By Yiping Zhao

The constitution of a progress or an etch entrance on a floor isn't just a topic of serious curiosity from the sensible perspective but additionally is of basic medical curiosity. quite often surfaces are created lower than non-equilibrium stipulations such that the morphology isn't consistently gentle. as well as a close 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 fundamental ideas of genuine and diffraction thoughts for quantitative characterization of the tough surfaces. The publication therefore comprises the newest improvement at the characterization and measurements of a wide selection of tough surfaces. The complementary nature of the genuine area and diffraction concepts is totally displayed.

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**Extra info for Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications**

**Sample text**

5. Sample #10 has he largest interface width and lateral correlation length among these three amples. However, the roughness exponents for all three samples are very lose, judging from the slopes of the log-log plots at the small r region. 10), to fit the heightLeight correlation data. 05 #m, 40 EXAMPLES OF RANDOM ROUGH SURFACES ! . . . ! 10~ --o--- Sibk#10 10~ 104 / . . . 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.

The bias depends on the ratio L/~. 12 shows how the ratio L/~ affects the estimation. When L >> ~c, the estimation is close to w 2, and the bias is small. When L _< ~, the estimation is much smaller than w 2. In this case, even though the number of data points N is huge, the estimation still is not good. 0 0 FIG. 12 20 E{< w 2 40 60 80 100 > L } / W 2 as a f u n c t i o n of r a t i o L/$~. 4]. There is a famous theorem, Shannon's sampling theorem, which gives the estimation of a sampling step.

The two-dimensional forms of the characteristic functions. For the auto-covariance function, obviously G(r) = G ( - r ) and one has Gs(p,q) G(r) = G(r) 1 (Ny-q)(Nx-p) Ny --q N~ - p E E l--1 n--1 h ( p + n , l + q ) h ( n , 1 ) , and 1 Gs ( - p , q) - (Ny - q)(Nx - p) • Ny--q N ~ - p E E h(Nx - p - n, 1 + q)h(n, 1). 2 Height-height correlation ]unction The simplest way to calculate the height-height correlation function for an isotropic surface is along the fast scan direction (assumed to be the x direction)" 1 N~ N ~ - p H(r) ~ Hs(p) - Ny(N~ - p) E l--1 E [h(p + n, l) - h(n, /)]2.