MBFIT (Many-Beam dynamical-simulations and least-squares FITting).²⁴ The PACBED method was selected as it enables acquisition of the CBED pattern from a selected nanometer range area, providing high spatial resolution and also high sensitivity to the local polarity.^20,25

Similar to the findings in the original work by Böscke et al.,¹⁰ a characteristic hysteretic behavior of both polarization, P, and relative permittivity, k, as a function of the electric field, E, were obtained, as displayed in Figure 2. The purely dielectric k-value (not affected by an enhancement around the switching fields of the ferroelectric) is between what would be expected for a low-symmetry monoclinic P2₁/c (Refs. 18 and 19) and a high-symmetry cubic $Fm3¯m$ phase.^1,18,19 Close examination of the structures in Figure 1 reveals that the reference structures share both common and distinct features (highlighted in each projection by gray boxes). In the case of the monoclinic structure, only the $[ 001 ]$ is comparable with the orthorhombic structures. For polar phases, Pmn2₁ and Pca2₁, the projected Hf arrangements are significantly different in all projections except $[ 100 ]$⁠. We also notice that the other three orthorhombic phases Pca2₁, Pbcm, and Pbca exhibit very similar arrangement of Hf atom columns along all four zone axes with only difference in O atom column arrangement. Thus, the highlighted features in Figure 1 enable the lattice type to be directly determined from HAADF STEM images along different crystal projections.

An overview of the thin film microstructure is shown in Figure 3(a), where the layered structure is resolved with the growth direction (G.D.) indicated. The HfO₂ grain size is around 10–30 nm, on the order of the film thickness. Two different types of grains, the monoclinic phase and an orthorhombic phase, have been generally observed in this HfO₂ film. As the monoclinic phase always exists in the reported HfO₂ thin films, which is also evident from the two shoulder peaks at 28.6° and 31.6° in GIXRD pattern (Figure 1(b)), we focus our discussion here on the orthorhombic phase. Atomic resolution STEM images of the film major phase component acquired along four zone axes (acquired from four different orthorhombic grains) are shown in Figure 3(b). Because O atoms are much lighter than Hf atoms, it is only possible to visualize and locate Hf atoms as seen in the four major zone axes. For the observed Hf atom columns in Figure 3, the arrangement is in excellent agreement with the projected crystal structure for Pca2₁, Pbca, and Pbcm. These results provide direct evidence of existence of an orthorhombic phase in the Gd:HfO₂ thin films. Furthermore, the results are inconsistent with the Pmn2₁ structure which has a unit cell that is too small, see Table I, and which does not incorporate the “zigzagging” behavior of the Hf atom column arrangement highlighted with lines in Figures 1(a) and 3.

For additional evidence of an orthorhombic phase, the lattice parameters are directly measured from the atom column positions in the STEM images.^21,23 The lattice constants measured directly in real-space are listed in Table I and are compared to literature values. The lattice parameters measured by RevSTEM are the averages from three different grains. The XRD values for Pca2₁ suffer from the error from peak broadening and phase mixture. Note that the reference values for other HfO₂ phases determined by DFT in Ref. 15 generally agree well with the experimental values. The DFT values from Ref. 16 do not agree with the other sources, which may be from the algorithms selected for DFT calculations. Moreover, the three structures possess a nearly identical arrangement of Hf, though they vary slightly in their arrangement of oxygen. While these measurements, combined with arrangement of projected atom columns, rule out Pmn2₁ and higher symmetry phases, it is evident that the lattice constants for the orthorhombic structures are difficult to distinguish from lattice parameters alone.

To distinguish between the Pbca, Pbcm, and Pca2₁ phases, we turn to electron diffraction measurements. Under dynamical conditions, the diffraction intensities for a non-centrosymmetric crystal no longer obey Friedel's rule (reciprocal lattice pairs are no longer required to be of equal intensity). This benefit of electron diffraction has been used to determine the polarity at the nanoscale using CBED methods.^26,27 The spontaneous polarization in BaTiO₃, for example, manifests as the removal of a mirror plane in the pattern.^20,28 In other words, by examining the symmetry of a CBED pattern, we can rapidly determine if the crystal is centrosymmetric or non-centrosymmetric.^26,29 Furthermore, nanoscale thin films often have the potential for overlapping grains. It is therefore important to target specific regions of the film for CBED where overlap does not occur, which can be readily achieved with the PACBED technique.^20,25

A representative HfO₂ thin film region for PACBED analysis is shown in Figure 4(a). The central grain analyzed by PACBED is oriented along $[ 110 ]$⁠, as shown in the inset. It is important to note that the $[ 001 ]$ axis, which is polar for Pca2₁, is nearly parallel to the film G.D. This orientation is consistent with the observed out-of-plane ferroelectricity. Furthermore, the intensity distribution of the corresponding PACBED pattern in Figure 4(b) shows a mirror plane (solid bars) along the horizontal direction, but lacks one along the vertical direction (dashed bars), i.e., the left side of the center disc is more intense than the right half. Simulated PACBED patterns along equivalent directions for the non-centrosymmetric Pca2₁, centrosymmetric Pbca, and centrosymmetric Pbcm phases are presented for comparison in Figures 4(c), 4(d), and 4(e), respectively. In contrast to the experiment, the Pbca and Pbcm PACBED patterns in Figures 4(d) and 4(e) show two perpendicular mirror planes as expected for a centrosymmetric structure. The Pca2₁ PACBED pattern in Figure 4(c), however, is asymmetric and in near-perfect agreement with experiment. Together with the STEM results in Figure 3, these results confirm the presence of the Pca2₁ phase, which was found throughout the thin film.

In conclusion, we have quantitatively analyzed the structural origins of ferroelectricity in Gd:HfO₂ thin films using STEM imaging and diffraction. We confirm that the source of ferroelectricity of thin-film Gd:HfO₂ likely arises from the non-centrosymmetric Pca2₁ orthorhombic phase. Having confirmed that this phase is present, the ferroelectric response can thus arise from spontaneous polarization of this structure, consistent with first-principle calculations.¹⁵ Moreover, while Gd doped HfO₂ has been examined here, we expect the structural origin observed here is common amongst other cases of ferroelectricity reported in HfO₂ and ZrO₂ based thin films.

The authors gratefully acknowledge the support from the National Science Foundation (Award No. DMR-1350273). E.D.G. was supported by the National Science Foundation through a Graduate Research Fellowship (Award No. DGE-1252376). X.S., E.D.G., and J.M.L. acknowledge the use of the Analytical Instrumentation Facility (AIF) at North Carolina State University, which is supported by the State of North Carolina and the National Science Foundation. Christoph Adelmann from Imec, Belgium is gratefully acknowledged for depositing the TiN-Gd:HfO₂-TiN stacks. Tina Sturm and Almut Pöhl from Leibniz IFW Dresden, Germany are acknowledged for FIB preparation of the lamellas. Moreover, the German Research Foundation (Deutsche Forschungsgemeinschaft) is acknowledged for funding part of this research in the frame of the “Inferox” project.