Reciprocal-space formulation and prediction of misfit accommodation in rigid and strained epitaxial systems
作者:Max W. H. Braun、Jan H. Van Der Merwe
DOI:10.1007/s11661-002-0370-4
日期:2002.8
Geometrical properties form a key aspect of any description of heteroepitaxial systems in which orientation, symmetry, and lattice parameters differ. An energetically founded epitaxial criterion, which is geometric in nature, for matching at a planar interface is derived from a generalization of the Frank-van der Merwe theory and the rigid models introduced by Reiss and van der Merwe. The criterion is most naturally formulated in reciprocal space as the matching of overgrowth and substrate reciprocal lattice vectors and is visualized with a construction analogous to the Ewald construction. Structure factors are introduced and account for rigid translations and the nonprimitive nature of substrate and overgrowth surface unit cells. This article focuses on the derivation of the epitaxial criterion and its consequences as a basis of a description of epitaxial configurations, pseudomorphism, and the parameters of dislocation or misfit vernier arrays, in terms of crystallographic conventions. The strength of the description is its general nature, as it is general and applicable to any combination of crystal symmetries or mismatch and can be used to predict, or interpret, interfacial structure.
几何特性在任何异质外延系统的描述中都是一个关键方面,其中方向、对称性和晶格参数各不相同。本文从Frank-van der Merwe理论的推广和Reiss与van der Merwe引入的刚性模型出发,推导出了一个基于能量的、本质上是几何性质的外延准则,用于平面界面的匹配。该准则最自然地以倒空间形式表述,即外延生长层和衬底的倒易晶格矢量匹配,并通过类似于Ewald构造的构建方法进行可视化。本文引入结构因子,考虑刚性平移以及衬底和外延生长层表面单胞的非原始性质。文章重点讨论了外延准则的推导及其后果,并将其作为描述外延结构、假同晶以及位错阵列或失配角尺阵列参数的基础,从晶体学的角度出发。该描述的优点在于其普遍性,因为它适用于任何晶体对称性或失配的组合,并可用于预测或解释界面结构。