Local Thomas-Fermi approximation for modeling the electronic structure of planar devices

Local estimates to the two-dimensional electron-electron electrostatics, i.e., Hartree energy, are obtained, which allows the formulation of a fully local, exactly solvable Thomas-Fermi approach. We also included Dirac's local exchange and Fermi-Amaldi's exchange correction. The method is applied to the problem of two-dimensional devices like quantum dots and quantum dot arrays, where we give estimates to ground-state properties like electron density, energy, chemical potential, and differential capacitance. Analytic expressions for the above properties are given for parabolic circular quantum dots. Numeric examples are shown for arrays of quantum dots using a Gaussian confining potential. The method's computational complexity is shown to be linear in the number of electrons and centers.