中国物理B ›› 2000, Vol. 9 ›› Issue (11): 833-836.doi: 10.1088/1009-1963/9/11/007

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ACCURATE DETERMINATION OF FILM THICKNESS BY LOW-ANGLE X-RAY REFLECTION

于文学1, 杨宁2, 陶琨2, 徐明3, 杨涛3, 刘翠秀3, 麦振洪3, 赖武彦3   

  1. (1)Department of Materials Science, Jilin University, Changchun 130023, China; (2)Department of Materials Science, Tsinghua University, Beijing 100083, China; (3)Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2000-03-03 修回日期:2000-07-03 出版日期:2000-11-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the the Foundation for Key Research Programs of the China 9th 5-year Plan, from Chinese Academy of Sciences (Grant No. KJ951-AL-401) and the National Natural Science Foundation of China (Grant No. 19890310).

ACCURATE DETERMINATION OF FILM THICKNESS BY LOW-ANGLE X-RAY REFLECTION

Xu Ming (徐明)a, Yang Tao (杨涛)a, Yu Wen-xue (于文学)b, Yang Ning (杨宁)c, Liu Cui-xiu (刘翠秀)a, Mai Zhen-hong (麦振洪)a, Lai Wu-yan (赖武彦)a, Tao Kun (陶琨)c   

  1. a Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, China;  b Department of Materials Science, Jilin University, Changchun 130023, China;  c Department of Materials Science, Tsinghua University, Beijing 100083, China
  • Received:2000-03-03 Revised:2000-07-03 Online:2000-11-15 Published:2005-06-12
  • Supported by:
    Project supported by the the Foundation for Key Research Programs of the China 9th 5-year Plan, from Chinese Academy of Sciences (Grant No. KJ951-AL-401) and the National Natural Science Foundation of China (Grant No. 19890310).

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摘要： A modified Bragg law for straightforward determining the film thickness by low-angle X-ray reflection was derived based on the geometrical optical theory. We showed that this modified Bragg law and its inference formulae could be used to accurately determine the thickness of the monolayer or multilayer film. Furthermore, the modified Bragg law for determining the superlattice period presented earlier by others can be derived from the above modified Bragg law. The similar inference formulae were also given. The precision in determining the film thickness and/or superlattice period by the above formulae was discussed.

Abstract: A modified Bragg law for straightforward determining the film thickness by low-angle X-ray reflection was derived based on the geometrical optical theory. We showed that this modified Bragg law and its inference formulae could be used to accurately determine the thickness of the monolayer or multilayer film. Furthermore, the modified Bragg law for determining the superlattice period presented earlier by others can be derived from the above modified Bragg law. The similar inference formulae were also given. The precision in determining the film thickness and/or superlattice period by the above formulae was discussed.

Key words: film, modified Bragg law, X-ray reflection

中图分类号:  (X-ray reflectometry (surfaces, interfaces, films))

  • 61.05.cm
68.55.-a (Thin film structure and morphology) 68.65.Ac (Multilayers) 68.65.Cd (Superlattices)