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Article

Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN

by
Xi Yu
1,†,
Lei Zhu
2,†,
Xin Li
3,
Jia Zhao
2,
Tingjun Wu
2,
Wenjie Yu
2,3 and
Weimin Li
1,2,3,*
1
School of Microelectronics, Shanghai University, Shanghai 201899, China
2
State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
3
Shanghai Institute of IC Materials Co., Ltd., Shanghai 201899, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Materials 2023, 16(5), 1778; https://doi.org/10.3390/ma16051778
Submission received: 21 November 2022 / Revised: 22 December 2022 / Accepted: 27 December 2022 / Published: 21 February 2023
(This article belongs to the Topic Advances in Computational Materials Sciences)
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Versions Notes

Abstract

:
The piezoelectric and elastic properties are critical for the performance of AlN-based 5G RF filters. The improvement of the piezoelectric response in AlN is often accompanied by lattice softening, which compromises the elastic modulus and sound velocities. Optimizing both the piezoelectric and elastic properties simultaneously is both challenging and practically desirable. In this work, 117 X0.125Y0.125Al0.75N compounds were studied with the high-throughput first-principles calculation. B0.125Er0.125Al0.75N, Mg0.125Ti0.125Al0.75N, and Be0.125Ce0.125Al0.75N were found to have both high C33 (>249.592 GPa) and high e33 (>1.869 C/m2). The COMSOL Multiphysics simulation showed that most of the quality factor (Qr) values and the effective coupling coefficient (Keff2) of the resonators made with these three materials were higher than those with Sc0.25AlN with the exception of the Keff2 of Be0.125Ce0.125AlN, which was lower due to the higher permittivity. This result demonstrates that double-element doping of AlN is an effective strategy to enhance the piezoelectric strain constant without softening the lattice. A large e33 can be achieved with doping elements having d-/f- electrons and large internal atomic coordinate changes of du/dε. The doping elements–nitrogen bond with a smaller electronegativity difference (ΔEd) leads to a larger elastic constant C33.

1. Introduction

Piezoelectric materials, which can be applied to Radio Frequency (RF) filters, have drawn much attention with the commercialization of 5G communication technologies [1,2,3,4]. Aluminum nitride with wurtzite structure (w-AlN) is the prevailing piezoelectric material for the body acoustic wave (BAW) filters owing to the advantages of high acoustic velocity, minimal acoustic loss, high thermal stability, and good compatibility with Complementary Metal Oxide Semiconductor (CMOS) technology [5,6]. The critical parameters to evaluate the performance of piezoelectric materials for 5G filters are the mechanical quality factor (Q) and the longitudinal electromechanical coupling constant (k332). The higher the Q, the lower the mechanical loss. The higher the k332, the larger the frequency bandwidth. In general, the Q value of 5G RF filters based on w-AlN thin film (Q = 400) is higher than that based on ZnO thin film (Q = 350), achieving low acoustic loss [7]. However, the k332 (6.1%) [8] of undoped w-AlN is lower than some well-known piezoelectric materials, such as lead zirconate titanate perovskite (PZT) (k332 = 8–15%) [8] and ZnO (k332 = 7.5%) [8]; therefore, undoped w-AlN needs further optimization [9].
As shown in Equations (1) and (2), the characteristic Q and k332 of a BAW RF filter are affected by the piezoelectric strain constant (e33) and elastic constant (C33) of the piezoelectric material [10,11,12],
1 k 33 2 = C 33 ε 33 s e 33 2 + 1 ,
Q = C 33 + e 33 2 / ε 33 s ω η 33 ,
where Q, ε33s, ω, and η33 are the acoustic quality factor, the clamped permittivity, the angular frequency, and the viscosity coefficient (details are shown in the support information) along the c-axis direction, respectively. A high C33 is favorable to Q, and a high e33 is favorable to k332. The piezoelectric material coupling coefficient k332 and resonator effective coupling coefficient Keff2 are positively related. It is not hard to design a resonator with a high Keff2 from a material having a high k332 value [13].Consequently, w-AlN should be tailored to have a high C33 and e33, simultaneously, which has been proven to be a difficult task.
For example, first-principles calculations [14] and experiments [15] showed that an ~400% increase in the piezoelectric coefficient (d33 ≈ e33/C33) of w-AlN can be achieved with Sc doping. The increase in the e33 is caused by the increase in the sensitivity of the internal atomic coordinates in response to the strain (du/dε) [16]. However, there also exists an elastic softening, owing to the elongated energy landscape in the c/a direction [17]. The e33 of w-Xa/2Ya/2Al1−aN (X = Li; Y = V, Nb, Ta; a = 0.125, 0.25, 0.375) is enhanced compared to that of undoped w-AlN [18], while the C33 decreases simultaneously due to the fact that these dopants can lead to a phase transition to a non-polar hexagonal structure. Hirata et al. [19] used first-principles calculations to investigate the enhancement in piezoelectric properties and the reduction in elastic properties by co-doping w-Xa/2Ya/2Al1−aN (X = Mg; Y = Nb, Ti, Zr, Hf; a = 0.125). The bonding analysis of the metal–nitrogen pairs by co-doping Mg + Y into w-AlN was carried out by the crystal orbital Hamilton population (COHP), which showed that weaker bonding energy is one of the reasons for the elastic softening.
The above results showed the need for a new mechanism to achieve a high C33 and e33 simultaneously. Manna et al. [20] found that the co-doping of Y and B elements in w-AlN improved the elastic properties while retaining good piezoelectric performance. Subsequently, Jing et al. [21] discovered that the C33 of B0.125Scx-0.125Al1−xN is higher than that of ScxAl1−xN with a small enhancement of the e33. These results confirm the feasibility of improving the piezoelectric and elastic properties by dual-element co-doping [22,23]. However, there is still a lack of systematic analysis leading to a clear strategy to choose doping elements for the enhancement of both the C33 and e33. Therefore, expanding the map of doping elements and the understanding of the adjustment mechanism is critical to finding new doping schemes with excellent performance.
In this work, a high-throughput workflow is designed to calculate the piezoelectricity and elasticity of 117 X0.125Y0.125Al0.75N compounds. Filtered by the non-magnetic criteria, semiconductor criteria, stability criteria, and performance criteria, three dopants are finally screened out, which are B0.125Er0.125Al0.75N (e33 = 2.11 C/m2, C33 = 262.2 GPa, d33 = 8.05 pC/N), Mg0.125Ti0.125Al0.75N (e33 = 2.41 C/m2, C33 = 261.1 GPa, d33 = 9.22 pC/N), and Be0.125Ce0.125Al0.75N (e33 = 2.12 C/m2, C33 = 272.0 Gpa, d33 = 7.78 pC/N). All have higher piezoelectric and elastic properties than Sc0.25Al0.75N (e33 = 1.87 C/m2, C33 = 249.59 GPa, d33 = 7.49 pC/N). It is found that the primary factor influencing the C33 is the electronegativity difference (ΔEd) of the metal–nitrogen bonds, and the primary factor influencing the e33 is the du/dε of the doping atoms. The bonds with a small ΔEd in the doped-AlN between the doping elements and nitrogen with stronger strength leads to a larger elastic constant C33. The energy competition between the doping atoms and Al mainly affects the internal structural response (du/dε) of the crystal due to the transition elements doping into tetrahedral Al sites, tending to form non-tetrahedral coordinates, and undergoing excursions. The increasing of C33 from the electronegativity difference and e33 from the du/dε of the doping atom with d-/f- electrons provides clear ideas to design new piezoelectric materials for 5G filters.

2. Computational Details

The 2 × 2 × 2 supercells for w-X0.125Y0.125Al0.75N (Figure 1b) were built with the special quasi-random structures (SQS) method [24]. The first-principles calculations were performed with the Vienna Ab initio Simulation Package (VASP) [25,26,27]. The Perdew–Burke–Ernzerhof (PBE) type generalized gradient approximation (GGA) as the exchange–correlation function was implemented [24]. The elastic tensor was determined by performing the finite differences method. Six finite distortions of the lattice were taken, and the corresponding elastic constants could be derived from the strain–stress relationship [28]. The strains for the original structure along each of the Cartesian directions were ±0.5% and ±1%. The piezoelectric tensors were evaluated from the phonon and dielectric response calculations performed from the density functional perturbation theory (DFPT) [29,30,31]. The Monkhorst−Pack method [32] was used to set the k-point mesh. The k-grids used in the calculation of the structural optimization, self-consistent, and Cij/eij were 30/L+1, 60/L+1, and 30/L+1, respectively, where L is the lattice constant of the systems. The cutoff energy of all calculations was 520 eV. The convergence criteria for the energy and force were set to 10−4 eV and 10−2 eV/Å, respectively. The Hubbard U values were from Wang et al. and Dudarev et al. [33,34].
The two-dimensional sandwich structure of the resonator and its geometric parameters is shown in Figure S1. The resonator consists of a piezoelectric material with top and bottom electrodes. COMSOL Multiphysics 6.0 is used to simulate the resonator quality factor(Qr) and effective electromechanical coupling coefficient (Keff2) of the resonator by using the finite element method [35]. Among them, the 2nd order Taylor approximation was performed to simulate the Keff2 [36]. The Qr value was calculated using the method proposed by Bode et al. [37]. The physical parameters of the materials utilized in the simulation are shown in Table S1.

3. Results

To explore the theoretical feasibility of doping engineering to obtain materials with a high performance of large e33 and C33, 117 dopants of X0.125Y0.125Al0.75N without toxic elements were tested. As shown in Figure 1a, the orange, green, blue, and gray spheres indicate X, Y, Al, and N, respectively. Considering the charge conservation law, the reasonable elements X and Y are substituted to the Al sites by 1:1. Moreover, Sc, Y, La Er, B, Ga, and In elements can be doped into either the X site or Y site due to the valence of +3. To effectively screen the piezoelectric and elastic performance of X0.125Y0.125Al0.75N materials, a high-throughput workflow was designed (Figure 1c). First, the entries with complex magnetism were removed due to the difficulties to accurately calculate the properties of the magnetic materials for the high-throughput method. Second, the non-semiconductor systems were removed. If the band gap of X0.125Y0.125Al0.75N is less than 0, it indicates that the system is metallic and is not suitable for making piezoelectric layers for 5G filters. Then, the mechanical criterion was tested by the Born–Huang criteria of hexagonal structures [38]: C11 > C12, 2C132 < C33 (C11 + C12), C44 > 0, C66 > 0. It is clear that all of the models we considered were mechanically stable, and the detailed results are listed in Table S2. Finally, three dopants (B0.125Er0.125Al0.75N, Mg0.125Ti0.125Al0.75N, and Be0.125Ce0.125Al0.75N) were screened out as having better performance than Sc0.25Al0.75N. For comparison purposes, the calculation results of Sc0.25Al0.75N were e33 = 1.87 C/m2, C33 = 249.59 GPa, and d33 = 7.49 pC/N, consistent with the results reported by Caro et al., Tasnadi et al., etc. [14,15,39,40,41]. (Details can be found in Figure S2).
The detailed results of the 67 mechanically stable dopants are shown in Table 1. The modulation ranges of the e33 and C33 are 0.064~2.408 C/m2 and 165.556~396.671 GPa, respectively. Table 1 shows that the e33 of the dopants with small atomic radii elements and transition elements is high. The e33 of the dopants with large atomic radii, such as K, Rb, Ca, Sr, Ba, and La, is smaller than that of those with small atomic radii, such as Li and Mg. Furthermore, the dopants that have one small radii element and one transition element (e.g., Mg co-doped with Ce, Ti, Hf, and Zr) show a higher e33 than Mg co-doping with carbon group elements (i.e., C, Si, Ge, Sn, and Pb). For the C33, when the difference between the electronegativity of the doping atom and the N element is small, the C33 is always high. For example, Be0.125C0.125Al0.75N has an ΔEd = 0.98 and a C33 = 346.605 GPa. Comprehensively considering the e33 and C33, B0.125Er0.125Al0.75N, Mg0.125Ti0.125Al0.75N, and Be0.125Ce0.125Al0.75N, all having non-transition elements and a small atomic radii atom with a small ΔEd and transition elements co-doping, have good performance. It is worth noting that Li0.125Ta0.125Al0.75N, Mg0.125Hf0.125Al0.75N, and Mg0.125Zr0.125Al0.75N, which have a C33 only somewhat smaller than Sc0.25Al0.75N and both an e33 and a d33 larger than Sc0.25Al0.75N, are also excellent choices. Better performance can be expected if the doping concentration is further regulated.

4. Discussion

4.1. Analysis of Elastic Properties

As shown in Figure 2, we explored in detail the mechanism of co-doping to enhance the characteristics of the C33 and e33, respectively. The hardness of the crystal is positively related to the bond density and negatively related to the ionicity indicator fi [42,43,44]. Figure 2a is the relationship of the C33 and the electronegativity difference ΔEd,
Δ E d = E X + E Y − 2 E N 2 ,
where EX, EY, and EN are the electronegativity of elements X, Y, and N, respectively. The electronegativity difference indicates the ionicity indicator (fi) of the chemical bonds according to the Pauling for AB-type compounds [45],
f i % = ( 1 − e − 1 4 Δ E d 2 ) × 100 ,
where fi indicates the degree of ionization of the hybrid bonds with a larger fi indicating that the chemical bond is closer to an ionic bond. Figure 2a shows that the C33 is negatively related to the ΔEd (i.e., the smaller the difference of electronegativity, the smaller the fi and the larger the C33). Moreover, other factors, such as the bond density induced by lattice distortion, also slightly influence the C33. A specific mechanistic explanation of the effect of lattice distortion on the C33 can be found in the supporting information. Generally, the smaller the electronegativity difference, the smaller the degree of ionization of the metal-N in X0.125Y0.125Al0.75N and the larger the hardness of the crystal. Thus, the electronegativity difference could be a criterion for the selected doped-AlN with a high C33.

4.2. Analysis of Piezoelectric Properties

Figure 2b shows the distribution of the e33, which comprises an electronic-response part and ion-polarization part [46].
e 33 = e 33 clamped + e 33 non_clamped
e33clamped represents the electronic response under strain, which is evaluated by fixing the internal atomic coordinates at their equilibrium positions. e33non_clamped represents the ion polarization under strain, which is derived from the internal atomic coordinate changes. The mean and standard deviation of the e33non_clamped are 2.001 and 0.689, respectively. However, the mean and standard deviation of the e33clamped are −0.435 and 0.077, respectively. Obviously, the e33non_clamped mainly contributes the e33 of w-AlN, owing to wider adjustable values and larger weights. Here, we focus on the derivation of the ion-polarization part,
e 33 non_clamped = ∑ n 2 e Z 33 n 3 a 2 d u n d ε ,
where n runs on all atoms in the supercell, e is the elementary charge, and a is the equilibrium lattice constant. Z33 is the c-axis component of the dynamic Born charge tensor, and du/dε is the strain sensitivity. u is the ratio of the length of the metal-N along the c-axis (uc) to the lattice constant c in w-AlN (Figure 2c), which can be changed by the strain in the c direction. du/dε is the factor about the c-structure change, and Z33 is the factor about the piezoelectric polarization variation on the structure change. Based on the first-principles calculation, the average Z33 is 2.77 and can be adjusted from −6.48% to 8.53%; the average du/dε is 0.17 and can be adjusted from −90.89% to 27.10%. The variation of the du/dε is particularly large, which may significantly affect the e33non_clamped [16,47].
Figure 3a shows that there is a linear correlation between the du/dε along the c-axis and the e33. The du/dε of w-AlN is calculated by varying the doping atoms with an adjustment of the internal structure parameter, especially the structure parameter along the c-axis. For example, Mg0.125Ti0.125Al0.75N, Li0.125Ta0.125Al0.75N, and B0.125Er0.125Al0.75N have large distortions along the c-axis with a du/dε = 0.221, 0.224, and 0.225, respectively, and an e33 reaching 2.41, 2.24, and 2.11 C/m2, respectively. In contrast, Mg0.125Ge0.125Al0.75N, Li0.125Sb0.125Al0.75N, and B0.125Ga0.125Al0.75N have a small distortion along the c-axis with a du/dε of 0.178, 0.0152, 0.152, respectively, and an e33 of only 1.492, 0.155, and 1.202 C/m2, respectively. Figure 3b shows that the variation range of |du/dε| of the doping elements X and Y is much larger than that of Al and N. The average |du/dε| of the doping elements X and Y is 0.195 and 0.184, respectively, while that of the elements Al and N is only 0.0597 and 0.0836, respectively. Thus, the doping elements affect the e33 dominantly compared to Al and N. The systems with large lattice distortion are doped by Sc, Y, and other transition elements with d-electrons and f-electrons.
To further discuss the mechanism of transition elements affecting the lattice distortion, the band structures and wave functions of the Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N system were calculated. The doping atoms replace the Al sites, thus the valence band of the undoped and doped w-AlN are all the p-electrons of the N atom. The doping atoms mainly change the electronic state of the conduction band. As shown in Figure 4a,b, the conduction bands of Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N are occupied by the d-electrons of Ti and s-electrons of Ge, respectively. The sp3 hybridization of w-AlN leads to a tetrahedral coordination geometry of Al; in addition, the doping atoms only have s- and p- electron orbitals (e.g., tetrahedral coordination of Figure 4f). For the transition elements X or Y, such as Ti, Zr, Hf, Er, and Ta, they tend to format other non-tetrahedral coordination (e.g., octahedral coordination of Figure 4e). Octahedral coordination will compete against the tetrahedral coordination of the substituted Al and is more unstable than the tetrahedral coordination of Al. Figure 4c,d shows the wave functions of the conduction band minimum of Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N. As shown in Figure 4d, for a non-transition element, the electron cloud of the regular tetrahedron geometry to bond to the nitrogen atom does not aggregate in the c-axis. For a transition element, it might bond to the nitrogen atom along the c-axis (Figure 4c). When a strain is performed on Mg0.125Ti0.125Al0.75N with unstable coordination, atoms move away from their regular tetrahedral positions and induce a larger du, which is due to the bond along the c-axis. As a result, the non-tetrahedral coordination of transition elements X or Y is easier to increase |du/dε| than the main group doping atoms with tetrahedral coordination under sp3 hybridization. It should be noted that the atomic radius also affects the e33. While the atomic radius of the doping atom is excessively large, it will produce a large local distortion in the lattice leaving a small space for an atom to move under the strain. For example, in Ba0.125Ti0.125Al0.75N, the atomic radius of Ba is 2.78 Å, and the du/dε is only 0.139. In a word, a small atomic radius and d/f-electrons are two parameters for finding doped-AlN with a large e33.
As shown in Table 2, the Qr value of all three selected systems is higher than that of Sc0.25Al0.75N. The trends are the same for the k332 about co-doped w-AlN material and the Keff2 about the resonator. The Keff2 and k332 of B0.125Er0.125AlN and Mg0.125Ti0.125AlN are both higher than that of Sc0.25Al0.75N, except for Be0.125Ce0.125AlN, due to the high permittivity according to Equation (1).

5. Conclusions

Based on the high-throughput workflow, more than 117 X0.125Y0.125Al0.75N compounds were examined. In addition, B0.125Er0.125Al0.75N, Mg0.125Ti0.125Al0.75N, and Be0.125Ce0.125Al0.75N were screened out as having a higher e33, C33, and d33 than Sc0.25Al0.75N. The Qr of the resonators made with these three systems was higher than that of Sc0.25AlN. The effective coupling coefficient (Keff2) of B0.125Er0.125AlN and Mg0.125Ti0.125AlN was also higher than that of Sc0.25AlN, except for Be0.125Ce0.125AlN due to the high permittivity. The C33 is affected by the electronegativity difference. There is a negative correlation between the ΔEd and C33. The doping elements–nitrogen bond with a small ΔEd leads to a larger elastic constant C33 of the doped-AlN because the strength of the bond is stronger. The e33 is affected by the du/dε of the doping atoms. The large du/dε comes from the competition between the tetrahedra coordinates [AlN4] of w-AlN and the non-tetrahedra coordinates of the doping elements with d-/f- electrons. This work provides a new way to find promising doped-AlN materials for 5G filters.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ma16051778/s1, Figure S1: The two-dimensional sandwich structure of the resonator; Figure S2: The calculated and experimented e33, C33, and d33 of ScxAl1−xN (x = 0~0.5); Figure S3: (a,b) Wave function analyses of Li0.125Ta0.125Al0.75N and Li0.125Sb0.125Al0.75N; Table S1: Physical parameters of the materials utilized in the simulation; Table S2: Dopants considered in this study and the result of C11-C12, 2C132-C33(C11 + C12), C66. Reference [48] are cited in the supplementary materials.

Author Contributions

Conceptualization, X.Y., X.L. and W.L.; methodology, X.L.; software, X.Y., J.Z. and X.L.; validation, X.Y., X.L. and T.W.; formal analysis, X.Y. and X.L.; investigation, X.Y.; resources, W.L.; data curation, X.Y. and J.Z.; writing—original draft preparation, X.Y.; writing—review and editing, X.L., T.W. and W.L.; visualization, X.Y.; supervision, L.Z. and W.L.; project administration, L.Z., W.L. and W.Y.; funding acquisition, L.Z., W.L. and W.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Project supported by Shanghai Technology Innovation Action Plan 2020-Integrated Circuit Technology Support Program, grant number No. 20DZ1100603.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

The authors would like to thank Huirong Jing at Shanghai Jiao Tong University for their discussion.

Conflicts of Interest

The authors declare no conflict of interest.

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Materials 16 01778 g001 550
Figure 1. High-throughput workflow of screening piezoelectric material w-X0.125Y0.125Al0.75N. (a) Dopants considered in this study. The blue line separates elements X and Y according to an ΔEd less than/more than 1.7. (b) Crystal structure of w-X0.125Y0.125Al0.75N. (c) High-throughput workflow of screening X0.125Y0.125Al0.75N with a high e33 and high C33. The red numbers indicate the number of remaining systems after screening.
Figure 1. High-throughput workflow of screening piezoelectric material w-X0.125Y0.125Al0.75N. (a) Dopants considered in this study. The blue line separates elements X and Y according to an ΔEd less than/more than 1.7. (b) Crystal structure of w-X0.125Y0.125Al0.75N. (c) High-throughput workflow of screening X0.125Y0.125Al0.75N with a high e33 and high C33. The red numbers indicate the number of remaining systems after screening.
Materials 16 01778 g001
Materials 16 01778 g002 550
Figure 2. (a) The relationship of the C33 and electronegativity difference. The result of the quadratic fitting is shown as a solid line. (b) The e33non_clamped and e33clamped of X0.125Y0.125Al0.75N. (c) Wurtzite structure with the internal parameter u = uc/c.
Figure 2. (a) The relationship of the C33 and electronegativity difference. The result of the quadratic fitting is shown as a solid line. (b) The e33non_clamped and e33clamped of X0.125Y0.125Al0.75N. (c) Wurtzite structure with the internal parameter u = uc/c.
Materials 16 01778 g002
Materials 16 01778 g003 550
Figure 3. (a)The relationship of the e33 and du/dε. du/dε is measured by calculating the response of the u(n) under a macroscopic strain (η = 0.5%). The result of the linear fitting is shown as a solid line. (b)The |du/dε| of X, Y, Al, and N in X0.125Y0.125Al0.75N alloys.
Figure 3. (a)The relationship of the e33 and du/dε. du/dε is measured by calculating the response of the u(n) under a macroscopic strain (η = 0.5%). The result of the linear fitting is shown as a solid line. (b)The |du/dε| of X, Y, Al, and N in X0.125Y0.125Al0.75N alloys.
Materials 16 01778 g003
Materials 16 01778 g004 550
Figure 4. (a,b) Band structures of Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N. The blue error bar respectively represents the contribution of the d-electrons of Ti and s-electrons of Ge. (c,d) Wave function analyses of Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N are shown in red circles. Blue represents bonding orbitals, and yellow represents anti-bonding orbitals. (e,f) The structure of Ti3N4 (Octahedral coordinates) and Ge3N4 (Tetrahedral coordinates).
Figure 4. (a,b) Band structures of Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N. The blue error bar respectively represents the contribution of the d-electrons of Ti and s-electrons of Ge. (c,d) Wave function analyses of Mg0.125Ti0.125Al0.75N and Mg0.125Ge0.125Al0.75N are shown in red circles. Blue represents bonding orbitals, and yellow represents anti-bonding orbitals. (e,f) The structure of Ti3N4 (Octahedral coordinates) and Ge3N4 (Tetrahedral coordinates).
Materials 16 01778 g004
Table
Table 1. Properties of the e33, C33, d33, and band gap of the 67 dopants considered in this study.
Table 1. Properties of the e33, C33, d33, and band gap of the 67 dopants considered in this study.
GroupChemical FormulaC33 (GPa)e33 (C/m2)d33 (pC/N)Band Gap (eV)
IA(X) + VA/VB(Y)Li0.125As0.125Al0.75N294.3971.5395.2271.026
Li0.125Nb0.125Al0.75N224.5982.2219.8901.809
Li0.125Sb0.125Al0.75N183.1510.1550.8491.234
Li0.125Ta0.125Al0.75N245.2012.2429.1432.177
Na0.125Ta0.125Al0.75N177.6791.7409.7931.950
K0.125Nb0.125Al0.75N258.4510.9613.7171.308
K0.125Ta0.125Al0.75N213.9030.0640.3011.704
Rb0.125Ta0.125Al0.75N222.5890.7043.1651.095
Rb0.125V0.125Al0.75N249.9361.0374.1511.011
IIA(X) + IVA/IVB(Y)Be0.125C0.125Al0.75N346.6051.7494.6271.808
Be0.125Ce0.125Al0.75N271.9922.1157.7761.434
Be0.125Ge0.125Al0.75N350.5461.1953.4083.149
Be0.125Hf0.125Al0.75N288.1431.9856.8883.504
Be0.125Pb0.125Al0.75N326.4511.2243.7481.573
Be0.125Si0.125Al0.75N356.1151.1763.3033.959
Be0.125Sn0.125Al0.75N328.4471.5084.5912.490
Be0.125Ti0.125Al0.75N294.0692.0426.9453.098
Be0.125Zr0.125Al0.75N274.4192.0427.4403.471
Mg0.125C0.125Al0.75N317.8551.6415.1642.604
Mg0.125Ce0.125Al0.75N247.0401.8087.3171.050
Mg0.125Ge0.125Al0.75N314.8391.4924.7402.355
Mg0.125Hf0.125Al0.75N245.9352.2159.0083.124
Mg0.125Pb0.125Al0.75N294.8741.5445.2381.025
Mg0.125Si0.125Al0.75N321.2181.6325.0812.891
Mg0.125Sn0.125Al0.75N304.0801.5455.0802.273
Mg0.125Ti0.125Al0.75N261.1052.4089.2232.744
Mg0.125Zr0.125Al0.75N243.2352.1808.9622.947
Ca0.125Ce0.125Al0.75N253.3721.4845.8581.282
Ca0.125Ge0.125Al0.75N258.3181.5495.9951.677
Ca0.125Hf0.125Al0.75N260.8801.6606.3632.644
Ca0.125Pb0.125Al0.75N252.1451.4405.7120.532
Ca0.125Si0.125Al0.75N291.2831.5955.4772.523
Ca0.125Sn0.125Al0.75N256.7271.6286.3401.549
Ca0.125Ti0.125Al0.75N259.0201.8417.1072.370
Ca0.125Zr0.125Al0.75N219.5111.8998.6502.425
Sr0.125Ge0.125Al0.75N239.6830.1610.6721.509
Sr0.125Hf0.125Al0.75N182.9130.5953.2511.400
Sr0.125Si0.125Al0.75N276.9800.4661.6822.327
Sr0.125Sn0.125Al0.75N257.7220.9503.6871.620
Sr0.125Ti0.125Al0.75N202.5101.4407.1121.597
Sr0.125Zr0.125Al0.75N265.4551.3585.1141.824
Ba0.125C0.125Al0.75N173.1681.2807.3931.644
Ba0.125Ce0.125Al0.75N240.3870.8503.5380.973
Ba0.125Hf0.125Al0.75N217.6070.8363.8411.757
Ba0.125Si0.125Al0.75N278.2750.4441.5961.423
Ba0.125Sn0.125Al0.75N309.3240.5201.6820.382
Ba0.125Ti0.125Al0.75N227.2111.2895.6721.582
Ba0.125Zr0.125Al0.75N165.5560.7454.4970.929
IIIA/IIIB(X) + IIIA/IIIB(Y)B0.125Er0.125Al0.75N262.2482.1128.0522.883
B0.125Ga0.125Al0.75N396.6711.2023.0303.533
B0.125La0.125Al0.75N253.8810.6832.6901.918
B0.125Sc0.125Al0.75N309.8081.8886.0933.005
B0.125Y0.125Al0.75N284.7592.0457.1802.659
Sc0.125Ga0.125Al0.75N300.2261.5435.1413.532
Sc0.125La0.125Al0.75N249.5831.4405.7692.098
Sc0.125Y0.125Al0.75N222.8072.0269.0922.729
Er0.125Ga0.125Al0.75N293.1871.3594.6342.848
Er0.125La0.125Al0.75N273.6221.2294.4901.972
Er0.125Sc0.125Al0.75N225.1941.8778.3372.788
Er0.125Y0.125Al0.75N231.7361.7067.3622.339
In0.125B0.125Al0.75N349.7981.3423.8372.462
In0.125Ga0.125Al0.75N348.9351.2603.6112.844
In0.125Sc0.125Al0.75N281.1141.6245.7782.898
In0.125Y0.125Al0.75N271.0971.4045.1802.318
La0.125Ga0.125Al0.75N270.6191.3685.0562.001
Y0.125Ga0.125Al0.75N306.7061.4184.6232.886
Y0.125La0.125Al0.75N265.5151.4075.2981.950
w-AlN359.8621.4714.0874.056
Sc0.25Al0.75N249.5921.8697.4883.287
Table
Table 2. Resonant characteristics of the resonator based on doped/undoped w-AlN. fs and fp represent resonant frequency and anti-resonant frequency. Keff2 and Qr are calculated by COMSOL software. k332 is calculated according to Equation (1).
Table 2. Resonant characteristics of the resonator based on doped/undoped w-AlN. fs and fp represent resonant frequency and anti-resonant frequency. Keff2 and Qr are calculated by COMSOL software. k332 is calculated according to Equation (1).
Piezoelectric Materialsfs
(GHz)		fp
(GHz)		Qr
(None)		Keff2
(None)		k332
(None)
w-AlN5.2375.3481603.2880.0500.063
B0.125Er0.125Al0.75N4.6964.9451420.6590.1180.143
Be0.125Ce0.125Al0.75N4.7634.9411438.4940.0860.100
Mg0.125Ti0.125Al0.75N4.7075.0101434.5930.1400.177
Sc0.25Al0.75N4.6324.8461407.9900.1040.123
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Yu, X.; Zhu, L.; Li, X.; Zhao, J.; Wu, T.; Yu, W.; Li, W. Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN. Materials 2023, 16, 1778. https://doi.org/10.3390/ma16051778

AMA Style

Yu X, Zhu L, Li X, Zhao J, Wu T, Yu W, Li W. Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN. Materials. 2023; 16(5):1778. https://doi.org/10.3390/ma16051778

Chicago/Turabian Style

Yu, Xi, Lei Zhu, Xin Li, Jia Zhao, Tingjun Wu, Wenjie Yu, and Weimin Li. 2023. "Doping Engineering for Optimizing Piezoelectric and Elastic Performance of AlN" Materials 16, no. 5: 1778. https://doi.org/10.3390/ma16051778

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