蓝宝石表面形貌的功率谱与分形特征分析

摘要

The surface morphology of the sapphire wafer has been analyzed by 2D power spectrum and correlation dimension of fractal theory.The application of power spectrum calculation by 2D FFT (Fast Fourier Transform) in the surface morphology of sapphire has been introduced;phase space was reconstructed through time delay technology and the correlation dimension of the surface morphology of sapphire was calculated by G-P algorithm.The topographic characteristics of the original surface,processed surface and individual sampling length of sapphire were analyzed through experiment by 2D power spectrum and correlation dimension.Result shows that the surface morphology of sapphire can be characterized by 2D power spectrum and correlation dimension.It avoid the shortcoming of the traditional characterization parameter which contains only information on the vertical direction and can not accurately characterize the surface morphology of the entire sapphire wafer.This type of characterization method has the advantages of being accurate,convenient and informative compared to the traditional methods.%运用二维功率谱和分形理论的关联维数分析了蓝宝石晶片的表面形貌特征.介绍了利用二维快速傅立叶变换计算二维功率谱在蓝宝石表面形貌中的应用方法;通过时间延迟技术重构相空间,利用G-P算法计算了蓝宝石表面形貌的关联维数.分别利用二维功率谱和关联维数对蓝宝石的原始表面、加工后表面和单个取样长度的形貌特征进行了实验分析.结果表明:二维功率谱和关联维数能够表征蓝宝石表面形貌,且克服了传统的表征参数只包含有垂直方向上的信息而不能准确表征整个蓝宝石晶片表面形貌特征的缺点,它比传统的表面形貌表征方法具有准确、便捷和信息量大等优势.