Over many years, group III-nitrides have been widely used in various types of electronic and optoelectronic devices. These materials are semiconductors with direct band gaps ranging from 0.7 eV for InN to 6.2 eV for AlN (Monemar et al., 2005; Edgar et al., 1990). Due to the great number of possible applications, group III-nitrides have gained significant attention in recent years. The possibility of forming ternary alloys, such as AlGaN or AlInN, allows for the tuning of the band gap of these compounds, making them potential candidates for optical applications (Pelá et al., 2011). One of the outstanding materials within the group III-nitrides is AlN, which due to its notable properties has been extensively utilized in acoustic, electronic, and optical devices. AlN owns a wide band gap (6.2 eV) (Edgar et al., 1990), high spontaneous polarization and break down voltage (1.351 C m 2 and 4–10 MV cm , respectively) (Dreyer et al., 2016; Ruemenapp and Peier, 1999), high thermal conductivity (321 W m . K ) (Cheng et al., 2020), and high thermal stability (T_m = 2200°C) (Berger, 1996). Due to its widespread use, numerous theoretical and experimental studies have been conducted on AlN.

One of the most important physical properties of AlN for applications is piezoelectricity. Piezoelectric materials are crucial components in microelectromechanical systems (MEMS) and are widely utilized in acoustic devices (BAW and SAW), radio frequency (RF) systems, and sensors. Beside AlN, a variety of piezoelectric materials exists, including lead zirconated titanite (PZT), quartz (SiO₂), zinc oxide (ZnO), and lithium niobite (LiNbO₃). Despite its lower piezoelectric coefficient, AlN has been extensively employed in device applications. The primary reasons for this preference include its high stiffness and sound velocity in addition to its ease of growth, high thermal stability, and compatibility with CMOS technology (Shelton et al., 2009). However, the relatively low piezoelectric coefficient of AlN (d ₃₃ ≅ 5 pC N ) remains a significant limitation for further improving device efficiency (Zhang M. et al., 2015).

In 2009, Akiyama et al. (2009) demonstrated that alloying AlN with the transition metal nitride ScN can significantly enhance its piezoelectric properties. For Al_0.6Sc_0.4N, an increase in the piezoelectric coefficient d ₃₃ of up to 25 pC N (approximately 400% improvement) was reported (Akiyama et al., 2009). This discovery opened up potential applications for Sc _x Al_1-x N alloys in various acoustic devices. Furthermore, in 2019, Fichtner et al. reported the first observation of ferroelectric properties in Sc _x Al_1-x N thin films (Fichtner et al., 2019). This discovery provides a wide range of potential applications for ferroelectric nitrides, such as non-volatile memory devices, ferroelectric resistive memory, and optical and tunable microwave components (Setter et al., 2006). Due to its high potential for device applications, numerous theoretical and experimental studies have been conducted on Sc _x Al_1-x N. Various growth techniques have been employed to produce this ternary alloy, such as sputtering (Akiyama et al., 2009), metal organic chemical vapor deposition (MOCVD) (Leone et al., 2019), and molecular beam epitaxy (MBE) (Hardy et al., 2017). Despite its outstanding properties and high potential in electromechanical devices, a significant drawback for the commercial implementation of Sc _x Al_1-x N is the high cost Sc, a rare earth material. Consequently, extensive researches have been undertaken to identify potential substitutes for Sc in this alloy system. One promising alternative of ScN as an alloying element for AlN is Yttrium Nitride (YN). Y belongs to the same group in the periodic table of elements as Sc, resulting in similar electronic configuration of their outer most shell, with Y having only one higher principle quantum number. This similarity leads to comparable chemical properties for both elements and their compounds. Notably, the cost of Y is approximately 100 times lower than that of Sc (ISE, 2024), making it a more economically viable option. Furthermore, Y has already found widespread use in industrial products, such as application of Y₂O₃ in LEDs, which could facilitate its implementation in commercial devices (Loewen, 2024). Theoretical and experimental studies have been conducted to investigate the structure and material properties of Y _x Al_1-x N. Computational predictions suggest that Y _x Al_1-x N exhibits similar trends in band gap, electrical, and optical parameters as Sc _x Al_1-x N (Žukauskaitė, 2012). From a structural perspective and based on thermodynamic calculations, Y _x Al_1-x N is expected to maintain its wurtzite structure up to a Y concentration of approximately x = 0.75. This high stability of the wurtzite phase could potentially lead to further enhanced piezoelectric coefficients, thus offering greater potential for applications in acoustic devices (Zukauskaite et al., 2012; Manna et al., 2017; Xie et al., 2020).

Despite the rapid progress in studies concerning Y _x Al_1-x N, to the best of the author’s knowledge, there has been no systematic review article that consolidates all available data on this material. This review article aims to provide a comprehensive and detailed overview of the advancements made in the research of Y _x Al_1-x N in recent years. The first three sections will discuss theoretical calculations and predictions related to the formation, structural, elastic, and thermal properties of Y _x Al_1-x N. Following this, various methods developed for the growth of Y _x Al_1-x N will be examined, along with experimental structural parameters. In section five, the article will present available data on material properties such as band gap, permittivity, piezoelectric coefficient, and spontaneous polarization. The subsequent section will explore potential device applications, and finally, the last section will summarize all data and discussions. This comprehensive review seeks to serve as a valuable resource for researchers and engineers interested in Y _x Al_1-x N and its applications.

AlN and YN are binary compounds composed of nitrogen atoms bonded to metal atoms (Al or Y). In binary compounds, nitrogen and metal atoms form stacks of monolayers (Sahin et al., 2009). However, in the alloys like Y _x Al_1-x N, the metal atoms (Y and Al) distribute randomly in the metal monolayers, with nitrogen atoms binding to either Al or Y atoms to form the crystal lattice. These compounds are referred to as ternary or pseudo binary systems. A ternary compound is made up of three different elements. Thus, it can apply to YAlN or ScAlN as they consist three distinct elements. On the other hand, a pseudo binary compound is a compound which is treated as a binary system, although it involves more than two elements. This approach is often utilized in order to simplify the properties by reducing the system into two effective components, in this case Y(Sc)N and AlN. Thus, the alloy can be viewed as a mixture of two binary nitrides. In this work, the alloy is referred to as a ternary system, and the fraction of Y is denoted by x, with the ratio of Y to Al atoms equal to x 1 − x .

AlN crystallizes in the hexagonal wurtzite structure (P6₃mc space group) under ambient conditions (Siegel et al., 2006). The electronic configuration of Al ( 1 s 2 2 s 2 2 p 6 3 s 2 3 p 1 ) and N ( 1 s 2 2 s 2 2 p 3 ) atoms play a crucial role in bond formation. During AlN crystal formation, Al atoms undergo 3 s p 3 hybridization, while N excites to 2 s 2 p 3 hybridization state (Cunha et al., 2022). This results in covalent bonds between the semi-complete sublevels of Al and N atoms, as well as an additional ionic bond between the complete sublevel of the N and the empty sublevel of Al. The covalent bonds in AlN have a length of l 1 = 1.89   Å and form a tetrahedron with the angle of 110.5 ° . The ionic bond has the length of l 2 = 1.92   Å , with an angle of 107.7 ° between the covalent and ionic bonds. Each N atom binds with four Al atoms, creating another tetrahedron and forming the wurtzite crystal structure. The unit cell of AlN consists of 14 N and Al atoms (Cunha et al., 2022). A schematic of the wurtzite unit cell of AlN is shown in Figure 1.

Additional to the stable wurtzite structure, theoretical studies have investigated the properties of rock salt, zinc blende, and layered hexagonal AlN (Ahmed and Sharma, 2021; Louhibi-Fasla et al., 2014). For small layer thicknesses of a few monolayers, calculations suggest that layered hexagonal AlN has a lower configuration energy compared to other structures (Louhibi-Fasla et al., 2014). This layered hexagonal form was experimentally observed by Tsipas et al in 2013 (Tsipas et al., 2013). Zinc blende AlN is stable only at very small thicknesses before transforming to the wurtzite structure (Hultman et al., 1992). Simulations predict a direct band gap of 3.44 eV (at Γ point) for layered hexagonal AlN (Bacaksiz et al., 2015), while the Zinc blende structure shows a bandgap of approximately 3.24 eV (Γ-X) at zero pressure (Silva et al., 2005). Ueno et al. (1992) has demonstrated that under high pressure (22.0 GPa), wurtzite AlN can transform into the cubic rock salt phase [NaCl (B1)]. In high pressure condition, AlN exhibits a band gap of 4.04 eV (Γ-X) (Ahmed and Sharma, 2021). The properties of different AlN structures are summarized in Table 1, providing a comprehensive overview of the material’s structural variations and their associated electronic properties.

Transition metal nitrides have various commercial applications, with ScN receiving significant attentions in recent years due to its potential in semiconductor technologies (Eklumd et al., 2016; Adamski et al., 2019). Given the electronic similarities between Sc and Y atoms, similar potential is expected for YN. The high thermal stability and melting temperature of transition metal nitrides also enable the formation of single crystals through annealing (Hultman, 2000). Theoretical calculations have predicted several interesting properties for YN, including strong anisotropic mechanical and electronic characteristics, as well as ferroelastic properties (Xu et al., 2018). Density Functional Theory (DFT) calculations indicate that the formation enthalpy of rock salt YN is lower than that of its hexagonal structure (Rowberg et al., 2021), suggesting that YN is expected to crystallize in the rock salt phase under ambient conditions. In its rock salt structure, YN exhibits an indirect band gap in the range of 0.9–1.3 eV (Rowberg et al., 2021; Liu et al., 2014; Ramirez-Montes et al., 2016). The calculated lattice parameter for rock salt YN is a = 4.88   Å (Rowberg et al., 2021). Notably, like ScN, YN is highly unstable in the wurtzite structure (Rowberg et al., 2021).

The first reports on the synthesis of YN dates back to 1950s, when Kempter et al. (1957) described the production of YN powder by converting metallic Y to YH₂ and then heating it up to 900°C in nitrogen environment. In recent years, researchers have reported growing YN on various substrates using techniques such as magnetron sputtering and metal organic chemical vapor deposition (Gregoire et al., 2008; Leone et al., 2023). However, the growth of YN has consistently presented challenges due to the high degree of oxidation observed in thin layers (Žukauskaitė, 2012; Leone et al., 2023). This oxidation issue results in n-type conduction in YN layers, more pronounced compared to that observed in ScN thin films (Rowberg et al., 2021; Biswas and Saha, 2019; Deng et al., 2015). To address this oxidation problem, researchers have found that using a protective passivation layer is important for YN applications. Specifically, the use of AlN as a passivation layer has shown positive results in reducing oxidation of YN thin layers (Gregoire et al., 2008). Despite the experimental instability of YN in structures other than rock salt, theoretical studies have investigated the structural parameters of alternative crystalline phases for YN, including wurtzite, zinc blende, and layered hexagonal phases (Mancera et al., 2003; Rowberg et al., 2021). The structural parameters for these different phases of YN, along with corresponding data for AlN, are summarized in Table 1.

DFT calculations have provided valuable insights into the mixing enthalpies and phase stability of Y _x Al_1-x N alloys across different compositions (Žukauskaitė, 2012; Manna et al., 2017; Xie et al., 2020). The calculations reveal that the wurtzite phase of Y _x Al_1-x N remains stable up to a high Y concentration of x = 0.75. Manna et al. (2017) calculated a temperature-composition phase diagram for the full range of Y _x Al_1-x N compositions, indicating a region between x = 0.2 and x = 0.9 were mixing enthalpies are not achievable under thermodynamic equilibrium. It is hypothesized that non-equilibrium growth techniques, such as reactive DC magnetron sputtering, could potentially overcome these thermodynamic limitations and enable the growth of compositions within this range.

The predictions for potential applications of wurtzite Y _x Al_1-x N, such as high piezoelectric coefficient d 33 with increasing Y content, provide strong motivation for thorough studies on the structural properties and type of phase transition of these alloys at high concentrations. The transition from wurtzite to the rock salt structure in materials like AlN and YN has been extensively studied both theoretically and experimentally. Corll initially described this transition using a continual deformation model (Corll, 1967), while Sowa later developed a more general crystallographic model that explained the transformation mechanism without breaking any bonds (Sowa, 2001). Several advanced models have since been generated from both experimental and theoretical data (Knudson and Gupta, 1998; Tolbert and Alivisatos, 1995; Wilson and Madden, 2002). In the wurtzite structure, two key structural parameters are the internal parameter u , which indicates the relative positions of metal and nitrogen atoms, and the c a ratio of lattice parameters. During the transition from wurtzite to rock salt, the internal parameter changes from approximately 0.38–0.50, while the c a ratio changes from about 1.6 to 1. This transformation process results in an intermediate layered hexagonal phase. In this intermediate structure, atoms are located in lateral planes, and the bond angles between the metal and nitrogen atoms in this plane is 60°. The final transition from the layered hexagonal to the rock salt phase involves a change in bond angles from 60° to 90°, with atoms moving horizontally within the lateral planes (Wilson and Madden, 2002). Based on calculations shown in Figure 2 for the mixing enthalpy of AlN and YN, the formation of a layered hexagonal intermediate lattice has not been predicted for Y _x Al_1-x N. Due to lack of experimental data at high Y concentrations, it has not been possible to draw conclusions about the formation of an intermediate phase and the nature of the phase transition in this system. In contrast, for Sc _x Al_1-x N, many studies initially predicted the formation of a layered hexagonal structure during the phase transition (Farrer and Bellaiche, 2002; Talley et al., 2018; Zhang et al., 2013; Furuta et al., 2021). However, recent experimental data have shown that the phase transition in Sc _x Al_1-x N occurs at around x = 0.45–0.5, with the crystalline structure changing directly from wurtzite to rock salt without an intermediate phase (Mihalic et al., 2023). Interestingly, as seen in Figure 2, the mixing enthalpies of different structures of Y _x Al_1-x N have close values in the range x = 0.65 to x = 0.80. This suggests that in this composition range, various growth parameters that can affect film strain, particularly the choice of the substrate and buffer layer, may have a significant effect on the resulting crystal structure (Afshar et al., 2024).

During the formation of Y _x Al_1-x N, beside Al atoms, Y atoms, which have an atomic radius approximately 1.3 times larger than Al ( r Y = 212  pm , r A l = 118  pm (Clementi et al., 1967) are incorporated into the crystal lattice. As the Y concentration ( x ) increases, more Y atoms participate in the lattice, leading to an increase in the bond length between metal and nitrogen atoms and consequently, an expansion of the lattice parameters (Žukauskaitė, 2012; Ramirez-Montes et al., 2016). The calculation of lattice parameters for wurtzite Y _x Al_1-x N and their comparison with Vegard’s law has been performed for both a and c lattice parameters (Žukauskaitė, 2012; Manna et al., 2017; Xie et al., 2020; Mayrhofer et al., 2015a; Assali et al., 2021), as illustrated in Figure 3A. Ramirez-Montes et al. (2016) simulated the a and c lattice parameters of wurtzite Y _x Al_1-x N and reported behavior similar to that of the lattice parameters in rock salt Y _x Al_1-x N. They calculated bowing parameters of - 0.262 Å for the a lattice parameter, and - 0.483 Å for the c lattice parameter in wurtzite Y _x Al_1-x N. Interestingly, the lattice parameters of wurtzite Y _x Al_1-x N exhibit less deviation from Vegard’s law compared to the rock salt structure. This smaller deviation is attributed to the closer values of lattice constants in the wurtzite structure of binary compounds (AlN and YN) compared to their rock salt counter parts (Ramirez-Montes et al., 2016).

For alloys that maintain the wurtzite structure throughout the entire composition range, such as Ga _x Al_1-x N and In _x Al_1-xN, both lattice parameters a and c rise with increasing alloy concentration (Ambacher et al., 2021). For alloys that undergo phase transition, like Sc _x Al_1-x N, the behavior of the lattice parameters differs significantly. In these cases, the c lattice parameter initially increases but begins to decrease as the phase transition approaches. At this critical point, the formation of an intermediate layered hexagonal structure is predicted, while the a lattice parameter increases in a manner similar to that observed in the rock salt structure. The structural transition from wurtzite (β-ZnS) to layered hexagonal (lh-MgO) and rock salt (NaCl) structures is characterized by a continuous decrease in the ratio of the lattice parameters, c a (Ambacher et al., 2021).

The calculated c to a ratio for wurtzite Y _x Al_1-x N are illustrated in Figure 3B. The data points from Ramirez-Montes et al. (2016)’s calculations show only a slight decrease in the c a ratio, which is attributed to their assumption of a stable wurtzite structure across the entire concentration range. In contrast, calculations by Zukauskaite et al. (2012) indicate a more significant decrease of c a ratio, dropping from 1.603 for AlN to 1.39 for Y_0.75Al_0.25N. For rock salt Y _x Al_1-x N, the ratio of the lattice parameters in an unstrained lattice reduces to a ∥ a ⊥ = 1 . However, there is currently no experimental data available to validate theoretical prediction regarding the phase transition of Y _x Al_1-x N.

The highest reported Y concentration in sputtered Y _x Al_1-x N films is around x = 0.7 to x = 0.8 (Afshar et al., 2024). However, experimental studies have faced challenges in maintaining a high-quality wurtzite structure above x = 0.4, with possible amorphization occurring at higher concentration (Afshar et al., 2024), a discrepancy that has not been fully addressed in theoretical predictions. As shown in Figure 2, calculations consistently predict the wurtzite phase to be stable for x < 0.7, while above x = 0.75, the rock salt structure becomes energetically favorable. Previous research conducted by our group has identified amorphization as a limiting factor for maintaining Y _x Al_1-x N at concentrations close to the predicted phase transition. This issue posed significant challenges in achieving the desired structural integrity at higher Y concentrations. These findings highlight both the potential and challenges in synthesizing Y _x Al_1-x N alloys across a wide composition range, emphasizing the need for further research to bridge the gap between theoretical predictions and experimental realities.

For the cubic rock salt structure, the calculated lattice parameter for AlN is 4.085 Å (Ahmed and Sharma, 2021) and for YN is 4.88 Å (Rowberg et al., 2021). To the authors’ knowledge, the only available data for rock salt Y _x Al_1-x N over the entire compositional range are those obtained by Ramirez-Montes et al. (2016), where they compared the calculated a lattice parameters of the rock salt phase with the predictions from Vegard’s law. Their results showed that the equilibrium lattice parameters vary non-linearly with Y concentration ( x ), deviating from Vegard’s law with an upward bowing parameter of - 0.203 Å. The calculated data for the binary compounds (AlN and YN) showed good agreement with the experimental values.

The knowledge of mechanical and elastic parameters is crucial for understanding different physical phenomena, such as stiffness, stability, elastic anisotropy, and properties relevant to device application like electroacoustic devices. The relation between stress and strain in a crystal is defined by the Hook’s law, expressed as in Equation 1: ε = S σ (1) where S is the elastic compliance. This equation can also be written in terms of elastic stiffness, C as in Equation 2: σ = C ε (2)

Given the elastic properties of crystals are directionally dependent, it is essential to define a standard orthogonal system. For hexagonal crystals, the standard axes are defined as x : 2 11 ¯ 0 , y : 01 1 ¯ 0 , and z : 0001 (Nye, 1985; Tromans, 2011) The elastic coefficients are described using Voigt’s notation as S m n , C m n m , n = 1 , … , 6 (Voigt, 1910). Using this notation, the Hook’s law can be rewritten as shown in Equation 3: σ m = ∑ n C m n ε n (3)

For describing the elastic properties in hexagonal crystals, only 5 independent stiffness coefficients are required due to their transverse isotropy, which means the elastic properties remain invariant under rotation around the z-axis (Mouhat and Coudert, 2014). This leads to equalities such as C 11 = C 22 , C 44 = C 55 , C 13 = C 22 , and C 66 = 1 2 C 11 − C 12 . Various studies have reported calculated elastic constants for different concentrations of wurtzite Y _x Al_1-x N, summarized in Table 2. Among the elastic coefficients, C 11 shows the highest value. As the concentration of Y atoms in the crystal increases, the values of C 11 , C 12 , C 33 , and C 44 decreases, while C 13 increases. Based on the Born mechanical stability criteria and the calculated elastic coefficients, wurtzite Y _x Al_1-x N is considered mechanically stable (Nye, 1985). Using the elastic coefficients and Voigt-Reus-Hill approximation (Hill, 1952; Reuss, 1929), polycrystalline elastic moduli, such as bulk or shear modulus can be calculated.

For hexagonal crystals, these parameters can be calculated using stiffness coefficients (Nye, 1985). Several theoretical calculations are available for bulk and shear moduli of wurtzite Y _x Al_1-x N (Ramirez-Montes et al., 2016; Assali et al., 2021; Laidoudi et al., 2022). All data show a decrease of the elastic moduli as the Y concentration increases, which is a result of the change in the bond angels. The only available data on the elastic properties of rock salt Y _x Al_1-x N is the bulk modulus provided by Ramirez-Montes et al. (2016). Based on the available data, the bulk modulus of the rock salt structure has higher values compared to the hexagonal Y _x Al_1-x N. The higher coordination number and structural uniformity of the rock salt crystal are the main reasons for these higher values (Ambacher et al., 2023). However, in both crystal systems, the lattice softening occurs as Y content increases. Similar behavior has also been reported for Sc _x Al_1-x N (Ambacher et al., 2023). Figure 4 represents the bulk modulus of hexagonal and rock salt structures of Y _x Al_1-x N as a function of Y concentration.

Further understanding of the elastic properties of Y _x Al_1-x N can be achieved by calculating the elastic compliance coefficients, which allows for the determination of useful elastic properties such as Young’s modulus, shear modulus, and Poisson’s ratio. The relationship between stiffness and compliance coefficients was established by Wei et al. (2019). Using this relationship and the stiffness coefficients calculated by Assali et al. (2021), the compliance coefficients of Y _x Al_1-x N were calculated and are shown in Figure 5. Notably, within the studied concentration range (x < 0.4), no extreme changes in compliance coefficients were observed, suggesting that the alloy is still far from its structural phase transition point. For Sc _x Al_1-x N, Ambacher et al. (2023) observed an extreme change in S 33 as the alloy approached the wurtzite to rock salt phase transition. The alloying process involves competition between Al and Y (or Sc) atoms for binding with nitrogen, which intensifies as the concentration of alloying atoms increases. Near the critical composition for structural transition, the crystal becomes highly sensitive to external forces, manifesting as extreme changes in elastic coefficients (Ambacher et al., 2023).

Young’s modulus is a material-specific property defined as the ratio of tensile stress σ to tensile strain ε , providing information about the materials’ deformability. In a crystal system, the Young’s modulus for an arbitrary crystal plane E h k i l , is defined as the ratio of stress to strain in the direction normal to the crystal plane h k i l . The directional dependence of Young’s modulus in a hexagonal crystal system can be calculated using the compliance coefficients, S m n , and as a function of the angle θ between the normal to the crystal plane and the axis [0001]. In hexagonal crystals, Young’s modulus is independent of the azimuth angle φ due to the six-fold rotation axis along [0001] (Gorodtsov and Lisovenko, 2019). This symmetry results in E h k i l being solely dependent on the polar angle θ . The polar angle can be defined using the following Equation 4 (Zhang et al., 2007): cos θ = a c l h 2 + h + 2 k 2 3 + a c l 2 (4) where a and c are lattice parameters, and h , k , and l are Miller-Bravis indices of the crystal plane.

Using the equations provided in previous studies (Zhang et al., 2007), a polar representation of the directional dependence of Young’s modulus can be generated for hexagonal crystals. These structures exhibit both rotational symmetry and mirror symmetry with respect to the [0001] axis, allowing the polar representation of elastic properties be limited to the interval θ = 0 ° , 90 ° . The directional dependency of other elastic properties, such as Shear’s modulus and Poisson’s ratio, can also be calculated using the compliance coefficients and considering the symmetries in hexagonal structures. Utilizing the equations given in referenced works for directionally dependent elastic properties in hexagonal crystals (Tromans, 2011; Zhang et al., 2007), and employing the compliance coefficients derived from the stiffness coefficients simulated by Assali et al. (2021), the Young’s modulus, Shear’s modulus, and Poisson’s ratio of wurtzite Y _x Al_1-x N were calculated and are presented in Figures 6A–C. The elastic modulus of AlN in each graph are calculated based on different data sets of elastic coefficients, and the average values are depicted (Assali et al., 2021; Kazan et al., 2007; McNeil et al., 1993; Tsubouchi and Mikoshiba, 1985). The shade around the values related to AlN are the error range resulted from using various reported data sets, showing a deviation of approximately 5% between different calculations and experimental values. This error bar can also be expected for the calculated values related to Y _x Al_1-x N. The elastic modulus of Y _x Al_1-x N exhibit a softening of the crystal structure as the number of Y atoms increases, a trend also observed in wurtzite Sc _x Al_1-x N (Ambacher et al., 2023). Additionally, anisotropies are evident in the elastic’s moduli. For Young’s modulus, higher values are observed in the [01–10] direction for x = 0, 0.0625, and 0.125. As the concentration increases to x = 0.25 and 0.375, the value in the [0001] becomes larger. A similar trend is observed for the Shear’s modulus. However, considering the possible errors resulted from the simulation of elastic coefficient, these results need further investigation. For having a better conclusion on the behavior of elastic modulus, comparison between different simulated and experimental data is of great importance. Notably, the symmetrical behavior of Young’s modulus becomes more pronounced at higher concentrations. Poisson’s ratio, which describes the ratio of transverse strain to axial strain under uniaxial stress, shows high anisotropy in hexagonal crystal across the entire concentration range, as illustrated in Figure 6C. From x = 0 to 0.25, the Poisson’s ratio exhibits higher values along the [01–10] axis, while at x = 0.375, an opposite behavior is observed. These trends in elastic properties are similar to those reported for Sc _x Al_1-x N (Ambacher et al., 2023), suggesting commonalities in the mechanical behavior of these III-nitride alloys.

Assali et al. (2021) have calculated the mass density and directional-dependent sound velocities in Y _x Al_1-x N crystals. The general relation between the sound velocities and stiffness coefficients is given by the following Equation 5, as (Ledbetter, 2006): v m n x = C m n x ρ x (5)

Where ρ x is the crystal’s mass density. Sound velocity in different crystal directions is crucial for acoustic devices, making polar representation of longitudinal v l , transversal v t , and quasi-transversal v q t velocities particularly useful. This visualization helps in understanding the anisotropic nature of sound propagation in Y _x Al_1-x N crystals, essential for designing and optimizing acoustic devices. Figure 7 shows the polar representation of these sound velocities, calculated based on the data sets provided by Assali et al. (2021) for Y _x Al_1-x N. The calculations related to AlN are done using different sets of data for elastic coefficients and the average values are shown in the graphs, with the shaded area showing the error related to calculations based on different reported values (Kazan et al., 2007; McNeil et al., 1993; Assali et al., 2021; Tsubouchi and Mikoshiba, 1985). In the case of Y _x Al_1-x N, since the number of elastic data available is very limited, the calculations were done only using one data set (Assali et al., 2021). However, based on the different reported values for AlN, an error bar of approximately 5% can also be expected for the data related to Y _x Al_1-x N. The longitudinal sound velocities exhibit the highest value for all concentrations in Y _x Al_1-x N alloys. As Y concentration increases, all sound velocities decrease due to crystal softening. The longitudinal velocity ( v l ) consistently shows the highest value along the [0001] axis. For transversal sound velocity, values in the basal plane exceed those along the c-axis [(0001)]. Notably, at 45°, the quasi-transversal sound velocity decreases significantly with increasing alloy concentration, indicating strong directional dependency.

Generally, wurtzite Sc _x Al_1-x N exhibits higher sound velocities than wurtzite Y _x Al_1-x N for the same values of x. This difference is due to Y’s larger atomic volume, resulting in longer bond lengths between Y and Al or N atoms, leading to more pronounced softening. Additionally, Y’s higher atomic mass increases mass densities, directly affecting crystal sound velocities as per Equation 9.

Compared to Sc _x Al_1-x N, there are fewer available data sets and first-principle studies on Y _x Al_1-x N, particularly regarding different structural phases and near the phase transition point. This limitation hinders comprehensive comparisons. More simulated data, especially near the predicted structural phase transition and considering various possible lattices, would enhance understanding of Y _x Al_1-x N’s elastic properties. Such knowledge is crucial for applications in devices like resonators and actuators, highlighting the need for further research in this area to fully exploit the potential of Y _x Al_1-x N in technological applications.

In crystals, the heat conduction is a temperature-dependent random process that can be divided into two parts: conduction by electrons and phonons. In metals, thermal conduction is dominant by the electronic part, which originates from the high density of electrons in metals and the fact that the Fermi velocity of electrons is much higher compared to sound velocities. In semiconductors, heat conduction is dominated by phonons and depends on the mean free path of the phonons, which can be affected by two major parameters: geometry and scattering from other phonons (Kittel and Holcomb, 2005). Phonon-related thermal conductivity depends on the average speed of the collective lattice vibrations and the average phonon mean free path, and is given by the following Equation 6, as: k = 1 3 C V v l (6) where k is the thermal conductivity, C V is the volumetric heat capacity, v is the average phonon velocity, and l is the phonon mean free path (Kittel and Holcomb, 2005).

Debye temperature is a material property in solids that determines the maximum vibration frequency of phonons. It is related to the elastic properties of crystals via sound velocities. The average Debye velocity is connected to the crystal’s elastic properties through a set of equations (Anderson, 1963) as is shown in Equations 7a–7c, v m x = 1 3 1 3 1 v l 3 x + 2 v s 3 x (7a) v s x = G x ρ x (7b) v l x = B x + 4 3 G x ρ x (7c) in which the first equation defines the average Debye velocity ( v m ) in terms of longitudinal ( v l ) and shear ( v s ) sound velocities, and subsequent equations express v s and v l in terms of shear modulus ( G ), bulk modulus ( B ), and density ( ρ ).

The Debye temperatures is a crucial parameter for determining important thermal properties such as specific heat ( C v x ), melting temperature ( T m x ), and minimum thermal conductivity, ( k min T , x ). The Debye temperature of Y _x Al_1-x N can be calculated as a function of elastic properties (Debye velocity) for each alloy concentration using a formula that incorporate Planck’s constant ( h = 6.6261 × 10 − 34 J . S ), Boltzmann’s constant ( k B = 1.3806 × 10 − 23 J K ), the number of atoms in the unit cell ( n ), which is equal to 4 for wurtzite and 8 for rock salt structures, Avogadro’s number ( N A ), mass density ( ρ x ), and the atomic masses of Y, Al, and N ( m Y , m A l , m N ), and can be represented as following in Equation 8 (Kittel and Holcomb, 2005), T D x = h k B   3 3 4 π n N A ρ x m Y x + m A l 1 − x + m N v m x (8)

Assali et al. (2021) have calculated the Debye temperature of Y _x Al_1-x N, finding that it decreases with increasing alloy composition, from approximately 920 K for AlN to 500 K for Y_0.375Al_0.625N. This decrease is attributed to the change in the bond angels which results in the bond softening and increased freedom of phonon vibrations at lower temperatures.

Various models have been proposed to understand and predict thermal conductivity in materials. Kittel modeled the phonon-deviated thermal conductivity by assuming the mean free path of phonons equals the bond length (Kittel and Holcomb, 2005). Cahill et al. (1992) took a quantum mechanical approach, dividing the sample into regions of size of λ 2 , and oscillation frequencies defined by ω = 2 π v λ and lifetime of τ = π ω . This model allows for the calculation of temperature-dependent thermal conductivity. In materials with high disorder, such as sputtered films with columnar structures where phonon heat transport is limited, a diffusive thermal conductivity model can be applied. This model considers heat transport as a random walk process resulting from atomic vibrations rather than phonon propagation (Allen and Feldman, 1993). Using this approach, Agne et al. (2018) established a relationship between a material’s eleastic properties and its minimum diffusive thermal conductivity.

Tran et al. (2023) have experimentally measured the thermal conductivity of wurtzite Y _x Al_1-x N and Sc _x Al_1-x N for concentrations up to x = 0.2. Both alloys demonstrated a similar decreasing trend in thermal conductivity as the alloy concentration increased, which is attributed to enhanced phonon-alloy scattering. Notably, Y _x Al_1-x N exhibited lower thermal conductivity compared to Sc _x Al_1-x N, a result of the further intensified phonon-alloy scattering due to the larger atomic size of Y relative to Sc.

Using the elastic property data sets for Y _x Al_1-x N provided by Assali et al. (2021), the minimum and minimum diffusive thermal conductivities of wurtzite Y _x Al_1-x N were calculated. Figure 8 illustrates the calculated values for minimum and diffusive thermal conductivities, as well as experimental values at room temperature, as a function of alloy composition (Tran et al., 2023). As evident in Figure 8, the diffusive thermal conductivity shows a higher incorporation compared to the minimum thermal conductivity, which is attributed to the high degree of disorder and alloy-phonon scatterings in Y _x Al_1-x N. This behavior aligns with similar observation reported by Ambacher et al for Sc _x Al_1-x N (Ambacher et al., 2023).

The observed reduction in both theoretical and experimental results, with the increase in alloy composition, can be a significant drawback for device applications, especially at higher Y concentration, where efficient heat dissipation becomes crucial. However, modern thermal management techniques offer potential solutions to mitigate this issue. Advanced material design strategies can be employed to enhance thermal properties while maintaining desired electrical and optical characteristics. In this case, Nano-structuring approaches or engineered interfaces can be utilized to manipulate phonon transport and potentially improve thermal conductivity (Dhumal et al., 2023). These innovative techniques can help reduce heating during device operation, thereby expanding the potential applications of Y _x Al_1-x N alloys in high-performance electronic and optoelectronic devices.

Transition metal nitrides, specifically Y _x Al_1-x N and Sc _x Al_1-x N, represent a class of novel materials with promising properties that are anticipated to play a significant role in future semiconducting devices. This study provides a comprehensive review of the structural, elastic, optical, electronic, and thermal properties of the ternary alloy system Y _x Al_1-x N, drawing from both simulated and experimental data. The structural analysis highlights the similarities between the structural characteristics and elastic parameters of Y _x Al_1-x N and Sc _x Al_1-x N. Alongside, optical and electronic properties of Y _x Al_1-x N and Sc _x Al_1-x N are also compared, further highlighting the similarities of the two alloy systems and emphasizing on the potential of Y _x Al_1-x N. Based on the available elastic properties, the thermal conductivity of Y _x Al_1-x N is evaluated and the limitation caused by insufficient thermal conductivity are discussed. In the following chapters, this study reviews the reported growth methods for the synthesis of Y _x Al_1-x N and the pros and cons are described. Additionally, the structural data, especially lattice parameters calculated from experimental results are summarized. By studying different material properties, such as electrical and optical parameters, this review also delves into the potential applications of Y _x Al_1-x N, such as acoustic resonators and high electron mobility transistors, by examining calculated sound velocities, elastic moduli, coupling coefficients, and carrier densities. A comparative analysis with Sc _x Al_1-x N, a reference material with well-documented and analogous properties, was conducted for each material property. A significant obstacle in advancing the understanding of Y _x Al_1-x N properties is the scarcity of experimental and simulated data. One of the critical challenges identified in experimental research is the oxidation and instability of films with high Y concentrations, which persist regardless of the growth methods employed. Therefore, systematic research, particularly focused on optimizing the growth processes of Y _x Al_1-x N, is imperative for a more detailed exploration of its material parameters. The data available thus far indicate that Y _x Al_1-x N exhibits behavior remarkably similar to Sc _x Al_1-x N, which serves as a compelling incentive for the research community to dedicate further time and resources to a wide array of studies on Y _x Al_1-x N. This investment is crucial for unlocking the full potential of these materials in various advanced technological applications.