We have calculated the tunneling through a three-dimensional box-shaped quantum dot with size in nanometer-scale. The quantum dot is embedded in a matrix serving as barrier for quantum confinement. We derived an integral equation to solve the electron wave function of the system. Our results show that with a given potential profile for the quantum dot and the barrier, the solution depends on the incident electron, as well as the volume and the surface of the quantum dot. A numerical calculation has been performed to model the wave confinement inside the quantum dot. The energies of the resonant sate for quantum dot with different size are obtained and compared. In our computed results, the dynamics of an electron density moving through the quantum dot at various energies is quite similar to the case for the quantum well except the density variation in the plane normal to the direction of propagation, which is quite similar to the case of an optical waveguide. Our approach is general, capable of modeling coupled quantum dots, as well as phase coherent schemes with possible application in quantum processing and quantum computing.
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