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

• Published in: Physica. B, Condensed matter Condensed matter, 2003, Vol.325 (1-4), p.149-156
• Main Authors: Pino, Ramiro, Markvoort, A.J, Hilbers, P.A.J
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron gas; Electron gas, Fermi gas; Electron states; Electron states and collective excitations in thin films, multilayers, quantum wells, mesoscopic and nanoscale systems; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Exact sciences and technology; Physics; Quantum dots; Statistical model calculations; Theories and models of many electron systems
• ISSN: 0921-4526; 1873-2135
• DOI: 10.1016/S0921-4526(02)01516-8

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.