title: Integration method for directly analyzing interface statistics of periodic multilayers from X-ray scattering.
abstract: An integration method is demonstrated for directly determining the average interface statistics of periodic multilayers from the X-ray scattering diagram. By measuring the X-ray scattering diagram in the out-of-plane geometry and integrating the scattered intensity along the vertical momentum transfer qz in an interval, which is decided by the thickness ratio Γ (ratio of sublayer's thickness to periodic thickness), the cross-correlations between different interfaces are canceled and only the autocorrelations are reserved. Then the multilayer can be treated as a `single interface' and the average power spectral density can be obtained without assuming any vertical correlation model. This method has been employed to study the interface morphology of sputter-deposited W/Si multilayers grown at an Ar pressure of 1-7 mTorr. The results show an increase in vertical correlation length and a decrease in lateral correlation length with increased Ar pressure. The static roughness exponent α = 0 and dynamic growth exponent z = 2 indicate the Edwards-Wilkinson growth model at an Ar pressure of 1-5 mTorr. At an Ar pressure of 7 mTorr, α = 0.35 and z = 1.65 indicate the Kardar-Parisi-Zhang growth model.
authors.affiliation: MOE Key Laboratory of Advanced Micro-structured Materials, Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092, People's Republic of China.
authors.forename: Haochuan
authors.initials: H
authors.lastname: Li
authors.affiliation: MOE Key Laboratory of Advanced Micro-structured Materials, Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092, People's Republic of China.
authors.forename: Jingtao
authors.initials: J
authors.lastname: Zhu
authors.affiliation: MOE Key Laboratory of Advanced Micro-structured Materials, Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092, People's Republic of China.
authors.forename: Zhanshan
authors.initials: Z
authors.lastname: Wang
authors.affiliation: MOE Key Laboratory of Advanced Micro-structured Materials, Institute of Precision Optical Engineering, Department of Physics, Tongji University, Shanghai 200092, People's Republic of China.
authors.forename: Hong
authors.initials: H
authors.lastname: Chen
authors.affiliation: Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, People's Republic of China.
authors.forename: Yuzhu
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, People's Republic of China.
authors.forename: Jie
authors.initials: J
authors.lastname: Wang
keywords: X-ray scattering; dynamic scaling; interface morphology; multilayer; power spectral density