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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 analysis 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 deposition 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.

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The total and partial densities of electronic states of gold monolayerstructures of different symmetry are calculated by the quantum mechanicalcalculations methods in the DFT approximation. It is shown that the firstcoordination sphere is determinant in the formation of the fine structureand the extent of the valence bands of the monolayer gold structures understudy. The peaks splitting of the TDOS curve, which leads to its finerstructure, is influenced not only by the lengths of interatomic bonds butalso by the mutual arrangement of atoms. The influence of long-rangeinteractions on the electronic structure of gold monolayers has beenestablished. For example, for the (110) plane, a change in the atomicordering in the third coordination sphere as a result of the introduction ofa vacancy leads to noticeable changes in the TDOS curve, which indicateseither a significant role of the atoms of the third coordination sphere or asignificant redistribution of the interaction of d-orbitals of differentsymmetries of close neighbours. A correlation between the packing density,as well as the number of neighbours in the first coordination sphere, andthe width of the energy band of gold monolayers has been established. Keywords: gold, monolayer, electron density, defects.\