Interaction between point defects and vertical inversion domain walls in wurtzite AlN

Technical Summary: Interaction between Point Defects and Vertical Inversion Domain Walls in Wurtzite AlN

Problem Statement
Alloyed aluminum nitride (AlN) compounds, particularly when doped with elements like Sc, B, or Gd, represent a promising class of ferroelectric materials due to their high remanent polarization, wide band gaps, and compatibility with Si substrates. However, their practical application in devices such as FeRAMs and RF components is hindered by large coercive fields ($E_c$) that approach the material's breakdown field. While strategies like strain engineering and co-alloying have been proposed to reduce $E_c$, the fundamental mechanisms governing polarization switching remain debated. Specifically, the role of point defects (vacancies, interstitials, substitutions) in interacting with domain walls (DWs)—which are central to switching kinetics and fatigue—is not fully understood. This study addresses the need to clarify how isolated point defects influence the stability and mobility of vertical inversion domain walls in wurtzite AlN.

Methodology
The authors employed first-principles calculations based on Density Functional Theory (DFT) using the Vienna ab initio Simulation Package (VASP) and the projector augmented-wave (PAW) method. The exchange-correlation energy was treated within the generalized gradient approximation (GGA) using the PBEsol parameterization.

The simulations utilized two supercell configurations:

1. A $4\times4\times3$ bulk supercell for reference calculations.
2. A $10\times4\times3$ supercell containing two equivalent vertical inversion domain walls (DWs) separated by ferroelectric domains of opposite polarization. The DWs were modeled as atomically sharp, electrically neutral, and oriented parallel to the polarization axis ([0001]), consistent with recent experimental evidence.

The study investigated nine specific neutral and charged point defects: two vacancies ($V_N$, $V_{Al}$) and seven substitutions ($X_N$ with $X=O, C$; $X_{Al}$ with $X=B, Si, Sc, Y, La$). The researchers calculated:

• The relative thermodynamic stability of defects at varying distances from the DW.
• The energy barriers ($\omega_i$) associated with DW displacement using Nudged Elastic Band (NEB) calculations, considering both "chain-by-chain" and coherent displacement mechanisms.
• Electronic properties, including Density of States (DOS), to assess the impact on band gaps and leakage currents.

Key Results

• Defect Stability: All studied point defects were found to be energetically more stable at or near the vertical DW compared to the bulk. This stabilization is most pronounced for vacancies ($V_{Al}$ and $V_N$). The authors attribute this primarily to the local reduction of the cation-anion rumpling parameter ($\Delta z$) at the DW (which is proportional to electric polarization). Since the energy cost of weakening ferroelectricity is lower where polarization is already reduced, defects are accommodated more easily. A linear correlation was observed between the energy gain at the DW and the variation in local $\Delta z$.
• Impact on Domain Wall Mobility: The presence of defects significantly alters the energy landscape for DW displacement:
  • Pinning Effects: Most defects, particularly $V_{Al}$ and $V_N$, act as pinning centers. While a $V_N$ defect lowers the initial barrier to switch the specific atomic chain containing it, it increases the barriers for subsequent chains, leading to a net increase in the total energy barrier ($\omega_{tot}$) for DW displacement (e.g., +4.63% for $V_N$ and +51.54% for $V_{Al}$).
  • Facilitation: Some substitutions, such as $Sc_{Al}$ and $Y_{Al}$, were found to lower the total energy barrier, potentially facilitating the initiation of resistive switching.
  • Detrimental Effects: Substitutions like $O_N$ and $B_{Al}$ were found to be particularly detrimental to polarization switching. $O_N$ prevents the formation of intermediate metastable states, effectively locking the DW, while $B_{Al}$ increases the initial switching barrier.
• Electronic Properties: The formation of a DW slightly reduces the band gap energy. The introduction of point defects further modifies the electronic structure:
  • $V_N$ introduces gap states near the valence and conduction band edges, closing the gap locally at the DW (creating a ~250 meV gap).
  • $O_N$ and $Si_{Al}$ substitutions lead to metallization.
  • These modifications suggest that defects at DWs can induce leakage currents, which is detrimental for ferroelectric retention but potentially beneficial for resistive switching applications.

Significance and Claims
The paper claims to provide a systematic theoretical understanding of how point defects interact with vertical inversion domain walls in wurtzite AlN. The authors assert that:

1. The enhanced stability of defects at DWs is driven by the local reduction of electric polarization (rumpling), which lowers the energetic penalty for defect formation.
2. Point defects play a dual role: they can either pin domain walls (increasing coercive fields and potentially degrading switching) or facilitate switching initiation (lowering barriers for specific defects like Sc substitutions).
3. The presence of defects, particularly vacancies and specific substitutions, can induce gap states or metallization, explaining observed leakage currents and degraded ferroelectric properties in real-world samples.
4. The study highlights that while isolated defects have specific effects, the collective behavior of defects in alloyed systems (e.g., AlScN) may lead to different outcomes, suggesting that disorder plays a critical role in the macroscopic properties of these materials.

The authors conclude that controlling point defects is a viable route for tuning coercive fields and that the interplay between defects and DWs is crucial for both preserving ferroelectric properties and enabling applications like resistive switching memories.