## 1 Introduction  
Semiconductor nanostructures form a basis for modern electronic technologies. Nowadays, they are employed in a wide range of applications in the fields of optoelectronics, photonics, photovoltaics, biosensing, photocatalysis, etc. By virtue of the quantum confinement effect, their electronic spectra and, consequently, the related optical properties depend on the nanostructure size. This feature is most pronounced for zero-dimensional (QD) objects, nanocrystals (NCs), where the conduction band electron motion is fully localized in all directions. Consequently, at least a part of the NC energy spectrum is completely discrete. In the limiting case of strong quantum confinement effect, when the NC size is much less than the effective exciton Bohr radius, the former strongly influences the electron and hole energies. It leads to the size-dependent energies of photons emitted or absorbed by the nanocrystals and allows one to control their optical spectra. For this reason, they sometimes are called \"artificial atoms\" [1]. A more scientific term to distinguish semiconductor NCs with strongly size-dependent electronic and optical properties is Quantum Dot (QD), which will be used in this article. (Let us note that the term Quantum Dot was originally proposed for a lithographic lateral nanostructure based on an AlGaAs/GaAs heterostructure with 2D electron gas, probably by [PERSON] in 1986. Beyond such structures and isolated nanocrystals, it covers also self-assembled epitaxial QDs and small transistor-like structures where discrete energy levels are created by electrostatic confinement. Here we shall employ this term just for semiconductor nanocrystals. )After the pioneering works by [PERSON] and [PERSON] [2] and [PERSON] [3] explaining the origin of size-dependent optical spectra of nanocrystals, the interest to these objects grew exponentially through the 1980s and 1990s. A variety of methods has been used for preparation of crystallites with sizes not greater than several nanometers, such as ion implantation [4; 5; 6], chemical vapour deposition from a gas phase, [7] magnetron sputtering [8], colloidal synthesis [9], electron beam epitaxy [10], etc. One of these methods, chemical growth in colloidal solutions, allows for obtaining good quality NCs of a broad range of semiconductors with an almost spherical shape and a rather narrow size distribution, characterized by rather narrow emission bands, which is, as a rule, extremely desirable for applications. This method was first suggested for II-VI NCs by [PERSON] et al. [11] and became widely employed later (see, e.g., chapters by [PERSON] et al., [PERSON], [PERSON] and [PERSON] in the book in [12] for review). The colloidal chemistry methods work fairly well for II-VI and III-V materials such as CdSe, CdS, CdTe, InAs, InP, etc. The authors of [12; 13] and several other groups have been able to produce good QDs of some IV-VI materials [14; 15] and silicon QDs (see, e.g., reviews in [16; 17]). Colloidal QDs of II-VI materials (especially CdSe and CdTe) are probably the most studied. During the last decade, a considerable research activity has been focused on the synthesis and investigation of the optical properties of ZnSe QDs. These nanocrystals exhibit large blue shift of the photoluminescence [18] and high enough (up to 50 percent) quantum yield [19]. Similarly to CdSe NCs, the ZnSe QDs can be synthesized with a sufficiently narrow size distribution, which is possible to control by temperature [20]. Due to ZnSe's lower toxicity, compared to many other II-VI semiconductors, these QDs turn out to be attractive objects also for biosensing [21]. Further improvement of the light emission properties of such QDs was achieved by fabrication of core-shell structures, successful for several pairs of II-VI [22] and IV-VI [23] materials, where the shell made of a wider band gap material provides a better protection of the quantized electronic states in the QD core [12].