Approaching to nanostructures using basic concepts of quantum mechanics

Abstract

In this work we discuss some concepts of quantum mechanics showing the result for the ground state energy of the infinite potential well that, together with elementary thermal physics concepts applied to semiconductors, help us to estimate the size of nanostructures. The energy value of the infinite potential well is compared with the finite potential well, some results were obtained with numerical calculations using basic quantum mechanics, particularly we used the BenDaniel-Duke model used for semiconductor junctions to analyze the structure GaAs-Al$_{1 - x}$Ga$_{x}$As, the energy levels were obtained of the confined states in the quantum well of the nanostructure in function of Al percentage. This system is representative of nanostructures quantum devices, currently under study in electronic solid state physics. This presentation could be very useful to teach in undergraduate applied physics courses.