Scaling-down of MOSFETs (metal-oxide-semiconductor field effect transistors can be divided to semi-classical and quantum mechanical one. In the regime of semi-classical scaling-down the behavior of electrons and holes can be well described with the effective mass approximation and in the regime of quantum mechanical scaling-down the characteristics of electrons and holes as wave becomes markedly. The minimum size limit of MOSFETs scaled down in semi-classical regime is mainly determined by the subthreshold characteristics and the short channel effect on the threshold voltage and 0.1 µm will be the minimum channel length from practical viewpoints. Scaling down of MOSFETs enhances their operational speed, but the substrates with high resistivity which are often used in SOI (silicon on insulator) substrates result longer dielectric relaxation time. While the dielectric relaxation time becomes longer than the reciprocal of signal frequency, the semiconductors work as lossy dielectrics and may lead to new types of dynamic circuits. Modification of material properties utilizing the wave nature of electrons is an illustration of quantum mechanical way to improve characteristics of MOSFETs. Suppression of optical phonon scattering of two dimensional electrons by introducing two dimensional array of quantum dots into substrates is expected to improve high field characteristics of material. Brillouin zone folding is another way to control the band structure of materials, especially to make the indirect transition band structure to the direct transition band structure. Heat transfer from a chip severely limits the number of devices which can be integrated on the chip. Reduction of signal charge to electronic elementary charge, that is quantum limit, is expected to be useful for realization of nano-power electronics.