In this paper, a model of etch rates of crystallographic planes of sapphire based on step flow mechanism is proposed, which explains the relationship between etch rates of and atomic structures of crystallographic planes accurately. By analyzing the atomic structure of sapphire, a method of identifying step-terrace structures of crystallographic planes is established. Step-terrace structures of crystallographic planes of sapphire can be composed of crystal units (cluster atoms) of terrace types, edge-terrace types and step types by different combinations. Etch rates of crystallographic planes of sapphire can be expressed as functions of removal rates of crystal units. Thus, the relationship between etch rates and atomic structures of crystallographic planes of sapphire is established. The values of removal rates of crystal units can be obtained by the established matrix equations of removal rates of crystal units and experimental etch rates of key crystallographic planes. Under the different experimental conditions, high coincidence between etch rates calculated by the model and experimental etch rates in the $ < -1\,\,1\,\,0\,\,0>$ and $ < 1\,\,1-2\,\,0>$ crystallographic zones is achieved. It proves the validity of the proposed model. [2020-0089]

中文翻译：

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基于阶梯流动机制的蓝宝石晶面蚀刻速率模型

本文提出了一种基于阶梯流动机制的蓝宝石晶面刻蚀速率模型，准确解释了晶面刻蚀速率与原子结构之间的关系。通过分析蓝宝石的原子结构，建立了一种鉴定晶面阶梯状结构的方法。蓝宝石晶面的阶梯-阶梯结构可以由阶梯型、边缘阶梯型和阶梯型的晶体单元（簇原子）通过不同的组合构成。蓝宝石晶面的蚀刻速率可以表示为晶体单元去除速率的函数。因此，建立了蚀刻速率与蓝宝石晶面原子结构之间的关系。晶体单元去除率的数值可以通过建立的晶体单元去除率矩阵方程和关键晶面的实验蚀刻率得到。在不同的实验条件下，模型计算的刻蚀率与实验刻蚀率在$ < -1\,\,1\,\,0\,\,0>$和$<1\,\的高度吻合，实现了 1-2\,\,0>$ 晶区。证明了所提出模型的有效性。[2020-0089] 证明了所提出模型的有效性。[2020-0089] 证明了所提出模型的有效性。[2020-0089]