Realizing Giant Ferroelectricity in Stable wz-Al1-xBxN Alloys by Controlling the Microstructure and Elastic Constant

Realizing Giant Ferroelectricity in Stable wz-Al1-xBxN Alloys by Controlling the Microstructure and Elastic Constant | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Realizing Giant Ferroelectricity in Stable wz-Al1-xBxN Alloys by Controlling the Microstructure and Elastic Constant Jie Su, Zhengmao Xiao, Xinhao Chen, Yong Huang, Zhenhua Lin, Jingjing Chang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4575186/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Feb, 2025 Read the published version in npj Computational Materials → Version 1 posted 12 You are reading this latest preprint version Abstract The emerged wurtzite-type (wz) ferroelectric Al 1 − x B x N alloys have drawn increasing attention due to superior ferroelectricity and excellent compatibility with microelectronics. Revealing and controlling the microstructure and ferroelectric origin is vital to design and fabricate stable wz-Al 1 − x B x N alloy with giant ferroelectricity. We find that the β-BeO-like rather than h-BN-like structure is the non-polar intermediate phase in the polarization inversion process of stable wz-Al 1 − x B x N alloy. The stability and ferroelectric switching pathway of wz-Al 1 − x B x N alloy are dominated by the covalent bond strength and elastic constant C 14 . Due to the reduced internal parameter u and enhanced C 14 of wz-Al 1 − x B x N alloy, the spontaneous polarization and polarization switching barrier respectively raises and declines as the B concentration increases. Meanwhile, the spontaneous polarization is enlarged by the compression along horizontal direction and tension along c-axis direction, while the polarization switching barrier and band gap are reduced by the all the tension. Moreover, the polarization switching fields are lower than the breakdown fields of wz-Al 1 − x B x N alloys with tension. As a result, the giant ferroelectricity with larger spontaneous polarization than wz-Al 1 − x Sc x N alloy and comparable polarization switching barrier to the common ferroelectric oxide is designed in for wz-Al 1 − x B x N alloy. It should be noted that the phase transformation concentration of about 0.1875 for wz-Al 1 − x B x N alloy is reduced by both tension and compression. These findings give a deeply understanding of ferroelectricity wz-Al 1 − x B x N alloy, and provide a guideline to design high-performance ferroelectric wz-Al 1 − x B x N alloys. Physical sciences/Physics/Electronics, photonics and device physics Physical sciences/Materials science/Theory and computation/Electronic structure Wurtzite Al1 − xBxN alloy Ferroelectric Spontaneous polarization Switching barrier Strain Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 INTRODUCTION Although the wurtzite AlN (wz-AlN) with a strong spontaneous polarization has been extensively studied in piezoelectricity and pyroelectricity, its ferroelectricity has been a subject of prolonged debate since the polarization cannot be switched by external electric field 1 , 2 . Until 2019, the polarization reversal of wz-AlN was realized by Sc-doping 3 , which enabling the exploitation of the ferroelectricity in wz-AlN. This discovery of ferroelectric wz-Al 1 − x Sc x N alloys not only breaks through the polarization application of wz-AlN limited in pyroelectric and piezoelectric, but also provides a new routine to explore the novelty ferroelectric semiconductor with wurtzite structure beyond the ferroelectric oxide 4 – 7 . On one hand, its polarization reversal originates from the local bond ionicity and ionic displacement induced by Sc ions instead of the simple change in the lattice parameter of the wurtzite structure 8 , 9 . On the other hand, the wz-Al 1 − x Sc x N alloy exhibits the higher ferroelectric polarization than the conventional ferroelectric oxides 3 . Moreover, the low temperature preparation of wz-Al 1 − x Sc x N alloy is compatible with the mainstream semiconductor technology 10 , 11 . Where the interfacial oxidization and ferroelectric degradation induced by oxide migration that commonly exist in the ferroelectric oxide device can be overcame in the ferroelectric wz-Al 1 − x Sc x N alloy. Recently, the ferroelectric semiconductor with wurtzite structure is expanded into the Al 1 − x B x N alloys 12 , 13 . Compared to wz-Al 1 − x Sc x N alloy, this ferroelectric semiconductor consists exclusively of elements and structures that are already common and essential in the silicon complementary metal-oxide semiconductor front end. The ferroelectric Al 1 − x B x N alloys thin film integrated on silicon with large remnant polarization of 136 µC/cm 2 and low coercive field has been fabricated by sputtering 10 . These ferroelectric parameters of wz-Al 1 − x B x N alloys continuously improve with the increment of B composition 14 , 15 . The reported optimal remnant polarization and coercive field of wz-Al 1 − x B x N alloys are respectively to be 150 µC/cm 2 and 5.1 MV/cm, which are superior to those of wz-Al 1 − x Sc x N alloy 13 . It is thought that wz-Al 1 − x B x N alloy is a promising ferroelectric material. However, it is noted that the ferroelectric characteristics and stability of wz-Al 1 − x B x N alloy are debate. For examples, Zagorac et al. claimed that the Al 1 − x B x N alloys remain the wurtzite structure over the composition range 0.125 < x < 0.375 16 , whereas Liu et al. found that the wurtzite stability remains only up to 0.19 15 . Several different polarization switching pathways have been reported in literatures 9 , 15 , 17 , 18 . Consequently, there is a significant difference among the reported polarization reversal barrier which directly determines the coercive field. To better design Al 1 − x B x N alloys for application, more research is required to understand the structure and ferroelectronic polarization of Al 1 − x B x N alloys. In addition, the epitaxial strain often exists in the epitaxial ferroelectric film 3 , 19 , which can tune the ferroelectric polarization and coercive field presumably by atomic microstructure and polarity switch 20 . It provides an effective way to design the giant ferroelectricity for wz-Al 1 − x B x N alloys, while is not revealed yet. In this work, we deeply unveil the structural stability and polarization reversal mechanisms of wz-Al 1 − x B x N alloys by atomic-scale simulation based on the first-principles calculations and modern polarization theory. Here, more accurate phase transformation concentration of about 0.1875 for wz-Al 1 − x B x N alloy was obtained by the chemical bond characteristic and elastic constant rather than the formation enthalpy and volume variations. Meanwhile the phase transition origin and polarization switching pathway of wz-Al 1 − x B x N alloy were revealed by the elastic constant C 14 . In addition, optimizing and designing the giant ferroelectricity of stable wz-Al 1 − x B x N alloys with high spontaneous polarization, low polarization switching barrier, low polarization reversal field, and large bandgap by controlling the strain in wz-Al 1 − x B x N alloys. The ferroelectricity of tuned wz-Al 1 − x B x N alloy is superior to that of wz-Al 1 − x Sc x N alloy and ferroelectric oxide. Such phenomena were deeply understood by the variation of elastic constant, orbital distribution and dipole moment. RESULTS AND DISCUSSION Although wz-AlN and wz-BN show similar atomic structures ( see Fig. 1 a), a phase transformation occurs in their alloy system 15 , 21 , 22 . For an instance, several Al-N octahedrons, which are the basic structures of zb-AlN, are observed for the wz-Al 1 − x B x N alloys with high concentration B, as the AIMD simulation structure exhibited in Fig. 1 b. To reveal the phase transformation concentration of wz-Al 1 − x B x N alloy, the formation enthalpies of wz-Al 1 − x B x N and zb-Al 1 − x B x N alloys as displayed in Fig. 1 c. It is obvious that the ground phase of Al 1 − x B x N alloy with x > 0.27 is zinc blende structure rather than the wurtzite structure, due to its lower formation enthalpy. In other words, a phase transformation of wz-Al 1 − x B x N alloy occurs at the B concentration of 0.27. Moreover, the phase transformation concentration significantly reduces when wz-Al 1 − x B x N alloy undergoes strain, irrespective of the direction and character of strain, because the formation enthalpy reduction of strained wz-Al 1 − x B x N alloy is smaller than that of strained zb-Al 1 − x B x N alloy (see Fig. 1 c-d and Supplementary Fig. 1). It maybe the underlying reason why the high-quality wz-Al 1 − x B x N alloy film with high concentration B is difficult to be deposited at the heterogeneous substrate 10 , 12 . To understand the phase transformation mechanism of wz-Al 1 − x B x N alloy, the elastic constants C ij s are calculated and illustrated in Fig. 2 and Supplementary Fig. 2. Although the wurtzite structure has six independent elastic constants, but just the C 12 , C 13 , C 14 , and C 44 are related to the elasticity in shape 23 – 25 . It is thought that a phase transformation can be revealed by these elastic constants. As seen in Fig. 2 , these elastic constants of wz-Al 1 − x B x N alloys show a non-monotonic variation rather than linear variation with the increment of B concentration. It further confirms the phase transformation of wz-Al 1 − x B x N alloy occurs at the high B concentration. Although the variation inflexions of most elastic constants (including C 12 , C 13 , C 44 ) are about 0.25, which is close to the above analyzed phase transformation concentration, these elastic constants are not the dominant factor for the phase transformation of wz-Al 1 − x B x N alloy. Because the variation inflexions of these elastic constants are unaffected by the external strain (see Fig. 2 b and Supplementary Fig. 2), which is inconsistent with the previous report 26 , 27 . Just the variation inflexion of elastic constant C 14 are affected by the external strain. The variation of elastic constant C 14 is thought as the dominant factor for the phase transformation of wz-Al 1 − x B x N alloy. Thus, the actual phase transformation of wz-Al 1 − x B x N alloy begins from the x = 0.1875 since the elastic constant C 14 breaks down at such concentration (see Fig. 2 a). Moreover, the phase transformation concentration of strained wz-Al 1 − x B x N alloy can further decrease, regardless of the direction and character of strain. In addition, the elastic constant C 14 associates with the shear stress, indicating the phase transformation of wz-Al 1 − x B x N alloy is accompanied by horizontal movement of atoms. In general, the structural and physical properties mainly origin from the novelty bonding characteristics. Figure 3 a gives the electron localization functions (ELFs) of Al-N and B-N bonds for wz-Al 1 − x B x N alloys. Different to the wz-Al 1 − x Sc x N alloys 8 , both the Al-N bonds and B-N bonds of wz-Al 1 − x B x N alloys show the covalent bonds characters with an apparent charge accumulation between Al (or B) and N atoms, irrespective of the concentration and strain. Meanwhile, the latter exhibits the stronger covalent bond strength than the former since the charge accumulation of B-N bond is higher than that of Al-N bond. The bond strengths are quantitatively evaluated by the integrated crystal orbital Hamilton population (ICOHP) as illustrated in Fig. 3 (b-c) . The larger -ICOHP suggests the stronger covalent bond strength. The -ICOHPs of Al-N bonds for all wz-Al 1 − x B x N alloys are lower than that of B-N bonds. It further confirms the stronger covalent bond strength for B-N bond than Al-N bond. Moreover, the covalent bond strength of Al-N bond decreases at first and then slowly weakens and then enhances as the B concentration enlarges, while the opposite variation occurs for the B-N covalent bond. Because the -ICOHP of Al-N bond of wz-Al 1 − x B x N alloy drops at first ( x < 0.1875) and then gradually reduces (0.1875 < x 0.25) with the increment of B concentration, while that of B-N bond shows an opposite variation, as demonstrated in Fig. 3 (b-c) . The abrupt change of -ICOHP for Al-N and B-N bonds further confirms that the wz-Al 1 − x B x N alloy begins a phase transformation at the x = 0.1875. When wz-Al 1 − x B x N alloy undergoes the strain, the variation of -ICOHP for Al-N bond and B-N bond keep remains, but the first transition concentration becomes smaller. It suggests that the phase transformation concentration of wz-Al 1 − x B x N alloy can be reduced by strain. In addition, both the horizontal and c-axis compression enlarges the covalent bond strengths of Al-N and B-N bonds with the higher –ICOHPs, while the horizontal and c-axis tension weakens the covalent bond strengths of Al-N and B-N bonds with the smaller -ICOHPs. In general, the stronger covalent bond strength suggests the shorter covalent bond length. Supplementary Fig. 3 exhibits the bond lengths of Al-N and B-N bonds of wz-Al 1 − x B x N alloy with and without strain. The variations of bond lengths are opposite to those of the -ICOHPs for Al-N and B-N bonds, but the transition concentration keep remains. It further confirms the phase transformation concentration for wz-Al 1 − x B x N alloy. However, the variations of Al-N and B-N bond lengths induce the linear change rather than the nonmonotonic linear change for the volume of wz-Al 1 − x B x N alloy, as seen in Fig. 3 d. Due to the change of bond length and volume, the internal parameter u of wz-Al 1 − x B x N alloy is lower than 0.5, and it decreases with the increment of B concentration, as illustrated in Fig. 3 e. The hexagonal structure with u = 0.5 means a phase without polarization along [0001], where the smaller u indicates the stronger polarization 6 , 28 . It means that wz-Al 1 − x B x N alloy possesses a strong polarization which enlarges as the B concentration increases. In addition, the c-axis compression and horizontal tension can enlarge the internal parameter u with the reduced polarization, while the c-axis tension and horizontal compression can shrink down the internal parameter u with the raised polarization. To further understand the polarization characteristic of wz-Al 1 − x B x N alloys, Fig. 4 illustrates the polarization reversal pathways and characteristics of wz-Al 1 − x B x N alloys. For the wz-AlN, the calculated spontaneous polarization ( viz . P sp ) is about 1.33 C/m 2 , which is consistent with previous reports 9 , 15 , 17 , 29 . There is just one peak, which corresponds to the intermediate nonpolar structure, in the polarization reversal pathway of wz-AlN (see Fig. 4 a). Moreover, the intermediate nonpolar structure is a nonpolar hexagonal (h)-BN-like structure (see Fig. 4 b). Such model can be regarded as the structure that Al-atom of wz-AlN moves along [000–1] direction to N-atoms plane. Because the elastic constant C 13 associates with the shear stress is lowest among the elastic constant of wz-AlN, which promotes the atom prefers to move along the c-axis with small change in the lattice parameter of the wurtzite structure. As a result, there is a large polarization switching barrier ( viz . E Barrier ) for the polarization reversal pathway of wz-AlN. The calculated E Barrier of wz-AlN of about 0.51 eV/f.u. is in good agreement with the previous report value 9 . Upon forming wz-Al 1 − x B x N alloys, the P sp is enlarged compared to the wz-AlN. But there are several peaks and valleys in the polarization reversal pathway of wz-Al 1 − x B x N alloy, which is different to that of wz-AlN. Such characteristics have been widely observed in the ternary alloy with wurtzite-type ferroelectric 17 . Because the new elastic constant C 14 with the smaller value appears when B composition is introduced into wz-AlN. It suggests that Al-atom of wz-Al 1 − x B x N alloy can also move along the horizontal direction, except for the c-axis direction. As a result, the intermediate nonpolar structure in the polarization reversal pathway of wz-Al 1 − x B x N alloy is β-BeO-like structure rather than the h-BN-like structure (see Fig. 4 b). This funding is consistent with the experimental observation 9 . Due to the additional horizontal movement of Al-atom, the calculated E Barrier of wz-Al 1 − x B x N alloy is lower than that of wz-AlN. Since the elastic constant C 14 of wz-Al 1 − x B x N alloy enlarges at first and then decreases as the B concentration rises, the E Barrier of wz-Al 1 − x B x N alloy reduces at first ( x 0.1875) with the increment of B concentration (see Fig. 4 c). The E Barrier s of wz-Al 1 − x B x N alloys ( x = 0.0625, 0.125, 0.1875, 0.25) are 0.188, 0.175, 0.171, and 0.187 eV/f.u., respectively. In addition, the P sp of wz-Al 1 − x B x N alloy monotonously enlarges as the B concentration increases (see Fig. 4 c), which is consistent the above internal parameter analysis. The P sp s of wz-Al 1 − x B x N alloys ( x = 0.0625, 0.125, 0.1875, 0.25) are 1.36, 1.39, 1.44, and 1.47 C/m 2 , respectively. It is noted that the increasing P sp for wz-Al 1 − x B x N alloy mainly originates from the enlarged electron dipole moment and reduced volume of wz-Al 1 − x B x N alloy, as seen in Fig. 4 d. Figure 5 illustrates the E Barrier and P sp of wz-Al 1 − x B x N alloys dependent of the strain. The E Barrier s of wz-Al 1 − x B x N alloys enlarges with the increasing compression, while reduce with the increasing compression, irrespective of the strain direction, as illustrated in Fig. 5 a-b. Because the compression shifts up the elastic constant C 13 and shifts down elastic constant C 14 , while the tension shifts down the elastic constant C 13 and shifts up elastic constant C 14 (see Fig. 2 and Supplementary Fig. 2). Interestingly, the P sp s of wz-Al 1 − x B x N alloys decease from the compression to tension along the horizontal direction, the opposite variations are observed for wz-Al 1 − x B x N alloys with strain along the c-axis. Moreover, the enlarged P sp s of wz-Al 1 − x B x N alloys with tension along the c-axis will decrease again when the tension is larger than 5%, as illustrated in Fig. 5 c-d. The main reason is that the P sp of wz-Al 1 − x B x N alloy is dominated by the electron dipole moment which possesses the similar variation (see Fig. 5 e). Figure 5 f comparatively lists the P sp s and E Barrier s of wz-Al 1 − x B x N alloys and other ferroelectric semiconductors 3 , 7 , 15 , 17 , 29 – 34 . It can be found that the P sp s of wz-Al 1 − x B x N alloys are not only far larger than those of ferroelectric oxides, but also higher than the wz-Al 1 − x Sc x N alloy with the same concentration. Moreover, no matter what the alloying concentration, the E Barrier s of all wz-Al 1 − x B x N alloys are far lower than those of wz-Al 1 − x Sc x N alloys. Meanwhile the E Barrier continues to decline and is comparable to that of HfO 2 when wz-Al 1 − x B x N alloys undergo the controllable tensile strain. Figure 6 and Supplementary Fig. 4 demonstrate the projected band structures of wz-Al 1 − x B x N alloys. The wz-AlN shows the direct band gap of about 6.18 eV, where the conduction band minimum (CBM) at the Γ point is dominated by s orbitals and the valence band maximum (VBM) at the Γ point is mainly composed of N-p z orbitals (see Supplementary Fig. 4). These characteristics are consistent with previous experimental and theoretical results 35 , 36 . When the B element is introduced into wz-AlN to form wz-Al 1 − x B x N alloy, the mainly orbital compositions of CBM and VBM keep remains. Meanwhile, additional orbitals, such as B-p z and Al-p (x,y) orbitals, begin to contribute to the CBM, as displayed in Fig. 6 (a-c) . Since the bond strength of Al-N covalent bond gradually weakens as the B concentration enlarges, the CBM of wz-Al 1 − x B x N alloy would be shifted down with the increment of B concentration. As a consequent, the band gap of wz-Al 1 − x B x N alloy reduces with the increasing B concentration. The band gaps of wz-Al 1 − x B x N alloy ( x = 0.0625, 0.125, 0.1875) are 5.77, 5.70, and 5.11 eV, respectively. When the B concentration is larger than 0.1875, these additional orbitals (B-p z and Al-p (x,y) orbitals) dominate the CBM of wz-Al 1 − x B x N alloy. Moreover, the position of CBM turns from Γ point to K point because the wz-Al 1 − x B x N alloy with such high B concentration undergoes a large atomic arrangement disorder and a phase transformation, as illustrated in Supplementary Fig. 4 (c-f) . Consequently, the wz-Al 1 − x B x N alloy exhibits a direct-to-indirect band gap transition when x > 0.1875, which is consistent with the previous report 35 . It means that the wz-Al 1 − x B x N alloy ( x > 0.1875) exhibits a direct-to-indirect band gap transition when the phase transformation occurs. At the moment, such high B concentration coupling with phase transformation enhance the bond strength of Al-N covalent bond, which can shift up the CBM. Thus, the indirect band gap of wz-Al 1 − x B x N alloy enlarges when B concentration is higher than 0.1875, as displayed in Fig. 6 d. It is noted that the band gaps of wz-Al 1 − x B x N alloys reduce when wz-Al 1 − x B x N alloys undergo tension, regardless of the strain direction. However, the compression along the horizontal direction enlarges the band gap, while the compression along the c-axis reduces the band gap. In common, the reduced band gap suggests the lowering breakdown filed for semiconductor 37 . In order to evaluate the effect of strain on the ferroelectric switching characteristics of wz-Al 1 − x B x N alloys, the theoretical polarization switching field and breakdown field of strained wz-Al 1 − x B x N alloys are calculated and compared, as displayed in Supplementary Fig. 5. It can be found that both the polarization switching field and breakdown field of wz-Al 1 − x B x N alloys are declined by the tension. Moreover, the polarization switching fields of wz-Al 1 − x B x N alloys with tension, except for the wz-Al 0.75 B 0.25 N alloy with tension along the horizontal direction, are lower than those of breakdown fields. It is thought that the tension is beneficial to improve the polarization switching characteristic of wz-Al 1 − x B x N alloy. CONCLUSION Here, we deeply unveiled the structural stability and polarization reversal mechanisms of wz-Al 1 − x B x N alloys by atomic-scale simulation based on the first-principles calculations and modern polarization theory. We found that the accurate phase transformation concentration of wz-Al 1 − x B x N alloy is about 0.1875, and which can be reduced by both tension and compression. The β-BeO-like structure is the non-polar intermediate phase in the polarization inversion process of wz-Al 1 − x B x N alloy, which is different to that of wz-Al 1 − x Sc x N alloy. Notably, the stability and ferroelectric switching pathway of wz-Al 1 − x B x N alloy are dominated by the covalent bond strength and elastic constant C 14 . As the B concentration increases, the spontaneous polarization and polarization switching barrier of stable wz-Al 1 − x B x N alloy respectively raises and declines due to the reduced internal parameter u and enhanced C 14 . Meanwhile, the spontaneous polarization is enlarged by the compression along horizontal direction and tension along c-axis direction, while the polarization switching barrier and band gap are reduced by the all the tension. Moreover, the polarization switching fields are lower than the breakdown fields of wz-Al 1 − x B x N alloys with tension. Consequently, the giant ferroelectricity with larger spontaneous polarization than wz-Al 1 − x B x N alloy and comparable polarization switching barrier to common ferroelectric oxide is designed in for wz-Al 1 − x B x N alloy. These findings give a deeply understanding of ferroelectricity wz-Al 1 − x B x N alloy, and provide a guideline to design high-performance ferroelectric wz-Al 1 − x B x N alloys. METHODS The wz-Al 1 − x B x N alloy was modelled by the 2 × 2 × 2 supercell wz-AlN with B substitution, where the substitution position of B atom was constructed by the quasirandom structure (SQS) methods 38 . To reveal the phase transformation character of wz-Al 1 − x B x N alloy, the zinc blende (zb) Al 1 − x B x N alloy was modelled by the 2×1×1 supercell zb-AlN. The formation enthalpies ( ∆H s) of Al 1 − x B x N alloys were calculated by the following equation: ∆H s = [ E (Al 1 − x B x N)- (1- x ) E (AlN) - xE (ScN)]/n(N), where x is B composition concentration, E (Al 1 − x B x N), E (AlN), and E (BN) are the total energy of Al 1 − x B x N, AlN and ScN, respectively, the n(N) is the number of N atom in the Al 1 − x B x N alloy 29 , 39 . These models were calculated by the first-principles density functional theory calculations on the basis of projector augmented wave (PAW) method, as implemented in the Vienna ab initio simulation package (VASP) 40 , 41 . The gneralized gradient approximation (GGA) coupling with Perdew-Burke-Ernzerhof (PBE) functional was adopted to describe the exchange and correlation interactions 42 . The cutoff energy was set to 500 eV, and Γ-centered k-mesh with k-spacing of 0.015 Å −1 in the Brillouin zone are used for geometry optimization and self-consistent calculation. The lattice constants and atomic positions were fully relaxed until the energy convergence within 1 × 10 − 5 eV and the residual force on each atom less than 0.01 eV/Å. The band structures were corrected by the screen hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) with the mixing parameter of 0.32 43 . The ab initio molecular dynamic simulations (AIMDs) were undertaken at 300 K for 3 ps with a time step of 1 fs. Nudged-elastic-band (NEB) simulations were conducted to determine the polarization reversal pathways. 44 15 and 31 images were generated for intrinsic switching in wz-AlN and sequential switching in wz-Al 1 − x B x N, respectively. The spontaneous polarization was calculated for each image along the pathway using the modern polarization theory together with Berry phase methods 45 . Declarations Data availability The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. ACKNOWLEDGMENTS This work was financially supported by the National Key Research and Development Program of China (2021YFA0715600); National Natural Science Foundation of China (Grant 62274125, 52192611); Key Research and Development Program of Shaanxi Province (Grant 2024GX-YBXM-410). Guangdong Basic and Applied Basic Research Fund (2023A1515030084). The numerical calculations in this paper have been done on the HPC system of Xidian University. AUTHOR INFORMATION Authors and Affiliations State Key Laboratory of Wide Bandgap Semiconductor Devices and Integrated Technology, Faculty of Integrated Circuit, Xidian University, Xi’an, 710071, China. Jie Su, Zhengmao Xiao, Xinhao Chen, Yong Huang, Zhenhua Lin, Jingjing Chang, Jincheng Zhang, Yue Hao Xidian-Wuhu Research Institute, Wuhu, 241002, China Jie Su, Zhengmao Xiao, Yong Huang Guangzhou Wide Band Gap Semiconductor Innovation Center, Guangzhou Institute of Technology, Xidian University, Guangzhou, 51055, China Jie Su Contributions J. S. performed the computational study and wrote the first draft of the manuscript. Z. M. X. performed the hybrid functional calculations and polarization calculation. All authors participated in discussions and the final preparation of the manuscript. Corresponding authors Correspondence to Jie Su or Yong Huang or Jingjing Chang ETHICS DECLARATIONS Competing interests The authors declare no competing interests. ADDITIONAL INFORMATION Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References Wang, H., Adamski, N., Mu, S. & Van de Walle, C. G. 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Reduced coercive field in epitaxial thin film of ferroelectric wurtzite Al 0.7 Sc 0.3 N. Applied Physics Letters 118, 162903 (2021). McMitchell, S. R. C. et al. Engineering Strain and Texture in Ferroelectric Scandium-Doped Aluminium Nitride. ACS Applied Electronic Materials 5, 858–864 (2023). Gunning, B. P., Moseley, M. W., Koleske, D. D., Allerman, A. A. & Lee, S. R. Phase degradation in B x Ga 1–x N films grown at low temperature by metalorganic vapor phase epitaxy. Journal of Crystal Growth 464, 190–196 (2017). Tran, T. B., Liao, C.-H., AlQatari, F. & Li, X. Demonstration of single-phase wurtzite BAlN with over 20% boron content by metalorganic chemical vapor deposition. Applied Physics Letters 117, 082102 (2020). Mouhat, F. & Coudert, F.-X. Necessary and sufficient elastic stability conditions in various crystal systems. Physical Review B 90, 224104 (2014). Luan, S., Dong, L. & Jia, R. Analysis of the structural, anisotropic elastic and electronic properties of β-Ga 2 O 3 with various pressures. Journal of Crystal Growth 505, 74–81 (2019). Fuller, E. R. & Weston, W. F. Relation between elastic-constant tensors of hexagonal and cubic structures. Journal of Applied Physics 45, 3772–3776 (1974). Johnson, G. R., Holmquist, T. J. & Beissel, S. R. Response of aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures. Journal of Applied Physics 94, 1639–1646 (2003). Beckstein, O., Klepeis, J. E., Hart, G. L. W. & Pankratov, O. First-principles elastic constants and electronic structure of α-Pt 2 Si and PtSi. Physical Review B 63, 134112 (2001). UETSUJI, Y. et al. First-Principles Study on the Spontaneous Polarization of Wurtzite Zn 1 – x Mg x O Alloy Crystals. Journal of the Society of Materials Science, Japan 58, 243–250 (2009). Furuta, K. et al. First-principles calculations of spontaneous polarization in ScAlN. Journal of Applied Physics 130, 024104 (2021). Noor-A-Alam, M., Z. Olszewski, O. & Nolan, M. Ferroelectricity and Large Piezoelectric Response of AlN/ScN Superlattice. ACS Applied Materials & Interfaces 11, 20482–20490 (2019). Moriwake, H. et al. Ferroelectricity in wurtzite structure simple chalcogenide. Applied Physics Letters 104, 242909 (2014). Beckman, S. P., Wang, X., Rabe, K. M. & Vanderbilt, D. Ideal barriers to polarization reversal and domain-wall motion in strained ferroelectric thin films. Physical Review B 79, 144124 (2009). Clima, S. et al. Identification of the ferroelectric switching process and dopant-dependent switching properties in orthorhombic HfO 2 : A first principles insight. Applied Physics Letters 104, 092906 (2014). Liu, C. et al. Multiscale Modeling of Al 0.7 Sc 0.3 N-based FeRAM: the Steep Switching, Leakage and Selector-free Array. in 2021 IEEE International Electron Devices Meeting (IEDM) 8.1.1–8.1.4 (IEEE, 2021). Shen, J.-X., Wickramaratne, D. & Van de Walle, C. G. Band bowing and the direct-to-indirect crossover in random BAlN alloys. Physical Review Materials 1, 065001 (2017). Yan, Q., Rinke, P., Janotti, A., Scheffler, M. & Van de Walle, C. G. Effects of strain on the band structure of group-III nitrides. Physical Review B 90, 125118 (2014). Kim, C., Pilania, G. & Ramprasad, R. From Organized High-Throughput Data to Phenomenological Theory using Machine Learning: The Example of Dielectric Breakdown. Chemistry of Materials 28, 1304–1311 (2016). Zunger, A., Wei, S.-H., Ferreira, L. G. & Bernard, J. E. Special quasirandom structures. Physical Review Letters 65, 353–356 (1990). Zhu, N., Wang, B., Ma, K., Xue, X. & Su, J. Structural characters and band offset of Ga 2 O 3 –Sc 2 O 3 alloys. Applied Physics Letters 120, 053503 (2022). Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B 54, 11169–11186 (1996). Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B 59, 1758–1775 (1999). Paier, J., Hirschl, R., Marsman, M. & Kresse, G. The Perdew–Burke–Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set. The Journal of Chemical Physics 122, 234102 (2005). Paier, J. et al. Screened hybrid density functionals applied to solids. The Journal of Chemical Physics 124, 154709 (2006). Henkelman, G., Uberuaga, B. P. & Jónsson, H. Climbing image nudged elastic band method for finding saddle points and minimum energy paths. Journal of Chemical Physics 113, 9901–9904 (2000). Spaldin, N. A. A beginner’s guide to the modern theory of polarization. Journal of Solid State Chemistry 195, 2–10 (2012). Additional Declarations (Not answered) Supplementary Files supportinginformation.pdf Cite Share Download PDF Status: Published Journal Publication published 14 Feb, 2025 Read the published version in npj Computational Materials → Version 1 posted Editorial decision: revise 21 Aug, 2024 Review # 3 received at journal 18 Aug, 2024 Review # 2 received at journal 11 Aug, 2024 Review # 1 received at journal 06 Aug, 2024 Reviewer # 3 agreed at journal 01 Aug, 2024 Reviewer # 2 agreed at journal 01 Aug, 2024 Reviewer # 1 agreed at journal 01 Aug, 2024 Reviewers invited by journal 17 Jul, 2024 Submission checks completed at journal 22 Jun, 2024 First submitted to journal 19 Jun, 2024 Unknown event 18 Jun, 2024 Editor assigned by journal 13 Jun, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4575186","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":328179509,"identity":"a037a68e-ebf5-4923-a7fc-6e0581a94b88","order_by":0,"name":"Jie Su","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYHCChAMMFQw8DIfBHGZitZwhUQsDA2MbkDhArBb5GQkPD3ycd1iG7zjzswcMFdaJDexnD+DVYnAjIeHgzG1pPJKH2cwNGM6kJzbw5CXg1yKRkHCYd5sNj8FhBjMJxrbDiQ0SPAaEHJZw+O8coLLD7N8kGP8RoYUB6LDDjA0gW3iAtjQQocXgzIOEgz3HQH7hKZNIOJZu3MaTQ8Bh7TnJH37UHLbnO398m8SHGmvZfvYzBBzGwJOAYIOYbATUAwH7AcJqRsEoGAWjYGQDAKMPRbcpBTjYAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-2132-1597","institution":"xidian university","correspondingAuthor":true,"prefix":"","firstName":"Jie","middleName":"","lastName":"Su","suffix":""},{"id":328179510,"identity":"02811ce3-820d-494d-a8f9-c5f515ddda4e","order_by":1,"name":"Zhengmao Xiao","email":"","orcid":"","institution":"xidian univeristy","correspondingAuthor":false,"prefix":"","firstName":"Zhengmao","middleName":"","lastName":"Xiao","suffix":""},{"id":328179511,"identity":"dda59a0e-ae54-46f4-b925-4ff14fe07d78","order_by":2,"name":"Xinhao Chen","email":"","orcid":"","institution":"xidian university","correspondingAuthor":false,"prefix":"","firstName":"Xinhao","middleName":"","lastName":"Chen","suffix":""},{"id":328179512,"identity":"a3f9819c-f602-44a9-b7a1-a320b030b535","order_by":3,"name":"Yong Huang","email":"","orcid":"https://orcid.org/0000-0001-8776-3577","institution":"xidian university","correspondingAuthor":false,"prefix":"","firstName":"Yong","middleName":"","lastName":"Huang","suffix":""},{"id":328179513,"identity":"ec6d030f-9746-4137-8cbb-ec4ce4b5df1b","order_by":4,"name":"Zhenhua Lin","email":"","orcid":"","institution":"Xidian University","correspondingAuthor":false,"prefix":"","firstName":"Zhenhua","middleName":"","lastName":"Lin","suffix":""},{"id":328179514,"identity":"5eb4d145-519f-4ab0-85bb-65da62409823","order_by":5,"name":"Jingjing Chang","email":"","orcid":"https://orcid.org/0000-0003-3773-182X","institution":"Xidian University","correspondingAuthor":false,"prefix":"","firstName":"Jingjing","middleName":"","lastName":"Chang","suffix":""},{"id":328179515,"identity":"add02410-41cd-4397-b1f7-791aa0a5abf8","order_by":6,"name":"Jincheng Zhang","email":"","orcid":"","institution":"Xidian University","correspondingAuthor":false,"prefix":"","firstName":"Jincheng","middleName":"","lastName":"Zhang","suffix":""},{"id":328179516,"identity":"7ef1385a-8bba-4305-ad48-087dc6960d3e","order_by":7,"name":"Yue Hao","email":"","orcid":"","institution":"Xidian University","correspondingAuthor":false,"prefix":"","firstName":"Yue","middleName":"","lastName":"Hao","suffix":""}],"badges":[],"createdAt":"2024-06-13 09:41:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4575186/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4575186/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41524-025-01517-5","type":"published","date":"2025-02-14T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62304730,"identity":"44ddbcee-cdae-4e16-bd6a-920ae129ac08","added_by":"auto","created_at":"2024-08-12 17:49:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1781134,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Atomic structures of wz-BN and wz-AlN. (b) Atomic arrangements of wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN (\u003cem\u003ex\u003c/em\u003e=0.375) alloys after 3000 fs AIMD simulation at 300 K. (c) Formation enthalpies \u003cem\u003e∆H\u003c/em\u003e of wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys and zb-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys with and without 5% tension along the horizontal direction. (d) The phase transition concentration between wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN and zb-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys varies with the horizontal (viz.\u003csub\u003e//\u003c/sub\u003e) and c-axis (viz.\u003csub\u003e⊥\u003c/sub\u003e) strain.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/1cacd69c93fdb6aec42de8f2.png"},{"id":62305274,"identity":"f6ba64dc-8357-45fd-9a75-824e8f98ebe1","added_by":"auto","created_at":"2024-08-12 17:57:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":189639,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Elastic constants Cij of wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys. (b) The elastic constants C\u003csub\u003e14\u003c/sub\u003e of wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys with different strains.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/2d7383a2583cbab7a9cbb543.png"},{"id":62304728,"identity":"c6a4ac78-4f42-415b-9ac2-4fe741ead90c","added_by":"auto","created_at":"2024-08-12 17:49:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4961821,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Cross-sectional of isosurface of electron localization function (ELF) of wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys with and without 5% horizontal compression. The (b) ICOHP and (c) bond length of Al-N and B-N bonds in the wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys. The (d) volume and (e) internal parameter \u003cem\u003eu\u003c/em\u003e in the wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/3524f1db1be141ecb2296d0c.png"},{"id":62305275,"identity":"3fd7f99e-8518-42bf-a4bc-d5d0f62d04a4","added_by":"auto","created_at":"2024-08-12 17:57:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":866398,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Nudged-elastic-band simulation of polarization reversal pathways for wz-AlN and wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys. (b) The intermediate nonpolar structures of wz-AlN (left) and wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys (right) polarization inversion process. (c) Polarization switching barrier (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e) and spontaneous polarization (\u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e) of wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys as a function of B concentration. (d) The electron dipole moment, ion dipole moment, and total dipole moment of wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys depend on the B concentration.\u0026nbsp;\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/7e124750a66ece18febfafdb.png"},{"id":62304733,"identity":"d995afa3-9f1c-4970-8601-bb14117cf28d","added_by":"auto","created_at":"2024-08-12 17:49:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":420568,"visible":true,"origin":"","legend":"\u003cp\u003eThe \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e of wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy dependent of the strain along the (a) horizontal direction and (b) c-axis. The \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e of wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy dependent of the strain along the (c) horizontal direction and (d) c-axis. (e) The dipole moment of wz-Al\u003csub\u003e0.9375\u003c/sub\u003eB\u003csub\u003e0.0625\u003c/sub\u003eN alloy with different strain. (f) The lowest \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e of strained wz-Al\u003csub\u003e1-\u003c/sub\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy comparing with those of the common ferroelectric semiconductors in literatures\u003csup\u003e3,7,15,17,29–34\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/eeffe721dc1902df68056120.png"},{"id":62304732,"identity":"c1312ebc-c7bf-40d6-82ab-0578c223bcc1","added_by":"auto","created_at":"2024-08-12 17:49:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":816534,"visible":true,"origin":"","legend":"\u003cp\u003e(a-c) Orbitals of Al, B, N atoms projected band structures for wz-Al\u003csub\u003e0.9375\u003c/sub\u003eB\u003csub\u003e0.0625\u003c/sub\u003eN alloy. (d) The band gap of wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy as a function of B concentration. The band gaps of wz-Al\u003csub\u003e1-x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys dependent of the strain along the (e) horizontal and (f) c-axis direction.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/b61c92aaf154b1b76122b213.png"},{"id":76345266,"identity":"c1a45c50-c041-4a34-8c54-3299153400ec","added_by":"auto","created_at":"2025-02-15 08:06:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":14119482,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/5ff22a4d-2ee3-46d9-a3fe-018eab8ce9c9.pdf"},{"id":62304735,"identity":"5670a818-91e1-4dd5-87f9-395b6b16e667","added_by":"auto","created_at":"2024-08-12 17:49:44","extension":"pdf","order_by":8,"title":"","display":"","copyAsset":false,"role":"supplement","size":899743,"visible":true,"origin":"","legend":"","description":"","filename":"supportinginformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4575186/v1/4b5404b3e64494b276fbd89e.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"Realizing Giant Ferroelectricity in Stable wz-Al1-xBxN Alloys by Controlling the Microstructure and Elastic Constant","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eAlthough the wurtzite AlN (wz-AlN) with a strong spontaneous polarization has been extensively studied in piezoelectricity and pyroelectricity, its ferroelectricity has been a subject of prolonged debate since the polarization cannot be switched by external electric field\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Until 2019, the polarization reversal of wz-AlN was realized by Sc-doping\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, which enabling the exploitation of the ferroelectricity in wz-AlN. This discovery of ferroelectric wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloys not only breaks through the polarization application of wz-AlN limited in pyroelectric and piezoelectric, but also provides a new routine to explore the novelty ferroelectric semiconductor with wurtzite structure beyond the ferroelectric oxide\u003csup\u003e\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. On one hand, its polarization reversal originates from the local bond ionicity and ionic displacement induced by Sc ions instead of the simple change in the lattice parameter of the wurtzite structure \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. On the other hand, the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy exhibits the higher ferroelectric polarization than the conventional ferroelectric oxides\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Moreover, the low temperature preparation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy is compatible with the mainstream semiconductor technology\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. Where the interfacial oxidization and ferroelectric degradation induced by oxide migration that commonly exist in the ferroelectric oxide device can be overcame in the ferroelectric wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy.\u003c/p\u003e \u003cp\u003eRecently, the ferroelectric semiconductor with wurtzite structure is expanded into the Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Compared to wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy, this ferroelectric semiconductor consists exclusively of elements and structures that are already common and essential in the silicon complementary metal-oxide semiconductor front end. The ferroelectric Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys thin film integrated on silicon with large remnant polarization of 136 \u0026micro;C/cm\u003csup\u003e2\u003c/sup\u003e and low coercive field has been fabricated by sputtering\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. These ferroelectric parameters of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys continuously improve with the increment of B composition\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. The reported optimal remnant polarization and coercive field of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys are respectively to be 150 \u0026micro;C/cm\u003csup\u003e2\u003c/sup\u003e and 5.1 MV/cm, which are superior to those of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. It is thought that wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy is a promising ferroelectric material. However, it is noted that the ferroelectric characteristics and stability of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy are debate. For examples, Zagorac et al. claimed that the Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys remain the wurtzite structure over the composition range 0.125\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.375\u003csup\u003e16\u003c/sup\u003e, whereas Liu et al. found that the wurtzite stability remains only up to 0.19\u003csup\u003e15\u003c/sup\u003e. Several different polarization switching pathways have been reported in literatures\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Consequently, there is a significant difference among the reported polarization reversal barrier which directly determines the coercive field. To better design Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys for application, more research is required to understand the structure and ferroelectronic polarization of Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys. In addition, the epitaxial strain often exists in the epitaxial ferroelectric film\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, which can tune the ferroelectric polarization and coercive field presumably by atomic microstructure and polarity switch\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. It provides an effective way to design the giant ferroelectricity for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys, while is not revealed yet.\u003c/p\u003e \u003cp\u003eIn this work, we deeply unveil the structural stability and polarization reversal mechanisms of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys by atomic-scale simulation based on the first-principles calculations and modern polarization theory. Here, more accurate phase transformation concentration of about 0.1875 for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy was obtained by the chemical bond characteristic and elastic constant rather than the formation enthalpy and volume variations. Meanwhile the phase transition origin and polarization switching pathway of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy were revealed by the elastic constant C\u003csub\u003e14\u003c/sub\u003e. In addition, optimizing and designing the giant ferroelectricity of stable wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys with high spontaneous polarization, low polarization switching barrier, low polarization reversal field, and large bandgap by controlling the strain in wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys. The ferroelectricity of tuned wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy is superior to that of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy and ferroelectric oxide. Such phenomena were deeply understood by the variation of elastic constant, orbital distribution and dipole moment.\u003c/p\u003e"},{"header":"RESULTS AND DISCUSSION","content":"\u003cp\u003eAlthough wz-AlN and wz-BN show similar atomic structures (\u003cb\u003esee\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea), a phase transformation occurs in their alloy system\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. For an instance, several Al-N octahedrons, which are the basic structures of zb-AlN, are observed for the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys with high concentration B, as the AIMD simulation structure exhibited in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb. To reveal the phase transformation concentration of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, the formation enthalpies of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN and zb-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys as displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. It is obvious that the ground phase of Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy with x\u0026thinsp;\u0026gt;\u0026thinsp;0.27 is zinc blende structure rather than the wurtzite structure, due to its lower formation enthalpy. In other words, a phase transformation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy occurs at the B concentration of 0.27. Moreover, the phase transformation concentration significantly reduces when wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy undergoes strain, irrespective of the direction and character of strain, because the formation enthalpy reduction of strained wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy is smaller than that of strained zb-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec-d and Supplementary Fig.\u0026nbsp;1). It maybe the underlying reason why the high-quality wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy film with high concentration B is difficult to be deposited at the heterogeneous substrate\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo understand the phase transformation mechanism of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, the elastic constants C\u003csub\u003eij\u003c/sub\u003es are calculated and illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Supplementary Fig.\u0026nbsp;2. Although the wurtzite structure has six independent elastic constants, but just the C\u003csub\u003e12\u003c/sub\u003e, C\u003csub\u003e13\u003c/sub\u003e, C\u003csub\u003e14\u003c/sub\u003e, and C\u003csub\u003e44\u003c/sub\u003e are related to the elasticity in shape\u003csup\u003e\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. It is thought that a phase transformation can be revealed by these elastic constants. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, these elastic constants of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys show a non-monotonic variation rather than linear variation with the increment of B concentration. It further confirms the phase transformation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy occurs at the high B concentration. Although the variation inflexions of most elastic constants (including C\u003csub\u003e12\u003c/sub\u003e, C\u003csub\u003e13\u003c/sub\u003e, C\u003csub\u003e44\u003c/sub\u003e) are about 0.25, which is close to the above analyzed phase transformation concentration, these elastic constants are not the dominant factor for the phase transformation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy. Because the variation inflexions of these elastic constants are unaffected by the external strain (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and Supplementary Fig.\u0026nbsp;2), which is inconsistent with the previous report \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Just the variation inflexion of elastic constant C\u003csub\u003e14\u003c/sub\u003e are affected by the external strain. The variation of elastic constant C\u003csub\u003e14\u003c/sub\u003e is thought as the dominant factor for the phase transformation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy. Thus, the actual phase transformation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy begins from the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1875 since the elastic constant C\u003csub\u003e14\u003c/sub\u003e breaks down at such concentration (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Moreover, the phase transformation concentration of strained wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy can further decrease, regardless of the direction and character of strain. In addition, the elastic constant C\u003csub\u003e14\u003c/sub\u003e associates with the shear stress, indicating the phase transformation of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy is accompanied by horizontal movement of atoms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn general, the structural and physical properties mainly origin from the novelty bonding characteristics. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea gives the electron localization functions (ELFs) of Al-N and B-N bonds for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys. Different to the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eSc\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, both the Al-N bonds and B-N bonds of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys show the covalent bonds characters with an apparent charge accumulation between Al (or B) and N atoms, irrespective of the concentration and strain. Meanwhile, the latter exhibits the stronger covalent bond strength than the former since the charge accumulation of B-N bond is higher than that of Al-N bond. The bond strengths are quantitatively evaluated by the integrated crystal orbital Hamilton population (ICOHP) as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(b-c)\u003c/b\u003e. The larger -ICOHP suggests the stronger covalent bond strength. The -ICOHPs of Al-N bonds for all wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys are lower than that of B-N bonds. It further confirms the stronger covalent bond strength for B-N bond than Al-N bond. Moreover, the covalent bond strength of Al-N bond decreases at first and then slowly weakens and then enhances as the B concentration enlarges, while the opposite variation occurs for the B-N covalent bond. Because the -ICOHP of Al-N bond of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy drops at first (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.1875) and then gradually reduces (0.1875\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.25) and then enlarges (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.25) with the increment of B concentration, while that of B-N bond shows an opposite variation, as demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(b-c)\u003c/b\u003e. The abrupt change of -ICOHP for Al-N and B-N bonds further confirms that the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy begins a phase transformation at the \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.1875. When wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy undergoes the strain, the variation of -ICOHP for Al-N bond and B-N bond keep remains, but the first transition concentration becomes smaller. It suggests that the phase transformation concentration of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy can be reduced by strain. In addition, both the horizontal and c-axis compression enlarges the covalent bond strengths of Al-N and B-N bonds with the higher \u0026ndash;ICOHPs, while the horizontal and c-axis tension weakens the covalent bond strengths of Al-N and B-N bonds with the smaller -ICOHPs. In general, the stronger covalent bond strength suggests the shorter covalent bond length. Supplementary Fig.\u0026nbsp;3 exhibits the bond lengths of Al-N and B-N bonds of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy with and without strain. The variations of bond lengths are opposite to those of the -ICOHPs for Al-N and B-N bonds, but the transition concentration keep remains. It further confirms the phase transformation concentration for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy. However, the variations of Al-N and B-N bond lengths induce the linear change rather than the nonmonotonic linear change for the volume of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed. Due to the change of bond length and volume, the internal parameter u of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy is lower than 0.5, and it decreases with the increment of B concentration, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee. The hexagonal structure with u\u0026thinsp;=\u0026thinsp;0.5 means a phase without polarization along [0001], where the smaller u indicates the stronger polarization \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. It means that wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy possesses a strong polarization which enlarges as the B concentration increases. In addition, the c-axis compression and horizontal tension can enlarge the internal parameter u with the reduced polarization, while the c-axis tension and horizontal compression can shrink down the internal parameter u with the raised polarization.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further understand the polarization characteristic of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the polarization reversal pathways and characteristics of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys. For the wz-AlN, the calculated spontaneous polarization (\u003cem\u003eviz\u003c/em\u003e. \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003esp\u003c/em\u003e\u003c/sub\u003e) is about 1.33 C/m\u003csup\u003e2\u003c/sup\u003e, which is consistent with previous reports\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. There is just one peak, which corresponds to the intermediate nonpolar structure, in the polarization reversal pathway of wz-AlN (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). Moreover, the intermediate nonpolar structure is a nonpolar hexagonal (h)-BN-like structure (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). Such model can be regarded as the structure that Al-atom of wz-AlN moves along [000\u0026ndash;1] direction to N-atoms plane. Because the elastic constant C\u003csub\u003e13\u003c/sub\u003e associates with the shear stress is lowest among the elastic constant of wz-AlN, which promotes the atom prefers to move along the c-axis with small change in the lattice parameter of the wurtzite structure. As a result, there is a large polarization switching barrier (\u003cem\u003eviz\u003c/em\u003e. \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e) for the polarization reversal pathway of wz-AlN. The calculated \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e of wz-AlN of about 0.51 eV/f.u. is in good agreement with the previous report value\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Upon forming wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys, the \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e is enlarged compared to the wz-AlN. But there are several peaks and valleys in the polarization reversal pathway of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, which is different to that of wz-AlN. Such characteristics have been widely observed in the ternary alloy with wurtzite-type ferroelectric\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Because the new elastic constant C\u003csub\u003e14\u003c/sub\u003e with the smaller value appears when B composition is introduced into wz-AlN. It suggests that Al-atom of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy can also move along the horizontal direction, except for the c-axis direction. As a result, the intermediate nonpolar structure in the polarization reversal pathway of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy is β-BeO-like structure rather than the h-BN-like structure (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). This funding is consistent with the experimental observation\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Due to the additional horizontal movement of Al-atom, the calculated \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy is lower than that of wz-AlN. Since the elastic constant C\u003csub\u003e14\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy enlarges at first and then decreases as the B concentration rises, the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy reduces at first (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.1875) and then raises (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.1875) with the increment of B concentration (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). The \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0625, 0.125, 0.1875, 0.25) are 0.188, 0.175, 0.171, and 0.187 eV/f.u., respectively. In addition, the \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy monotonously enlarges as the B concentration increases (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec), which is consistent the above internal parameter analysis. The \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0625, 0.125, 0.1875, 0.25) are 1.36, 1.39, 1.44, and 1.47 C/m\u003csup\u003e2\u003c/sup\u003e, respectively. It is noted that the increasing \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy mainly originates from the enlarged electron dipole moment and reduced volume of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys dependent of the strain. The \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys enlarges with the increasing compression, while reduce with the increasing compression, irrespective of the strain direction, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea-b. Because the compression shifts up the elastic constant C\u003csub\u003e13\u003c/sub\u003e and shifts down elastic constant C\u003csub\u003e14\u003c/sub\u003e, while the tension shifts down the elastic constant C\u003csub\u003e13\u003c/sub\u003e and shifts up elastic constant C\u003csub\u003e14\u003c/sub\u003e (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Supplementary Fig.\u0026nbsp;2). Interestingly, the \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys decease from the compression to tension along the horizontal direction, the opposite variations are observed for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys with strain along the c-axis. Moreover, the enlarged \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys with tension along the c-axis will decrease again when the tension is larger than 5%, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec-d. The main reason is that the \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy is dominated by the electron dipole moment which possesses the similar variation (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ee). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ef comparatively lists the \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003es and \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys and other ferroelectric semiconductors\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan additionalcitationids=\"CR30 CR31 CR32 CR33\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. It can be found that the \u003cem\u003eP\u003c/em\u003e\u003csub\u003esp\u003c/sub\u003es of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys are not only far larger than those of ferroelectric oxides, but also higher than the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy with the same concentration. Moreover, no matter what the alloying concentration, the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003es of all wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys are far lower than those of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloys. Meanwhile the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eBarrier\u003c/sub\u003e continues to decline and is comparable to that of HfO\u003csub\u003e2\u003c/sub\u003e when wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys undergo the controllable tensile strain.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Supplementary Fig.\u0026nbsp;4 demonstrate the projected band structures of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys. The wz-AlN shows the direct band gap of about 6.18 eV, where the conduction band minimum (CBM) at the Γ point is dominated by s orbitals and the valence band maximum (VBM) at the Γ point is mainly composed of N-p\u003csub\u003ez\u003c/sub\u003e orbitals (see Supplementary Fig.\u0026nbsp;4). These characteristics are consistent with previous experimental and theoretical results\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. When the B element is introduced into wz-AlN to form wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, the mainly orbital compositions of CBM and VBM keep remains. Meanwhile, additional orbitals, such as B-p\u003csub\u003ez\u003c/sub\u003e and Al-p\u003csub\u003e(x,y)\u003c/sub\u003e orbitals, begin to contribute to the CBM, as displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e\u003cb\u003e(a-c)\u003c/b\u003e. Since the bond strength of Al-N covalent bond gradually weakens as the B concentration enlarges, the CBM of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy would be shifted down with the increment of B concentration. As a consequent, the band gap of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy reduces with the increasing B concentration. The band gaps of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0625, 0.125, 0.1875) are 5.77, 5.70, and 5.11 eV, respectively. When the B concentration is larger than 0.1875, these additional orbitals (B-p\u003csub\u003ez\u003c/sub\u003e and Al-p\u003csub\u003e(x,y)\u003c/sub\u003e orbitals) dominate the CBM of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy. Moreover, the position of CBM turns from Γ point to K point because the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy with such high B concentration undergoes a large atomic arrangement disorder and a phase transformation, as illustrated in Supplementary Fig.\u0026nbsp;4\u003cb\u003e(c-f)\u003c/b\u003e. Consequently, the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy exhibits a direct-to-indirect band gap transition when \u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.1875, which is consistent with the previous report\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. It means that the wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy (\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.1875) exhibits a direct-to-indirect band gap transition when the phase transformation occurs. At the moment, such high B concentration coupling with phase transformation enhance the bond strength of Al-N covalent bond, which can shift up the CBM. Thus, the indirect band gap of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy enlarges when B concentration is higher than 0.1875, as displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed. It is noted that the band gaps of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys reduce when wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys undergo tension, regardless of the strain direction. However, the compression along the horizontal direction enlarges the band gap, while the compression along the c-axis reduces the band gap.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn common, the reduced band gap suggests the lowering breakdown filed for semiconductor\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. In order to evaluate the effect of strain on the ferroelectric switching characteristics of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys, the theoretical polarization switching field and breakdown field of strained wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys are calculated and compared, as displayed in Supplementary Fig.\u0026nbsp;5. It can be found that both the polarization switching field and breakdown field of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys are declined by the tension. Moreover, the polarization switching fields of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys with tension, except for the wz-Al\u003csub\u003e0.75\u003c/sub\u003eB\u003csub\u003e0.25\u003c/sub\u003eN alloy with tension along the horizontal direction, are lower than those of breakdown fields. It is thought that the tension is beneficial to improve the polarization switching characteristic of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy.\u003c/p\u003e"},{"header":"CONCLUSION","content":"\u003cp\u003eHere, we deeply unveiled the structural stability and polarization reversal mechanisms of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys by atomic-scale simulation based on the first-principles calculations and modern polarization theory. We found that the accurate phase transformation concentration of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy is about 0.1875, and which can be reduced by both tension and compression. The β-BeO-like structure is the non-polar intermediate phase in the polarization inversion process of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy, which is different to that of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy. Notably, the stability and ferroelectric switching pathway of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy are dominated by the covalent bond strength and elastic constant \u003cem\u003eC\u003c/em\u003e\u003csub\u003e14\u003c/sub\u003e. As the B concentration increases, the spontaneous polarization and polarization switching barrier of stable wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy respectively raises and declines due to the reduced internal parameter \u003cem\u003eu\u003c/em\u003e and enhanced \u003cem\u003eC\u003c/em\u003e\u003csub\u003e14\u003c/sub\u003e. Meanwhile, the spontaneous polarization is enlarged by the compression along horizontal direction and tension along c-axis direction, while the polarization switching barrier and band gap are reduced by the all the tension. Moreover, the polarization switching fields are lower than the breakdown fields of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys with tension. Consequently, the giant ferroelectricity with larger spontaneous polarization than wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy and comparable polarization switching barrier to common ferroelectric oxide is designed in for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy. These findings give a deeply understanding of ferroelectricity wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy, and provide a guideline to design high-performance ferroelectric wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003eThe wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy was modelled by the 2 \u0026times; 2 \u0026times; 2 supercell wz-AlN with B substitution, where the substitution position of B atom was constructed by the quasirandom structure (SQS) methods\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. To reveal the phase transformation character of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy, the zinc blende (zb) Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloy was modelled by the 2\u0026times;1\u0026times;1 supercell zb-AlN. The formation enthalpies (\u003cem\u003e∆H\u003c/em\u003es) of Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN alloys were calculated by the following equation: \u003cem\u003e∆H\u003c/em\u003es = [\u003cem\u003eE\u003c/em\u003e(Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN)- (1-\u003cem\u003ex\u003c/em\u003e)\u003cem\u003eE\u003c/em\u003e(AlN) - \u003cem\u003exE\u003c/em\u003e(ScN)]/n(N), where \u003cem\u003ex\u003c/em\u003e is B composition concentration, \u003cem\u003eE\u003c/em\u003e(Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN), \u003cem\u003eE\u003c/em\u003e(AlN), and \u003cem\u003eE\u003c/em\u003e(BN) are the total energy of Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN, AlN and ScN, respectively, the n(N) is the number of N atom in the Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. These models were calculated by the first-principles density functional theory calculations on the basis of projector augmented wave (PAW) method, as implemented in the Vienna ab initio simulation package (VASP)\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The gneralized gradient approximation (GGA) coupling with Perdew-Burke-Ernzerhof (PBE) functional was adopted to describe the exchange and correlation interactions\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. The cutoff energy was set to 500 eV, and Γ-centered k-mesh with k-spacing of 0.015 \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e in the Brillouin zone are used for geometry optimization and self-consistent calculation. The lattice constants and atomic positions were fully relaxed until the energy convergence within 1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV and the residual force on each atom less than 0.01 eV/\u0026Aring;. The band structures were corrected by the screen hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) with the mixing parameter of 0.32\u003csup\u003e43\u003c/sup\u003e. The ab initio molecular dynamic simulations (AIMDs) were undertaken at 300 K for 3 ps with a time step of 1 fs. Nudged-elastic-band (NEB) simulations were conducted to determine the polarization reversal pathways.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e 15 and 31 images were generated for intrinsic switching in wz-AlN and sequential switching in wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eN, respectively. The spontaneous polarization was calculated for each image along the pathway using the modern polarization theory together with Berry phase methods\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eACKNOWLEDGMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was financially supported by the National Key Research and Development Program of China (2021YFA0715600); National Natural Science Foundation of China (Grant\u0026nbsp;62274125, 52192611);\u0026nbsp;Key Research and Development Program of Shaanxi Province (Grant 2024GX-YBXM-410). Guangdong Basic and Applied Basic Research Fund (2023A1515030084).\u0026nbsp;The numerical calculations in this paper have been done on the HPC system of Xidian University.\u003c/p\u003e\n\u003cp\u003eAUTHOR INFORMATION\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors and Affiliations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eState Key Laboratory of Wide Bandgap Semiconductor Devices and Integrated Technology, Faculty of Integrated Circuit, Xidian University, Xi\u0026rsquo;an, 710071, China.\u003c/p\u003e\n\u003cp\u003eJie Su, Zhengmao Xiao, Xinhao Chen, Yong Huang, Zhenhua Lin, Jingjing Chang, Jincheng Zhang, Yue Hao\u003c/p\u003e\n\u003cp\u003eXidian-Wuhu Research Institute, Wuhu, 241002, China\u003c/p\u003e\n\u003cp\u003eJie Su, Zhengmao Xiao, Yong Huang\u003c/p\u003e\n\u003cp\u003eGuangzhou Wide Band Gap Semiconductor Innovation Center, Guangzhou Institute of Technology, Xidian University, Guangzhou, 51055, China\u003c/p\u003e\n\u003cp\u003eJie Su\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eJ. S. performed the computational study and wrote the first draft of the manuscript. Z. M. X. performed the hybrid functional calculations and polarization calculation. All authors participated in discussions and the final preparation of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding authors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence to Jie Su or Yong Huang or Jingjing Chang\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eETHICS DECLARATIONS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eADDITIONAL INFORMATION\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePublisher\u0026rsquo;s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang, H., Adamski, N., Mu, S. \u0026amp; Van de Walle, C. G. 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Journal of Solid State Chemistry 195, 2\u0026ndash;10 (2012).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Wurtzite Al1 − xBxN alloy, Ferroelectric, Spontaneous polarization, Switching barrier, Strain","lastPublishedDoi":"10.21203/rs.3.rs-4575186/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4575186/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe emerged wurtzite-type (wz) ferroelectric Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys have drawn increasing attention due to superior ferroelectricity and excellent compatibility with microelectronics. Revealing and controlling the microstructure and ferroelectric origin is vital to design and fabricate stable wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy with giant ferroelectricity. We find that the β-BeO-like rather than h-BN-like structure is the non-polar intermediate phase in the polarization inversion process of stable wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy. The stability and ferroelectric switching pathway of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy are dominated by the covalent bond strength and elastic constant \u003cem\u003eC\u003c/em\u003e\u003csub\u003e14\u003c/sub\u003e. Due to the reduced internal parameter \u003cem\u003eu\u003c/em\u003e and enhanced \u003cem\u003eC\u003c/em\u003e\u003csub\u003e14\u003c/sub\u003e of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy, the spontaneous polarization and polarization switching barrier respectively raises and declines as the B concentration increases. Meanwhile, the spontaneous polarization is enlarged by the compression along horizontal direction and tension along c-axis direction, while the polarization switching barrier and band gap are reduced by the all the tension. Moreover, the polarization switching fields are lower than the breakdown fields of wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys with tension. As a result, the giant ferroelectricity with larger spontaneous polarization than wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eSc\u003csub\u003ex\u003c/sub\u003eN alloy and comparable polarization switching barrier to the common ferroelectric oxide is designed in for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy. It should be noted that the phase transformation concentration of about 0.1875 for wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy is reduced by both tension and compression. These findings give a deeply understanding of ferroelectricity wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloy, and provide a guideline to design high-performance ferroelectric wz-Al\u003csub\u003e1\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eB\u003csub\u003ex\u003c/sub\u003eN alloys.\u003c/p\u003e","manuscriptTitle":"Realizing Giant Ferroelectricity in Stable wz-Al1-xBxN Alloys by Controlling the Microstructure and Elastic Constant","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-12 17:49:39","doi":"10.21203/rs.3.rs-4575186/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2024-08-21T04:07:46+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-08-18T19:15:10+00:00","index":3,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-08-11T07:54:38+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-08-06T08:59:26+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-08-01T09:14:36+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-08-01T08:48:59+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-08-01T08:05:27+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-07-17T11:24:42+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-22T11:31:51+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Computational Materials","date":"2024-06-19T06:14:14+00:00","index":"","fulltext":""},{"type":"checksFailed","content":"","date":"2024-06-18T20:02:42+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-06-13T09:38:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b0da4300-ea5f-40f6-a98f-790b9ccb1f07","owner":[],"postedDate":"August 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":34734195,"name":"Physical sciences/Physics/Electronics, photonics and device physics"},{"id":34734196,"name":"Physical sciences/Materials science/Theory and computation/Electronic structure"}],"tags":[],"updatedAt":"2025-02-15T08:05:53+00:00","versionOfRecord":{"articleIdentity":"rs-4575186","link":"https://doi.org/10.1038/s41524-025-01517-5","journal":{"identity":"npj-computational-materials","isVorOnly":false,"title":"npj Computational Materials"},"publishedOn":"2025-02-14 05:00:00","publishedOnDateReadable":"February 14th, 2025"},"versionCreatedAt":"2024-08-12 17:49:39","video":"","vorDoi":"10.1038/s41524-025-01517-5","vorDoiUrl":"https://doi.org/10.1038/s41524-025-01517-5","workflowStages":[]},"version":"v1","identity":"rs-4575186","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4575186","identity":"rs-4575186","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}