Creation and Evaluation of Atomically Ordered Side- and Facet-Surface Structures of Three-Dimensional Silicon Nano-Architectures

The realization of three-dimensional (3D)-architected nanostructures, that is, the transformation from novel two-dimensional (2D) film-based devices to 3D complex nanodevices, is of crucial importance with the progress of scaling down devices to nanometer order. However, little attention has been devoted to controlling the atomic ordering and structures of side-surfaces on 3D structures, while techniques for controlling and investigating 2D surfaces, namely, surface science, have been established only for planar 2D surfaces. We have established an original methodology that enables atomic orderings and arrangements of surfaces with arbitrary directions to be observed on 3D figured structures by developing diffraction and microscopy techniques. An original technique, namely, directly and quan-titatively viewing the side- and facet-surfaces at the atomic scale by reflection high-energy electron diffraction (RHEED) and low-energy electron diffraction (LEED), can be used to determine process parameters in etching. This chapter introduces methods of evaluation by RHEED and LEED based on a reciprocal space map and methods of creating various atomically flat 111 f g and {100} side-surfaces of 3D Si nano-architectures and tilted 111 f g facet-surfaces fabricated by lithography dry and wet etching processes, followed by annealing treatment in vacuum.


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.
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][7][8][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.
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][13][14][15][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 a * ¼ 2π=a in the x direction (Figure 2(b)). This can be explained by the Bragg interference condition a cos θ out À a cos θ in ¼ nλ, that is, Here, λ is wavelength, and k ! in and k ! out are incident and outgoing wave-number vectors, respectively, satisfying k 0 ¼ k Since the intersection of reciprocal lattice planes with an Ewald sphere of radius k 0 produces a diffraction pattern (Figure 2(c)), diffraction rings are observed as the diffraction patterns of 1D materials.
A 2D material with lattice constants a and b, that is, unit vectors a ! and b ! (Figure 2(d)), shows reciprocal lattice rods with reciprocal lattice unit vectors of , corresponding to the intersection of orthogonal reciprocal lattice planes (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 is called an h k ð Þ rod, which produces an h k ð Þ 2D diffraction ! * , and c ! * (Figure 2(g)). The intersection of reciprocal lattice points with an Ewald sphere produces a pattern of diffraction spots arrayed on a lattice. A reciprocal lattice point at position ha ! * , kb ! * , and l c ! * produces an h k l ð Þ3D diffraction spot. From diffraction patterns (e.g., diffraction rings or spots) projected on a detection screen, the original reciprocal structure pattern (e.g., reciprocal lattice planes, rods, or points) in a 3D RSM can be regenerated by changing the incident angle of the electron beam to the crystalline material (i.e., the direction of k ! in ) or the beam energy (i.e., k 0 ), as illustrated in Figure 3 for a 3D material with azimuth angle rotation [12][13][14][15]. For example, Figure 4 ð Þsubstrate as a function of the azimuth angle around the substrate surface normal direction [14]. Indeed, the conversion of diffraction spots on a lattice (indicated by orange arrows) in different diffraction patterns generates reciprocal lattice points in a 3D RSM, as indicated by orange arrows in Figure 4(c)-(e). In this 3D RSM, we can recognize the existence of a certain 3D crystalline structure, in this case the structure is α-FeSi 2 , among candidate crystal structures [17,18]; the crystalline orientations are α-FeSi 2 110 ð Þ∥ Si 001 ð Þand α-FeSi 2 001 ½ ∥ Si 110 h i from the reciprocal structure pattern. In Figure 4(a) and (b), there are also diffraction spots on arcs indicated by red arrows. These spots are often observed under a glancing condition of an electron beam nearly parallel to a substrate surface in RHEED with a primary energy E p of typically 10-15 keV. The conversion of the spots generates reciprocal lattice rods perpendicular to the substrate surface in a 3D RSM, as indicated by red arrows in Figure 4(c)-(e). The existence of spots on arcs or reciprocal lattice rods implies that the surface perpendicular to the rods is atomically well-ordered; in this case, it implies the formation of a well-defined clean Si 001 ð Þsubstrate surface. The width of a reciprocal lattice rod is finite (full width at half maximum ≃ 2π=D) and reflects the crystalline domain size D. Thus, the intersection of the rod with an Ewald sphere is elongated along the rod direction, that is, the surface normal direction. Indeed, in Figures 4(a) and (b) and 5(a), there are the surface spots (red arrows) elongated along the Si 001 ½ substrate surface normal direction.

Diffraction patterns from side-surfaces of 3D structured sample
One of the advantages of RHEED is its ability to observe atomically ordered surfaces in any direction, as described later in Sections 3.2 and 4. RHEED has been used to investigate crystalline structures on planar substrate surfaces. Recently, for    3D fabricated materials, the authors have demonstrated that not only substrate surfaces but also surfaces inclined from or perpendicular to a substrate plane exhibit atomically ordered structures where surface spots elongated along directions inclined from or perpendicular to the substrate normal direction appear in RHEED patterns ( Figure 5(b)) [6,7,9]. We emphasize that a simple surface property of 3D fabricated materials, that is, a surface direction, can be confirmed by the elongation of surface spots. Low-energy electron diffraction (LEED) with a typical E p of 50-100 eV focuses the interference caused by the backward scattering of an electron incident to an atom, while RHEED focuses the interference caused by forward scattering. Both LEED and RHEED are sensitive to surface structures. A LEED pattern at the normal incidence corresponds to a top view of reciprocal lattice rods intersecting with an Ewald sphere from the surface normal direction. The diffraction spots move to the 00 ð Þspot arising from the 00 ð Þrod with increasing E p [8,18]. For an inclined surface, the arrangement of diffraction spots in alignment changes that in an arc, the center of which is the 00 ð Þ spot. The diffraction spots also move to the 00 ð Þspot with increasing E p . Thus, we can confirm the surface direction of 3D fabricated materials by the arrangement and E pdependent motion of diffraction spots.

Experimental procedure
The authors demonstrated the creation of atomically ordered side-and facetsurfaces owing to the arbitrary selection of planes ( Figure 6). Atomically reconstructed Si 100 f g, 110 f g, and 111 f g vertical side-surfaces and 111 f g tilted facet-surfaces were first realized on 3D patterned Si substrates, and the perfection of the 3D surface structures was examined. The 100 f g2Â1, 110 f g16Â2, and 111 f g 7 Â7 diffraction spots from the 3D surfaces were confirmed by RHEED and LEED.

Sample fabrication with combination of dry and wet etching processes
The 3D architected Si samples with arbitrary faces discussed here were produced on commercial mirror-polished Si substrates by the following dry and wet etching procedures. All processes were performed at room temperature (RT). First, a line mask pattern was drawn using a photoresist. To produce the vertical side-surfaces (Figure 7(a)-(c)), Si was etched in an inductive coupled plasma (ICP)-reactive ion etching system (RIE-400iPB, Samco). The process parameters were an ICP source power of 300 W, a bias power of 10 W, and a working pressure of 4 Pa. Mixture gases of 10 sccm SF 6 , 5 sccm O 2 , and 200 sccm Ar were used in the etching cycle, and 40 sccm C 4 F 8 , 5 sccm O 2 , and 200 sccm Ar were used in the passivation process [6][7][8][9]. Depending on dry RIE conditions, various curved structures from trapezoid to triangle shapes were obtained. When we produced tilted facet-surfaces (Figure 7(d) and (e)), the optimized conditions for a triangle-like shape were a flow rate of 51 sccm, a pressure of 4.0 Pa, and a bias power of 60 W using an RIE system (RIE-10 NR, Samco) with SF 6 gas [9].
After dry etching, wet etching was performed to reduce the side-and facetsurface roughnesses. The base solution used in the wet process removes the damage and contaminants [19][20][21], and flash annealing promotes reconstruction through the sublimation of the contaminants [22]. Unoptimized conditions never led to reconstructed patterns on side-or facet-surfaces. In this process, the etching recipe was optimized by considering the plane-dependent etching properties [23]. A 100 f g sample was dipped in 25 wt% tetramethylammonium hydroxide (TMAH) at 70°C for 3 min. A 110 f g sample was etched in 25 wt% TMAH with 0.1 vol% surfactant (iso-octylphenoxy polyethoxyethanol) at 70°C for 1 min [7]. Then, the sample was rinsed with pure water, dried by blowing with N 2 , and introduced into an ultra-high vacuum (UHV) chamber. The 3D Si sample was degassed and flashed by directcurrent heating at $1150-1200°C at a pressure below 2 Â 10 À8 Pa.

RHEED observation of 3D structured samples
RHEED patterns were obtained at RT using an electron beam with an E p of 15 keV and a diameter of $0.5 mm. Au advantage of the RHEED technique is the accessibility of various 3D surfaces; that is, the diffraction pattern consists of all diffractions from the substantial crystal surfaces in 3D space. Actually, the selection of the incident e-beam direction enables the identification of 3D surface structures. In this study, the direction of the incident electrons was defined by the glancing angle θ and azimuth angle ϕ for the top and bottom Si surfaces (Figure 8). The RHEED patterns were also obtained from the 3D samples with vertical side-surface or tilted facet-surfaces by controlling θ and ϕ. For instance, for 3D Si with a vertical 111 f g side-surface, θ is the angle between the incident electron beam and the top 110 ð Þ surface, which was changed from À0.4°to +1.2°. ϕ, which is defined as the angle from 112 Â Ã in the in-plane direction, was changed from À4.5°to +4.7°. The RHEED patterns were filtered by a computer to emphasize the spot features in the background. LEED can also be used to observe 3D surface ordering, while 3D accessibility is less than that of RHEED because of the limited range of diffraction conditions. LEED patterns were also observed using a typical E p of 40-200 eV and a beam size of $1 mm. ð Þsurface (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  ð Þand 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 7Â7 pattern with faint 2Â16 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 = À1.6°) 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 (L 1/7 -L 6/7 ) 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 g7Â7 reconstruction [4], having shadow edges in the horizontal and vertical directions. Figure 9(c) (Figure 9(d)) corresponds to Si 111 À Á (Si 111 À Á ) 7Â7 diffraction on the surface of the left-side (right-side) wall of the 3D patterned structure. Note that a specular spot 00 ð Þ 111 ð Þ ( 00 ð Þ 111 ð Þ ) 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 À Á rightside surface, and the 111 À Á left-side surface, have atomically ordered structures. Figure 10 shows the LEED patterns observed from the figured 111 À Á 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 7Â7 pattern can be seen in Figure 10(a), where the incident electron beam is along a direction almost normal to the 111 À Á side-surface. Characteristic LEED patterns were observed when the sample was rotated; the electron beam probed both a 111 À Á side-surface and a 110 ð Þtop-surface. An example with an incident angle of $37°i s shown in Figure 10(b), which reflects surface reconstructions for both the figured 111 À Á 7Â7 side-surface and the pristine 110 ð Þ16Â2 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 111 À Á and 110 ð Þ surfaces in the patterns, demonstrating the observation of atomic crystalline ordering for the 3D surfaces using LEED.

100
f gvertical side-surfaces Figure 11(a) shows a typical filtered RHEED pattern obtained from 3D Si with 100 f gside-surfaces. The 100 f gside-surfaces were created on a commercial mirrorpolished Si 100 ð Þsubstrate (Figure 6(a)). In Figure 11(a) (θ = +0.4°and ϕ = À1.2°), the two overlapping Si 100 f g2Â1 reconstructed diffraction patterns [4,24] originated from the top/bottom and left-side surfaces. One is a 100 ð Þ2Â1 pattern with a semicircular shape having a shadow edge SE (100) in the horizontal direction. The other is a 001 ð Þ 2Â1 pattern on the left quarter side with a shadow edge SE (100) in the vertical direction.
We can see that the diffraction spots on the left side are slightly elongated in the horizontal direction, which is a characteristic of a RHEED pattern from a sidesurface [6]. The diffractions from the top-/bottom-surfaces disappeared and those from the left-side surface remained when we changed θ from +0.4°to 0.0°. When we set θ = +0.0°and ϕ = À1.2°, only a quarter circle 2Â1 pattern with strong Kikuchi lines and bands can been seen, corresponding to the relationship between θ and ϕ, that is, the glancing and azimuth angles for each surface, respectively, similarly to that observed in Figure 9(a). Quarter circle 2Â1 patterns were also observed on the right when ϕ was positive.
The left part of Figure 11 Þleft-side surfaces in 3D reciprocal space in our experimental setup, namely, the simulated RHEED patterns at θ = +0.4°and ϕ = À1.2° (Figure 11(b) right panel), show good agreement with the observed RHEED pattern (Figure 11(a)). These results indicate that atomically flat side-surfaces were achieved on the 100 f gsample.

110 f g vertical side-surfaces
Finally, the RHEED pattern from the vertical 110 f g side-surface is shown in Figure 12(a). Here, a 110 f g side-surface was produced on a 2D 100 ð Þsubstrate (Figure 6(b)). Figure 12 Figure 12(a). In Figure 12(a), domain A is only considered as a 011 À Á eye guide. The incident electron direction was the 011 ½ direction, and the first Laue zone arc of Si 100 ð Þof L 100 ð Þ 1 (Figure 12(b)) is the same as L 011 ð Þ 1 (Figure 12(d)).

111
f g tilted facet-surfaces Figure 13(a) shows a typical filtered RHEED pattern obtained from the 111 f g facet sample at θ g = +0.7°and ϕ = +2.7°after flashing in UHV. The RHEED pattern showed notable characteristics, consisting of tilted 7Â7 spots (some are marked by yellow circles, and 1/7th-order Laue zones, L 1/7 -L 6/7 , are recognized) and   faint horizontal 16Â2 spots (cyan circles). The 7Â7 pattern was tilted in the counterclockwise direction around DB, and the tilt angle was $36°, which is consistent with θ F . Figure 13(b) shows a simulated RHEED pattern from the 111 ð Þ facet-surface, corresponding to Ewald sphere cross sections of 2D 7Â7 reciprocal lattice rods of the tilted Si 111 ð Þ. The excellent agreement between Figure 13(a) and (b) indicates the creation of an atomically ordered Si 111 ð Þ7Â7 facet-surface. The fabricated 3D structure shows that the relative glancing and azimuth angles to the tilted Si 111 ð Þ facet-surface are 2.1 and 1.8°, respectively, under this condition. These RHEED patterns clearly show the existence of three different atomically ordered surfaces on the 111 f gfacet sample, that is, the 110 ð Þbottom, 111 ð Þfacet, and 111 À Á facet-surfaces. One can see the characteristic ϕ dependence of the RHEED patterns in Ref [9].

Application of 3D architected Si
The creation and observation methods for well-defined surfaces enable the epitaxial growth of an arbitrary geometry, a key technique for nanoconstruction in 3D space [26][27][28][29][30][31]. Therefore, our established methodology contributes to the realization of well-ordered 3D nanofabrication, where the material stacking direction can be perfectly switched between the out-of-plane and in-plane directions. Novel 3D nanostructures are also expected to help unveil the underlying 3D surface science phenomena. Finally, two demonstrations utilizing a 3D architected Si platform are shown.

Platform for material growth on 3D surfaces
Atomically well-defined side-surfaces on a substrate can make an enormous contribution to nanofabrication [26][27][28][29][30][31]. To demonstrate the applicability of material growth on such side-surfaces, we produced Si 111 f g-Fe and Si 111 f g-Ag reconstructed side-surface structures on 3D Si with vertical 111 f g7Â7 side-surfaces. Ag and Fe layers with thickness of 1.0 and 0.4 nm were deposited on the 111 À Á leftside and 111 À Á right-side surfaces, respectively, and the sample was subsequently annealed at 500°C in UHV. Figure 14(a) and (b) show typical RHEED patterns obtained from the left-side and right-side surfaces, respectively. We can confirm ffiffi ffi 3 p Â ffiffi ffi 3 p (streaky) spots in L 0 (orange arrows) in Figure 14(a). In Figure 14(b), we can confirm 2Â2 (streaky) spots (orange arrows), showing the formation of c-FeSi [18]. Simultaneously, [4,24,31,32] was obtained on the left-side surface. These results show that highly developed thin-film formation techniques are applicable for the vertical side-surface of 3D patterned substrates and the material stacking direction can be perfectly switched between the out-of-plane and in-plane directions. right-side surface (Figure 14(d)), where a smooth in-plane heteroepitaxial interface with a length of 50 nm or more was formed between α-Fe and Si.  (Figure 14(c)) showed that fcc-Ag epitaxially grew with an atomically matched interface, Ag 111 À Á ∥ Si 111 À Á , without any visible defects or dislocations. Our results clearly show that a coherently grown (ultra) thin film was realized on the vertical side-surface with the growth alternating between the out-of-plane and inplane directions. The siliciding reaction can be controlled on the side-surfaces. Therefore, highly developed thin-film formation techniques are applicable for the vertical side-surface of 3D patterned substrates, and the material stacking direction can be perfectly switched between the out-of-plane and in-plane directions.

Novel conductivity on interconnected 100
f gvertical side-surfaces Three-dimensional integrated circuits, which contain multiple layers of active devices, have the potential to dramatically enhance chip performance, functionality, and device packing density. Recent 3D structured field-effect transistors (FETs) have surfaces with different orientations; for instance, a fin-type tri-gate structure has one top-surface and two side-surfaces [35,36].
The electric connection between metal wires on these surfaces-that is, the wiring interconnects at sharp edges of top-and side-surfaces-is one of the issues in the development of 3D devices. Although the conductivity in metal wires on isolated 2D planar or side-surfaces has been well discussed, there are no reports on the metal conductivity of interconnections between 3D surfaces with different orientations, probably owing to the difficulty in measuring the intrinsic conductivity in 3D angular interconnects, which is mainly caused by diffuse scattering on rough surfaces [37][38][39][40][41][42][43][44][45][46][47][48]. One of the most outstanding factors contributing to the conductivity in the 3D angular interconnects is the facet-edge, which is a boundary of two surfaces with different crystalline orientations. To extract an intrinsic conductive property for metal wires interconnected at facet-edges, atomically flat surfaces in 3D structured substrates are required for the evaluation of the 3D interconnect resistivity by eliminating extra factors, such as roughness. To elucidate the impact of the 3D geometric effect on the conductive property, angularly interconnected Au wires with two configurations, crossing over and parallel to the facet-edges, were produced on atomically flat facet 111 f g surfaces (Figure 13). Figure 15(a) shows a typical cross-sectional SEM image of a 111 f g facet sample on which a 10-nm-thick Au layer was deposited. The SEM image indicates that Au was uniformly grown on the Si facet-surface with a smooth interface without any depressions or protrusions. No breaks or discontinuity of the Au wires was observed in SEM images, even at the top facet-edges. Figure 15(b) shows current-voltage properties at 100 K for 3D angularly interconnected Au wires of 2 μm width (circles) and 5 μm width (squares) in the parallel (red) and perpendicular (blue) configurations (insets). The length of the Au wires was 100 μm. Both perpendicular wires have an approximately one-order larger resistance (smaller current) than the parallel wires of the same width. For the other wire widths, the resistance in the perpendicular configuration was also larger than that in the parallel configuration.
The simplified resistance ratio, defined as the inverse of the current ratio at a fixed voltage, was 3-10 for the measured wire widths. Note that the dimensions (cross section and length) and crystallinity of the Au film were almost the same in the parallel and perpendicular configurations. Thus, the significant anisotropic resistance in these configurations is ascribed to the properties of the geometric shapes of the Au wires, that is, 3D angular interconnects. Indeed, the perpendicular wires have more facet-edges than the parallel wires; the perpendicular channel crossed over 11 top and 23 bottom facet-edges, while the parallel channel crossed over one top and two bottom facet-edges for a wire width of 5 μm. Au wires on the 3D facet structure can be separated into four regions: flat bottom-surface, flat facet-surface, convex top facet-edge, and concave bottom facet-edge regions with resistances of R B , R F , R TE , and R BE , respectively, as shown in the inset of Figure 15(b). The geometries of crystal grain boundaries in the polycrystalline Au wire may increase the electrical resistance [49]. The aggregation of crystal grain boundaries in the interconnect region, leading to the reduction in effective cross-sectional area, was attributed to the large α (≈30-180), i.e., We found that the conductivity passing through the interconnects is sensitive to the alignment of the facet-edges in the electric path, and the series configuration showed a 3-10-fold larger resistance than the parallel configuration, which originated from the increased resistivity across the facet-edges by a factor of $30-180, as calculated from the circuit model. This work provides a fundamental understanding of the impact of the 3D angular interconnects of a metal wire on electric transport and guidelines for the comprehensive investigation of the intrinsic interconnect transport properties on 3D structures, which is expected to produce critical benefits in the semiconductor industry.

Conclusion
This chapter demonstrated the creation and evaluation of atomically ordered side-surfaces and inclined facet-surfaces in nanofabricated 3D Si architectures toward the realization of sequentially 3D integrated and stacked devices for More Moore [3]. Atomically flat and well-ordered 3D structured surfaces play an important role in creating high-performance films on arbitrarily oriented 3D surfaces, similar to films grown on ordinary planar substrates. We emphasized that electron diffraction techniques such as RHEED and LEED are convenient for evaluating atomically ordered 3D surfaces, while conventional SEM has no atomic resolution. The points for recognizing 3D surfaces in diffraction patterns were explained along the basic concept of diffraction in reciprocal space; the intersection of reciprocal lattice rods with an Ewald sphere led to diffraction spots on arcs, and the spots elongate in the surface normal direction.
By diffraction, we evaluated several systems with side-or facet-surfaces of Si 111 f g or 100 f gon Si 110 ð Þ or Si 001 ð Þsubstrates, which were fabricated by lithography dry and wet etching processes, followed by annealing in vacuum. Metal deposition on the well-ordered 3D surfaces (followed by annealing) also produced well-ordered films of nanometer thickness fabricating with arbitrary orientations. This is one of the fundamental techniques for defect-free material construction on 3D architectures. The electrical conductivity of metal wires on atomically flat 3D facet-surfaces crossing facet-edges was also measured toward the design of nanoscale steric wiring. We consider that these techniques for creating and evaluating 3D surfaces are promising for the realization of future 3D architecture devices.