Introduction

Ferroelectric materials are polar non-centrosymmertric crystal structures having an electric polarization that can be switched between crystallographically degenerate states with the application of an electric field. The wurtzite structure (S.G.: P6 3 mc ) is a polar crystal structure as shown in Figure 1, but it has long been regarded to be non-ferroelectric (nonswitchable) because of the large atomic displacements and bond breaking necessary to transition from one polarization state to the other, especially in crystals with a high degree of polar covalent bonding. Here and subsequently, the term "wurtzite" also includes wurtzite-derived structures, including wurtzite-type solid solutions such as Al 1 x Sc x N. 1

Spontaneous polarization in wurtzite structures

Unlike perovskites, an initial challenge in wurtzites was to identify the correct nonpolar reference phase, which is intimately related to the magnitude of the spontaneous polarization ( P s ) and switching mechanism. Prior to the discovery of ferroelectricity, modeling and predicting P s in wurtzite materials was largely motivated by the need to understand polarization discontinuities at interfaces. 2 The sign and magnitude of P s , however, depend upon the reference structure, according to the modern theory of polarization. [3][4][5] With the discovery of ferroelectricity in wurtzites, it became apparent that different reference structures were being utilized in the literature, each giving a different value and sign for P s . 6 The early attempts at theoretically estimating P s in wurtzite materials from Bernardini et al., using zincblende as the reference state, resulted in underestimated P s 7 compared to the ones calculated by Dreyer et al. using a layered hexagonal structure. 6 Fichtner et al., using the modern theory of polarization, clarified the layered hexagonal BN-like (hBN-like) structure as the appropriate reference non-polar structure, as shown in Figure 1a. 8 Using this reference structure, the N-polar and metal(M)-polar phases of wurtzite MN exhibit P s vectors pointing downward (Figure 1b) and upward (Figure 1c), respectively. Utilizing this reference frame, the sign and magnitude of P s can be calculated from the structural parameters and the Born effective charges ( Z ) using Equation 1, which has been successfully applied to perovskite ferroelectrics. 9,10 (1) P = e s Z s,α r s,α , where r is the displacement from the reference centrosymmetric reference structure, e is the electronic charge, and is the unit cell volume. In the wurtzite structure, P s is constrained along the 〈0001〉 c-axis and this reduces to:

Taking wurtzite ZnO as an example, with a cell volume of 49.72 Å 3 , a Born effective charge of 2.163 for Zn and an average Zn displacement of 0.638 Å from the centrosymmetric structure, the resulting P s is 0.888 C/m 2 . 11 The direction of P s results from the displacement vector, positive (up) for metalpolar direction and negative (down) for oxygen-polar configuration, similar to wurtzite MN shown in Figure 1.

With this approach, P s can be experimentally determined by analyzing atomic positions within the structure (e.g., by structure refinement via scattering experiments or through atomic-resolution transmission electron microscopy techniques), which is more applicable to thin films. This structurebased method has been applied to a compositional series of Al 1 x B x N thin films, 12 enabling the calculation of P s even at the highest boron concentrations, where conventional polarization-electric field (P-E) loop measurements are hindered by significant leakage currents. The results reveal a strong correlation between P s and the crystalline quality of the films, as boron content increases, crystallinity deteriorates, leading to a corresponding reduction in P s .

The ability to probe polarization at the local scale opens new possibilities for investigating P s at interfaces and defective regions, down to the unit-cell level. Electron microscopybased calculations have demonstrated that with appropriate experimental configuration and careful sample preparation, polarization measurements in these structures can achieve accuracy within 5-15 percent. 13 Ultimately, such structurebased measurements of the spontaneous polarization should correlate with the remanent polarization measured in ferroelectric hysteresis loops. When inferring P s via the displacement currents induced by ferroelectric switching, however, it is important to recognize other potential contributions to the

measured current, including electrical leakage and contributions from piezoelectric displacement currents.

Switching mechanisms in wurtzite ferroelectrics

The P6 3 mc space group of the wurtzite structure means the polarization is symmetry permitted along the crystallographic c-axis. Figure 1 shows the two allowed polarization states, as well as a hypothetical prototype phase with space group P6 3 /mmc , which has zero polarization. In a perfect crystal, the two allowed polar states have identical energies, and are separated by a potential barrier (Figure 2a). In the case of ZnO, the barrier for ferroelectric switching has been estimated to be 0.25 eV/formula unit. 17,18 Among the open questions in the field are the manner in which composition changes by alloying, point defects, line defects, and area defects modify the potential profile to facilitate switching. The historic difficulty in fully switching materials with the wurtzite structure is not surprising. As a rule of thumb, the larger the atomic displacement required to switch between two configurations, the higher the potential barrier and, consequently, the larger the coercive field. However, this heuristic does not capture the full picture, as the potential barrier also depends on factors such as bonding character, structural softness, and the specific switching mechanism. For instance, in ZnO at room temperature, the Zn atom must be displaced by 1.25 Å-approximately three times greater than the atomic displacements involved in polarization switching in PbTiO 3 and yet, the calculated switching barriers are similar (0.25 eV/f.u. for ZnO versus 0.20 eV/f.u. for PbTiO 3 ). Early work by Onodera et al. on Li-doped ZnO reported values for the switchable polarization of 0.044 µC/cm 2 at room temperature; 19 this is too small by a factor of 1800-2000, suggesting that either a tiny fraction of the volume switched or that charge injection dominated the data. Similarly, Sawada et al. reported a polarization of 6 µC/cm 2 in wurtzite BeO, which is also anomalously low. 20 To assess whether ferroelectricity could be possible in wurtzites, Moriwake et al. conducted first-principles calculations for Zn and Be chalcogenides. 14 Many of the Zn and Be chalcogenides are quite ionic, such that the Born effective charges are comparable to the formal charges. They conclude that the barriers for intrinsic switching (e.g., in which the material uniformly/collectively changes polarization state, Figure 2a) are lower when the material is more ionic in character. The role of bond ionicity, in addition to anion-to-cation radius ratio 17 and bond stiffness, 15,21,22 in affecting the switching barriers has been recognized in subsequent works, and discussed in more detail in Reference 23. In the case of ZnO, the 0.25 eV/f.u. barrier is not that much higher than the 0.2 eV/f.u. barrier for intrinsic switching of PbTiO 3 . In the case of ZnO, the corresponding intrinsic coercive field is 7.2 MV/ cm. The models also predict that the intrinsic switching barrier should drop in cases where a c-axis oriented film is subjected to tensile stress. 14 This acts to flatten the tetrahedra by splaying the legs, and so reducing the distance that the atoms must displace for polarization reversal to occur. In practice however, intrinsic switching is rarely observed and the potential energy pathway, calculated with the solid-state nudged elastic band (SS-NEB) method, exhibits multiple barriers between the polar states, discussed next.

While the atomic-scale switching process involves phase transition(s) between polar and nonpolar states, the observation of P-E hysteresis is a result of mesoscopic switching that is understood to occur over longer length scales. Such mesoscopic switching requires the formation and motion of domains with distinct polarities. Polarization switching is inherently multiscale. The limited computational and experimental data that exist for wurtzite ferroelectrics point to significant differences in both the atomic-and domain-scale polarization switching compared to classic octahedrally bonded perovskite ferroelectrics. For example, recent computational studies have identified the structural disorder and chemical complexity as key factors enabling sequential switching of individual cation tetrahedra at the atomic scale 15 and the abrupt macroscale switching observed in Al 1 x Sc x N and Al 1 x B x N alloys requires extension of the classic Kolmogorov-Avrami-Ishibashi (KAI) model. 24 As such, a mechanistic understanding of this multiscale process is necessary to design wurtzite ferroelectrics and remediate challenges such as high coercive fields and low endurance.

As discussed in the previous section, the hBN-like structure is widely accepted as an appropriate nonpolar structure for calculating P s of wurtzite structures, including wurtzite-type alloys such as Al

However, the actual switching process may not involve a phase transition wherein the structure collectively transforms through a hBN-like structure. In other words, the hBN-like structure is an appropriate choice strictly for the purposes of calculating P s . The choice of the nonpolar structure for calculating P s is not unique, as shown in recent studies that found half-switched, nonpolar structures and the same magnitude of P s whether the hBN-like or the half-switched structures are used as reference non-polar structures. 15,16 The appropriate reference nonpolar structures depend on the number of unit cells considered in simulations.

Computational and experimental studies have revealed the complex nature of the atomic-scale switching mechanisms in wurtzite ferroelectrics. Early computational works by Moriwake et al. 14 to determine the intermediate non-polar structures along the switching pathway between the positive ( wz + ) and negative ( wz ) polar wurtzite structures of binary compounds, including ZnO, AlN, GaN, and InN. A collective (sometimes referred to as homogeneous) switching pathway going through the hBNlike intermediate, non-polar structure was proposed (Figure 2a).

More recent computational studies have used the NEB or SS-NEB method to deduce the minimum energy pathways between wz + and wz and found the same collective mechanism ( wz + hBN-like wz ) for undefective AlN and ZnO. 15,16,22 This collective mechanism is characterized by a single potential barrier where the non-polar structure is the transition state (Figure 2a). Lee et al. showed that increased chemical complexity of compounds associated with ternary and higher stoichiometries in wurtzite-derived structures (determined by group-subgroup symmetry relations 1 ) favors switching pathways with multiple potential barriers and intermediate metastable states that are transient during the switching process. 15,22 Unlike the collective mechanism, the "individual" (or sequential) cation tetrahedron undergo sequential switching in a cascading fashion; the non-polar structures are often "half-switched" (i.e., one half of the tetrahedra are one polarity and the other half of opposite polarity [Figure 2a]). Lee et al. identified five unique half-switched, nonpolar structures (Figure 2c), including the -BeO-like structure that has been proposed in a few computational studies 15,16 and imaged using scanning transmission electron microscopy (STEM) in Al 1 x B x N. 27 Alloying also increases chemical complexity, in addition to introducing site disorder. The combined effect of compositional complexity and disorder lends itself to interesting switching mechanisms in wurtzite alloys. Liu et al. used the NEB method to calculate the minimum energy pathways for Al 1 x B x N and found that at x >0.0625, the -BeO-like non-polar structure is metastable (Figure 2d). 16 Calderon et al. confirmed the same non-polar structure in Al 1 x B x N with STEM. 27 By combining STEM and theoretical calculations, Mi and co-workers proposed a charged domain wall with a buckled two-dimensional hexagonal phase in Ga 1 x Sc x N characterized by 4-8 rings reminiscent of the -BeO-like nonpolar structure. 28 There is now growing evidence that AlN-based alloys exhibit a composition-dependent switching mechanism. Using the SS-NEB method, Lee et al. computationally demonstrated that Al 1 x Sc x N alloys at low Sc compositions ( x 0.25-0.28) exhibit collective switching passing through a hBN-like nonpolar structure, but at higher Sc compositions gradually transitions to individual switching that passes through half-switched, nonpolar structures (Figure 3a). Such collective switching is still expected to occur on the scale of a few to many unit cells, but not throughout the thickness of the film. The Sc composition (x) around which the transition from collective to individual switching is observed in simulations also correspond to the compositions with onset of experimentally observed ferroelectricity in Al 1 x Sc x N, which provides indirect validation of the computational model. Additionally, the switching barrier decreases almost linearly with x (Figure 3a), consistent with the linear decrease in coercive field observed experimentally. 8 Similar transition behavior and correspondence with thin-film compositions at which ferroelectricity is observed at or near room temperature has been reported for Al 1 x B x N and Al 1 x Gd x N. 29 It must be noted that the specific compositions at which the transition in mechanism is observed are not "critical" compositions. Since the experimental realization of ferroelectricity relies on the coercive to breakdown field ratio, these specific composition ranges simply represent when the coercive fields are sufficiently larger than the breakdown fields to observe ferroelectricity at room temperature. Similar conclusions have been presented for Zn 1 x Mg x O in a somewhat related way. Baksa et al. showed that higher Mg substitutions induce larger local distortions and therefore, strain fluctuations that promote a change in the switching mechanism and lowering of the coercive field (Figure 3b). 25 In another study, reactive force fields were trained on density functional theory (DFT) data and used to perform molecular dynamics simulations that showed the coercive field decreases with increasing Mg substitution in Zn 1 x Mg x O. 30 Domain nucleation and motion in wurtzite ferroelectrics are central to understanding their polarization switching. Unlike conventional ferroelectrics, wurtzite materials exhibit unique anisotropic switching and possibly complex domain dynamics that challenge traditional theoretical models. Mesoscopic simulations are crucial for capturing these domain-scale switching mechanisms, as they bridge the gap between atomistic interactions and macroscopic behavior. Work by Andrew Rappe and co-workers has leveraged machine-learned interatomic potentials to perform largescale simulations, providing insights into the polarization reversal process in AlN (Figure 3c). 26 Experimental verification of ferroelectric switching pathways remains inherently challenging due to the ultrafast nature of the switching process, the high electric fields required, and the necessity for atomic-scale resolution to capture ionic displacements during the event. This demands experimental techniques capable of performing time-resolved, in situ biasing experiments at atomic resolution-such as transmission electron microscopy (TEM). However, accurately determining the position of every atomic species within the structure is nontrivial, requiring advanced TEM techniques and extremely thin, electron-transparent samples.

High-resolution STEM, particularly when using aberration-corrected instruments, is commonly employed. The high-angle annular dark-field (HAADF) imaging mode is widely used due to its sensitivity to atomic number (Z-contrast), but it provides limited information about light elements such as oxygen and nitrogen. To overcome this limitation, annular bright-field (ABF) and phase contrast techniques such as differential phase contrast (DPC) and center of mass (CoM) imaging have emerged, enabling simultaneous visualization of both light and heavy elements. However, it is important to note that conventional TEM provides a two-dimensional projection of the structure along the beam direction, effectively averaging the structure over the sample thickness. This projection effect complicates the interpretation of transient or spatially varying features, such as those present during polarization switching. For instance, conventional STEM techniques may result in ambiguous interpretations of the domain walls structure in Al 1 x B x N and Al 1 x Sc x N, 31 hindering the distinction between an inclined domain wall or the presence of a non-polar, -BeO-like phase, predicted by NEB calculations. 15,16 One promising approach to addressing some of these limitations is electron ptychography, which has the potential to recover structural information as a function of sample thickness. 32 However, its application to dynamic switching processes remains an open challenge.

Defects in wurtzites and their role in ferroelectric switching

While substitutional point defects are critical to the switching energetics and can engender ferroelectricity, they and other point defects can have deleterious effects on the dielectric and ferroelectric properties, as in oxide perovskites 33 and hafnia. 34 However, the defect chemistry of wurtzite alloys and its effect on the ferroelectric behavior remain unclear. We know from fundamental physics that defects-from atomic-scale point defects to extended defects (stacking faults, dislocations, interfaces)-are likely to affect ferroelectric properties as well as dielectric breakdown. 35,36 Deep defects that introduce midgap states localize electronic carriers and minimize the leakage current but may also lead to premature defectmediated dielectric breakdown. Shallow defects, on the other hand, contribute to increased leakage currents but may not reduce dielectric breakdown fields as strongly as deep defects. These tradeoffs are well-known qualitative concepts but quantifying these effects in wurtzite ferroelectrics is critical for future developments. Point defects are well known to modify locally the polarization switching and domain-wall motion in perovskite oxide ferroelectrics. 37 By extension, similar effects are expected in wurtzite ferroelectrics although the actual mechanisms may differ. While our discussion here focuses mainly on point defects, the importance of extended defects in III-nitrides is also widely reported. 38 Our current understanding of the defect chemistry of wurtzite alloys is mostly based on binary wurtzite compounds, AlN, GaN, and ZnO. AlN and GaN are direct bandgap materials, with AlN classified as ultrawide bandgap ( 6.2 eV) and GaN as wide bandgap ( 3.4 eV). 39,40 The substantial difference in their bandgaps influences the nature and energy levels of native defects and impurities (Figure 4).

Native Defects: First-principles point defect calculations provide useful guidance in identifying the dominant MRS BULLETIN • VOLUME 50 • SEPTEMBER 2025 • mrs.org/bulletin defects and their energy levels in the bandgap. We will follow the modified Kröger-Vink notation to represent defects, A C B , where A is the defect (V for vacancy), B is the defect site (i for interstitial), and C is the charge state q, denoted by q+ or q-instead of q . and q . The formation energy of charged defects vary with the position of the Fermi energy, E F , which intimately depends on the growth conditions. In native AlN and GaN, cation (V 3 Al , V 3 Ga ) and nitrogen (V 1+ N ) vacancies are the dominant defects under both metal-rich (Al-rich or Ga-rich) and N-rich conditions (Figure 4b and c). [41][42][43] Under Al-rich growth conditions, nitrogen vacancies have relatively low formation energies in both AlN and GaN. However, the defect states are deeper in AlN compared to GaN, which is a consequence of the larger bandgap of AlN. For example, V N +3/+1 and +1/0 defect states in AlN reside 5.1 eV and 1.5 eV below the conduction-band minimum (CBM) while in GaN the same states are at 3.0 eV and 0.2 eV, respectively (Figure 4a). 44,45 Experimentally, a 5.9-eV photoluminescence band in ion-implanted AlN has been attributed to a band-to-defect transition involving V 1+ N , where the defect state is estimated to lie approximately 0.3 eV below CBM. 46 The equilibrium Fermi energy ( E F,eq ) in undoped AlN is around 2.9 eV and 1.8 eV below CBM under N-rich and Al-rich growth conditions, respectively, consistent with its highly insulating nature. The high formation energy of the dominant defects V 3 Al and V 1+ N at E F,eq , for example, >3 eV under Al-rich growth conditions, ensures very low defect concentrations. However, in practice, unintentional dopants (impurities) such as oxygen and silicon and complexes such as V Al -2(O N ) dictate the phase equilibria in AlN (Figure 4b). 44 The effect of impurities is discussed later in this section.

Unlike AlN, the only dominant defect in native GaN is 4c) under Ga-rich growth conditions. As such, V 1+ N are not charge compensated by V 3 Al . Here, V 1+ N introduces donor defect states 2.9 eV and 0.25 eV below CBM. The observed n-type conductivity of GaN 47 was initially attributed to the presence of V N , partly due to the limited accuracy of DFT functionals such as local density approximation (LDA) and generalized gradient approximation (GGA). 48,49 While V N is a relatively shallow donor (compared to V N in AlN), higher accuracy DFT calculations later clarified that V N concentrations are too low to be responsible for n-type conductivity. Instead, unintentional incorporation of impurities such as oxygen and silicon is found to be the source of n-type conductivity in GaN. Cation interstitials (e.g., Ga i ) as well as antisite defects (e.g., Ga N ) are generally unfavorable in III-nitrides (Figure 4c). Recent first-principles calculations of the defect energetics in AlN-based alloys show qualitatively similar behavior to the parent III-nitrides. For example, V 1+ N , V 3 Al , and V 3 Sc are the dominant defects in native Al 1 x Sc x N and oxygen is a readily soluble impurity that forms deep-level DX centers. 50 The bandgap of wurtzite ZnO (3.4 eV) is similar to GaN. Under Zn-rich/O-poor growth conditions, oxygen ( V O ) and zinc vacancies ( V Zn ) are the dominant defects, followed by zinc interstitials (Zn i ). 51,52 Under O-rich growth conditions, the neutral split oxygen interstitial (O i ) also becomes a dominant defect, in addition to V O and V Zn . The V O (+2/0) defect level has been debated in computational studies because of the sensitivity to the DFT method. 51,53,54 Early models attributed the ubiquitous n-type conductivity of ZnO to the donor oxygen vacancies ( V 2+ O ), presumed to act as shallow donors. However, hybrid DFT calculations showed that V O in ZnO introduces a deep donor level approximately 1.2 eV below CBM with relatively high formation energy to explain the n-type conductivity. 55,56 Thus, V O is unlikely to contribute significantly to roomtemperature free carriers. Zinc interstitials (Zn i ), by contrast, are shallow donors, but they exhibit high formation energies (>2 eV under O-poor conditions), rendering their equilibrium concentrations low. V Zn introduce deep acceptors states (0/-1 and -1/-2), but their concentrations are low regardless of the growth conditions. 55,56 Impurities: In 1973, Slack posited that oxygen incorporation in AlN occurs via substitution on the nitrogen sublattice, with charge compensation provided by Al vacancies (i.e., one Al vacancy for every three O atoms substituting N). 57 The increased V 3 Al concentration contributes to contraction of the unit cell and reduction in thermal conductivity. Once the oxygen level exceeds a critical threshold (0.75 at.%), a new defect species emerges, wherein an Al atom adopts an octahedral coordination with O atoms. The formation of this defect mitigates the Al vacancies favored at lower O concentrations, thereby restoring the lattice parameter. Additionally, such octahedrally coordinated Al centers can serve as nucleation sites for extended O-rich defects (e.g., inversion domain boundaries [IDBs] and stacking faults). 58,59 Donor O 1+

N introduces an energy level approximately 0.6 eV below the conduction band. Upon capture of two electrons, O 1+

N undergoes structural relaxation that forms a DX center, O 1+

N transitioning into a deeper DX center, giving rise to an absorption band peaked at 2.22 eV. 60 Substitutional oxygen donors likely form deep-level defect complexes with V 3 Al , resulting in acceptor levels that lie deeper in the bandgap. The ( V 3 Al -O 1+ N ) 2 and ( V 3 Al -2O 1+ N ) 1 complexes correspond to acceptor levels around 1.4-1.6 eV and 1.8-2.0 eV above the valence band, depending on bonding configurations (Figure 4). [61][62][63][64][65] Additionally, ( V 3 Al -O 1+ N ) 2 complexes produce 2.2 eV yellow luminescence via recombination from the shallow donor state. 66 Similarly, in GaN, O substituting for N introduces a donor level, O 1+ N , 0.27 eV below the conduction band. 45,67,68 This donor can also capture an extra electron to form a DX center. 45 Silicon is another unintentional impurity that can substitute for Al or Ga, acting as a donor. In AlN, the shallow Si 1+ Al donor level transitions to deeper DX states, with ionization energies ranging from 70 to 300 meV, depending on the Si concentration. 69 In GaN, Si remains a shallow donor under pressure up to 25 GPa 70 and in Al x Ga 1 x N alloys up to x = 0.44. 71 Its donor level lies approximately 0.2 eV below the conduction-band minimum in GaN, thereby enhancing n-type conductivity. 71 Certain growth methods, such as metal-organic chemical vapor deposition (MOCVD), can introduce high concentrations of hydrogen, which acts as an amphoteric interstitial ion in AlN and GaN. Due to the larger bandgap of AlN, the solubility of hydrogen can be substantially higher in AlN than in GaN. In p-type GaN, hydrogen behaves as a donor H + , thereby compensating acceptors. Its preferred sites are the antibonding position behind a nitrogen atom or the bond-center site, where it forms a strong bond with nitrogen. The diffusion barrier for H + is about 0.7 eV, indicating high diffusivity at moderate to elevated temperatures. Conversely, in n-type GaN, hydrogen acts as an acceptor H , most stably occupying the antibonding site near a Ga atom. This configuration has a high migration barrier, leading to very low diffusivity. When the Fermi level lies below approximately 2.1 eV, H + is favored; for higher Fermi-level positions, H predominates. [72][73][74] Extrinsic hydrogen plays a dominant role in ZnO defect chemistry, often unintentionally incorporated during crystal growth or annealing processes. Hydrogen can exist as interstitial hydrogen (H i ) or substitutional hydrogen at an oxygen site (H O ), both acting as shallow donors. The 0/+ transition level for H i lies close to the CBM ( 30 meV below), making it a highly efficient donor at room temperature. 75 Formation energy of H i is notably lower than V O , leading to significant incorporation even without deliberate doping. The 30-meV donor state in ZnO has also been attributed to a defect complex, Zn i -O N , 76 although overwhelming evidence attributes the donor state to H.

Role of alloying and defects on dielectric breakdown

In the discussion of wurtzite ferroelectrics, the changes in breakdown field ( E b ) strength is often overlooked because it is generally large, but because the switching fields are very close to the E b , it is essential that breakdown strengths are not compromised. Indeed, the key to inducing ferroelectricity in wurtzite materials is to lower E c relative to E b . 22 The intrinsic dielectric breakdown strength is intimately related to the bandgap, permittivity, and phonon properties, which all change with alloying. Typically, semiconductors with wide ( E g > 3 eV) and ultrawide ( E g > 5 eV) bandgaps, large dielectric constants ( > 10), and strong electron-phonon coupling (avalanche theory by von Hippel, 77 Fröhlich 78 ) exhibit large intrinsic E b . Various phenomenological models 79,80 as well as machine-learned relations 81 suggest the strong dependence of E b on the bandgap of the material.

While alloying may flatten and lower switching barriers (Figure 3a), and by extension, reduce coercive fields, it is essential that the chemical modifications do not significantly reduce the material bandgap nor introduce appreciable concentrations of deep defects with midgap states, which facilitate carrier hopping and lower E b . Figure 5 compares the bandgap variations with compositions of AlN-and ZnO-based alloys.

Because rocksalt ScN has a small bandgap, 85 increasing Sc composition in Al 1 x Sc x N causes the bandgap to shrink rapidly, reaching 3 eV at x > 0.3. 82 In contrast, B alloying has an advantage in that the bandgap reduces less rapidly while the computed switching barriers are lowered sharply, 29 providing better E b /E c ratio. Zn 1 x Mg x O bandgap increases with Mg alloying, consistent with the ultrawide bandgap of rock salt MgO. MRS BULLETIN • VOLUME 50 • SEPTEMBER 2025 • mrs.org/bulletin

Defect charge transition levels in AlN

Extrinsic effects on E b are also important, as any increases in electrical conduction can lead to thermal breakdown via Joule heating 86 or avalanche breakdown due to increased carrier hopping. The dominant defects in IIInitrides and some AlN-based alloys introduce deep defects with midgap states (Figure 4), which may be beneficial for carrier trapping that suppresses leakage currents, but facilitate carrier hopping under high electric fields leading to dielectric breakdown. Breakdown caused by the formation of conductive filaments of V N has also been proposed, 87 although the migration barrier of V N is known to be significantly higher than for V O . 88

Role of defects on film polarity, endurance, and leakage characteristics of wurtzite ferroelectrics

Oxygen and silicon impurities play a pivotal role in promoting IDBs and, thus facilitating polarity inversion in AlN films. Youngman and Harris showed that at O concentrations higher than 0.75 at.%, the formation of V 3 Al -nO 1+ N defect clusters reach a threshold where aluminum coordination changes from tetrahedral to octahedral. This structural change promotes IDB formation and ultimately drives the polarity inversion. 64 Bruley et al. reported that incorporating an equivalent of 1.5 basalplane monolayers of oxygen into the IDB is required to satisfy the Pauling charge compensation rule requirement. 89 Stolyarchuk et al. later confirmed that this same amount of oxygen enables the formation of Al x O y N z , which is crucial for switching from N-polar to Al-polar in AlN films grown on sapphire. 90 The formation of Al x O y N z phase was achieved through (1) a reaction between sapphire and ammonia during nitridation; and (2) O 2 annealing or O 2 plasma treatment, which converts a mixed-polar AlN epitaxial film to Al-polar. 91,92 Figure 6(a)-(f) presents a high-resolution HAADF-STEM image of the AlN/ sapphire interface after postannealing in N 2 at 1750°C. During annealing, Al atoms near the interface in the sapphire diffuse upward into the AlN layer, occupying V 3 Al sites and creating an O-terminated sapphire surface, which leads to N-polar AlN formation. Simultaneously, O atoms from sapphire also diffuse into the AlN layer, forming an Al x O y N z layer and lead to the polarity inversion from N-polar to Al-polar. 93 A similar process has been proposed for Si-doped AlN, where the V 3 Al -n Si 1+ Al defect cluster is energetically favored. At low Si concentrations (<1 at.%), these clusters remain sparse and exert little impact on the wurtzite structure, preserving an Al-polar orientation. However, when Si content increases (1-15 at.%), the increasing density of V 3 Al -n Si 1+ Al clusters promotes a transition from tetrahedral to octahedral coordination, forming IDBs and switching the film polarity from Al-polar to N-polar. 94 Defects also found to have an effect on switching barrier for polarization reversal in Al 1 x Sc x N films at low Sc compositions ( x < 0.36). Figure 6g shows the minimum energy switching pathways for both pristine AlN and defected AlN (2.8 at.% V 1+ N or O 1+ N ). Introducing these defects lowers ω s , switching barrier, relative to the pristine structure (Figure 6h).

It was proposed that increased bond ionicity and softness reduce ω s . Specifically, V 1+ N locally softens the bonds, while O 1+ N introduces more ionic, yet stronger, Al-O bonds. The resulting local distortions resemble those caused by Sc doping in AlN: Al-N bonds in the basal-plane shorten, and those along the c-axis elongate, shifting the local structure closer to the hBN-like phase. 21 In both cases, the structural changes lower ω s . 50 Endurance and Leakage Current Characteristics: While several wurtzite ferroelectrics are promising candidates for nonvolatile ferroelectric memories due to their high thermal stability, high remanent polarization, and CMOS compatibility, the reported endurance values 10 4 -10 7 remain far below the required 10 12 cycles. [95][96][97] Recently, Uehara et al. demonstrated that Sc x Ga 1 x N exhibited no change in remanent polarization up to 1 10 8 cycles. 98 Although the intrinsic breakdown strength is approximately 15 MV/cm, the presence of defects leads to breakdown at lower electric fields, ultimately resulting in low endurance. Limited studies have explored the physical phenomena of fatigue and breakdown in wurtzite ferroelectrics under AC cycling. One study proposed that V N exist in asdeposited Al 0.78 Sc 0.22 N films, with additional vacancies forming during switching cycles. Prolonged cycling leads to electron trapping, which pins ferroelectric domains and reduces P s . Newly generated V N lower the Schottky barrier at the interface, enhancing electron tunneling and ultimately causing dielectric breakdown due to increased Joule heating (Figure 7a-b). 86 He et al. demonstrated that in the pristine state, the bulk conductivity of Al 0.93 B 0.07 N is primarily governed by electron trapping at V N sites. In the fatigued state, electron transitions between V 3+ N and deeper defects, such as V 3 Al -nO 1+ N , become more prominent, controlling bulk conductivity (Figure 7c-d). 99 A more recent study demonstrated that another defect level, O 1+ N , also contributes to increased leakage current levels in Al 0.65 Sc 0.35 N films subjected to AC cycling. It was observed that oxygen migrates and penetrates through grain boundaries, leading to an increase in oxygen content from 2.3 to 12.8% after 10 7 cycles (Figure 7d). Each oxygen atom substituting for nitrogen introduces an extra electron, creating conductive channels that lead to increased leakage current, a significant reduction in remanent polarization, and eventual electrical breakdown. When the film was exposed to AC cycling in fluorinated oil, the fatigue lifetime increased significantly, along with a slower increase in leakage current (Figure 7e). 100 The adverse effect of V N and O N on endurance was mitigated by postannealing the Al 1 x Sc x N films under NH 3 environment at 700 C, leading to improved endurance by more than two orders of magnitude (Figure 8a). Following NH 3 annealing, the oxygen concentration within the Al 1 x Sc x N film decreased from 3.5% to 2.3%, while the oxygen content at the TiN/Al 1 x Sc x N interface also showed a reduction. Effective removal of V N and O N reduced density of trapped charges, leading to lower leakage current and increased E b (Figure 8b-c). 101 Chen et al.

observed a similar increase in E b and a reduction in leakage current when H 2 gas was introduced into the Ar/N 2 gas mixture during growth. This led to an improvement in the fatigue lifetime of Al 1 x Sc x N films. The effect was more pronounced in films with higher Sc content (x = 0.26), suggesting that a reduction in concentration of V 3 Al -nO 1+ N defects may be responsible for the enhanced endurance (Figure 8d-f). 102 Intriguingly, it was demonstrated that introducing O into bulk Al 0.73 Sc 0.27 N through an external gas source during the reactive sputter process suppressed the leakage current by fourfold near the coercive field. In this study, the O concentration was high enough to form extended defects where Al is octahedrally bonded to oxygen. These defects act as structural units for forming IDBs, which facilitate polarization reversal. The authors demonstrated gradual transition from N-to M-polar orientation as the oxygen content in the film increased. MRS BULLETIN • VOLUME 50 • SEPTEMBER 2025 • mrs.org/bulletin

Outlook

The recent discovery and rapid development of wurtzite ferroelectrics opens numerous possibilities for their use in an array of electronic and electro-optical devices. Over the past five years, experimental and computational studies have provided fundamental insight into switching mechanisms and pathways in these alloyed materials. Less, however, is known about the mechanisms of domain movement and their dynamics, necessitating ongoing investigation. The relative simplicity of the wurtzite structure, chemical simplicity of many ferroelectric compositions, and low-temperature synthesis conditions also facilitate scaling to wafer sizes at back-end-of-line (BEOL)-compatible temperatures. In particular, these materials offer a potential avenue to achieve high density non-volatile memory. Among the key factors that will need to be overcome to move these materials forward in this application space are adequate reliability over the lifetime of the memory element. Improved reliability demands better understanding and control of deleterious point defects. In parallel, there is also a need to further reduce the coercive field to reduce carrier injection during the switching process. Reduced coercive fields will also facilitate their use in ferroelectric field-effect transistors (FeFETs). Beyond their interest in memory applications, the large electro-optic coefficients of the wurtzite materials also provide the tantalizing prospect of nonlinear optical components, which could be integrated on semiconductors without the need for wafer bonding (as is currently required for lithium niobate and lithium tantalate). For this latter application, the ability to create controlled (and potentially rewriteable) polarization patterns is appealing for second-harmonic generation. Here, it may be necessary to develop new approaches to induce local polarization reversal without electrodes, to minimize optical losses. Likewise, reduction of midgap defect states to reduce the propensity for absorption at the use wavelengths will also be required.

While ongoing research is needed to better understand domain dynamics and to control point defects in this new class of ferroelectrics, the field continues to rapidly advance. Since (Al, Sc)N is already widely adopted in piezoelectric resonators for acoustic filters in cellular communications, a preexisting industrial base for materials deposition and patterning exists, which may accelerate adoption into these new application spaces. a b c f e d Figure 8. (a) Fatigue behavior, (b) Weibull distribution of breakdown voltage, (c) leakage current characteristics of Al, ScN films in their pristine state and after annealing under NH 3 at 500 C, 700 C, and 900 C. Reprinted with permission from Reference 101. © 2023 Royal Society of Chemistry. (d) Variation in leakage current density, (e) endurance characteristics for the sputtered films with different Al/Sc ratios and input gas: Sample A: Al 0.53 Sc 0.47 N in Ar/N 2 , Sample B: Al 0.53 Sc 0.47 N in Ar/N 2 /3%H 2 , Sample C: Al 0.80 Sc 0.20 N in Ar/N 2 , and Sample D: Al 0.80 Sc 0.20 N in Ar/N 2 /3% H 2 . Reprinted with permission from Reference 102. © 2024 IOP Publishing. She is also a Fellow of the Materials Research Society, The American Ceramic Society, the Microscopy Society of America, and AAAS. She has ~25 years of experience in developing processing-structure-property relationships for ceramics and ceramic composites for advanced aerospace and electronic-device applications. She is regarded as a leader in the application of electron microscopy to understand the role of material defects on electrical and chemical transport and polarization in electronic ceramics. Dickey can be reached by email at ecdickey@cmu.edu.

Prashun Gorai is an Assistant Professor in Chemical and Biological Engineering at Rensselaer Polytechnic Institute and holds a joint appointment at the National Renewable Energy Laboratory. He combines quantum mechanical calculations, highthroughput computing, and machine learning to accelerate the discovery and design of materials for energy and microelectronics. His current work aims to discover novel wurtzite ferroelectric materials and uncover polarization switching mechanisms. He has received several honors, including the International Thermoelectric Society Young Investigator Award and Chemistry of Materials Lectureship Award. Gorai can be reached by email at goraip@rpi.edu.