Investigation of Elastic Properties of Sc Doped AlN: A First principles and Experimental Approach ^†

Abstract

Aluminum Nitride (AlN) is a promising piezoelectric material for microelectromechanical systems owing to its attractive physical and chemical properties and CMOS compatibility. It has a moderate piezo response compared to its rival material bound to its wide application. This obstacle can be overcome by doping or alloying. Sc alloying increases the piezo response of AlN up to four-fold; it also increases the electromechanical coupling coefficient, which is a prominent figure of merit for any MEMS device application. Sc doping induces elastic softening in wurtzite AlN, enhances polarization, and increases piezoelectric constants. However, the possibility of phase separation at higher Sc concentrations, and the wurtzite phase of AlN, which is responsible for piezoelectricity, becomes negligible. Therefore, knowing the optimum concentration of Sc for device applications is necessary. In this work, using density functional theory, we calculated the lattice parameter, band and density of states along with the physical properties such as Young’s modulus, the bulk modulus, Poisson’s ratio, and elastic constants of pristine AlN and Sc doped AlN. The DFT calculations show that the geometrical optimized lattice parameters agree with the literature. As a function of increased Sc concentration, the calculated Young’s modulus and elastic constants decrease, indicating a decrease in hardness and elastic softening, respectively. Meanwhile, the bulk modulus and Poisson’s ratio increase with an increase in Sc concentration, representing an increase in the crystal cell parameters and elastic deformation. AlN and AlScN thin films were grown on Si (111) substrate using magnetron sputtering to study the structural properties experimentally. The deposited films show the required c-axis (002) preferential crystallographic orientation. The XRD peaks of Sc doped AlN thin films have shifted to a lower angle than pristine AlN, indicating elastic softening/tensile stress in grown thin films. So, from our observation, we can conclude that Sc doping induces elastic softening in AlN and deposited films have a preferential crystallographic orientation that can be applied in MEMS devices.

1. Introduction

Wurtzite Aluminum nitride (AlN) is one of the most promising piezoelectric materials owing to its unique physical and chemical properties [1,2,3]. Its compatibility with CMOS (Complementary Metal-Oxide-Semiconductor) technology enables the monolithic integration of PEHs into ICs (Integrated Circuits) [4,5]. Therefore, the growth and assessment of piezoelectric properties of AlN at CMOS-compatible temperatures with high piezoelectric response is essential [6]. Lead Zirconate Titanate (PZT)-based materials are superior in Piezoelectric Energy Harvesters (PEHs) but have disadvantages such as lead-based toxicity, instability at high temperatures, and CMOS incompatible processing temperature [7,8]. Although AlN has moderate piezoelectric constant, it is eco-friendly and, most importantly, has a good figure of merit ($=e_{31}^2/{\mathrm{Ɛ}}_0{\mathrm{Ɛ}}_r$, where e_ij is the piezoelectric co-efficient and ${\mathrm{Ɛ}}_0$ and ${\mathrm{Ɛ}}_r$ are the permittivity of vacuum and relative permittivity, or dielectric constant, respectively) compared to PZT-based materials [9]. Recently, it was shown that Sc alloying in AlN improves the piezo response four-fold and that one of the critical factors that results in enhanced piezo response is elastic softening [10]. Sc doping induces elastic softening in w-AlN, enhancing polarization, thereby increasing the piezoelectric constants [11,12]. In this direction, the proposed work aims to correlate the effect of Sc alloying in AlN and elastic softening through first principles calculations and its verification through experiments.

2. Materials and Methods

2.1. Computational Method

Density Functional Theory (DFT) is a first principles study employed to predict the different properties of materials through computations. The present work employs the Kohn–Sham equation to solve plane wave basis sets using Perdew–Burke–Ernzerhof (generalized gradient approximation) exchange–correlation and hence to predict materials properties like electronegativity, bandgap, lattice parameters, density of states, dielectric constants, elastic constants, etc. We used Quantum Espresso codes [13,14,15] to predict the properties such as structural, elastic, and density of states for pristine AlN and Sc alloyed AlN. We have employed a supercell (2 × 2 × 2) containing 32 atoms for structural optimization, Density of States (DOSs), and an elastic constant calculation. Initially, we performed relax calculations to optimize atomic positions; later, we performed variable cell relax calculations for obtaining the lattice parameters, and then optimized parameters were used to calculate the projected density of states for all atomic orbitals involved in bonding. Then, elastic properties were predicted by applying variable strain to the relaxed structures. The irreducible elastic tensor components corresponding to wurtzite structure C₁₁, C₁₂, C₁₃, C₃₃, C_31, and C₄₄ were computed from specific strain matrices from which constants are calculated.

2.2. Experiments

To deposit AlN and dope Sc into AlN, we have used magnetron sputtering of Al and Sc targets in a co-sputtering geometry. During the co-sputtering, the concentration of the individual target material in the deposited films can be controlled by power applied to each target. In our experiments, we have fixed Al target power and varied Sc target power to obtain different Sc concentrations in the deposited films. Before each sputtering run, the sputter chamber (Excel Instruments, Maharashtra, India) was evacuated to base pressure below 6 × 10⁻⁷ mbar using a turbo molecular pump (Pfeiffer, Emmeliusstraße, Germany).

During sputtering, the sputtering parameters, such as sputtering power, temperature, pressure, and gas flow rate, played a significant role in sample preparation and the crystal quality. Initially, we grew AlN thin films at different sputtering powers and with other sputtering parameters, we have chosen the sputtering parameters that yielded a high amount of c-axis orientation films. Later, AlScN thin films were deposited with a fixed nitrogen-to-argon ratio of 1:3, and an Sc power that varied from 50 W to 60 W by keeping other sputtering parameters constant. The sputtering parameter details are given in

Table 1. Sputtering parameters for sputtered AlScN thin-films on Si (111) substrates.

Parameters	Value
Targets	Aluminum (99.999%), Scandium (99.9%)
Base pressure	1 × 10−6 mbar
Sputtering Pressure	6.6 × 10−3 mbar
Sputtering temperature	300 °C
Argon	15 sccm (99.999%)
Nitrogen	5 sccm (99.999%)
Sputtering power	Al-175 W, Sc-50 W & 60 W

.

3. Results and Discussion

3.1. Computations

The relaxed lattice parameters a and c for the wurtzite structure are listed in

Table 2. Calculated lattice parameter and elastic tensor components.

Composition Al1−xScxN	c-Axis (Å)	c/a	C11 GPa	C12 GPa	C13 GPa	C33 GPa	C44 GPa
AlN (x = 0)	5.062 (4.98)	1.6118 (1.60)	374.2 (376.0)	123.5 (129.0)	92.0 (98.0)	357.7 (353.0)	110.7 (113.0)
AlScN (x = 0.6)	5.083	1.6115	368.7	141.7	114.5	345.1	103.2
AlScN (x = 0.25)	5.142	1.6138	352.4	203.4	176.2	332.1	83.8

The values in the bracket refer to those found in https://next-gen.materialsproject.org/ (accessed on 25 July 2023).

, and the values are in agreement with the literature [16]. For a stable wurtzite structure, the c/a ratio should be maintained at 1.6. We observed that the ratio was maintained for both AlN and ScAlN. The total Density of States (DOSs) gives the number of electrons that occupy a particular energy level at different allowed states and the Partial Density of States (PDOSs) gives the contribution of each valence orbital to the total DOSs of the material. By calculating the DOSs and PDOSs of a material, one can predict the nature of the bonding, hybridization, and Fermi level arrangement with respect to the valence band and conduction band.

The DOSs and PDOSs of AlN and Sc doped the AlN for different Sc concentrations (6% and 25%) were calculated, as seen in Figure 1. As one can see from the PDOSs, with increased Sc concentration, the Fermi level is pushed towards the conduction band, indicating that the probability of finding electrons in the conduction band reduces the energy band gap of the material. The calculated energy band gap of AlN and Al_0.75 Sc_0.25 N was found to be 5.7 eV and 3.5 eV, respectively, equal to experimental values reported in the literature [17].

In Figure 1, we can observe that the s and p orbitals of Al and N are mainly employed in the hybridization to form AlN, while in Figure 2 and Figure 3, we can see the involvement of the d-orbital of Sc along with that of the s and p orbitals of Al, and N attributing the effective substitution of Al by Sc in a host material.

From the group theory of symmetry elements, wurtzite AlN has five irreducible elastic tensor components: C₁₁, C₁₂, C₁₃, C₃₃, and C₄₄. The calculated elastic tensor for AlN is presented, and for better understanding, elastic tensor components of pristine AlN and Sc doped AlN are tabulated in

Table 3. Elastic-constant-derived properties of Al_1-xSc_xN.

Composition Al1-xScxN	Bulk Modulus GPa	Young’s Modulus GPa	Shear Modulus GPa	Poisson’s Ratio
AlN (x = 0)	191.2 (195.0)	303.0 (306.0)	122.5 (122.2)	0.236 (0.24)
AlScN (x = 0.6)	184.1	282.5	111.4	0.267
AlScN (x = 0.25)	178.2	217.1	80.5	0.348

The values in the bracket refer to that found in https://next-gen.materialsproject.org/ (accessed on 25 July 2023).

. The calculated elastic tensor obtained for pristine AlN is given below (the values are in GPa).

$$\left(\begin{array}{cccccc}374.2& 123.5& 92.0& 0.00& 0.00& 0.00\\ 123.5& 374.2& 92.0& 0.00& 0.00& 0.00\\ 90.7& 90.7& 357.7& 0.00& 0.00& 0.00\\ 0.00& 0.00& 0.00& 110.7& 0.00& 0.00\\ 0.00& 0.00& 0.00& 0.00& 110.7& 0.00\\ 0.00& 0.00& 0.00& 0.00& 0.00& 125.3\end{array}\right)$$

From the elastic tensor, the Bulk modulus, Young’s modulus, shear modulus, and Poison’s ratio have been tabulated in Table 3. One can observe from the table that, as the Sc concentration increased in Al_1−xSc_xN, the bulk modulus decreased, which accounts for the increase in the overall compressibility of the cell. The hardness of the material or resistance to compression is denoted by Young’s modulus of the material. Here, as the Sc concentration increases, Young’s modulus decreases, indicating the material is undergoing elastic softening, which is favorable for enhancing the piezo response. A similar observation was reported in the literature [18,19]. Poisson’s ratio increases with Sc concentration, and it has a positive value due to tensile deformation in the material. So, one can conclude that all the elastic properties of the pristine AlN and Sc doped AlN show that the material is undergoing tensile deformation, which induces elastic deformation.

3.2. Experiments

The grown AlN and AlScN thin films have a thickness of 1 micron. To study the structural properties of the grown films, an X-ray diffraction characterization was carried out using a Rigaku Ultima 4 with a 1°/min scan rate. Wurtzite AlN has (002) (c-axis orientation plane) characteristic peaks around 36.05° obtained from JCPDS file no: 96-900-8861. We used Bragg’s law, the Debye Scherrer equation, and its derived equations to calculate the lattice parameters, crystallite size, and microstrain of the deposited films. The calculated parameters mentioned above are listed in

Table 4. Structural parameters obtained from XRD data.

Sample	Power (W)	2 Theta (°)	FWHM (°)	c-Axis (Å)	Crystallite Size (nm)	Micro Strain (10−3)
AlN	Al-175	36.06	0.34	0.497	24.27 ± 1.45	4.61 ± 0.28
AlScN 1	Al-175 Sc-50	35.59	0.40	0.504	20.82 ± 1.25	5.44 ± 0.33
AlScN 2	Al-175 Sc-60	35.63	0.27	0.503	30.91 ± 1.85	3.66 ± 0.22

.

The XRD plots show that all the pristine and Sc doped AlN thin films show preferential orientation. The FWHM of (002) initially tend to increase with Sc doping; however, for the increased Sc concentration, the lowest FHWM was observed, indicating the improvement in the crystallinity upon doping. One can observe from Figure 4 that in both Sc doped samples (002), the peak shift toward the lower angle indicates an increase in the c-axis and tensile stress in the films compared to the pristine sample. This accounts for the elastic softening in the films.

We have carried out an Energy Dispersive X-ray (EDAX) analysis to quantitatively confirm the Sc and Al elemental composition in the films (see Figure 5). The Sc concentration in the AlScN1 and AlScN2 samples are 22.01 and 25.65 atomic %, respectively. The variation of Sc concentration with Sc power is not a linear relation. We have also carried out elemental mapping to confirm the absence of Sc agglomeration. Figure 5 shows the elemental mapping for 25% of Sc concentration, and similar results were also obtained for 22.01% Sc concentration.

4. Conclusions

We have calculated the elastic stiffness tensor for AlN and Sc doped AlN through DFT. The obtained elastic properties are in agreement with the literature. We have grown AlN and Sc doped AlN thin films by magnetron sputtering to aid the obtained results. The deposited films show a required preferential orientation along c-the axis (002). From both the first principles and experimental studies, we have observed that Sc alloying in AlN undergoes tensile deformation as a consequence of DFT studies. Young’s modulus reduced from 303.0 GPa to 217.1 GPa, and the Bulk modulus decreased from 191.2 GPa to 178.2 GPa for AlN and Al_0.75 Sc_0.25 N, respectively. From the experimental results for the AlN- and Sc-doped AlN thin films, the XRD peaks corresponding to (002) planes are shifted to lower 2$\mathsf{\theta }$ values. The overall result is aiding to induce elastic softening. The lower FWHM values of the grown films indicate good crystallinity, and the deposited films have preferential crystallographic orientation, which can be used for better application in piezoelectric-energy-harvesting devices in the future.