Energy calculations of quantum dot

We calculated the total energy of a semiconductor quantum dot formed in gate and etching defined devices. A 3D Poisson equation is solved self-consistently to obtain the electron density and potential profile. The total energies of electrons in the quantum dots with two different sizes are calculated with three different approximations by using the density and potential obtained from self-consistent procedure. In our calculation we used a recently developed energy functional called “orbital-free energy functional”, Thomas–Fermi approximation and standard local-density approximation within density functional theory. The comparison of these methods reveals the efficacy of the used newly developed orbital-free energy functional which facilitates the calculation of Hartree integral for treatment of electron–electron interaction.