Steps, array

Fluctuations of an isolated step are also suppressed by the microscopic energy cost to form kinks. On coarse-graining, this translates into an effective stiffness or line tension that tends to keep the step straight. Standard microscopic 2D models of step arrays incorporating both of these physical effects include the free-fermion model and the Terrace-Step-Kink (TSK) model. Both models have proved very useful, though their microscopic nature makes detailed calculations difficult. 

Figure 9 (a) The network of crossing steps, and (b) a combination of two step arrays of different orientation, after the phase separation, predicted by (5) for e > 0, has occurred. The + and - indicate the opposite reconstruction phases induced by the clockwise steps. 

Finally in Fig. 7 the dashed lines show the truncation of the equilibrium shape of the (110) facet by ridges connecting the facet to rounded areas and Fig. 10(c) shows the expected arrangement of steps around the truncated facet. Notice that in this case there are sharp ridges between rounded regions covered by networks of steps and regions covered by non-crossing step arrays. 

M.E. Keeffe, C.C. Umbach, and J.M. Blakely. Surface self-diffusion on Si from the evolution of periodic atomic step arrays. J. Phys. Chem. Solids, 55 965-973, 1994. 

Fig. 4. Schematic of a single-step array fabrication process for in vivo biotinylated proteins. Step a A cmde lysate containing the desired biotinylated recombinant protein is printed onto a streptavidin-coated surface coderivatized with a polymer that resists nonspecific protein absorption. Step b Unbound proteins are washed away to leave the purified recombinant protein, specifically immobilized and oriented on the array surface via the biotin moiety on the BCCP tag.

Stepped Surfaces. Steps on vicinal surfaces are interesting because they represent a set of one-dimensional (ID) nanostructures. A regular step array is most often observed [155-158] though at low temperatures the energetic minimum can be a faceted surface [159]. The origin of this order is the step-step... 

Figure 2.16 (a) Schematic of the simulation geometry model for a Nafion-coated HOPG surface (i), where the numbers are indicative of the film-solution interface (1), periodic boundaries from which the step array response can be determined (2a, 2b), step-edge plane (3), and basal plane (4a, 4b), respectively, and simulated concentration profiles for a Nafion-Ru(bpy)3 +... 

Figure 6.11 Pattern type and pattern density within a die of an SKW7-2 test wafer (Fan, 2012) (a) layout of a die on SKW7-2 wafer (MIT standard oxide CMP characteization layout). A P preceding a number indicates a pitch structure with 50% density, with the number following in microns. All other numbers are localized densities, with the number indicating the density. Density stmctures have a fixed 100 pm pitch, (b) Topography of the 70% STEP array in a die.

A strong PD dependence is observed from the simulated up area thickness and step height evolutions in Figure 6.12. Center points of STEP arrays are selected as monitor sites. Both material removal (up area thickness reduction) and local planarization (step height reduction) are faster in lower PD areas. This is caused by higher local pressure in these low PD up areas. 

Figure 6.12 Pattern density (PD) dependence of CMP process (Fan, 2012) (a) monitor sites in STEP arrays of MIT standard layout (b) up area thickness evolution (c) step height evolution.

Calculated electron diffraction pattern from the surface of figure (3) for normal incidence at 94 eV. The observed patterns are in good agreement with these calculations for an ordered step array. [After Ellis and Schwoebel( )] The split diffraction spots are characteristic of the pattern from a stepped surface. 

The formation of step bunches and/or facets on hydrogen-etched Si- and C-faces of 6H-SiC has been studied by Nie et al. [38], using both nominally on-axis and intentionally miscut (i.e., vicinal) substrates. For nominally on-axis substrates, H2-etching produced uniformly distributed step-terrace arrays on both Si- and C-faces, as shown in Figure 4.10. The step arrays form because of the miscut of the surface (the average miscut values for the substrates of Figure 4.10a and b are... 

About half the code in the listing (between lines 26 and 40) is devoted to setting possible limits on the step sizes for each variable. If no step size limitations are set by the input step[] array, this code is bypassed. The step size limitation code is almost identical to that previously discussed in connection with Newton s method for a single variable. A limitation may be specified for each variable independently using either a negative number for a + - limitation or a positive number for a relative step size limitation. The reader is referred back to Chapter 3 for a more detailed discussion of step size limitation in connection with the newton() function. In addition the convergence criteria (on line 52) is based upon the maximum relative error in any one of the variables and the code tries to obtain a maximum relative error below that specified by the ERROR value (2.e-6 in the code on line 57). 

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