The electronic band structure of silicon (Si) crystals is significantly modified when the size is reduced to below the exciton Bohr radius ($4.9 nm) of bulk Si crystals due to the quantum size effect. The quantum size effect manifests itself as a high-energy shift of the luminescence band and an enhancement of the spontaneous emission rate. Furthermore, enlargement of the singlet-triplet splitting energy of exciton states with decreasing size has been demonstrated [1-4]. The modified band structure opens up new application of Si nanocrystals in the fields where bulk Si crystal has not been involved. Besides well-known high-efficiency visible photoluminescence (PL), one of the most exotic new feature of Si nanocrystals is their ability to generate a kind of active oxygen species called singlet oxygen by energy transfer from excitons to oxygen molecules (O 2 ) adsorbed onto the surface of Si nanocrystals [5]. This feature is due to the molecule-like energy structure of Si nanocrystals and is a direct consequence of the quantum size effects. Similarly, efficient photosensitization of rare earth ions by Si nanocrystals has been reported and this phenomenon is expected to lead to the development of an efficient planar waveguide-type optical amplifier operating at the optical telecommunication wavelength. Since almost all new features of Si nanocrystals arise from the modified electronic band structure, its deep understanding is indispensable to explore new nano-Si-based research fields and devices. Fortunately, the energy structure of Si nanocrystals is almost clarified, at least qualitatively, by detailed optical spectroscopy. In Section 3.2, we briefly summarize fundamental optical properties of intrinsic Si nanocrystals [1][2][3][4][5][6][7][8].The properties of Si nanocrystals can be controlled by the size, shape, surface termination, and so on. An additional freedom of material design can be introduced by impurity doping. The introduction of shallow impurities in a semiconductor significantly modifies its optical and electrical transport properties. Actually, a precise control of an impurity profile is key to achieve desirable functions in almost all kinds Silicon Nanocrystals: Fundamentals, Synthesis and Applications. Edited by Lorenzo Pavesi and Rasit Turan