No strain, no piezoelectric gain: pushing piezoelectric boundaries via composition-dependent strain engineering in wurtzite scandium-doped aluminum nitride

Abstract

This study presents an investigation of the structural and piezoelectric properties of scandium-doped aluminum nitride (Al_1−xSc_xN) alloys over a wide composition range, using first-principles calculations. We explore compositions ranging from pure AlN to Al_0.5Sc_0.5N under various biaxial strain conditions, revealing the complex interplay between composition, strain, and piezoelectric response. Our findings demonstrate that the piezoelectric coefficient d₃₃ of unstrained Al_1−xSc_xN reaches a maximum at x = 0.4375, significantly surpassing that of pure AlN. Remarkably, we show that applying biaxial strain dramatically enhances d₃₃, with values peaking at compositional-dependent critical strains. These peak values, ranging from 519.03 pC N⁻¹ for strained AlN to an extraordinary 5121.58 pC N⁻¹ for strained Al_0.625Sc_0.375N, represent improvements of over two orders of magnitude compared to their unstrained counterparts. We attribute this enhancement to a strain-induced phase transition from wurtzite to non-polar hexagonal layered structures, similar to the structural change observed with enhanced Sc concentration, accompanied by significant changes in elastic and piezoelectric constants. Notably, we demonstrate that this phenomenon can be exploited through changes in both tensile strain in Al-rich compositions and compressive strain in Sc-rich compositions, highlighting the exceptional tunability of Al_1−xSc_xN. These insights provide a fundamental understanding of Al_1−xSc_xN behavior and offer valuable guidance for optimizing its properties in next-generation piezoelectric devices.

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1. Introduction

Piezoelectric materials, capable of converting mechanical stress into electrical charge and vice versa, play a crucial role in a wide range of technological applications, from sensors and actuators to energy harvesting devices.^1–4 Among these materials, aluminum nitride (AlN) has garnered significant attention due to its prominent piezoelectric properties, high thermal conductivity, and compatibility with semiconductor processing.^5–7 However, the quest for materials with enhanced piezoelectric performance has led researchers to explore alloying strategies, with scandium-doped aluminum nitride (Al_1−xSc_xN) emerging as a promising candidate for next-generation piezoelectric applications.

The incorporation of Sc into the AlN matrix has been shown to significantly enhance the piezoelectric response of the material. This enhancement is attributed to the larger atomic radius of Sc compared to Al, which induces structural distortions and increases the polarizability of the crystal lattice.⁸ Previous studies have demonstrated that the piezoelectric coefficient d₃₃ of Al_1−xSc_xN is several times higher than that of pure AlN, making it an attractive option for various applications, including surface acoustic wave devices, bulk acoustic resonators, and microelectromechanical systems (MEMS).^9–11 However, the structural and piezoelectric properties of Al_1−xSc_xN are highly dependent on both composition and strain state. As the Sc content increases, the material undergoes a transition from the polar wurtzite structure characteristic of AlN (space group: P6₃mc) to a non-polar hexagonal layered structure (space group: P6₃/mmc) resembling hexagonal boron nitride (hBN) at high Sc concentrations.^12,13 This structural evolution, coupled with the effects of strain arising from lattice mismatch in thin film growth, significantly influences the piezoelectric response of the material.¹⁴ Understanding these complex relationships is therefore crucial for optimizing the performance of Al_1−xSc_xN in practical applications.

In this study, we present a comprehensive investigation of the structural and piezoelectric properties of Al_1−xSc_xN alloys across a range of compositions and under various biaxial strain conditions. Using first-principles calculations based on density functional theory (DFT) and the special quasi-random structure (SQS) approach to model the random alloys, we explore the intricate interplay between Sc concentration, strain, phase transitions, and piezoelectric response. We aim to provide fundamental insights into the behavior of Al_1−xSc_xN and elucidate strategies for tailoring its properties to meet the diverse requirements of advanced piezoelectric devices.

2. Computational methodology

2.1 Cluster expansion (CE) method

To efficiently explore the configuration space of Al_1−xSc_xN alloys, we employed the cluster expansion (CE) method.^15–17 In this formalism, a particular alloy configuration on a fixed lattice is described using a set of occupational variables. For our Al_1−xSc_xN system, we generated substitutional alloys on the metallic sublattice with varying Al and Sc percentages, while maintaining the fraction of N.

We utilized the thermodynamic tool-kit (TTK) code^18–20 to perform CE calculations. The process involved constructing an initial CE Hamiltonian by fitting the effective cluster interactions (ECIs) from a learning set of DFT-calculated mixing enthalpies ΔH_mix of 861 alloy configurations with wurtzite, non-polar hexagonal layered, and rock-salt phases. ΔH_mix of a given configuration σ at 0 K is calculated relative to the most stable wurtzite AlN and rock-salt ScN constituents:

ΔH_mix(Al_1−xSc_xN, σ) = E(Al_1−xSc_xN, σ) − (1 − x)E(wz-AlN) − xE(rs-ScN) (1)

where E(wz-AlN), E(rs-ScN), and E(Al_1−xSc_xN, σ) are the total energies per atom of wurtzite AlN, rock-salt ScN, and a particular σ of Al_1−xSc_xN alloy, respectively.

We next screened over 3 × 10⁶ alloy structures with unique configurations to obtain their corresponding CE energies. The CE was considered properly truncated when no new ground-states were predicted and/or CE ΔH_mix were reproduced accurately within <0.005 eV atom⁻¹. Using the ECIs, the CE-predicted ΔH_mix of the Al_1−xSc_xN solid solutions could then be determined.²¹

For the systematic selection of the disordered solid solution Al_1−xSc_xN alloys for first-principles simulations, we utilized the special quasi-random structure (SQS) approach²² by sieving out from the 10⁶ different wurtzite alloy configurations with x = 0.0000, 0.0625, 0.1250, 0.1875, 0.2500, 0.3125, 0.3750, 0.4375, 0.5000, consisting of 64-atom pseudo-orthorhombic supercells, and selecting those configurations with cluster correlations of two- and three-body interactions closest to those of a random alloy.²³ While this supercell size may have limitations in capturing very long-range strain fields, it is adequate for modeling the critical local atomic distortions and competing structural motifs that drive the phase transition at high Sc concentrations.²⁴

2.2 Density functional theory (DFT) calculations

First-principles calculations were performed using density functional theory (DFT)²⁵ via the Perdew, Burke, and Ernzerhof (PBE) exchange–correlation functional based on the generalized gradient approximation (GGA)^26,27 as implemented in the Vienna ab initio simulation package (VASP).^28,29 The projector augmented wave (PAW) method³⁰ was used to describe the electron–ion interactions, using the PAW potentials Al, Sc_sv, and N. Plane-wave cut-offs were set to 500 eV and an electronic convergence criterion of 10⁻⁸ eV was applied. All atomic coordinates were fully relaxed until the calculated Hellmann–Feynman force on each atom was less than 0.01 eV Å⁻¹. Brillouin zone sampling was performed with Monkhorst–Pack (MP) k-point meshes³¹ inclusive of the Γ-point. A k-point mesh of 2 × 4 × 2 which translates to a density of around 20 k-points per Å⁻¹ was used for the disordered solid solution Al_1−xSc_xN alloy supercells.

To investigate the effects of strain on the piezoelectric properties of Al_1−xSc_xN, we applied biaxial strains ranging from −5% to +8% to our optimized structures in steps of 0.5%, with finer steps close to phase transitions, allowing for the study of phase transitions and their effects on piezoelectric properties. The strain was applied in the a–b plane while allowing relaxation along the c-axis. For each strained configuration, we calculated the elastic tensor elements C_ij including ionic relaxations via the finite differences method³² and the piezoelectric tensor elements e_ij using density functional perturbation theory (DFPT).³² The piezoelectric coefficient d₃₃ could then be estimated from the piezoelectric constants e₃₃ and elastic constants C₃₃ according to the relationship:⁸

The elastic constants were obtained by applying small strains to the relaxed structures and calculating the resulting stress tensors. This approach allowed us to systematically study the evolution of piezoelectric properties as a function of both composition and strain state, with a focus on identifying the critical strain levels where d₃₃ peaks.

3. Results and discussion

3.1 Phase properties of scandium-doped aluminum nitride Al_1−xSc_xN alloys

Fig. 1 illustrates the relative stability of various Al_1−xSc_xN alloy structures by examining the mixing enthalpies of wurtzite, rock-salt, and non-polar hexagonal layered phases, calculated using eqn (1). Our analysis reveals that the wurtzite phase exhibits a lower mixing enthalpy and greater thermodynamic stability compared to the rock-salt phase for compositions up to x = 0.6. This finding indicates that the wurtzite phase represents the ground-state structure for both pure AlN and Al-rich Al_1−xSc_xN alloys. Our findings are in excellent agreement with both experimental and computational work. Talley et al. reported a wurtzite-to-rock-salt transition in Al_1−xSc_xN between x = 0.4 and 0.65 via XRD measurements,¹³ while Höglund et al. showed that single-phase wurtzite films are achievable up to x = 0.6, above which the material phase-separates into wurtzite and rock-salt domains.³³ Likewise, Zhang et al.'s first principles study located the same composition transition (x = 0.6) and found mixing enthalpies rising from 0 to 0.2 eV atom⁻¹ at that point, using an approach analogous to ours.¹²

Fig. 1 Plot of the calculated mixing enthalpies of Al_1−xSc_xN alloys in wurtzite, rock-salt, and non-polar hexagonal layered phases. Each of the grey, blue, and orange points correspond to the mixing enthalpy of a particular alloy configuration of Al_1−xSc_xN in wurtzite, rock-salt, and hexagonal layered phases, respectively, with filled and unfilled points referring to the mixing enthalpies determined from the cluster expansion (CE) approach and density functional theory (DFT) calculations. The grey, blue, and orange dashed curves correspond to the CE-derived mixing enthalpy of the perfectly disordered Al_1−xSc_xN alloy in wurtzite, rock-salt, and hexagonal layered phases, respectively. The purple vertical dotted line at x = 0.6 corresponds to the wurtzite–rock-salt phase transition composition, with the shaded region in grey or blue showing concentration range where wurtzite or rock-salt phase is the most stable, respectively.

A noteworthy observation is the behavior of the non-polar hexagonal layered phase. While it does not represent the ground-state for all compositions, its mixing enthalpies converge with those of the wurtzite phase under Sc-rich conditions. This convergence is consistent with the optimized structure of initial wurtzite ScN being similar to the non-polar hexagonal layered structure. Fig. S1 in the ESI† further elucidates this phenomenon, demonstrating that both the structural and absolute energy differences between Al_1−xSc_xN configurations in wurtzite and non-polar hexagonal layered phases diminish with increasing Sc content, approaching zero for pure ScN.

The transformation from wurtzite to non-polar hexagonal layered structure can be attributed to the larger atomic size of Sc (1.60 Å) compared to Al (1.25 Å).³⁴ As the Sc content increases, it induces an expansion in the crystalline volume of wurtzite Al_1−xSc_xN. This expansion facilitates the structural transformation. The process likely involves a gradual distortion of the wurtzite lattice, with atomic rearrangements leading to the formation of the non-polar hexagonal layered structure.

This phase transition has profound implications for the material's piezoelectric response. The wurtzite structure is inherently polar (space group P6₃mc), with a spontaneous polarization along the c-axis. In contrast, the non-polar hexagonal layered structure with the presence of inversion center lacks this intrinsic polarization (space group P6₃/mmc). As we shall explore in the subsequent sections, the transition between these phases will lead to significant changes in the piezoelectric coefficients, which are directly related to the material's ability to convert mechanical stress into electrical charge and vice versa.

Given that extensive research has already been conducted on the structural and phase transitions of Al_1−xSc_xN,^12,13 the focus of the following section will be in providing a detailed description and analysis of the piezoelectric properties of both non-strained and strained Al_1−xSc_xN alloys. This includes examining how these properties vary with Sc concentration and the associated phase transformations, providing a comprehensive understanding of the material's potential for piezoelectric applications.

3.2 Piezoelectric properties of non-strained and strained Al_1−xSc_xN alloys

Using the 64-atom pseudo-orthorhombic special quasirandom structures (SQS) supercells of Al_1−xSc_xN with Sc fractions ranging from 0 to 50% (0 ≤ x ≤ 0.5), we calculated the piezoelectric coefficients (d₃₃) from the piezoelectric constants (e₃₃) and elastic constants (C₃₃) via eqn (2). As shown in Fig. 2a, for the non-strained Al_1−xSc_xN alloys, the d₃₃ value exhibits a strong dependence on the Sc concentration. It increases from 4.57 pC N⁻¹ in pure AlN to a maximum of 29.88 pC N⁻¹ when x = 0.4375, before falling to 13.36 pC N⁻¹ at 50% Sc. This calculated peak d₃₃ of 29.88 pC N⁻¹ at x = 0.4375 aligns well with the reported experimental range, which varies from ∼25 pC N⁻¹ (Teshigahara et al.)¹⁰ to over 30 pC N⁻¹ (Lu et al.),¹¹ with the minor deviation attributable to the ideal, defect-free nature of the SQS model compared to experimental films, which often contain performance-limiting defects, grain boundaries, and residual stress.

Fig. 2 (a) Plot of piezoelectric coefficients, d₃₃, versus different Sc fraction, x, for Al_1−xSc_xN SQS supercells. The blue squares, red circles, and green diamonds, correspond to values obtained via simulation for this work, and experimental results by Teshigahara et al.¹⁰ and Lu et al.¹¹ (b) Plot of lattice constants, a and c, and c/a ratio versus different Sc fraction, x, for Al_1−xSc_xN SQS supercells. The filled symbols correspond to values calculated from optimized structures in this work, while the hollow symbols correspond to experimental data from Teshigahara et al.¹⁰ (c) Plot of piezoelectric constants, e₃₃, and elastic constant, C₃₃, versus different Sc fraction, x, for Al_1−xSc_xN SQS supercells. The purple circles and olive squares correspond to e₃₃ and C₃₃, respectively. Vertical dotted lines at x = 0.4375 highlight how a significant increase in C₃₃ results in a decrease in d₃₃.

To explain this behavior, we can examine the structural changes induced by Sc doping. Fig. 2b illustrates that increasing Sc content leads to a gradual increase in lattice parameter a, while lattice parameter c decreases, leading to the reduction in c/a ratio. The increase in a is primarily attributed to the larger atomic radius of Sc which expands the basal plane of the wurtzite structure. As the lattice structure becomes more planar-like, the axial Al/Sc–N bond weakens and causes an elastic softening and mechanical weakening of the structure along the axial or z-axis,³⁵ reflected in the decrease in the elastic constant C₃₃ in Fig. 2c. The reduction in C₃₃ contributes to the increase in d₃₃, as the piezoelectric coefficient is inversely proportional to the elastic constant. In addition to the changes in lattice parameters, the piezoelectric constant e₃₃ also critically impacts the piezoelectric coefficient. As Sc concentration increases, e₃₃ initially rises due to the enhanced polarization induced by the larger and more polarizable Sc atoms substituting for Al. The substitution leads to a stronger piezoelectric response in the crystal.

However, these trends for C₃₃ and e₃₃ do not continue indefinitely. Above 43.75% Sc, there is a notable decrease in c, resulting in the c/a ratio decreasing from ∼1.6 to ∼1.2, which is characteristic of the non-polar hexagonal layered phase. This shift signals a transition in Al_1−xSc_xN from the wurtzite structure to a non-polar hexagonal layered crystalline structure at high scandium content. In the hexagonal layered phase, the structure becomes mechanically stiffer, resulting in an increase in C₃₃ compared to the wurtzite phase. This is in stark contrast to just prior to the transformation, where the weakening of the axial Al/Sc–N bonds softens C₃₃. Instead, once the structure transitions to the hexagonal layered phase, its planarity leads to more uniform axial interactions across atoms in adjacent layers, enhancing the stiffness of the lattice. The significant increase in C₃₃ offsets the much smaller increase in e₃₃, leading to a net reduction in d₃₃. Here, assuming constant e₃₃, an increase in C₃₃ from ∼130 to ∼290 GPa corresponds to a decrease in d₃₃ from ∼30 to ∼13 pC N⁻¹, a 2.2-fold reduction.

It is noteworthy that our calculated values align well and are consistent with those measured experimentally from synthesized Al_1−xSc_xN alloys,^10,11 validating our chosen SQS supercells in representing the random alloy structure (see Fig. 2a). This agreement also underscores the predictive power of our computational approach in studying these complex alloy systems.

Typically, in deposited Al_1−xSc_xN films, strain arises from lattice mismatch with the substrate and the incorporation of Sc atoms into the AlN matrix, significantly influencing piezoelectric properties. To investigate these effects, we have applied a series of in-plane biaxial (along the a and b directions) tensile strains on the Al_1−xSc_xN SQS supercells (with 0 ≤ x ≤ 0.4375, and the structures begin in the wurtzite phase before being strained) as shown in Fig. 3 to assess their impact on the structural and piezoelectric properties. When positive (tensile) biaxial strain is applied, we observe a dramatic increase in the piezoelectric coefficient d₃₃ of Al_1−xSc_xN, which peaks at a specific biaxial tensile strain value for each Sc concentration before dropping abruptly to near zero. Remarkably, the peak d₃₃ values range from 519.03 pC N⁻¹ in strained AlN to an exceptionally high 5121.58 pC N⁻¹ in strained Al_0.625Sc_0.375N, both at least two orders of magnitude larger than their unstrained counterparts. For context, commercial PZT (lead zirconate titanate) ceramics exhibit d₃₃ values in the range of 300 to 1000 pC N⁻¹, whereas BTO (barium titanate) ceramics typically lie in the few-hundred pC N⁻¹ regime (e.g., 100 to 460 pC N⁻¹ in BTO nanoparticles).¹ Our peak d₃₃ of 5121.58 pC N⁻¹ in strained Al_0.625Sc_0.375N therefore exceeds these classic materials by more than an order of magnitude. Moreover, unlike PZT which contains toxic lead and is not compatible with standard CMOS back-end processes, and BTO which suffers from lower Curie temperature and integration challenges,^1,36 Al_1−xSc_xN is both lead-free and fully CMOS-compatible, making these exceptionally large d₃₃ values particularly compelling for on-chip applications.

Fig. 3 Plots of (a) piezoelectric coefficients, d₃₃, (b) lattice parameter c/a ratio, (c) piezoelectric constant, e₃₃, and (d) elastic constant, C₃₃, versus biaxial strain applied for different Sc fraction, x, for Al_1−xSc_xN SQS supercells. The black horizontal dashed lines represent the abscissa.

While these peak values occur at relatively high strain levels that may be challenging to achieve experimentally, the significant enhancement in d₃₃ even at moderate strain levels provides valuable insights into the fundamental mechanisms of strain-enhanced piezoelectric response in these materials. Notably, as the Sc concentration increases, the amount of biaxial tensile strain required to achieve the maximum d₃₃ value decreases from 7.18% in AlN to 2.37% in Al_0.5625Sc_0.4375N which indicates that the maximum piezoelectric coefficient is more easily attainable with less tensile strain as Sc content increases. To place these values in context, biaxial tensile strains in state-of-the-art epitaxial films are typically limited to 1% to 2.5% to avoid material degradation. For instance, tensile strains of ∼1% are common for AlN on Si and SiC substrates,^37,38 while growth on a GaN template can induce a tensile strain of approximately 2.4%.^39,40 Although the 7.18% strain required to maximize d₃₃ in pure AlN is likely unattainable, the predicted 2.37% strain for Al_0.5625Sc_0.4375N is remarkedly close to what is practically achievable via heteroepitaxy on GaN. This suggests that near-maximal d₃₃ enhancement in Sc-rich Al_1−xSc_xN is a tangible goal for experimental realization. Furthermore, strain engineering via flexible substrates or in MEMS structures offers alternative pathways to apply the necessary mechanical loads to harness this predicted giant piezoelectric effect.^41,42

Interestingly, at low biaxial strains, Al_1−xSc_xN alloys with different Sc contents but the same x–y biaxial unit area coincidentally exhibit nearly identical d₃₃ values (Fig. S2, ESI†). This behavior, though seemingly unexpected, suggests a dominant role of strain-induced polarization effects in the wurtzite structure that may momentarily override composition-dependent variations. This observation reinforces the robustness of strain as a tuning parameter and highlights a potential design strategy where targeted strain levels, rather than precise control over Sc content, can achieve a consistent enhancement of piezoelectric properties.

To understand the underlying mechanisms behind this behavior, we examine Fig. 3b–d, which illustrate the contributing factors to the piezoelectric coefficient. The observed trends can be rationalized by considering the interplay between structural changes, electronic polarization, and elastic properties as a function of both Sc concentration and applied strain:

(I) Structural evolution: as shown in Fig. 3b, the lattice parameter c/a ratio decreases in general with increasing strain for all concentrations of Sc. This is expected due to the Poisson effect, whereby the tensile strain leads to an expansion of in-plane lattice parameters a and b and corresponding compression in the out-of-plane lattice parameter c. This decrease is not linear, and for each Sc concentration, there is a steep abrupt decrease in the c/a ratio to ∼1.25. This abrupt change coincides with the respective value of biaxial tensile strain at which the d₃₃ value peaks; it also marks the transition point between the wurtzite and non-polar hexagonal layered phase.

(II) Piezoelectric constants: Fig. 3c demonstrates that the piezoelectric constants, e₃₃, increase with increasing biaxial tensile strain, peaking at the transition points before decreasing rather abruptly to close to zero. The maximum e₃₃ values are higher with more Sc content (from 5.22 C m⁻² in AlN to 12.44 C m⁻² in Al_0.5625Sc_0.4375N), which can be attributed to the enhanced polarization induced by the larger and more polarizable Sc atoms substituting for Al.⁴³ This increased polarization strengthens the piezoelectric response until the structural transition occurs.

(III) Elastic properties: in Fig. 3d, we observe drastic changes in the elastic constants, C₃₃, at the transition points. Before reaching the critical biaxial tensile strain, C₃₃ decreases with increasing strain, likely due to the elastic softening as the wurtzite structure becomes increasingly distorted under tensile stress. This softening leads to values between 1.4 to 10.1 GPa. However, after the transition to the non-polar hexagonal phase, C₃₃ increases significantly to above 300 GPa, reflecting the increased mechanical rigidity of the new phase.

The changes in both e₃₃ and C₃₃ modify d₃₃ following eqn (2), where d₃₃ is the ratio of e₃₃ to C₃₃. As the structure approaches the phase transition, it becomes highly polarizable (high e₃₃) and extremely compliant (low C₃₃), resulting in the observed large values of d₃₃ at the applied biaxial tensile strains at the transition points. The subsequent abrupt drop of d₃₃ to near-zero is the definitive hallmark of this structural phase transition; it is a direct consequence of the system adopting the higher-symmetry, non-polar hexagonal layered structure (space group P6₃/mmc), which, as a centrosymmetric phase, forbids piezoelectricity. It is important to note that the actual peak values of d₃₃ may be subject to estimation errors, particularly due to the small values and potential inaccuracies in determining C₃₃ at the transition point. However, despite these uncertainties, we can assert that a significant increase in d₃₃ values occurs as the applied biaxial tensile strain is increased just below its critical value.

Building on the observed transition between the wurtzite and non-polar hexagonal layered structures, we explored whether the piezoelectric properties of Al_0.5Sc_0.5N, which naturally adopts a non-polar hexagonal layered structure in its unstrained form, could be enhanced by applying biaxial compressive strain instead of tensile strain. Indeed, as shown in Fig. S3 (ESI†), applying compressive strain induces a polar, wurtzite-like character, resulting in a significant enhancement of the d₃₃ value at a critical compressive strain of 1.69%. To clarify the nature of this change, this is not a formal phase transition back to the P6₃mc space group, but rather a strain-induced distortion of the disordered hexagonal structure. Interestingly, this strain-induced phase distortion in Al_0.5Sc_0.5N does not produce the same abrupt changes in the c/a ratio, e₃₃, and C₃₃ values as observed in Al_1−xSc_xN alloys with x ≤ 0.4375 under tensile strain (Fig. 3). This can be attributed to the more inherently distorted structure of Al_0.5Sc_0.5N from its higher Sc content, where the larger Sc atoms create local structural irregularities and varying bond lengths throughout the crystal. These pre-existing distortions provide multiple avenues for structural accommodation of strain, allowing the material to respond more gradually to applied stress, rather than undergoing the sharp, collective transitions seen in the more uniform, less distorted structures of Al-rich compositions. This prevents a collective, abrupt symmetry change and instead, favors a progressive distortion towards a polar, wurtzite-like state. As for AlN and Al_1−xSc_xN alloys with x ≤ 0.4375, compressive strains within our investigative range simply lead to a more rigid wurtzite structure, accompanied by reduced piezoelectric properties. This dichotomy in behavior between Sc-rich and Al-rich compositions highlights the complex interplay between composition, structure, and strain in determining the piezoelectric response of these alloys.

These findings lead to a crucial insight: regardless of the initial structure, if Al_1−xSc_xN is subjected to either compressive or tensile strain, to the point of transition between the wurtzite and non-polar hexagonal layered phases, it becomes possible to greatly enhance the piezoelectric properties. This highlights the exceptional versatility of Al_1−xSc_xN as a tunable piezoelectric material. By strategically engineering strain and modulating Sc composition, it is possible to tailor the structural and piezoelectric properties of Al_1−xSc_xN to meet the diverse requirements of piezoelectric device applications, making Al_1−xSc_xN alloys a promising candidate for next-generation piezoelectric materials.

4. Conclusion

Our comprehensive study of Al_1−xSc_xN alloys reveals the exceptional tunability and versatility of this material system for piezoelectric applications. Through careful analysis of the structural, electronic, and piezoelectric properties across a range of compositions and strain states, we uncovered several key insights. First, we showed that the wurtzite phase is the ground-state structure for Al_1−xSc_xN at low Sc concentrations, with a transition to a non-polar hexagonal layered phase occurring at moderate Sc concentration before transforming to rock-salt above 60% Sc. Second, we observed that the piezoelectric coefficient d₃₃ of unstrained Al_1−xSc_xN reaches a maximum at x = 0.4375, demonstrating a significant enhancement over pure AlN. More strikingly, we found that applying biaxial tensile strain can dramatically increase d₃₃, with values peaking at specific critical strains for each composition. These peak values, ranging from 519.03 pC N⁻¹ for strained AlN to an extraordinary 5121.58 pC N⁻¹ for strained Al_0.625Sc_0.375N, represent improvements of at least two orders of magnitude over their unstrained counterparts.

The observed enhancement in piezoelectric properties is intimately linked to the structural evolution of Al_1−xSc_xN under strain, particularly the transition between the wurtzite and non-polar hexagonal layered phases. This phase transition, occurring at composition-dependent critical strain values, is accompanied by a significant softening of the elastic constant C₃₃ and a peak in the piezoelectric constant e₃₃. Importantly, we demonstrated that this phenomenon can be exploited not only through tensile strain in Al-rich compositions but also through compressive strain in Sc-rich compositions like Al_0.5Sc_0.5N. This bidirectional tunability underscores the remarkable adaptability of Al_1−xSc_xN as a piezoelectric material, which opens up new avenues for material design and device optimization, potentially enabling the development of highly efficient and versatile piezoelectric devices for a wide range of applications, from high-frequency acoustics to sensitive pressure sensors and efficient micro-scale actuators.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

Data that supports the findings of this study are presented within figures and tables of the article and ESI.† Additional data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgements

This work is supported by the Agency for Science, Technology and Research (A*STAR) of Singapore (Grant ID: A20G9b0135). The authors would like to acknowledge the use of high-performance computing facilities provided by the National Supercomputing Centre Singapore (NSCC) (Grant No. 13002487) and A*STAR Computational Resource Centre (A*CRC).

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Footnote

† Electronic supplementary information (ESI) available: Plot of structural difference versus absolute energy difference between wurtzite and non-polar hexagonal layered phases of Al_1−xSc_xN of particular alloy configurations; plots of piezoelectric coefficients d₃₃ versus biaxial unit area of Al_1−xSc_xN SQS supercells; plots of piezoelectric coefficients d₃₃, lattice parameter c/a ratio, piezoelectric constant e₃₃, and elastic constant C₃₃ versus biaxial strain applied for Al_0.5Sc_0.5 SQS supercell and AlN. See DOI: https://doi.org/10.1039/d5tc01075f

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