Steps on Si

D. J. Chadi, Stabilities of single-layer and bilayer steps on Si(001) surfaces, Phys. Rev. Lett. 59, 1691 (1987). 

Later the barrier puzzle was resolved in a close collaboration between experiment and electronic structure calculations. It turned out that it is not sufficient to just consider the H2 dissociation on clean Si(l 0 0). Instead it was realized that it is very important to take into account the exact surface structure and surface coverage in the determination of the adsorption/desorption barriers [64, 72]. At surface imperfections such as steps the reactivity of a surface can be extremely modified. It was found experimentally on vicinal Si(l 0 0) surfaces that the sticking coefficient at steps is up to six orders of magnitude higher than on the flat terraces [71]. This finding was supported by DFT studies which showed that non-activated dissociation of H2 on the so-called rebonded DB steps on Si(l 0 0) is possible [71, 78], while on the flat Si(l 0 0) terraces the dissociative adsorption is hindered by a barrier of 0.4 eV [37],... 

Fig. 18. STM images of Si in ambient conditions, (a) Pattern generated by the tip on Si(l 11) etched in HF (after [98]) and (b) image showing the resolution of atomic steps on Si(lOO) (after [100]).

Later work on diffusion rates led Wu et al. [86] to reject diffusion as the rate-limiting step on Si(lOO). They fit a potential surface to results of their calculations and used Monte Carlo transition state theory to calculate rate constants. Surface relaxation effects that were neglected in their first prin-... 

Table 9.5 Step formation energy per unit length fl(ooi) for single and double steps on Si(OOl) and Ge(OOl) [70, 71].

Cu and Ag on Si(lll) surfaces. In the last example, we come back to surfaces. It is well known (44-46) that Cu catalyzes the formation of dimethyl-dichlorosilane from methylchloride and solid silicon, which is a crucial technological step in the synthesis of silicone polymers. Even today, the details of the catalytic mechanism are unclear. Cu appears to have unique properties for example, the congener Ag shows no catalytic activity. Thus, the investigation of the differences between Cu and Ag on Si surfaces can help in understanding the catalytic process. Furthermore, the bonding of noble metal atoms to Si surfaces is of great importance in the physics and chemistry of electronic devices. 

Silastannation similarly appears to involve intermediates based on Si-PdL -Sn complexes, the rate-determining step being the insertion of the alkyne into the Sn-Pd bond (Equation (32)). 

D Gratings on Si(OOl) There are some fundamental differences in the evolution of 1- and 2-D modulations on singular or vicinal surfaces. As illustrated in figure 1 and discussed by Rettori and Villain[4] the 2-D modulations will generally involve closed step contours so that decay is promoted by differences in curvature of neighbouring steps and also interactions among steps in... 

The Saddle Point Features of the 2-D Gratings For an ideal 2-D sinewave the saddle point features should appear to have 4-fold symmetry when viewed in LEEM images. From the sketch of figure 13 it can be seen that the hypocycloid shaped terrace at the saddle point has the same type of monoatomic step on all four sides due to the difference in the free energies of the two steps, Sa and Sb, on Si(OOl) there should be a strong preference for Sa steps and hence each maximum would prefer to be flanked by two white domains and two "black ones as is the case in figure 10. (A similar conclusion follows if the the saddle point terrace is surrounded by two Sa steps and two double steps of Db type[31]). 

Figure 13. Schematic showing the probable configuration of atomic steps surrounding the (001) terrace at a saddle point of a 2-D grating on Si(OOl). Note that if the surrounding steps are mono-atomic they are all of the same type and will prefer to be all of the low energy type(SA) if the saddle point moves up or down by one step unit the surrounding steps will all be of the high energy type. This is believed to be the basic reason for the preference in type of saddle point terrace.

Step-mobility-limited models can be further separated into two limits conserved and non-conserved [20]. This terminology refers to the local conservation of mass transport is said to be conserved if a surface defect generated at a step edge eventually annihilates at the same step or at one of the two adjacent steps. Thus, the motion of adjacent steps is coupled. The 1-D conserved model of Nozieres [21] predicts T a L, independent of Zo. On the other hand, in a non-conserved model the motion of adjacent steps is uncorrelated surface defects generated at a step edge can annihilate at any step edge on the surface. Uwaha [22] has considered this case and found x a L L/zay. In the discussion below, we will use these two limiting cases of step-mobility-limited models [21, 221 to extract the step-mobilities on Si(OOl) and Ge(OOl) surfaces from experiments on relaxation kinetics. 

Keefe et al. [12] observed that the relaxation of micron-sized 1-D gratings on Si(OOl) is consistent with Eq. 1. But as discussed above, the derivation of Eq. 1 is not strictly valid at r < Tr. We show here that these experiments are also in agreement with dynamics of the conserved, step-mobility-limited model derived by Nozieres [21] ... 

Next, the step-mobilityof Si(OOl) is estimated at lower temperatures, T 500°C, from the experiments of Webb et al. [25] on the relaxation kinetics of non-equilibrium step-spacings. In this experiment, the average terrace size was large, and therefore, due to the stress anisotropy of the 2 x 1 surface reconstruction, a long range interaction of the form... 

Figure 6. Compilation of step-mobilities derived from several experiments on Si(OOl) and Ge(OOl). The temperatures for the two data points for Ge(OOl) (filled triangles) have been scaled by the ratio of the cohesive energy of Si to Ge, 1.20. The dashed line shows a thermally activated process with an activation energy of 1.8 eV and a prefactor b kQ/k, 0 is the Debye temperature of Si, 650 K, and b = 0.38 nm.

To proceed, we must describe the effective driving force and the effective interactions between steps on this mesoscopic scale. We focus here on two cases of recent experimental and theoretical interest current-induced step bunching on Si( 111) surfaces - " and reconstruction-induced faceting as seen a number of systems including the O/Ag(110) and Si(lll) surfaces" In both cases interesting 2D step patterns can arise from the competition between a driving force that promotes step bunching, and the effects of step repulsions, which tend to keep steps uniformly spaced. 

To construct an approximation to the relaxation process in the reaction network iV, we also need to restore cycles, but for this purpose we should start from the whole glued network V on si (not only from fixed points as we did for the steady-state approximation). On a step back, from the set si to si and so on some of glued cycles should be restored and cut. On each step we build an acyclic reaction network, the final network is defined on the initial vertex set and approximates relaxation of if. 

Butadiene has also been reported to form a [4 + 2] cycloaddition-like product at the Si(l 11)—7 x 7 surface. Theoretically, the reaction has been predicted to occur between a rest atom-adatom pair via a step-wise, diradical path pathway that is unactivated [19,249]. Recent STM studies of butadiene adsorbed on Si(l 11)—7 x 7 have observed the formation of either a [4+ 2]-like or a [2+ 2]-like product with the Si adatom-rest atom pair, but were not able to definitely assign the product as one or the other [250]. Interestingly, the STM images also reveal that about a third of the cycloaddition product forms between two Si adatoms. Because both adatoms are positively charged, the stepwise reaction does not seem likely, and the authors suggest that this reaction occurs in a concerted fashion [250]. 

The basic steps of the lithographic process are shown schematically in Figure 1. The example shown corresponds to photolithography in which the photosensitive resist or photoresist is applied as a thin film to the substrate (Si02 on Si) and subsequently exposed in an image-wise fashion through a mask. The mask contains clear and opaque features that define the circuit pattern. The areas in the photoresist that are exposed to light are made either... 

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