Energy Calculations of The Realistic Quantum Slab

We calculated the total energy of a semiconductor quantum dot which is defined by the trench gate method. In our calculation we used a recently developed energy functional called ``orbital-free energy functional". We compared the total energies obtained by Thomas-Fermi approximation, orbital-free energy functional and standard local-density approximation for the square quantum slab geometry. We have seen that this newly developed energy functional is numerically very efficient, superior to the Thomas-Fermi approximation and is in good agreement with the local-density approximation for two different sizes of quantum dot systems.