Recent progress made in the growth techniques has led to the fabrication of the artificial semiconductor systems of lower dimension. Electrons and holes in these materials have quantization different from those of the three dimensional systems presenting unusual electronic properties and novel device applications. In this work, the important features of the free carriers in semiconductor superlattices are examined, and the electronic structure of some novel 2D semiconductor systems are investigated theoretically. This thesis studies various systems of lower dimensionality such as: the strained Si/Ge superlattices, i-doping. Si (100) surface and the tip-sample interaction in scanning tunneling microscopy (STM) study of this surface, and Wannier-Stark localization in finite length superlattices. The electronic energy structure of pseudomorphic Ge„i/Si„ superlattices is investigated by using the empirical tight binding method. Effects of the band offset, sublattice periodicity and the lateral lattice constant on the transition energies have been investigated. It is found that Ge„i/Si„ superlattices grown on Ge (001) can have a direct band gap, if m + n = 10 and m = 6. However, optical matrix elements for in-plane and perpendicular polarized light are negligible for the transition from the highest valence band to the lowest conduction band state at the center of the superlattice Brillouin zone. The electronic structure of the Si i-layer in germanium is explored by using the Green’s function formalism with layer orbitals. We found two dimensional parabolic subbands near the band edges. This approach is extended to treat the electronic structure of a single quantum well without invoking the periodically repeating models. Quantum well formation in Ge,„Si„ superlattices is also studied by using different number of ^-layers. Subband structure is observed by changing the height of the Si quantum well. The confinement of acoustical modes within 2DEG due to only the electronphonon interaction is proposed. The confined modes split out from the bulk phonons, if the 2DEG is created by means of modulation doping. This occurs even if the lattice has uniform parameters. The effect is more pronounced when the wave vector q of the modes increases and is maximum a,t q = 2kp {kp is the Fermi wave vector). In the case of several electron sheets the additional features of the confinement effect appear. Green’s function method is also applied to treat the modifications of electronic state density in STM. The tip-sample interaction in STM study of Si (100) surface is explored by calculating the Gieen’s function within the empirical tight binding method. Both of the proposed reconstruction models, buckled and symmetrical dimer model, is investigated. A dip occurs in the change of density of states of surface atoms at the energy of surface states for small tip-sample distances, and it decreases with increasing tip-sample separation. Although, in-plane tip position (above the up- or down-surface atom) affects the surface atoms differently in buckled dimer model, it influences the surface atoms symmetrically in symmetric dimer model. Recent experimental studies revealed the significant information on the Wannier-Stark localization. Following these experimental results, the WannierStark ladder is investigated by carrying out numerical calculations on a multiple quantum well structure under an applied electric field. The variation of the Wannier-Stark ladder energies and localization of the corresponding wave II function are examined for a wide range of applied electric field. Our results show that Wannier-Stark ladder do exist for finite but periodic system which consists of a large number of quantum well having multi-miniband structure. It is found that the miniband states are localized in the well regions with the applied electric field, while the continuum states preserve their extended character. Energies of the well states show a linear shift with the electric field except the small field values in which a nonlinear shift is resulted. Multiband calculations show that there is a mixing between the different band states although they are localized in different well regions.