NOWADAYS QUANTUM STRUCTURES AS QUANTUM DOT AND WIRES HAVE DRAMATICALLY CHANGED electronIC OPTOelectronIC DEVICES.THAT IS TO SAY, SOLAR CELLS, PHOTODETECTORS, LASERS AND OPTICAL AMPLIFIERS ARE JUST A FEW DEVICES WHOSE transport AND OPTICAL PROPERTIES HAVE BEEN IMPROVED BY THESE NANOMETER STRUCTURES. IN THIS WORK, WE HAVE EMPLOYED A TWO-DIMENSIONAL MODEL OF electron TUNNELING transport IN INAS-GAAS QUANTUM HETEROSTRUCTURE, AND THE DIFFERENCE BEHAVIOR OF QUANTUM DOT AND WIRE HAS BEEN PRESENTED. IN THIS REGARD, FINITE DIFFERENCE METHOD, TRANSFER MATRIX METHOD AND TRANSFORMATION UPON ENVELOP FUNCTIONS HAVE BEEN EMPLOYED TO GET THE TRANSMISSION MATRIX, AND FINALLY THE RESULT HAS BEEN APPLIED IN LANDAUER FORMALISM TO GET THE CONDUCTANCE OF THE SYSTEM AT ZEROTEMPERATURE.THE RESULTS SHOW THAT IN NANOSTRUCTURES THE CONDUCTANCE OCCURS AT DISCRETE ENERGIES. MOREOVER, IN THE QUANTUM WIRE CASE SOME CERTAIN CONDUCTANCE ENERGIES HAVE EXPERIENCED A RED-SHIFT WHICH IS IN AGREEMENT WITH THE QUANTUM MECHANICS CONCEPTS.