Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon

The review article deals with ‘quantum engineering’ of growing of silver films on semiconductor substrates that allows obtaining new forms of matter. The results on the energy dispersion of electron states in epitaxial Ag (111) films obtained on Si (001) and Si (111) are presented.

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Дата:	2019
Автори:	Karbivska, L.I., Karbivskyy, V.L., Romanskyy, A.O.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут металофізики ім. Г.В. Курдюмова НАН України 2019
Назва видання:	Успехи физики металлов
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Цитувати:	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon / L.I. Karbivska, V.L. Karbivskyy, A.O. Romanskyy // Progress in Physics of Metals. — 2019. — Vol. 20, No 3. — P. 502-532. — Bibliog.: 61 titles. — eng.

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spelling	nasplib_isofts_kiev_ua-123456789-1679352025-02-09T15:23:39Z Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon Детермінізм симетрії монокристалічної поверхні межі поділу при одержанні 0D- і 2D-структур шляхетних металів та Індію на кремнії Детерминизм симметрии монокристаллической поверхности границы раздела при получении 0D-и 2D-структур благородных металлов и индия на кремнии Karbivska, L.I. Karbivskyy, V.L. Romanskyy, A.O. The review article deals with ‘quantum engineering’ of growing of silver films on semiconductor substrates that allows obtaining new forms of matter. The results on the energy dispersion of electron states in epitaxial Ag (111) films obtained on Si (001) and Si (111) are presented. Оглядову статтю присвячено «квантовій інженерії» вирощування плівок срібла на напівпровідникових підкладинках, яке уможливлює одержання нових форм речовини. Наведено результати з енергетичної дисперсії електронних станів у епітаксіальних плівках Ag (111), одержаних на Si (001) та Si (111). Обзорная статья посвящена «квантовой инженерии» выращивания пл нок серебра на полупроводниковых подложках, которое позволяет получать новые формы вещества. Приведены результаты по энергетической дисперсии электронных состояний в эпитаксиальных пл нках Ag (111), полученных на Si (001) и Si (111). 2019 Article Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon / L.I. Karbivska, V.L. Karbivskyy, A.O. Romanskyy // Progress in Physics of Metals. — 2019. — Vol. 20, No 3. — P. 502-532. — Bibliog.: 61 titles. — eng. 1608-1021 DOI: https: //doi.org/10.15407/ufm.20.03.502 https://nasplib.isofts.kiev.ua/handle/123456789/167935 en Успехи физики металлов application/pdf Інститут металофізики ім. Г.В. Курдюмова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The review article deals with ‘quantum engineering’ of growing of silver films on semiconductor substrates that allows obtaining new forms of matter. The results on the energy dispersion of electron states in epitaxial Ag (111) films obtained on Si (001) and Si (111) are presented.
format	Article
author	Karbivska, L.I. Karbivskyy, V.L. Romanskyy, A.O.
spellingShingle	Karbivska, L.I. Karbivskyy, V.L. Romanskyy, A.O. Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon Успехи физики металлов
author_facet	Karbivska, L.I. Karbivskyy, V.L. Romanskyy, A.O.
author_sort	Karbivska, L.I.
title	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon
title_short	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon
title_full	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon
title_fullStr	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon
title_full_unstemmed	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon
title_sort	determinism of the symmetry of a single-crystalline surface of interface at obtaining 0d- and 2d-structues of noble metals and indium on silicon
publisher	Інститут металофізики ім. Г.В. Курдюмова НАН України
publishDate	2019
url	https://nasplib.isofts.kiev.ua/handle/123456789/167935
citation_txt	Determinism of the symmetry of a single-crystalline surface of interface at obtaining 0D- and 2D-structues of noble metals and indium on silicon / L.I. Karbivska, V.L. Karbivskyy, A.O. Romanskyy // Progress in Physics of Metals. — 2019. — Vol. 20, No 3. — P. 502-532. — Bibliog.: 61 titles. — eng.
series	Успехи физики металлов
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first_indexed	2025-11-27T08:46:31Z
last_indexed	2025-11-27T08:46:31Z
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fulltext	502 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 © L.I. KARBIVSKA, V.L. KARBIVSKYY, A.O. ROMANSKYY, 2019 https://doi.org/10.15407/ufm.20.03.502 L.I. KARBIVSKA, V.L. KARBIVSKYY, and A.O. ROMANSKYY G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine DETERMINISM OF THE SYMMETRY OF A SINGLE-CRYSTALLINE SURFACE OF INTERFACE AT OBTAINING 0D -AND 2D -STRUCTUES OF NOBLE METALS AND INDIUM ON SILICON The review article deals with ‘quantum engineering’ of growing of silver films on semiconductor substrates that allows obtaining new forms of matter. The results on the energy dispersion of electron states in epitaxial Ag (111) films obtained on Si (001) and Si (111) are presented. The splitting of bands is explained, and analysis of the Shockley’s surface states is given. Superstructures, which are formed on the surface of monolayer silver nanostructures, are analysed in detail. A detailed analy- sis of the energy states of the noble-metal quantum wells is given. The mechanism of formation of a noble-metal nanorelief on the (111) and (110) surfaces of Si single crystal during multistage thermal deposition is investigated. The symmetry of the interface surface of the single-crystal Si (111) 7 × 7 silicon plane is deterministic in the growth mechanism of the hexagonal-pyramidal structures of copper, silver, and gold. The morphological features of the indium surface during its thermal deposi- tion on the Si (111) and Si (110) surfaces are investigated. The formation of clusters of a regular cubic shape is observed that indicates the formation of In nanocrystals. The formation of In nanoclusters (of ≈10 nm size) on the Si (111) surface and the subsequent modification of the single-crystal surface morphology response in the calculated curves of electron density of states. Keywords: quantum wells, energy dispersion, noble metals, surface, morphology, scanning tunnelling microscopy, thermal deposition. 1. Introduction For specialists involved in the study of the growth processes of thin films and the study of the surfaces of materials, the fabrication of me- tallic nanostructures on the atomic-clean surfaces of semiconductor sin- ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 503 Determinism of the Symmetry of a Single-Crystalline Surface gle crystals is one of the most important areas of research. Among other things, it is so because in many electronic devices the metal-semi- conductor boundary section is a working component. Many years of in- tensive research in this direction eloquently prove its importance. Nev- ertheless, despite that, fundamental research in this area is still interesting and relevant. This topic still attracts a lot of attention, in- cluding due to a number of interesting effects associated primarily with preparation technology and size effects. It is known that the growth modes (regimes) of substances on differ- ent substrates can be described by three main types [1]: two-dimensional (2D) mode or layer-by-layer growth (Frank–van der Merve growth mode); combined growth mode, which begins as layer-by-layer growth but then proceeds to three-dimensional island growth (Stranski–Krastanov growth mode); three-dimensional island film growth (Volmer–Weber growth mode). When we vary thermodynamic parameters based on the analysis of boundary energy and surface energy, these three growth modes may have differences [2]. The growth of metals on surfaces of semiconductors has heteroepitaxial character. For a long time, it was thought that the growth of metals on semiconductor surfaces obeys the aforementioned growth regimes. However, in 1996, a new approach was published [3]. This approach was based on the critical film thickness during the growth of silver on the GaAs(110) substrate surface. In the aforementioned work, it was shown that with a less critical film thickness, they are un- even, and with increasing thickness, they grow into a smooth, even layer. A new method for growing thin films was proposed when Smith et al. [3] applied the two-step method described earlier by Evans et al. [4] for growing silver on the surface of GaAs (110) at ≈135 K and further an- nealing at room temperatures. It was discovered that the initially uneven Ag film consisting of nanoscale 3D clusters self-organizes into an atom- ically flat film, when the system is warmed to room temperature. More- over, such a transition from cluster organization of the surface to an atomically smooth one can take place only when the total number of lay- ers is no less than six monolayers (ML) [3]. Due to the study of nature of this new type of critical thickness of growth, the ‘electronic growth’ model was proposed [5]. Electrons in thin films are quantized along the direction of the surface normal and some of these electrons can be scattered at the interface of film substrate. Consequently, as the thickness changes, there will be a change in the electron energy, which includes oscillations of electrons along the nor- mal direction to the surface and electrostatic potential due to the ap- pearance of an electrical double layer with scattered electrons at the interface. The balance between these phenomena determines the thick- ness at which the total electron energy has a local minimum [5]. Thus, the film tends to align and acquires an atomically flat morphology. 504 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 The study of Cu, Ag, and Au nanostructures formation during their thermal deposition on semiconductor single-crystal surfaces provides a valuable information about organization of metallic nanostructures, in par ticular, metallic single-component ones. In view of that, it is very im- portant from a fundamental point of view. On the other hand, given the applications in electronics for example, they are no less important from a purely practical side. Nowadays, noble metal nanostructures are used in various consumer technologies that use their physical properties, particu- larly optical, electrically conductive, antibacterial, and others [6–10]. This paper focuses on an overview of the study of the electronic, spectral, morphological, and structural properties of monolayer films of noble metals on the surfaces of single crystals. 2. Energy Dispersion in Ag (111) Epitaxial Films Obtained on Si (001) and Si (111) The authors of Ref. [11] investigated the dispersion of the quantum- well states (QWS) in Ag (111) epitaxial films grown on Si (001) and on Si (111). The studies were carried out via photoelectron spectroscopy with angular resolution (ARPES). It was found that the planar band structure of a thin Ag film is essentially determined by the interface of the substrate (Fig. 1). The s and p valence electrons of silver in the film are spatially lim- ited and quantized along the normal to the Ag (111) film. For a bulk metal, the Ag (111) E(k║) is isotropic, but the size of the dispersion be- comes significant, if 4d states participate in the hybridization with an increase of the binding energy [13, 14]. As established by Müller et al. [12], in-plane effective mass m* ║ increases with binding energy Ebind (the solid line in Fig. 1). Such a tendency of the s–p band m* ║ of bulk Ag is explained by the electron states of quantum wells in the Ag/Cu (111) system [12]. However, this trend does not correspond to the ARPES data for QWS in Ag/Si (001) and Ag/Si (111), which show completely opposite aspirations of m* ║ with respect to the binding energy. The change in plane dispersion can be caused by transverse deforma- tion of film, which is caused by the lattice mismatch of the interface and the film [15]. This deformation effect was theoretically calculated and, as it turned out, it is quite insignificant, and, if there is one, it is homogeneous in the entire energy range. However, this does not explain the results for the QWS in Ag/Si (001) and Ag/Si (111), which are sig- nificantly different from bulk Ag. Herewith, the possibility that the lattice deformation changes m* ║ cannot be ruled out, thus, affecting the hybridization of the Ag 4d and s, p valence states. Another factor that was considered in explaining the anomalous plane band dispersion was the small size of the planar coherent region. L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 505 Determinism of the Symmetry of a Single-Crystalline Surface Although this effect of transverse size of film is unlikely, since the Ag (111) film had an area size of less than 200 Å, which was observed with scanning tunnelling microscopy (STM) and low-energy electron dif- fraction (LEED) [16–19], which goes far beyond the quantum limit <50 Å [20]. During the photoelectron investigation of deposited Ag layers on the V(100) surface, Valla et al. [21] observed a large discrepancy be- tween the Ag s–p planar band dispersion and the behaviour of free elec- trons. From the similarity between such an unexpected dispersion of the QWS and that on the V (100) substrate with the 3d band, Valla et al. [21] suggested a strong hybridization between these two electronic states. Such hybridization with electron states of the substrate can cause unu- sual dispersions of QWS observed in Ag/Si (001) and Ag/Si (111). Shaded areas in Fig. 1 correspond to the valence region of the sili- con substrate below the maximum of the valence band. When QWS are located within this energy range, they can hybridize with the electron states of the substrate. Apparently, this unusual behaviour of m* ║ in Ag/ Si (001) and Ag/Si (111) occurs inside such regions. Note also that the masses m* ║ for Ag/Si (001) and Ag/Si (111) differ little, when the corre- sponding QWS are located outside the region of the substrate: the QWS with n = 1 in Ag/Si (001) has m* ║ = 0.3me at Ebind = 0.5 eV (Fig. 1). It is assumed that the wave functions of the electrons of the Ag (111) s–p band and the Si (001) s–p band do not hybridize with each other. It is also not entirely clear how hybridization can affect a planar band dis- persion of film with a thickness of 14–16 ML with shielding values in- side the metal [22, 23]. A correct theoretical description with necessity required knowledge of the band structure of Ag films on monocrystal- line silicon substrates. Another unusual aspect of the planar dispersion of QWS is the fact that the QWS with n = 2 in Ag/Si (001) splits into two subbands with significant dispersion (Fig. 2). Such a splitting is less likely to occur Fig. 1. Ratios of (topo- logical) effective mass (m* ║) to the free electron mass (m0) as a function of the binding energy of the QWS at k║ = 0 for Ag (111) film on Cu (111) [12], Si (111), and Si (001) substrates. The data were obtained at hν = = 22.7, 10.3, and 9.3 eV, respectively (–, ●, ■, ♦) 506 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 with large quantum numbers, e.g., n = 3. Analysing the splitted bands, it is necessary to analyse in detail the possibility of the influence of photoemission from the surface of the substrate itself. The STM and electron diffraction results [17, 18] show that Ag (111) films uniformly cover the substrate surface, while the mean free path for the corre- sponding photoelectrons is no more than ≈10 Å [24], which is about one third of film thickness Ag (111). It can be assumed that splitting can be caused due to contributions from different parts of the silver film, which have different thickness. However, this explanation is also not plausible, as it was shown that silver films are homogeneous with a height variation of ±1 or ±2 ML and the expected energy splitting for such variations in height is much less than the observed one [25, 26]. The parabolic dispersion law should describe the expected dispersion of the QWS from slightly different film thicknesses. Such splittings were observed for the Ag (111) films on Si (001) with different thicknesses. The authors of [11] proposed an explanation of such a splitting of QWS within the framework of the quantization rule of the phase shift. It has been established that the difference in the phase shift between the inner and outer side of the valence band of the substrate corres- ponds to 0.3 π, which, with using theoretical calculations, gives the dif- ference between the split Ebind branches for QWS with n = 2 equal to 0.10 ± 0.04 eV. This ratio agrees quite well with the observed energy splitting at 0.13 ± 0.03 eV for QWS with n = 2 (Fig. 2). Similar calcula- tions were performed for QWS with n = 3 and 4 in accordance with the observed energy splittings, e.g., 0.13–0.18 eV for n = 3. These calcula- L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Fig. 3. The same as in the previous figure, but for 16 ML film on Si (111) substrate [11] Fig. 2. Binding energy Ebind vs. wave vector kǀǀ for 14 ML thick Ag (111) film on Si (001) substrate along the [101] axis of the substrate (hν = 22.7 eV) [11] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 507 Determinism of the Symmetry of a Single-Crystalline Surface tions confirm the idea of a phase break at the substrate edge during emission not normal. However, such a model is not sufficiently complete to describe in detail dispersion of the split QWS. If we apply such theoretical calculations for the Ag/Si(111) system, the change of the binding energy of QWS near the edge of the bulk Si band at Ebind ≈ 0.5 eV [QWS with n = 1 in Ag/Si(111)] will be around 0.03 ± 0.03 eV. Such a small value is determined by flattening of the s–p band of silver close to the top of the band (Fig. 3). 3. Shockley’s Surface States The Shockley’s surface electron states on silver epitaxial films grown on a Si (111) 7 × 7 surface were studied in the work of Neuhold et al. [16]. The films were obtained by a two-step method [3]. The LEED method showed that, before the annealing, only blurred spots were observed, and after that, distinct hexagons were revealed (Fig. 4). If we consider a silver layer as a quantum well with valence elec- trons, the wave vectors of stationary states in the well have the values, which are described via the equation kz = nπ/Na + C, where a — atomic- layer width, N — the number of atomic layers in the metal film, n — principal quantum number. Amendment C occurs due to the finite height of the walls forming the pit. This value can be found theoretically and vary very slightly in a certain energy range [27, 28]. Therefore, this equation describes the quantiza- tion condition for the k values, which, due to the monotony of the band structure, lead to dis- crete energy levels, first observed by means of the photoelectron spectroscopy by Wachs et al. [29]. Figure 4 [30] compares the spectra of Ag (111)/Si (111) 7 × 7 Fig. 4. Comparison of photoelectron spectra obtained with excitation photon energy of 47 eV and emission normal to ≈50 Å thick Ag (111) on the HOPG and Si (111) 7 × 7. The diagram below shows the characteristic part of the Ag band structure near the L point (L' 2 — edge of the band). The wave vector is taken as the radius vector of the Brillouin zone along the Γ–L direction. The in- sert in the figure shows the LEED of the Ag (111) film on Si (111) 7 × 7 [30] 508 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 and Ag (111)/HOPG (0001) systems (here, HOPG abbreviates the highly oriented pyrolytic graphite) obtained by photoelectron spectroscopy at a temperature of 130 K (the substrate temperature during Ag depo- sition). In the band gap along the Γ–L direction (the shaded area below Fig. 4), there are Shockley’s surface states, which give a peak near the Fermi energy EF in the Ag/HOPG spectrum in Fig. 4. Its energy is 50 meV below EF at the temperature of 130 K [31]. It is noteworthy that the peak is absent in the spectrum of the Ag (111)/Si (111) 7 × 7 system obtained in a similar way. The so-called phase accumulation model was used to explain the differences in the spectra (Fig. 4). In this model, the surface states are stationary states in a one-dimensional (1D) quantum well containing a potential barrier from the vacuum side and a band gap of the crystal on the other side [32]. Quantum-mechanical solutions are in the form of phase shifts in the reflection of the wave functions of electrons from these barriers [27, 28]. It is easy to show that the energy of the Shockley’s surface state, which is the lowest proper state of this well, depends on the height of the vacuum barrier, that is, on the work function [27], and on the energies of the band edges [31]. An experimen- tal evaluation of the dependence of the energy of surface states on the L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Fig. 5. Photoelectron spectra of Ag films on HOPG (left) and Si (111) (right) substrates coated with Cs submonolayer. Vertical bars indicate shift of peaks (ħω = = 47 eV) [27] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 509 Determinism of the Symmetry of a Single-Crystalline Surface work-function magnitude was made. The use of the adsorption of the alkali-metal submonolayer leads to a significant decrease in the work function. The effect of reducing the work function and its effect on the experimental spectra of surface states is shown in Fig. 5. The upper left curve (in Fig. 5) for the Ag (111) surface contains peaks and significant emission of surface states near EF. As an amount of precipitated Cs increases, a decrease in the work function is observed. Such behaviour was previously observed for Cs/Cu (111) and Na/Cu (111) in Refs. [33, 34]. The decrease of the intensity of the peaks of surface states with the deposition of Cs occurs due to the redistribution of its charge in the energy-momentum space [35]. The unperturbed electron wave function can be detected in a limited region, and when surface states cross the edge of the L' 2 band at the level of 0.3 eV below EF, their wave function spreads into the bulk, and the electrons corresponding to this state will have less sensitivity to surface photoemission. In order to quantify the shift of the energy of surface states with a change in the work function, the peaks of the surface states of the quantum well were modelled using the Voigt peaks described by the Fermi function with experimentally determined parameters. On the left in Fig. 6, the re- sults of this analysis for Ag (111) spectra on HOPG are shown by circles. Given solid line reflects the energies of surface states taken from the phase accumulation model, in which the effect of adsorption of Cs is assumed to lead to a change in the work function [27]. One can see that a simple model describes well the behaviour of surface states. Fig. 6. Shift of the surface states with changes of the work function and strain. On the left, the energies of the surface states (from Fig. 5) are compared with the ener- gies of the phase accumulation model (solid line). On the right, there are calculated energies of the L' 2 edge of s–p band. The circle marks the point on the theoretical curve, where the energy of the surface states is shifted by 150 meV relative to the equilibrium value, as it is the case in Ag (111)/Si (111) 7 × 7 [31] 510 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 In Figure 5 to the right, we can see the results of the effect of Cs adsorption on the x-ray photoelectron spectra of the 54 Å thick Ag (111) film obtained on Si (111). The upper curve reflects the spectrum of the clean surface. Figure 4 shows only the peaks of the quantum well in the s–p band. No signal from surface states was found in the vicinity of the Fermi edge. Nevertheless, with a decrease in the work function (Φ) upon the adsorption of Cs, an increase in the intensity of the peak below EF occurs. This peak is the most pronounced in the spectrum of the work function change ΔΦ = −1.31 eV. With a subsequent decrease in the work function, the intensity of this peak decreases. After its first manifesta- tion at ΔΦ = −0.74 eV, the energy of its maximum decreases with de- creasing work function. Thus, the emission from the surface states of the Ag (111) layers obtained on Si (111) 7 × 7 is due to the shift of the surface states to the unoccupied region. The downward shift caused by adsorption of Cs causes an intersection with the Fermi level. The ener- gies of the surface states obtained from the spectra are shown in Fig. 6. In order to model the spectra for the clean surface of the Ag (111)/Si system with a similar restrictive parameter obtained in the case of the Ag (111)/HOPG system, it is necessary to have a surface state almost 120 meV above EF. The surface states of the Ag (111)/Si (111) 7 × 7 sys- tem shift, on average, by 150 meV relative to the states in the Ag (111)/ HOPG system. This value is sufficient to empty completely the surface states of the clean Ag (111) surface at a given temperature [31]. Consequently, several effects can cause a shift in surface states. In thin epitaxial Ag layers, the surface states of Ag (111) demonstrate sig- nificant shifts, which are explained in terms of the interaction of the weakly damped wave function of the surface state in the substrate [36]. The film thickness of about 50 Å, which was used in the work [16], was much longer than the attenuation length ≈28 Å [37], which makes this explanation of the above observations impossible. The lateral localization of the wave function of the surface state on the tops of the islands, which was considered in Ref. [20], is equally unlikely, since the island size necessary to obtain a noticeable shift is much less than the lateral coherence length of LEED. Since the Ag/ Si (111) 7 × 7 interface boundary has significant distinctive parameters [38], this should lead to the disappearance of LEED. The LEED spots (Fig. 4) demonstrate that the localization of the surface states of Ag (111) cannot make a significant contribution to the observed energy shift. The effect of band edges on the energy of the surface state is a di- rect explanation of the shift of the surface state in Ag/Si (111) 7 × 7. Due to its close proximity, the lower band edge (L' 2) has a huge impact. Therefore, it is reasonable to assume that this quantity determines the observed shift. This view is supported by the fact that the highest peak of the quantum well, corresponding to the principal quantum number L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 511 Determinism of the Symmetry of a Single-Crystalline Surface n = N − 1, has a higher energy in Ag/Si (111) than in Ag/HOPG. Since the number of Ag layers is ca 21 in both cases, this peak should occupy the same position relative to the edge of the band. This means the ob- served energy difference indicates a shift in the edge of the L' 2 band. Nevertheless, variation of the correction coefficient C in equation kz = nπ/Na + C (see designations above) for Ag films on two substrates may affect the energy positions of the QWS. Since deformation is a widespread characteristic of film growth on substrates with lattice mismatch and was observed on epitaxial silver films of the same thickness [39], its effect on the L' 2 energy should be considered. The Ag band structure for deformed (stressed) lattices was calculated through the empirical pseudopotential method (EMP) in Ref. [40]. The described scheme is sufficient to describe the properties of a simple band structure of Ag s–p electrons. In order to reproduce the experimental value of −0.3 eV for the energy L' 2 [41] in an unstressed lattice, the bands after the calculation were shifted by 225 meV. Since the L' 2 value is determined using the EMP, the energy of the surface state is derived from the phase accumulation model. This scheme can be verified by using the temperature dependence of the energy of the sur- face state, as made by Paniago et al. [31]. The temperature expansion coefficient relates the sample temperature to the isotropic deformation of the silver lattice. If we use the value 19 ⋅ 10−6 K−1 [42], then using the described procedure, we obtain the value 0.12 meV/K for the shift of the surface state depending on temperature. This result well agrees with the experimentally determined value of 0.17 meV/K obtained in Ref. [31]. The deviation may be due to the narrowing of the band gap L with lattice vibrations that was calculated by Larsson and Pendry [43]. It is assumed that the stress that exerts pressure on the lattice and accompanies the process of forming epitaxial Ag (111) films changes the lattice constant of the (111) plane. As a result, the lattice constant of the plane perpendicular to this one also changes. During deformation, the volume of the crystal will be maintained. This condition was used in calculations when describing lattice deformation. In the right part of Fig. 6, the results of a theoretical review are shown. The calculated en- ergy of the surface state is already strongly shifted at low tensile stress- es in the (111) plane (compressed along the [111] direction). In order to explain the observed shift of 150 meV, the Ag (111) lattice grown epi- taxially on Si (111) must be deformed by approximately 0.95%. A ten- sile stress of this magnitude observed in silver films of comparable thickness on MgF2, Si (100) and mica [39] was attributed to the poly- crystalline growth of Volmer–Weber. It was suggested that its nature belongs to the relaxation of grain boundaries and the effects of recrys- tallization in a silver layer. Increased recrystallization due to the subse- quent annealing stage should lead to a further increase in the tensile 512 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 stress. In addition, the lattice order is improved, as evidenced by LEED spots, and the surface is levelled that is a necessary condition for ob- serving QWS in the s–p band (Figs. 4 and 5). Differences in the tem- perature expansion of silicon and silver cannot contribute to the defor- mation presented in this system, since the deposition and measurement were carried out at the same temperature. Due to the limited attenua- tion length of 28 Å [37], the energy of the surface state during deforma- tion changes only for the uppermost layers of film. Silver layers obtained in a similar way on GaAs (110) substrates also show quantum-mechanical peaks indicating uniform growth morpholo- gy, but with no surface states. In Ref. [3], using scanning tunnelling microscopy, it was shown that the surface state is absent on the Ag (111) structure. However, there are data for which the deformation is a con- troversial issue. Jiang et al. [44] described the procedure of measurements of both the surface structure and electronic properties of thin silver films. Us- ing scanning tunnelling spectroscopy (STS), thin Ag films grown on a GaAs (110) substrate and obtained by a two-step method were studied [3]. The STS method allows us to study unoccupied electron states on the surface of films, which are above the Fermi level, in contrast to the photoelectron-spectroscopy method used earlier, in which the range of recorded energies is limited to the Fermi level. The STS spectra, which show the dependence (dI/dV)/(I/V)mean of the voltage V, are shown in Fig. 7. All spectra have three significant peaks in the density of states. Two of them are associated with occupied (V < 0) electronic states and one with unoccupied (V positive) state. The peaks that are observed below EF, i.e., associated with the occupied states, change with a change in the film thickness, although the peak of free electronic state did not respond to the film thickness. The occupied states can be associated with QWS that appeared under the restriction on z of the Ag film, while the unoccupied states are the Shockley’s sur- face states (energetically, they occupy the positions at the level of ≈180 meV). The authors of Ref. [44] used the quantization condition for the wave vector of stationary QWS given above to determine the kz value. Using the data in Fig. 7, the authors plotted the dependence of the en- ergy levels (peaks in Fig. 7) on the film thickness (Fig. 8). Analysis of the energy positions of the QWS and the thickness of films allows one to derive the s–p band dispersion in thin Ag films. The principal quantum number n in the first Brillouin zone must be between 1 and N (N is the number of atomic layers). Therefore, the first occu- pied state below EF corresponds to the QWS with n = N − 1 and the wave vector will be kz = (N − 1) π/Na. The wave vector at the boundary of the Brillouin zone (point L) is then reads as kzL = π/a − kz = π/Na. By anal- L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 513 Determinism of the Symmetry of a Single-Crystalline Surface ogy, for the wave vector of the neighbouring state, the formula will be as follows: kzL = 2π/Na. Figure 9 shows the band structure along the direction of Γ–L. The solid line describes the band structure of bulk silver. Around point L, the data behaves similarly to pure Ag(111) (solid line). Nevertheless, the experimentally observed energy values shifted upward by 190 ± 20 meV relative to theoretical values. With increasing distance from point L, they deviate more significantly towards higher energies. Thus, the dis- persion and the width of the band of thin Ag films on GaAs(110) sub- strates are smaller than those are known for the theoretical band struc- ture of pure Ag. During the construction of the experimental data of the band struc- ture, the correction C in the above-mentioned equation for kz was not taken into account that is associated with the influence of the inter- faces. Indeed, on the one hand, the amendment would introduce a hori- zontal shift, but would in no way affect the energy shift, since, around point L, the energy states are above the maximum of s–p band for pure Ag(111) (Fig. 9). On the other hand, the phase shift at the Ag–vacuum interface changes very little with a change in thickness and the contri- bution to the band structure of this interface is insignificant [4, 16]. In this case, EF lies at the level of the band gap of GaAs on the side of the Ag–GaAs interface. Therefore, electrons with energies close to EF should be Bragg reflected from this interface and the phase shift should be ap- proximately π. Fig. 8. Energy positions of the STS spectra peaks vs. the film thickness [44] Fig. 7. STS spectra of Ag films with thicknesses of 2.0–4.5 nm [45] ← 514 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 For a detailed analysis of the surface states, the authors of [44] de- posed potassium on the surface and compared the STS spectra. As Fig- ure 10 shows, after the deposition of potassium, energy of free states decreases by ≈190 meV, and these states are occupied. Deposition did not affect the occupied states. This potassium deposition effect can be explained, taking into account the fact that potassium reduces the work function of the sample. At the basis of the phase accumulation model, Shockley’s states are shifted to lower energies due to a decrease in the vacuum barrier, i.e. the work function. The ≈190 meV shift for Shock- ley’s states should be due to the decrease of the work function by 1.2 eV [16]. Similar shifts for Shockley’s states, with a decrease in the work function, were also observed for Ag films grown on Si (111) surfaces [16] and on surfaces of other noble metals [33, 34]. This experiment confirms the assumption that the main observed maximum in the free states belongs to the Shockley’s surface state. In Figure 10, potassium deposition does not change the QWS posi- tions, although lowering the work function should increase the length of the QWS wave function tails deep into the barrier in the direction of vacuum. According to rough estimates, a decrease in the work function of 1.2 eV leads to a change in the wave vector of first quantum-well state only by Δkz (n = N − 1) < 0.05 nm−1 that corresponds to the energy shift of the QWS less than 20 meV. Such a small shift cannot be resolved in measurements at the room temperature. L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Fig. 10. The STS spectra obtained for clean surface of 1.5 nm thick Ag film on GaAs (110) and after deposition of 0.2 nm of K on the Ag film surface [44] Fig. 9. The s–p band structure of the Ag film near the point L along the Γ–L. The circles show the energy states for QWS ob- tained via the STS method [44] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 515 Determinism of the Symmetry of a Single-Crystalline Surface After analyzing the energy positions of the surface states of the bulk (111), Jiang et al. [44] concluded that the surface states of thin Ag films on the GaAs (110) surface are shifted upwardly by 210 ± 30 meV. This shift in magnitude is comparable to the shift observed for the dis- persion of the s–p band. The energy shifts of the s–p band as well as a significant decrease in the width of the band during film dispersion as compared to the bulk material may be due to the lattice stress in thin films. It was shown that an increase in the temperature of noble metal crystals causes a shift of the band structure upward toward EF [31, 46] due to a temperature in- crease in the lattice constant at high temperatures. An increase in the lattice causes a decrease in the overlap of the wave functions, reducing the width of the band. Using the results of calculations based on the empirical pseudopotential method (EPM), the authors of [44] estimated that a shift of about 200 meV corresponds to a planar tensile strain Δa ≈ 1%. Ag thin film on GaAs(110) has a superstructure. The appear- ance of the superstructure confirms that the film is stressed. The LEED studies also confirm the presence of deformation. Therefore, [111] ori- entation of the Ag film is deviated by approximately 4° in accordance with the orientation [110] of the GaAs substrate [47, 48]. If we assume that the Ag–GaAs interface has the same slope, we can assume an Ag film as (667)-oriented film with (111) microfaces. In such a structure, the distance between two steps on the Ag(667) surface is 3.16 nm that is greater about 2 times than the average distance (1.5 nm) between the bands of the quasi-periodic modulated surface [49]. In such a structure, unrelaxed Ag (667) films should have a large lattice mismatch of ap- proximately 6% as compared with the GaAs (110) lattice along the [001] direction. It is likely that the lattice mismatch partially weakens the quasi-periodic superstructure, which leads to an internal lattice stress. The authors of [44] observed identical quasi-periodic superstructures in all Ag films, regardless of their thickness. In this connection, at a stress in a thin film, an upward shift of the electron s–p band occurs. Thus, the upward shift of surface states can be associated with the upward shift of the electron s–p band and the effect of lattice stress. In the model of the phase approach, Shockley’s states occupy the lowest state in the potential well limited by the potential barrier from the vacuum side and the band gap of the crystal from the other side. The energy of Shockley’s states depends on the work function as well as on the position of the edge of the band gap (point L). In this case, the last shifts upward by 190 ± 20 meV in comparison to the energy band struc- ture of the bulk material of f.c.c. Ag (111) at L point. Jiang et al. [44] proved why other unoccupied states did not arise for the QWS. The s–p band of electrons of f.c.c. Ag has a wide band gap of 4.2 eV along the Γ–L direction near the point L [50]. The range of 516 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 voltages applied to the sample from 0 to 1.5 V was within the energy limits of the band gap. Therefore, there could be no free QWS states along the Γ–L direction. The electron energy in this direction does not increase, but increases along the lateral directions (Γ–Õ and Γ–W). A group of Japanese scientists in the paper of Sawa et al. [51] stud- ied the thickness-dependent behaviour of Shockley’s surface states. They were interested in the question-challenge, due to what the upward shift of the bottom of the surface dispersion band occurs with a decrease in the thickness of the Ag film. The dI/dV graphs show the standing waves of surface electrons that appear at the edges of the steps, the monolayer well and partial dislocations (Fig. 11). Using these images, the wave- length of the surface electron was found. In the calculations, the dis- tance between the peaks of standing waves in the region distant from the defects and dislocations was used in order not to take into account the various quantum limitations of the electrons in these narrow sur- L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Fig. 13. Changing of the dispersion of the surface-state band because of the hy- bridization with n = 1 QWS [51] Fig. 12. Dispersion graphs of the surface states for the films of different thick- nesses and for bulk Ag [51] (see also Ref. [3] in [51]) Fig. 11. STM (a) and dI/dV (b)–(d) images (31.5 × 31.5 nm2) for 20 ML thick Ag (111) film, where the bias voltages VS is 0.35 V (a), 0.15 V (b), 0.25 V (ñ), and 0.35 V (d) [51] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 517 face regions. With the determination of the wavelength λ, the plane wave vector k║ = 2π/λ was actually computed. Having found the surface electron energy E (equals to bias voltage Vs), the authors of the work were able to construct the dependence E(k2 ║) plotted in Fig. 12. From this figure, several consequences were concluded. First, surface states have a parabolic dispersion. Secondly, a 40 ML thick film has dispersion close to the dispersion of the surface states of bulk Ag (111). Thirdly, the energy shifts upward with decreasing film thickness (for energies with k║ = 0, the shift is 77 meV for a film with a thickness of 40 ML, while 77 + 26 meV for a 7 ML thick film). The fact of the shift of the bottom of the surface-state band Å0 due to the hybridization of the latter with the valence band of the substrate was refuted. For the Si (111) substrate, the valence band maximum is at the level of −0.3 eV below the Fermi level, and the bottom of the surface state band Å0 for the bulk Ag is only at the level of −63 meV, conse- quently, the energy levels do not overlap, and thus, hybridization is impossible. Although, e.g., for Ge (111) substrates, it is impossible to say so clearly, since the maximum of the valence band in this case is very close to the Fermi level. The fact of hybridization of the surface state band with QWS inside the film was also refuted. One can observe in Fig. 13 the dispersion of the surface band (dashed line) and the QWS with n = 1 (dash-dotted line). These two states intersect at k║ = 2.51 nm−1. However, degenera- tion at the intersection begins and the two states are split into upper and lower branches when the hybridization interaction HSQ = 〈QWS\|V\|SS〉 is introduced between the surface state and the QWS with n = 1 at their intersection [51, 52], which are indicated in this figure as solid and dashed lines. The exact HSQ value is unknown in the presented system. Although, as reported, HSQ lies in the range from 20 to 180 meV in Bi/ Ag films on a Si (111) substrate [51, 52]. Thus, in this study, the vari- ance of split branches was calculated with HSQ = 100 and 200 meV. The theoretical and experimental data on Å0 and the plane effective mass m∗ are given in Table below. The thickness dependence of the theoretically and experimentally found Å0 and m∗ values for surface band and QWS film with n = 1 Number of Ag ML E0 QWS (n = 1), eV Crossing, nm–1 Experiment HSQ = 100 meV HSQ = 200 meV E0, meV m∗/m0 E0, meV m∗/m0 E0, meV m∗/m0 7 −1.08 4.07 26 0.37 −54 0.42 −27 0.41 10 −0.83 3.54 −6 0.37 −52 0.41 −18 0.40 20 −0.45 2.51 0 0.34 −52 0.38 −19 0.36 30 −0.38 2.26 −11 0.39 −53 0.37 28 0.35 40 −0.31 2.01 −51 0.42 −49 0.34 46 0.34 Determinism of the Symmetry of a Single-Crystalline Surface 518 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 Due to hybridization, it is assumed that E0 moves downward and m∗ becomes larger with decreasing thickness. However, in the experiment, inverse dependences on thickness were observed (the 4-th and 5-th col- umns in Table). Therefore, it was excluded from consideration about the hybridization of the surface state and QWS as the cause of the observed shift of the surface states of the Ag(111) films. This calculation indi- cates that HSQ is very small, and no significant splitting occurred in the presented Ag/Si(111) system. Sawa et al. considered the change in the electronic structure of Ag films caused by stress [16]. The lattice constant for Ag is 25% less than for Si. The calculation using the EPM demonstrated that the plane ten- sile strain shifts E0 upward on the surface of the Ag(111) film [16]. Indeed, as the film thickness increases, the misfit stress gradually weakens in the heteroepitaxial system [53]. From this point of view, it is reasonable to assume that E0 shifts upward, since the thickness of the Ag film decreases, since a decrease in thickness increases the flat tensile strain. This explanation also agrees with the results of the previous study using photoelectron spectroscopy of the temperature-dependent shift E0 on the surfaces of bulk Ag(111) [31]. Application of the method of photoelectron spectroscopy shows that the shift upward of E0 at the temperature increase is observable. The same effect is observed due to the stress. In addition, the calculation with the usage of the EPM indicates that 0.95% of the value of flat tensile stress causes E0 to be shifted upward by 150 meV [16]. This result confirms that the accumulated stress in the film was not 25%, even for an Ag film with a thickness of 7 ML on the Si(111) substrate. STM studies showed that Ag films con- tain many dislocations even at a very early stage of the growth [54]. That is why the authors of Ref. [51] interpreted the small shift E0 by stress relaxation. 4. Quasi-Periodic Superstructures of Ag on Single-Crystal Surfaces The appearance of the superstructure, which is formed by an Ag film deposited on a GaAs(110) surface, has been studied by Ebert et al. [49]. They found that 1D quasi-crystals acting as a quasi-periodic self-similar superstructure are formed on the film. The nature of defects changing the surface superstructure of film is also ascertained. The 1D quasi-periodic structure is observed in the formation of thin Ag layers with a thickness of 1.5–1.7 nm using the two-step method [3]. All Ag films exhibit 1D modulation in height leading to bands with 0.05 nm grooves on STM images (Fig. 14). Figure 14 demonstrates that the bands are clear, not having the same separation, and do not form an explicit periodic superstructure. L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 519 Determinism of the Symmetry of a Single-Crystalline Surface Two different basic separation intervals with distances between the bands of about 1.2 ± 0.2 and 1.7 ± 0.2 nm can be distinguished (Fig. 14, b). The authors identified them with short (S) and long (L) sec- tions, respectively. Figure 14, a shows that at low magnifications STM images show bands similar to those in Fig. 14, b. Nevertheless, in Fig. 14, a, there are significantly longer distances between the bands than in the case of two base bands. Large-size bands arise due to additional height modulation, which overlaps with base-height modulation, re- sulting in L and S regions. Figure 14, c shows the Fourier transform of the bands. The peaks in the Fourier transform are well described and numbered [55] in the basis of two basic elements whose lengths are related to each other according to the principle of the golden section in inverse space. Peaks beyond 1/S are associated with the substruc- ture of the bands and they exhibit properties, which are described by the golden section principle (peak 1.6/S). Due to the Fourier transform as well as spatial images, it was found that the ratio of the long band- separating interval to the short on the STM images is 1.55 ± 0.15. This Fig. 14. The STM images for the 1.5 nm thick Ag film su- perstructure [3] on the GaAs (110) surface (a, b) and the Fourier transform (c) [55] 520 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 ratio is consistent within the framework of errors with the ratio of two consecutive members of the Fibonacci sequence for large values of their numbers (Fn, Fn+1 are sequence members, Fn + 1/Fn = φ, where (1 5) 2ϕ = + equal to 1.618… is golden ratio). Self-similarity and Fourier transform do not contradict the quasi-periodic type of order. The bands form a sequence of long and short sections. Such a se- quence is indicated in the lower part of Fig. 14, b. A large number of such sequences were analysed (with lengths up to 135 areas and a total number of areas over 1500 taken from different Ag films) in order to determine statistically the structural model, which best fits the experi- mental observations. Comparison with the Fibonacci sequence shows that the experimen- tally observed data best fit the sequence of the Fibonacci golden section, since it has the least number of irrelevant sequences. The best observed in the experiment is described by a quasi-periodic golden section se- quence with a coherence length of approximately 12.5 nm. This conclu- sion is also consistent with the LEED data, which can be well explained with taking into account quasi-periodic ordering of the golden section. It cannot be excluded that such a structure can be described using a high-order approximating sequence. However, high-order approximat- ing sequences and quasi-periodic structures differ little, and recogni- tion at this level is beyond the limits of the statistical accuracy under consideration. The limited coherence length indicates that defects must be present in the sequences. It has been detected that the main defect is the fre- quent absence of a short section. This one leads to three, and sometimes even more consecutive, long sections. The importance of this type of defect is confirmed by observation of dislocations that correct these sequences from three long sections on the LLSL sequence. It has been L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Fig. 15. STM images (with different scales) of the LLL sequence and dislocation correcting this sequence [55] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 521 Determinism of the Symmetry of a Single-Crystalline Surface shown that the sequences defined by dislocations have much better agreement with the Fibonacci sequence. The coherence length of the cor- rected sequences increases to almost 11 regions or 17 nm. The number of L regions decreases from 66% to 62% when adjusted, providing a very good agreement with that for the ideal Fibonacci sequence (≈61.8%). Thus, the missing short sections are main defects. Three consecutive long intervals between areas are labelled as LLL. In the position indicated by the arrow, one additional strip is inserted, which shows a short separation interval with the adjacent strip (section S), i.e. the dislocation generates a short section. It was found that such properties were observed with a concentration of approximately 5⋅1010 cm−2. Each observed dislocation has a Burgers vector oriented parallel to the quasi-periodic direction ([001] direction of the GaAs(110) substrate) with a short separation interval length. A pair of dislocations with op- posite Burgers vectors was observed frequently, as shown in Fig. 15, a; however, isolated dislocations were observed as well. In Figure 15, a, we can see an STM image of such a LLL defect, which can be referred to as a domain wall or as a grain boundary. In addition to dislocations, there are still other defects responsible for a limited coherence length. Figure 16 shows the most common ones— phason defects. A large degree of disorder occurs due to phason defects. Phase defects by definition are a local displacement of one position of a quasi-periodic lattice to another neighbouring position, violating the quasi-periodic structure. Surface phason defects in Fig. 16 were ob- served with a concentration of circa 1012 cm−2 [55]. A significant part of phason defects is not uniformly distributed over the surface. Small light circles in Fig. 15, b show that phason de- Fig. 17. Distribution of phason de fects close to the dislocation cores Fig. 16. STM image of Ag film surface with a phason defect [55] 522 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 fects arise close to the core of the dislocation. The STM image indicates that phason defects propagate mainly along the [001] direction from the dislocation core. A statistical analysis of the distribution of phason de- fects close to the dislocation cores is represented in Fig. 17 [55]. The size of the points in Fig. 17 is proportional to the number of phason defects (within the range of 1–8) per area unit around 14 dislocations. One division along the axes in Fig. 17 corresponds to a length of 3 nm; the centre of coordinates coincides with the core of the dislocation; the strip inserted during dislocation is located on the left side of the x-axis [55]. The authors of Ref. [49] found that all the band shifts due to pha- son defects occur in the direction opposite to the dislocation core. Thus, dislocations cause oriented phason defects. The appearance of phason defects can be explained from the point of stress relieving; they are close to the core of the dislocation, since phason defects increase the size of the interband interval that is necessary when an additional band is added-on during dislocation. In this case, the static stress field around dislocations is a source of phason defects, whereas early work on icosa- hedral quasi-crystals reported that the appearance of phason and disor- der is associated with dislocation movements [56, 57]. 5. Morphological Features of Nanostructures of Noble Metals and In during Their Thermal Deposition on the Si Single Crystal Surfaces The studies of surface nanorelief were performed on a JSPM-4610 tun- nelling microscope (JEOL, Japan). The working vacuum quality during the experiment was such that the pressure was ≤10−8 Pa. Plates of sili- con Si(111) and Si(110) single crystal with a size of 7 × 1 × 0.3 mm3 were used. Preparation of single crystal surfaces was performed by standard methods. Initially, a current of ≈0.2 A was conducted through the sili- con plate for one day. In this way, the sample was heated up to ≈250 °C. After that, the current conducting through the sample raised to 3.0 A being maintaining for 30 s, which corresponded to the sample tempera- ture of about 950 °C. Then, the sample was cooled, after which the (111) and (110) surfaces were imaged via a tunnelling microscope (Fig. 18). All studies on a tunnelling microscope were performed in the dc regime. L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Fig. 18. STM images of the Si single- crystal surfaces: Si (111) (a) and Si (110) (b) [58] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 523 Determinism of the Symmetry of a Single-Crystalline Surface Gold, silver, copper, and indium were deposed on the surfaces pre- pared by the thermal evaporation method. As an evaporator, we used a spiral tungsten cuvette containing a metal sample; the cuvette occupied the middle of a metal cylinder with a hole of 3 mm. The distance be- tween the sample and the evaporator was ≈7 cm. The deposition oc- curred at a current of ≈5.0 A through a tungsten coil, which corre- sponded to the temperature of ≈100 °C above the melting point of the metal. The time of deposition was about 1–3 s. The deposition of metal on a single crystal surface was performed without heating or cooling the sample. Tunnel spectra were studied using a high-vacuum tunnel spec- trometer with atomic resolution of the company JEOL (Japan). Fig. 19. Gold nanos- tructures on the Si (111) (a–e) and Si (110) (f–h) surfac- es, and profile curves (i–k) for some images (a, e, g) [59]. Arrows (a, e, g) relate to scale 524 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy Noble metal nanostructures (Fig. 19) can be obtained by varying deposition parameters [58–61]: the deposition time, the distance from the cuvette to the sample, the pressure in the chamber, the melting temperature of the cuvette, or the cooling of the sample. Using the developed technology, we can obtain hexagonal clusters with a hexagon side of ≈5 nm (Fig. 19, a). The geometry of such struc- tures is close to that of the Si (111) 7 × 7 single crystal surface (Fig. 18). Figure 19, b shows the chain ordering of clusters. Under certain techno- logical conditions, we obtained ‘fractal’ leaf-like gold nanostructures (Fig. 19, c). Needle-like crystals (Fig. 19, d) can be grown under the longer deposition times (≈1 min). The study showed that the stable hex- agonal-pyramidal structures of gold could be obtained only on the Si (111) plane. Meanwhile, on the Si (110) plane, we obtained the structures shown in Fig. 19, f, which are characterized by the presence of hexagons Fig. 20. Flakes of gold on the Si (111) surface (a–c), where the arrows indicate a scale, and corresponding profiles (d–f) [59] ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 525 Determinism of the Symmetry of a Single-Crystalline Surface without the formation of pyramids. For short deposition times and vac- uum up to 10−6 Pa, we observed clusters with a small size distribution (6–8 nm). In this case, an increase of the time of deposition led to the formation of cluster conglomerates (Fig. 19, g). Currently, the investigation and production of monolayer metallic coatings in a higher vacuum is of the significant interest. Combining some methodical and technological characteristics, we reached such a deposition regime, which allowed us to obtain monolayer flake-like gold formations (Fig. 19, h). There are areas within the flakes not filled with atoms. After the spectral analysis using the tunnel spectroscopy, we revealed that electron states in these vacancies might possess specific features. Particularly, they can be quantized according to the quantum dots principle. The parameters of flake shown in Fig. 20. Earlier in [59], we sug- gested that free sagging flake edges might be possible. However, an adequate answer to this question one can provide by the 3D-microscopy only. The case of free existence of a metal monolayer (or its edges in this case) contradicts the solid-state physics general canons. Analysing vacancies (with diameter of ≈0.5 nm), we noticed that Au atoms are absent in amount of ≈1–3 atoms (Fig. 20, b). Similar situation was observed for Cu deposited with the same tech- nological parameters as Au; the behaviour of formed nanostructures is very close to the morphological features for gold described above. Hex- agonal-pyramidal nanostructures of copper are shown in Fig. 21. Thus, self-ordered hexagonal-pyramidal nanostructures are formed on Si (111) by thermal evaporation of both Cu and Au. The ordering is characterized by parallelism of the corresponding sides of the bipyramid as well as their respective orientation relative to the sides of the 7 × 7 hexagon of the structure of silicon. The heights of the bipyramidal formations belong to the range 1–1.5 nm, as can be seen from the vector profiles. The thickness of growth of steps is of ≈0.15 nm that corresponds to the size of an atom. Observed ‘texturing’ in all the figures indicates that all bipyramids Fig. 21. Pattern of copper nanostructures on the Si (111) surface: 2D diagram (a) and height curve (b). White arrow (a) relates to scale 526 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy have the same orientation with respect to the interface structure of the base. Therefore, the symmetry of the interface plane is crucial in ob- taining such ordered nanostructures. The observed growth of steps corresponds to atomic planes. The characteristic distance from the beginning of the plane to the next one is (as is in the case of Au) ≈3 nm [58, 59]. For Cu as well as for Au at- oms, it is energetically more advantageous to begin formation of the next plane from this distance. In the case of copper deposition on the (110) surface of a single Si crystal, the observed pattern of nanorelief is similar to the image obtained for Au deposition. Copper, like gold, does not form pyramidal nanostructures on the Si(110) surface (Fig. 19, f). Mentioned above may indicate that the deposition of the atomic Au and Cu gases is partially, but not completely, described by traditional schemes for the nanorelief formation. The dynamic image of a steady flow of atoms is defined by the difference between the flows to and from the surface. Varying the technological parameters of deposition [58–61], we can obtain one or another morphological pattern of the noble metal surface. In the case of the indium deposition on the (111) and (110) surfaces of the Si single crystals, a completely different mechanism of forma - tion of nanostructures is realized (Fig. 22). The formation of predomi- nantly spherical In clusters is observed on short deposition times (1– 3 s). In addition, clusters close to hexagonal or rectangular shape may Fig. 22. Indium nanostructures on the Si (111) surface Fig. 23. Profile of indium roughness on the Si (111) surface: 2D diagram (a) and height curve (b) ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 527 Determinism of the Symmetry of a Single-Crystalline Surface be observed (Fig. 22, a). The formation of hexagonal clusters on the surface of shapeless cluster (Fig. 22, b) was observed when the deposi- tion time was increased up to 5 s. Furthermore, one can see the position- ing of rectangular and square clusters. The formation of clusters of correct symmetry unambiguously indicates the formation of indium nanocrystals. Indium has a much lower melting point (156.6 °C) as compared to gold and copper. Under the same technological parameters of deposition as for gold and copper, we obtained molten indium, which is many times overheated. Its deposition onto the uncooled surface of silicon single crystal resulted to formation of the clusters of form mentioned above. When the deposition time was increased above 5 s, it led to the for- mation of the bunch of clusters of predominantly cubic form (Fig. 22, c). An average side size of such cubic formations: 4–5 nm. It is noteworthy that this type of samples has the profile of irregu- larities with a height of 0.6–3 nm (Fig. 23). There is also a periodic relief substructure in the form of line bunches (Fig. 22, d). Figure 24 shows the tunnel spectra for the two samples. Curve in Fig. 24, a demonstrates the density of electronic states (DOS) for image in Fig. 22, a. A certain band gap at the Fermi level indicates a non- metallic character of the cluster, which attributes to ≈10 nm size clus- ters of In. Figure 24, b shows modification of the DOS caused by the surface morphology completely filled with bunches of clusters. The DOS curve is much closer to that of indium in the metallic phase. The first peaks in the region of occupied states characterize the p states of indi- um. For a single cluster, they are localized at ≈1.8 eV and have a narrow peak. But this maximum has a practically non-zero value in the region of zero binding energies, shifts to the region of high binding energies upon transition to the coating. The same tendencies of the DOS curve changing have been observed for the region of free states. Fig. 24. Densities of elec- tronic states corresponding to images in Figs. 22, a (a) and d (b) 528 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy 6. Summary ‘Quantum engineering’ of the silver films growing on semiconductor substrates allows obtaining new forms of the matter. Analysis of the growth of ultrathin metal films convinces that quantum mechanics plays an important role in the design of atomically flat metal layers. The results on the energy dispersion of electronic states in epitaxial Ag(111) films obtained on Si(001) and Si(111) surfaces are presented. Splitting of energy bands is explained; analysis of the Shockley’s sur- face states is given. Superstructures, which are formed on the surface of monolayer silver nanostructures, are analysed in detail. A detailed analysis of the energy states of the noble metal quantum wells is given. The mechanism of formation of a nanorelief of a noble metal on the (111) and (110) surfaces of a Si single crystal during multi-stage ther- mal deposition is investigated. The symmetry of the interface surface of the Si(111) 7 × 7 plane acts as a determinant factor in the growth mecha- nism of the hexagonal-pyramidal structures of Cu, Ag, and Au. The In surface morphological features on the Si(111) and Si(110) surfaces investigated upon the thermal deposition. The regular cubic- shape cluster patterns are observed that indicates the indium nanocrys- tals formation. The density of electron states varies when the case of a separate ≈10 nm-size In clusters on the Si(111) changes into the case of bunch coating of the single crystal surface (coating thickness no more than 30–40 nm). REFERENCES H. Liu, Y.F. Zhang, D.Y. Wang, M.H. Pan, J.F. Jia, and Q.K. Xue, 1. Surf. Sci., 571: 5 (2004). https://doi.org/10.1016/j.susc.2004.08.011 E. Bauer, 2. Z. Kristallogr., 110: 372 (1958). https://doi.org/10.1524/zkri.1958.110. 1-6.372 A.R. Smith, K.-J. Chao, Q. Niu, and C.-K. Shih, 3. Science, 273: 226 (1996). https://doi.org/10.1126/science.273.5272.226 D.A. Evans, M.Alonso, R. Cimino, and K. Horn, 4. Phys. Rev. Lett., 70: 3483 (1993). https://doi.org/10.1103/PhysRevLett.70.3483 Z.Y. Zhang, Q. Niu, C.-K. Shih, 5. Phys. Rev. Lett., 80: 5381 (1998). https://doi. org/10.1103/PhysRevLett.80.5381 G. Yang, Y. Zhou, H. Long, Y. Li, and Y. Yang, 6. Thin Solid Films, 515: 7926 (2007). https://doi.org/10.1016/j.tsf.2007.03.027 M. Rai, A. Yadav, and A. Gade, 7. Biotech. Adv., 27: 76 (2009). https://doi.org/ 10.1016/j.biotechadv.2008.09.002 R.M. Tilaki, A. Irajizad, and S.M. Mahdavi, 8. Appl. Phys. A, 84: 215 (2006). https://doi.org/10.1007/s00339-006-3604-2 G. Yang, D. Guan, W. Wang, W. Wu, and Z. Chen, 9. Optical Mater., 25: 439 (2004). https://doi.org/10.1016/j.optmat.2003.11.002 H.-J. Lee, S.-Y. Yeo, and S.-H. Jeong, 10. J. Mat. Sci., 38: 2199 (2003). https://doi. org/10.1023/A:1023736416361 ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 529 Determinism of the Symmetry of a Single-Crystalline Surface I. Matsuda and H.W. Yeom, 11. J. Electron Spectrosc. Relat. Phenom., 126: 101 (2002). https://doi.org/10.1016/S0368-2048(02)00145-7 M.A. M12. üller, T. Miller, and T.-C. Chiang, Phys. Rev. B, 41: 5214 (1990). https:// doi.org/10.1103/PhysRevB.41.5214 H. Wern, R. Courths, G. Leschik, and S. Hufner, 13. Z. Phys. B, 60: 293 (1985). https://doi.org/10.1007/BF01304449 H. Erschbaumer, A.J. Freeman, C.L. Fu, and R. Podloucky, 14. Surf. Sci., 243: 317 (1991). https://doi.org/10.1016/0039-6028(91)90369-4 E. Bauer and J. van der Merwe, 15. Phys. Rev. B, 33: 3657 (1986). https://doi. org/10.1103/PhysRevB.33.3657 G. Neuhold and K. Horn, 16. Phys. Rev. Lett., 78: 1327 (1997). https://doi.org/10. 1103/PhysRevLett.78.1327 M.H.-v. Hoegen, T. Schmidt, M. Henzler, G. Meyer, D. Winau, and K.H. Rieder, 17. Phys. Rev. B, 52: 10764 (1995). https://doi.org/10.1103/PhysRevB.52.10764 M.H.-v. Hoegen, T. Schmidt, M. Henzler, G. Meyer, D. Winau, and K.H. Rieder, 18. Surf. Sci., 331–333: 575 (1995). https://doi.org/10.1016/0039-6028- (95)00320-7 G. Meyer and K.H. Rieder, 19. Appl. Phys. Lett., 64: 3560 (1994); idem, Surf. Sci., 331–333: 600 (1995). https://doi.org/10.1063/1.111197, https://doi.org/10. 1016/0039-6028(95)00325-8 R. Fischer, Th. Fauster, and W. Steinmann, 20. Phys. Rev. B, 48: 15496 (1993). https://doi.org/10.1103/PhysRevB.48.15496 T. Valla, P. Pervan, M. Milun, A. B. Hayden, and D.P. Woddruff, 21. Phys. Rev. B, 54: 11786 (1996). https://doi.org/10.1103/PhysRevB.54.11786 A. Zangwill, 22. Physics at Surfaces (Cambridge University Press: 1988). https:// doi.org/10.1017/CBO9780511622564 H. Luth, 23. Surface and Interfaces of Solid Materials (Berlin: Springer: 1995). https://doi.org/10.1007/978-3-662-03132-2 S. Hufner, 24. Photoelectron Spectroscopy, Springer Series in Solid-State Sciences. Springer Series. Vol. 82 (Berlin: Springer: 1995). https://doi.org/10.1007/978- 3-662-03150-6 J.J. Paggel, T. Miller, and T.-C. Chiang, 25. Phys. Rev. B, 61: 1804 (2000). https:// doi.org/10.1103/PhysRevB.61.1804 J.J. Paggel, T. Miller, and T.-C. Chiang, 26. Science, 283: 1709 (1999). https://doi. org/10.1126/science.283.5408.1709 N.V. Smith, 27. Phys. Rev. B, 32: 3549 (1985). https://doi.org/10.1103/PhysRevB. 32.3549 N.V. Smith, N.B. Brookes, Y. Chang, and P.D. Johnson, 28. Phys. Rev. B, 49: 332 (1994). https://doi.org/10.1103/PhysRevB.49.332 A.L. Wachs, A.P. Shapiro, T.C. Hsieh, and T.-C. Chiang, 29. Phys. Rev. B, 33: 1460 (1986). https://doi.org/10.1103/PhysRevB.33.1460 F. Patthey and W.-D. Schneider, 30. Phys. Rev. B, 50: 17560 (1994). https://doi. org/10.1103/PhysRevB.50.17560 P. Paniago, R. Matzdorf, G. Meister, and A. Goldmann, 31. Surf. Sci., 336: 113 (1995). https://doi.org/10.1016/0039-6028(94)00740 P.M. Echenique and J.B. Pendry, 32. J. Phys. C, 11: 2065 (1978). https://doi.org/ 10.1088/0022-3719/11/10/017 S.Å. Lindgren and L. Walld33. én, Solid State Commun., 28: 283 (1978). https:// doi.org/10.1016/0038-1098(78)90644-0 S.Å. Lindgren and L. Walld34. én, Solid State Commun., 34: 671 (1980). https:// doi.org/10.1016/0038-1098(80)90952-7 530 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 L.I. Karbivska, V.L. Karbivskyy, and A.O. Romanskyy S.D. Kevan and W. Eberhardt, 35. Angle-Resolved Photoemission. Theory and Cur- rent Applications (Ed. S. D. Kevan) (Amsterdam: Elsevier: 1992), p. 99; idem, Studies in Surface Science and Catalysis, 74: 99 (1992). https://doi.org/10.1016/ S0167-2991(08)61774-7 F. Patthey and W.-D. Schneider, 36. Surf. Sci. Lett., 334: L715 (1995); T.C. Hsieh and T.-C. Chiang, Surf. Sci., 166: 554 (1986). https://doi.org/10.1016/0039- 6028(95)80022-0, https://doi.org/10.1016/0039-6028(86)90696-5 T.C. Hsieh, T. Miller, and T.-C. Chiang, 37. Phys. Rev. Lett., 55: 2483 (1985). D. Aburano, H. Hong, J. M. Roesler, K. Chung, D.-S. Lin, P. Zschak, H. Chen, 38. and T.-C. Chiang, Phys. Rev. B, 52: 1839 (1995). https://doi.org/10.1103/ PhysRevB.52.1839 R. Abermann, 39. Vacuum, 41: 1279 (1990); R. Koch, D. Winau, A. Führmann, and K.H. Rieder, Phys. Rev. B, 44: 3369 (1991); R. Koch, D. Winau, K. Thümer, M. Weber, and K.H. Rieder, Europhys. Lett., 21: 213 (1993). https://doi.org/ 10.1016/0042-207X(90)93933-A, https://doi.org/10.1103/PhysRevB.44.3369, https://doi.org/10.1209/0295-5075/21/2/016 C.Y. Fong and M.L. Cohen, 40. Phys. Rev. Lett., 24: 306 (1970); C.Y. Fong, J.P. Walter, and M.L. Cohen, Phys. Rev. B, 11: 2759 (1975). https://doi.org/10.1103/ PhysRevLett.24.306, https://doi.org/10.1103/PhysRevB.11.2759 R.C. Jaklevic and J. Lambe, 41. Phys. Rev. B, 12: 4146 (1975). https://doi.org/ 10.1103/PhysRevB.12.4146 Gmelin Handbuch der Anorganischen Chemie42. , A-Z/8 (Ed.R. Warncke) (Berlin– Heidelberg: Springer-Verlag: 1978). https://doi.org/10.1007/978-3-662- 06224-1 G. Larsson and J.B. Pendry, 43. J. Phys. C, 14: 3089 (1981). https://doi.org/10. 1088/0022-3719/14/21/025 C.-S. Jiang, H.-B. Yu, X.-D. Wang, C.-K. Shih, and Ph. Ebert, 44. Phys. Rev. B, 64: 235410 (2001). https://doi.org/10.1103/PhysRevB.64.235410 R.M. Feenstra, 45. J. Vac. Sci. Technol. B, 7: 925 (1989); P. Martensson and R.M. Feenstra, Phys. Rev. B, 39: 7744 (1989); C.K. Shih, R.M. Feenstra, and G.V. Chandrashekhar, Phys. Rev. B, 43: 7913 (1991). https://doi.org/10.1116/1.584582, https://doi.org/10.1103/PhysRevB.39.7744, https://doi.org/10.1103/PhysRevB. 43.7913 N.E. Christensen, 46. Phys. Rev. B, 20: 3205 (1979). https://doi.org/10.1103/ PhysRevB.20.320 K.-J. Chao, Zhenyu Zhang, Ph. Ebert, and C.-K. Shih, 47. Phys. Rev. B, 60: 4988 (1999). https://doi.org/10.1103/PhysRevB.60.4988 G. Neuhold, L. Bartels, J.J. Paggel, and K. Horn, 48. Surf. Sci., 376: 1 (1997). https://doi.org/10.1016/S0039-6028(96)01393-3 Ph. Ebert, K.-J. Chao, Q. Niu, and C.-K. Shih, 49. Phys. Rev. Lett., 83: 3222 (1999). https://doi.org/10.1103/PhysRevLett.83.3222 A.-B. Chen and B. Segall, 50. Phys. Rev. B, 12: 600 (1975). https://doi.org/10.1103/ PhysRevB.12.600 K. Sawa, Y. Aoki, and H. Hirayama, 51. Phys. Rev. B, 80: 035428 (2009). https:// doi.org/10.1103/PhysRevB.80.035428 K. He, T. Hirahara, T. Okuda, S. Hasegawa, A. Kakizaki, and I. Matsuda, 52. Phys. Rev. Lett., 101: 107604 (2008). https://doi.org/10.1103/PhysRevLett.101.107604 H. Ibach, 53. Surf. Sci. Rep., 29: 195 (1997). https://doi.org/10.1016/S0167-5729- (97)00010-1 M. Miyazaki and H. Hirayama, 54. Surf. Sci., 602: 276 (2008). https://doi.org/10. 1016/j.susc.2007.10.02 ISSN 1608-1021. Usp. Fiz. Met., 2019, Vol. 20, No. 3 531 Determinism of the Symmetry of a Single-Crystalline Surface P. Mikul55. ík, Beyond Quasicrystals (Eds. F. Axel and D. Gratias) (Berlin–Heidelberg: Springer-Verlag: 1995), p. 229. https://doi.org/10.1007/978-3-662-03130-8 M. Feuerbacher, C. Metzmacher, M. Wollgarten, K. Urban, B. Baufeld, 56. M. Bartsch, and U. Messerschmidt, Mater. Sci. Eng. A, 226–228: 943 (1997); R. Wang, M. Feuer bacher, W. Yang, and K. Urban, Philos. Mag. A, 78: 273 (1998). https://doi.org/10.1016/S0921-5093(97)80097-4, https://doi.org/10.1080/ 01418619808241904 R. Mikulla, P. Gumbsch, and H.-R. Trebin, 57. Philos. Mag. Lett., 78: 369 (1998); R. Mikulla, J. Stadler, F. Krul, H.-R. Trebin, and P. Gumbsch, Phys. Rev. Lett., 81: 3163 (1998). https://doi.org/10.1080/095008398177760, https://doi. org/10.1103/PhysRevLett.81.3163 V.L. Karbivskyy, V.V. Vishniak, V.H. Kasiyanenko, 58. J. Adv. Microsc. Res. 6: 278 (2011). https://doi.org/10.1166/jamr.2011.1083 V. Karbivskyy, L. Karbivska, and V. Artemyuk, 59. Nanoscale Res. Lett., 11: 69 (2016). https://doi.org/10.1186/s11671-016-1291-2 V.A. Artemyuk, L.I. Karbivska, O.Ya. Kuznetsova, V.L. Karbivskyy, L.P. Klyu-60. yenko, and S.S. Smolyak, Usp. Fiz. Met., 18, No. 3: 235 (2017) (in Ukrainian). https://doi.org/10.15407/ufm.18.03.235 L.I. Karbivska, O.Ya. Kuznetsova, V.L. Karbivskyy, S.S. Smolyak, and V.A. Arte-61. myuk, Usp. Fiz. Met., 20, No. 1: 52 (2019) (in Russian). https://doi.org/10.15407/ ufm.20.01.052 Received May 5, 2019; in final version, July 30, 2019 Ë.². Êàðá³âñüêà, Â.Ë. Êàðá³âñüêèé, À.Î. Ðîìàíñüêèé ²íñòèòóò ìåòàëîô³çèêè ³ì. Ã.Â. Êóðäþìîâà ÍÀÍ Óêðà¿íè, áóëüâ. Àêàäåì³êà Âåðíàäñüêîãî, 36, 03142 Êè¿â, Óêðà¿íà ÄÅÒÅÐÌ²Í²ÇÌ ÑÈÌÅÒÐ²¯ ÌÎÍÎÊÐÈÑÒÀË²×ÍÎ¯ ÏÎÂÅÐÕÍ² ÌÅÆ² ÏÎÄ²ËÓ ÏÐÈ ÎÄÅÐÆÀÍÍ² 0D- ² 2D-ÑÒÐÓÊÒÓÐ ØËßÕÅÒÍÈÕ ÌÅÒÀË²Â ÒÀ ²ÍÄ²Þ ÍÀ ÊÐÅÌÍ²¯ Îãëÿäîâó ñòàòòþ ïðèñâÿ÷åíî «êâàíòîâ³é ³íæåíåð³¿» âèðîùóâàííÿ ïë³âîê ñð³áëà íà íàï³âïðîâ³äíèêîâèõ ï³äêëàäèíêàõ, ÿêå óìîæëèâëþº îäåðæàííÿ íîâèõ ôîðì ðå÷îâèíè. Íàâåäåíî ðåçóëüòàòè ç åíåðãåòè÷íî¿ äèñïåðñ³¿ åëåêòðîííèõ ñòàí³â ó åï³ òàêñ³àëüíèõ ïë³âêàõ Ag (111), îäåðæàíèõ íà Si (001) òà Si (111). Ïîÿñíåíî ðîç- ùåïëåííÿ çîí ³ íàäàíî àíàë³ç ïîâåðõíåâèõ ñòàí³â çà Øîêë³. Äåòàëüíî àíàë³çóþòüñÿ íàäñòðóêòóðè, ÿê³ óòâîðþþòüñÿ íà ïîâåðõí³ ìîíîøàðîâèõ íàíîñòðóêòóð ñð³áëà. Íàâåäåíî äåòàëüíèé àíàë³ç åíåðãåòè÷íèõ ñòàí³â êâàíòîâèõ ÿì øëÿõåòíèõ ìåòà- ë³â. Äîñë³äæåíî ìåõàí³çì ôîðìóâàííÿ íàíîðåëüºôó øëÿõåòíîãî ìåòàëó íà ïî âåðõ- íÿõ (111) ³ (110) ìîíîêðèñòàëó Si ïðè áàãàòîñòàä³éíîìó òåðì³÷íîìó íàïî ðîøåíí³. Ñèìåòð³ÿ ïîâåðõí³ ³íòåðôåéñó ìîíîêðèñòàë³÷íî¿ ïëîùèíè êðåìí³þ Si (111) 7 × 7 º äåòåðì³íóâàëüíîþ ó ìåõàí³çì³ ðîñòó ãåêñàãîíàëüíî-ï³ðàì³äàëüíèõ ñòðóêòóð ì³ä³, ñð³áëà òà çîëîòà. Äîñë³äæåíî ìîðôîëîã³÷í³ îñîáëèâîñò³ ïîâåðõí³ ³íä³þ ïðè éîãî òåðì³÷íîìó íàíåñåíí³ íà ïîâåðõí³ Si (111) ³ Si (110). Ñïîñòåð³ãàºòüñÿ óòâîðåííÿ êëàñòåð³â ïðàâèëüíî¿ êóá³÷íî¿ ôîðìè, ùî ñâ³ä÷èòü ïðî ôîðìóâàííÿ íàíîêðèñòàë³â In. Óòâîðåííÿ íàíîêëàñòåð³â In (ðîçì³ðîì ó ≈10 íì) íà ïîâåðõí³ Si(111) ³ ïîäàëüøå çì³íåííÿ ìîðôîëîã³¿ ïîâåðõí³ ìîíîêðèñòàëó ìîäèô³êóþòü ðîçðàõîâàí³ êðèâ³ ãóñ- òèíè åëåêòðîííèõ ñòàí³â. Êëþ÷îâ³ ñëîâà: êâàíòîâ³ ÿìè, åíåðãåòè÷íà äèñïåðñ³ÿ, øëÿõåòí³ ìåòàëè, ïîâåðõíÿ, ìîðôîëîã³ÿ, ñêàíóâàëüíà òóíåëüíà ì³êðîñêîï³ÿ, òåðì³÷íå íàïîðîøåííÿ. 532 ISSN 1608-1021. Prog. Phys. Met., 2019, Vol. 20, No. 3 V. Y. Bondar, V. E. Danilchenko, V. F. Mazanko, O. V. Filatov, and V. E. Iakovlev Ë.È. Êàðáîâñêàÿ, Â.Ë. Êàðáîâñêèé, À.À. Ðîìàíñêèé Èíñòèòóò ìåòàëëîôèçèêè èì. Ã.Â. Êóðäþìîâà ÍÀÍ Óêðàèíû, áóëüâ. Àêàäåìèêà Âåðíàäñêîãî, 36, 03142 Êèåâ, Óêðàèíà ÄÅÒÅÐÌÈÍÈÇÌ ÑÈÌÌÅÒÐÈÈ ÌÎÍÎÊÐÈÑÒÀËËÈ×ÅÑÊÎÉ ÏÎÂÅÐÕÍÎÑÒÈ ÃÐÀÍÈÖÛ ÐÀÇÄÅËÀ ÏÐÈ ÏÎËÓ×ÅÍÈÈ 0D- È 2D-ÑÒÐÓÊÒÓÐ ÁËÀÃÎÐÎÄÍÛÕ ÌÅÒÀËËÎÂ È ÈÍÄÈß ÍÀ ÊÐÅÌÍÈÈ Îáçîðíàÿ ñòàòüÿ ïîñâÿùåíà «êâàíòîâîé èíæåíåðèè» âûðàùèâàíèÿ ïë¸íîê ñåðå- áðà íà ïîëóïðîâîäíèêîâûõ ïîäëîæêàõ, êîòîðîå ïîçâîëÿåò ïîëó÷àòü íîâûå ôîð- ìû âåùåñòâà. Ïðèâåäåíû ðåçóëüòàòû ïî ýíåðãåòè÷åñêîé äèñïåðñèè ýëåêòðîííûõ ñîñòîÿíèé â ýïèòàêñèàëüíûõ ïë¸íêàõ Ag (111), ïîëó÷åííûõ íà Si (001) è Si (111). Îáúÿñíåíî ðàñùåïëåíèå çîí è äàí àíàëèç ïîâåðõíîñòíûõ ñîñòîÿíèé Øîêëè. Äåòàëüíî àíàëèçèðóþòñÿ ñâåðõñòðóêòóðû, êîòîðûå îáðàçóþòñÿ íà ïîâåðõíîñòè ìîíîñëîéíûõ íàíîñòðóêòóð ñåðåáðà. Ïðèâåä¸í äåòàëüíûé àíàëèç ýíåðãåòè÷åñêèõ ñîñòîÿíèé êâàíòîâûõ ÿì áëàãîðîäíûõ ìåòàëëîâ. Èññëåäîâàí ìåõàíèçì ôîðìèðî- âàíèÿ íàíîðåëüåôà áëàãîðîäíîãî ìåòàëëà íà ïîâåðõíîñòÿõ (111) è (110) ìîíî- êðèñòàëëà Si ïðè ìíîãîñòàäèéíîì òåðìè÷åñêîì íàïûëåíèè. Ñèììåòðèÿ ïîâåðõ- íîñòè èíòåðôåéñà ìîíîêðèñòàëëè÷åñêîé ïëîñêîñòè êðåìíèÿ Si (111) 7 × 7 ÿâ ëÿ åò ñÿ äåòåðìèíèðóþùåé â ìåõàíèçìå ðîñòà ãåêñàãîíàëüíî-ïèðàìèäàëüíûõ ñòðóêòóð ìåäè, ñåðåáðà è çîëîòà. Èññëåäîâàíû ìîðôîëîãè÷åñêèå îñîáåííîñòè ïîâåðõíîñòè èíäèÿ ïðè åãî òåðìè÷åñêîì íàíåñåíèè íà ïîâåðõíîñòè Si (111) è Si (110). Íàáëþ- äàåòñÿ îáðàçîâàíèå êëàñòåðîâ ïðàâèëüíîé êóáè÷åñêîé ôîðìû, ÷òî ñâèäåòåëüñòâó- åò î ôîðìèðîâàíèè íàíîêðèñòàëëîâ In. Îáðàçîâàíèå íàíîêëàñòåðîâ In (ðàçìåðîì ≈10 íì) íà ïîâåðõíîñòè Si(111) è äàëüíåéøåå èçìåíåíèå ìîðôîëîãèè ïîâåðõíî- ñòè ìîíîêðèñòàëëà ìîäèôèöèðóþò ðàññ÷èòàííûå êðèâûå ïëîòíîñòè ýëåêòðîí- íûõ ñîñòîÿíèé. Êëþ÷åâûå ñëîâà: êâàíòîâûå ÿìû, ýíåðãåòè÷åñêàÿ äèñïåðñèÿ, áëàãîðîäíûå ìå- òàëëû, ïîâåðõíîñòü, ìîðôîëîãèÿ, ñêàíèðóþùàÿ òóííåëüíàÿ ìèêðîñêîïèÿ, òåð- ìè÷åñêîå íàïûëåíèå.

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