**1. Introduction**

The significance of nanostructuring techniques has increased with the progress of scaling down devices to nanometer order in accordance with Moore's law [1]. The realization of three-dimensional (3D)-architected nanostructures, that is, the transformation from novel two-dimensional (2D) film-based planar devices to 3D complex and multifunctional nanodevices, is of crucial importance to future electronic applications [2, 3], the so-called More Moore. So far, various nanofabrication techniques have been proposed and developed with different levels of success. In many cases, materials grown on substrates are affected by substrate structural characteristics such as shape, roughness, and dimensionality. Three-dimensional patterned substrates

prepared by a conventional lithographic method can be used to form 3D nanostructures. Although considerable attention has been devoted to controlling the size, shape, and positioning in research on 3D patterning, little attention has been focused on the atomic ordering of arbitrarily oriented surfaces on 3D patterned substrates. The realization of perfect surfaces on 3D structures is required to produce high-quality samples. Since material growth starts on a surface, the surface condition clearly determines the structural and physical properties of the grown material.

for instance, *σ* � 4 Mb for a 15 keV electron and 0.002 Mb for a Cu K (�8 keV) X-ray to a Si atom [10, 11]. According to the kinematic diffraction theory, a diffraction pattern can be understood as a reciprocal structure pattern reflecting a crystalline structure (**Figure 2**) in a reciprocal space map (RSM). By comparing an experimental reciprocal structure pattern in an RSM with patterns of candidate crystalline structures, we can analyze the characteristics of crystalline materials, such as dimensionality, atomic structure, orientation, size, and strain [4, 12–16]. For instance, an ideal one-dimensional (1D) material with lattice constant *a* in the *x* direction in real space (**Figure 2(a)**) shows a characteristic reciprocal structure pattern consisting of reciprocal lattice planes with a reciprocal lattice unit length of *<sup>a</sup>*<sup>∗</sup> <sup>¼</sup> <sup>2</sup>*π=<sup>a</sup>* in the *<sup>x</sup>* direction (**Figure 2(b)**). This can be explained

*Creation and Evaluation of Atomically Ordered Side- and Facet-Surface Structures of Three…*

by the Bragg interference condition *a* cos *θout* � *a* cos *θin* ¼ *nλ*, that is,

and outgoing wave-number vectors, respectively, satisfying *k*<sup>0</sup> ¼ *k*

*<sup>x</sup>* ¼ 0. Here, *λ* is wavelength, and *k*

2*π=λ*. Since the intersection of reciprocal lattice planes with an Ewald sphere of radius *k*<sup>0</sup> produces a diffraction pattern (**Figure 2(c)**), diffraction rings are

(**Figure 2(d)**), shows reciprocal lattice rods with reciprocal lattice unit vectors of

*Schematics of (a)–(c) 1D, (d) and (e) 2D, and (f) and (g) 3D crystals: real space structures (a), (d), and (f) and corresponding reciprocal space structures (b), (c), (e), and (g). 1D, 2D, and 3D crystals show reciprocal*

*lattice planes, reciprocal lattice rods, and reciprocal lattice points, respectively.*

(**Figure 2(e)**). The intersection of reciprocal lattice rods with an Ewald sphere produces a pattern of diffraction spots arrayed on arcs. A reciprocal lattice rod at

, corresponding to the intersection of orthogonal reciprocal lattice planes

is called an ð Þ *h k* rod, which produces an ð Þ *h k* 2D diffraction

A 2D material with lattice constants *a* and *b*, that is, unit vectors *a*

!

*in* and *k* !

> ! *in*

 <sup>¼</sup> *<sup>k</sup>* ! *out* 

! and *b* !

*out* are incident

 ¼

*k* !

*a* ! <sup>∗</sup> *out* � *k* !

and *b* ! <sup>∗</sup>

position *ha*!<sup>∗</sup>

**Figure 2.**

**93**

*in* <sup>þ</sup> *na*<sup>∗</sup> <sup>∙</sup> *<sup>e</sup>*

> þ *kb* !<sup>∗</sup>

!

*DOI: http://dx.doi.org/10.5772/intechopen.92860*

observed as the diffraction patterns of 1D materials.

Although techniques for studying 2D surfaces, namely, surface science, have been intensively developed and established, little attention has been devoted to controlling the atomic ordering and structures of side-surfaces on 3D architectures. Fabrication techniques for 3D nanoscale structures that are promising for 3D integrated circuits have been individually developed from surface science.

The subject of study should be changed from 2D planar surfaces to 3D assembly surfaces to enable atomically ordered nanofabrication on vertical side-surfaces and/or tilted facet-surfaces in 3D space (**Figure 1**). For this purpose, a simple and accurate structure evaluation technique is required. Currently, scanning electron microscopy (SEM) is widely used for the observation of 3D nanostructures. However, SEM cannot be used to evaluate structures involving atomic ordering. On the other hand, transmission electron microscopy (TEM) is a powerful technique for examining the atomic structure of 3D nanomaterials, but it is destructive and not convenient. An alternative technique is a diffraction method. Reflection high-energy electron diffraction (RHEED) enables the examination of surface properties such as atomic ordering, surface roughness (flatness), and surface homogeneity [4]. Low-energy electron diffraction (LEED) is also a conventional and nondestructive surface observation technique [5]. To apply these techniques to 3D structured samples with various oriented surfaces, instead of 2D planar samples, an appropriate alignment of the incident electron beam considering the configuration in 3D space is indispensable [6–9].

In this chapter, we first show how to obtain and evaluate RHEED and LEED patterns from 3D structured samples by explaining the principle of diffraction. Then, we demonstrate creating and evaluating atomically ordered side- and facetsurface structures of 3D silicon nano-architectures. Finally, we discuss novel structures that have been constructed on 3D patterned Si to form 3D interconnected structures and their physical properties.
