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Download Characterization of Amorphous and Crystalline Rough Surface: by Yiping Zhao PDF

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By Yiping Zhao

The constitution of a development or an etch entrance on a floor is not just a subject matter of significant curiosity from the sensible perspective but additionally is of basic clinical curiosity. quite often surfaces are created less than non-equilibrium stipulations such that the morphology isn't continually tender. as well as an in depth description of the features of random tough surfaces, Experimental equipment within the actual Sciences, quantity 37, Characterization of Amorphous and Crystalline tough Surface-Principles and purposes will concentrate on the elemental rules of actual and diffraction ideas for quantitative characterization of the tough surfaces. The booklet therefore comprises the most recent improvement at the characterization and measurements of a large choice of tough surfaces. The complementary nature of the genuine house and diffraction options is totally displayed.

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Example text

This height-height correlation function works for both 1+ 1 dimensions and 2+1 dimensions. 10), the corresponding auto-correlation function R(r) is given by R(r)-e-(~ )2" . 11) [When a = 1, the 1+l-dimensional surface can be treated like a linear system with an independent Gaussian noise input ~(t). The system response function Y(t) is a Gaussian function with a correlation length ~. This correlation length determines the lateral correlation length of the output. 12) SELF-AFFINE SURFACES (a) a = 1 4,,a ~9 37 .

I . . . . 10~ i | | , 10~ r (tim) FIG. 5 T h e h e i g h t - h e i g h t c o r r e l a t i o n f u n c t i o n s c a l c u l a t e d f r o m t h e A F M i m a g e s obt a i n e d f r o m Si S a m p l e s # 3 , # 5 , a n d # 1 0 ( f r o m Ref. 11]). 02. As we discussed in Chapter 2, one also needs to make sure that the rough surface is homogeneous and ergodic. A simple way to test the homogeneity is to scan the sample in different places and compare the statistical properties obtained from different places.

49) i=1 Similar to the auto-correlation function, as m increases, the number of data points becomes smaller. Therefore, for a large m value, the corresponding estimation for the height-height correlation function would not be accurate. 2, the surface power spectrum is the Fourier transform of the auto-covariance function. 47), we can obtain the power spectrum. 50) 26 STATISTICAL NATURE OF ROUGH SURFACES (1, 1) ~ (Nx, 1) (1, Ny) FIG. 11 T h e c o o r d i n a t e s for t h e i m a g e m e s h used in the text.

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