We present a continuum model of ion-induced surface patterning. The model incorporates the atomic processes of sputtering, re-deposition and surface diffusion, and is shown to display the generic features of the damped Kuramoto-Sivashinsky (KS) equation of non-linear dynamics. Linear and non-linear stability analyses of the evolution equation give estimates of the emerging pattern wavelength and spatial symmetry. The analytical theory is confirmed by numerical simulations of the evolution equation with the Fast Fourier Transform method, where we show the influence of the incident ion angle, flux, and substrate surface temperature. It is shown that large local geometry variations resulting in quadratic non-linearities in the evolution equation dominate pattern selection and stability at long time scales.

中文翻译：

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离子诱导的表面构图的稳定性和对称性

我们提出了离子诱导的表面图案的连续模型。该模型结合了溅射，再沉积和表面扩散的原子过程，并显示出阻尼Kuramoto-Sivashinsky（KS）非线性动力学方程的一般特征。演化方程的线性和非线性稳定性分析提供了新兴图案波长和空间对称性的估计。通过使用快速傅立叶变换法对演化方程进行数值模拟，可以证实该分析理论，其中我们展示了入射离子角，通量和衬底表面温度的影响。结果表明，较大的局部几何变化会导致演化方程中出现二次非线性，从而在长时间尺度上支配了模式选择和稳定性。