Electron transport in a semiconductor nanosystem has been studied in detail. Especially, the investigation of the quantized conductance in the two-dimensional electron gas (2DEG) has been performed in a GaAs/AIGaAs heterostructure. As impurities, disorder, and imperfections may frequently exist in the actual experimental situation, it is of particular interest to investigate their influence on the conductance of this system. An extensive study of the case of impurity (delta-function, a single finite-size, attractive and repulsive potential) has been done in a quantum waveguide. Our project is concentrated to understand and explanation the effects of multiple finite-size impurities in a quantum waveguide. More specifically, we introduce double finite-size attractive impurities, located at the arbitrary position in the transverse direction, and investigate resonant conductance of the system by modulating the impurity strength and location.Fano resonance is a widespread phenomenon in physics, which can be observed in various systems. This effect arises from the interaction of a discrete state with a resonant continuum of states. In the presence of impurity in the quantum system, we expect to observe both Breit-Wigner (BW) and Fano resonances in the transmission. By increasing the strength and changing the location of the impurity, as asymmetric Fano resonance may evolve into a symmetric BW dip and subsequently into an inverted Fano resonance.We will be accomplishing computational analysis of 2DEG based on GaAs/AIGaAs heterostructure. This problem utilizes tight-binding approximation and reclusive Green's function technique. Numerical calculation will be done using existing FORTRAN code, modified where necessary, in the CCN Beowulf cluster. For the parallelizations, we use a LAM/MPI library, which was officially approved by ANSI (American National Standards Institute) and ISO (International Standard Organization).