First-principles study of the phase competition, mechanical and piezoelectric properties of pseudo-binary (SiC)(AlN) alloy

TL;DR

The paper addresses designing piezoelectric materials with a favorable balance between electromechanical response and other properties by studying the pseudo-binary $(\mathrm{SiC})_{1-x}(\mathrm{AlN})_x$ alloy with first-principles methods. It applies First-Principles Random Structure Sampling (FPRSS) to identify phase competition among wurtzite, zincblende, and rhombohedral structures, uses Special Quasi-random Structures (SQS) to model random alloys and evaluate mixing thermodynamics, and computes stiffness, dielectric, and piezoelectric tensors for the wurtzite phase across compositions via DFPT and finite-difference methods. Key findings show wurtzite is thermodynamically favored for most compositions, with a pronounced peak in the piezoelectric constant $d_{33}$ near $x \approx 0.875$ and a modest increase in the longitudinal sound speed $v_{l,z}$ around $x=0.5$, highlighting a tunable trade-off for bulk acoustic wave (BAW) filter applications. The work provides composition-specific design guidance and delivers full tensor data to support device-level optimization of AlN-SiC piezoelectrics.

Abstract

The ongoing search for new piezoelectric materials offering adequate balance between piezoelectric response and other application-relevant properties has lead to the investigation of various alloy systems. In this work we study the alloy of the widely used AlN with SiC for their relative abundance, current use in other electronics applications and expected phase competition between wurtzite and other polymorphs, the kind of which has lead to some of the most interesting results notably between AlN and ScN. Here the pseudo-binary (SiC)(AlN) alloy is studied from first-principles over the entire composition range. Relevant crystalline phases are identified using the First-Principles Random Structure Sampling approach which, in accordance with previous bulk experiments, finds wurtzite, zincblende and rhombohedral phases to be the only statistically relevant phases of the alloy. Further study of these phases is done through Special Quasi-random Structures (SQS) and, in the case of the wurtzite phase, predictions of the stiffness, piezoelectric and dielectric tensors. Analysis of these tensors is done through the scope of a Bulk AcousticWave (BAW) filter application, where trends and trade-offs between the c-axis acoustic velocity and piezoelectric response enable identification of relevant compositions.

Figures (5)

• Figure 1: An example of a 128 atom (SiC)$_{0.125}$(AlN)$_{0.875}$ SQS relaxed using the first-principles methods described in Section \ref{['sec:methods']}. Light blue, blue, white and brown spheres represent Al, Si, N and C atoms, respectively.
• Figure 2: Space group resolved thermodynamic density of states of the (SiC)$_{1-x}$(AlN)$_{x}$ alloy for $x=0.25$, $0.50$ and $0.75$. Each plot is derived from $\sim5000$ structures obtained from random structure sampling. Groups of structures with the same underlying/parent structure (see Section \ref{['ssec:methods_FPRSS']} for details) are designated by their parent-structure space group numbers and are ordered in ascending (minimal) total energy in each legend. For clarity low symmetry structures (space group #$<10$) have been grouped together. For better visualization, a Gaussian broadening of 0.005 eV has been applied to the data.
• Figure 3: Density and mixing enthalpy evolution over the entire range of the pseudo-binarry (SiC)$_{1-x}$(AlN)$_{x}$ alloy using 128 atoms SQSs in both Wurtzite (orange) and Zinc Blende (blue) phases and 144 atoms SQSs for the 9R phase.
• Figure 4: Evolution of lattice parameters $a$ and $c$ as well as the Isotropic Young's modulus and Poisson's ratio of the Wurtzite phase of the pseudo-binary (SiC)$_{1-x}$(AlN)$_{x}$ alloy over compositions. Experimental data taken from Lubis et al.alloy_3 and Rafaniello et al.alloy_5.
• Figure 5: Wurtzite pseudo-binary alloy (SiC)$_{1-x}$(AlN)$_{x}$ composition dependance of the longitudinal speed of sound along the $c$ axis (in green) and of the piezoelectric strain constant $d_{33}$ as defined in Section \ref{['ssec:methods_mecha_props']} (in blue). Inset shows the evolution of the electromechanical coupling coefficient $k^{2}_{33}$. Errorbars show maximal and minimal values of the sample while markers are averages. Complete stiffness, piezoelectric stress and dielectric tensors can be found in supplementary information