Enhanced Piezoelectric Response of AlN via CrN Alloying

Since AlN has emerged as an important piezoelectric material for a wide variety of applications, efforts have been made to increase its piezoelectric response via alloying with transition metals that can substitute for Al in the wurtzite lattice. We report on density functional theory calculations of structure and properties of the ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ system for Cr concentrations ranging from zero to beyond the wurtzite-rocksalt transition point. By studying the different contributions to the longitudinal piezoelectric coefficient, we propose that the physical origin of the enhanced piezoelectricity in ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ alloys is the increase of the internal parameter $u$ of the wurtzite structure upon substitution of Al with the larger Cr ions. Among a set of wurtzite-structured materials, we find that ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ has the most sensitive piezoelectric coefficient with respect to alloying concentration. Based on these results, we propose that ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ is a viable piezoelectric material whose properties can be tuned via Cr composition. We support this proposal by combinatorial synthesis experiments, which show that Cr can be incorporated in the AlN lattice up to 30% before a detectable transition to rocksalt occurs. At this Cr content, the piezoelectric modulus $d_{33}$ is approximately 4 times larger than that of pure AlN. This finding, combined with the relative ease of synthesis under nonequilibrium conditions, may position ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ as a prime piezoelectric material for applications such as resonators and acoustic wave generators.

Figure 1

Schematics of a cation sublattice of a ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ alloy. Al (Cr) sites are shown as gray (green) spheres. At a given Cr concentration, the Cr sites of each configuration have a different and random spin initialization with zero total spin in order to capture the paramagnetic state.

Figure 2

(a) DFT-calculated mixing enthalpies of the wurtzite and rocksalt phases of ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ as functions of the Cr concentration. (b) Calculated mixing enthalpies for several wurtzite-based nitride alloys grown experimentally.

Figure 3

The 18 components of the piezoelectric tensor calculated for SQS supercells with different spin configurations and compositions of Cr. At each Cr composition, the open circles represent the data for each SQS cell used, while the red solid circles represent the average values across the random initial configurations.

Figure 4

Variation of (a) $e_{33}^{\text{total}}$, (b) the $e_{33}^{\text{clamped}}$ component of $e_{33}$, (c) $e_{33}^{\text{nonclamped}}$, (d) the 33 component of the Born effective charge tensor, (e) the strain sensitivity of the internal parameter, and (f) the $c/a$ ratio with respect to the Cr addition.

Figure 5

(a) Variation of the internal parameter, $u$, with the Cr addition. (b) Crystal structure of wurtzite AlN.

Figure 6

Comparison of change in $e_{33}$ with the addition of different transition metals for the $x\le 25\%$ regime.

Figure 7

Variation of (a) $C_{33}$ and (b) $d_{33}$ for several nitride-based wurtzite alloys.

Figure 8

Variation of $e_{33}$ as a function of Cr concentration for wurtzite phase alloys of up to 50%.

Figure 9

(a) Representative TEM image and (b) an EDS line scan of an ${\mathrm{Cr}}_x{\mathrm{Al}}_{1-x}\mathrm{N}$ film cross section containing approximately 7% Cr, confirming the incorporation of Cr into the wurtzite solid solution. EDS data are collected along the dashed black line shown in (a).

Figure 10

X-ray diffraction patterns of the thin-film combinatorial libraries plotted against the film composition, with comparison to the patterns for wurtzite (Wz) [43] and rocksalt (Rs) [44] structures. For alloying content $x<30\%$, the films grow predominantly with the wurtzite structure. At higher Cr concentrations, $x>30\%$, both the rocksalt and wurtzite phases are detected, and the wurtzite exhibits a degraded texture. No films are produced with compositions in regions where no intensity is shown.