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arXiv 2402.09354cond-mat.mtrl-sci
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通过劈裂缺陷研究$β$-Ga$_2$O$_3$中的Ga间隙和空位扩散:基于主扩散方程的直接方法

Investigation of Ga interstitial and vacancy diffusion in $β$-Ga$_2$O$_3$ via split defects: a direct approach via master diffusion equations

Channyung Lee, Michael A. Scarpulla, Elif Ertekin

AI总结:

本研究基于第一性原理与主扩散方程直接求解,预测了$β$-Ga$_2$O$_3$中Ga间隙与空位的3D扩散率张量,发现3-劈裂缺陷使两者沿$c$轴扩散最快,且Ga自扩散主要由高浓度的V$_{Ga}^{3-}$介导。

摘要:

单斜$β$-Ga$_2$O$_3$的低对称性导致了复杂的本征缺陷,例如在多个晶格位点间发生劈裂的Ga空位。这些缺陷促成了快速且各向异性的Ga扩散,然而其复杂性使得理解主导扩散机制极具挑战。在此,我们通过第一性原理及直接求解主扩散方程,预测了Ga间隙(Ga${_i^{3+}}$)和空位(V${_{Ga}^{3-}}$)的3D扩散率张量。我们首先探究了构型复杂的“$N$-劈裂”Ga间隙和空位的最大程度。在识别出主导的低能缺陷后,我们枚举了连接各缺陷构型的所有可能基本跃迁,包括间隙跃迁。跃迁势垒通过微动弹性带模拟获取。最后,利用(i)缺陷构型及其能量和(ii)连接它们的跃迁势垒的综合集合,我们为Ga${_i^{3+}}$和V${_{Ga}^{3-}}$构建了主扩散方程。求解这些方程得出了Onsager输运系数,即Ga${_i^{3+}}$和V${_{Ga}^{3-}}$的3D扩散率张量$D_{{Ga}_i}$和$D_{V_{Ga}}$的各个分量。它进一步揭示了沿所有晶体学方向的活跃扩散路径。我们发现,由于3-劈裂缺陷沿$c$轴桥接了相邻晶胞并引导扩散物质绕过高能瓶颈,Ga${_i^{3+}}$和V${_{Ga}^{3-}}$的扩散均在沿$c$轴方向最快。尽管孤立的Ga${_i^{3+}}$比孤立的V${_{Ga}^{3-}}$扩散得更快,但由于在大多数热力学环境下V$_{Ga}^{3-}$缺陷浓度更高,Ga的自扩散主要由V$_{Ga}^{3-}$介导。

英文摘要:

The low symmetry of monoclinic $β$-Ga$_2$O$_3$ leads to elaborate intrinsic defects, such as Ga vacancies split amongst multiple lattice sites. These defects contribute to fast, anisotropic Ga diffusion, yet their complexity makes it challenging to understand dominant diffusion mechanisms. Here, we predict the 3D diffusivity tensors for Ga interstitials (Ga${_i^{3+}}$) and vacancies (V${_{Ga}^{3-}}$) via first principles and direct solution of the master diffusion equations. We first explore the maximum extent of configurationally complex ''$N$-split'' Ga interstitials and vacancies. With dominant low-energy defects identified, we enumerate all possible elementary hops connecting defect configurations to each other, including interstitialcy hops. Hopping barriers are obtained from nudged elastic band simulations. Finally, the comprehensive sets of (i) defect configurations and their energies and (ii) the hopping barriers that connect them are used to construct the master diffusion equations for both Ga${_i^{3+}}$ and V${_{Ga}^{3-}}$. The solution to these equations yields the Onsager transport coefficients, i.e. the components of the 3D diffusivity tensors $D_{{Ga}_i}$ and $D_{V_{Ga}}$ for Ga${_i^{3+}}$ and V${_{Ga}^{3-}}$, respectively. It further reveals the active diffusion paths along all crystallographic directions. We find that both Ga${_i^{3+}}$ and V${_{Ga}^{3-}}$ diffusion are fastest along the $c$-axis, due to 3-split defects that bridge neighboring unit cells along the $c$-axis and divert diffusing species around high-energy bottlenecks. Although isolated Ga${_i^{3+}}$ diffuse faster than isolated V${_{Ga}^{3-}}$, self-diffusion of Ga is predominantly mediated by V$_{Ga}^{3-}$ due to the higher V$_{Ga}^{3-}$ defect concentration under most thermodynamic environments.

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