**4.1 111** f g **vertical side-surfaces**

**Figure 9(b)**–**(d)** show typical filtered RHEED patterns obtained from 3D Si with a vertical 111 f g side-surface (**Figure 7(c)**) various *θ* and *ϕ* values. The 111 f g side-surfaces were produced on a 110 ð Þ surface (**Figure 6(c)**). The RHEED patterns showed curious characteristics, because half of the patterns were removed, which has not been reported to the best of our knowledge. The appearance of the left-side

#### **Figure 9.**

*(a) Dependence of observable conditions (orange) in the RHEED pattern on the polarity of* θ *and* ϕ*. (b)–(d) RHEED patterns from 3D Si with* f g 111 *vertical side-surfaces observed at (b)* θ *= 0.0*° *and* ϕ *= +1.9*°*, (c)* θ *= +0.3*° *and* ϕ *=* �*1.6*°*, and (d)* θ *= +0.3*° *and* ϕ *= +1.1*°*. Insets schematically show the relationship between the incident electron beam and the observable surfaces in 3D space.*

*Creation and Evaluation of Atomically Ordered Side- and Facet-Surface Structures of Three… DOI: http://dx.doi.org/10.5772/intechopen.92860*

and right-side Si 111 f g7�7 patterns depends on *ϕ*, as shown in **Figure 9(c)** and **(d)**. *ϕ* is the azimuth angle for the Si 110 ð Þ top-/bottom-surfaces and simultaneously corresponds to the glancing angle for the Si 111 f g side-surfaces. On the other hand, *θ* is the glancing angle for Si 110 ð Þ and is also the azimuth angle for Si 111 f g. **Figure 9(a)** summarizes the dependence of the observable and non-observable conditions in the RHEED patterns on the polarity of *θ* and *ϕ*. When *θ* (the glancing angle for Si 110 ð Þ) decreases, the RHEED pattern from Si 110 ð Þ disappears, while a pattern from Si 111 f g is present. Indeed, in **Figure 9(b)** (*θ* = 0.0° and *ϕ* = +1.9°), a quarter circle 7�7 pattern with faint 2�16 spot can be seen. The diffraction spots on the left and the right sides (**Figure 7(c)**) are slightly elongated in the horizontal direction. In general, the elongation (streaky) direction corresponds to the surface normal direction [4], as illustrated in **Figure 8**. Thus, these slightly streaky spots indicate the existence of vertical side-surfaces.

Let us analyze the curious RHEED patterns in more detail. In **Figure 9(c)** (*θ* = +0.3° and *ϕ* = �1.6°) and **Figure 9(d)** (*θ* = +0.3° and *ϕ* = +1.1°), diffraction spots from the direct beam (DB) can be observed in the 1/7th-order Laue zones (L1/7-L6/7) on the left and right quarter sides, respectively, as well as seven spots within the Kikuchi band width (e.g., indicated by a pink arrow in **Figure 9(c)**). These patterns clearly correspond to Si 111 f g7�7 reconstruction [4], having shadow edges in the horizontal and vertical directions. **Figure 9(c)** (**Figure 9(d)**) corresponds to Si <sup>111</sup> (Si 111 ) 7�7 diffraction on the surface of the left-side (right-side) wall of the 3D patterned structure. Note that a specular spot 00 ð Þð Þ <sup>111</sup> ( 00 ð Þð Þ <sup>111</sup> ) from the DB appears on the left (right) side. In addition, strong Kikuchi lines and bands were

observed in the side RHEED pattern. These results indicate that atomically flat sidesurfaces were achieved on 3D patterned Si 110 ð Þ by etching and UHV annealing.

One can see the characteristic *ϕ* and *θ* dependences of the RHEED patterns (movie) in Supporting Information of Ref [5]. These RHEED patterns clearly show that all the surfaces on 3D Si, that is, the 110 ð Þ top-/bottom-surfaces, the 111 rightside surface, and the 111 left-side surface, have atomically ordered structures.

**Figure 10** shows the LEED patterns observed from the figured 111 side-surface. Because in LEED we observe backscattering diffraction, while RHEED reflects forward scattering diffraction, a unique 3D Si sample with a wider side-surface was prepared [9]. A clear 7�7 pattern can be seen in **Figure 10(a)**, where the incident electron beam is along a direction almost normal to the 111 side-surface. Characteristic LEED patterns were observed when the sample was rotated; the electron beam probed both a <sup>111</sup> side-surface and a 110 ð Þ top-surface. An example with an incident angle of �37° is shown in **Figure 10(b)**, which reflects surface reconstructions for both the figured <sup>111</sup> <sup>7</sup>�7 side-surface and the pristine 110 ð Þ <sup>16</sup>�2 top-surface [6].

The LEED patterns are in good agreement with those simulated by considering the crystal orientation and electron beam (i.e., the cross sections of the reciprocal lattice rods and an Ewald sphere [22]) shown in the lower-right panels of **Figure 10**. It is possible to identify diffraction spots on Laue zones of both <sup>111</sup> and 110 ð Þ surfaces in the patterns, demonstrating the observation of atomic crystalline ordering for the 3D surfaces using LEED.
