Weizsacker correction in the Thomas-Fermi and Thomas-Fermi-Dirac models of static dielectric screening in undoped semiconductors: Impurity donor ions in silicon and germanium

Scarfone, Leonard M.

doi:10.1103/physrevb.45.8348

Cited by 4 publications

(6 citation statements)

References 32 publications

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“…The estimate (4.3) can be used to study the full non-linear response of the ground state to a nuclear impurity. We compare this to the results from the Thomas-Fermi (TF) [2,28,39] and TFW [18,35,40,29] theories of screening. Consider a nuclear arrangement m 1 ∈ M L 2 (M, ω) and model a nuclear impurity at the origin with positive charge Z by Zη(x), where η ∈ C ∞ c (R 3 ), η ≥ 0 and η = 1.…”

Section: 2mentioning

confidence: 99%

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Locality of the Thomas–Fermi–von Weizsäcker Equations

Nazar

Ortner

2017

Arch Rational Mech Anal

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We establish a pointwise stability estimate for the Thomas-Fermi-von Weizsäcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

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Section: 2mentioning

confidence: 99%

“…In both models, V satisfies the linear equation where k s > 0 is a material-dependent constant called the inverse screening length. In the TFW model, V and n satisfy [18,40,29,35] V…”

Section: 2mentioning

confidence: 99%

Locality of the Thomas–Fermi–von Weizsäcker Equations

Nazar

Ortner

2017

Arch Rational Mech Anal

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“…15 The TFW formula has also been used to study the dielectric function. 16 The advantage of the TFW formula is that the charge density is smooth and realistic near the atomic nucleus and in the classically forbidden regions. Since an explicit solution of the TFW equation for a given inhomogeneous system is expected to describe the dielectric function well, especially for small q components ͑the cause of the charge sloshing͒, its use for potential mixing should speed up convergence.…”

Section: ͑2͒mentioning

confidence: 99%

Thomas-Fermi charge mixing for obtaining self-consistency in density functional calculations

2001

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We present a method for charge mixing in self-consistent density functional calculations which uses the Thomas-Fermi-von Weizsäcker equation to solve implicitly for the charge density response function to the potential. This approach has significant improvements over existing methods, particularly for inhomogeneous systems with large unit cells which commonly suffer from poor convergence due to charge sloshing.

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“…The TFDW model has become a popular and powerful computational tool, however, most studies have been limited to the 'zero temperature' case, e.g. [4][5][6][7][8][9][10]. While in many situations this is a reasonable approximation, for example, for cold compressed materials or molecules, the 'zero temperature' theory is not adequate in the warm dense matter regime, when finite-temperature effects become important.…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature Thomas–Fermi–Dirac-Weizsäcker model in the warm dense matter regime

Petrov¹

2023

Plasma Phys. Control. Fusion

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The Thomas-Fermi-Dirac-Weizsäcker model for finite temperature is presented. Starting with the free energy density, consistent expressions for the Helmholtz free energy, total energy, pressure and virial theorem are derived. The exchange and correlation terms are cast in form that is suitable for derivation of their contributions to energy and pressure. The Euler-Lagrange equation is written in Schrödinger-like form and solved in spherical symmetry in a Wigner-Seitz cell. The challenges associated with its numerical solution have been discussed and a viable approach to obtain a non-negative solution is proposed. The model is benchmarked for two materials, Al and Cu, by comparing the pressure at solid density in the temperature range 0.1<T_e<10 eV, as well as the cold pressure curves.

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Weizsacker correction in the Thomas-Fermi and Thomas-Fermi-Dirac models of static dielectric screening in undoped semiconductors: Impurity donor ions in silicon and germanium

Cited by 4 publications

References 32 publications

Locality of the Thomas–Fermi–von Weizsäcker Equations

Locality of the Thomas–Fermi–von Weizsäcker Equations

Thomas-Fermi charge mixing for obtaining self-consistency in density functional calculations

Finite-temperature Thomas–Fermi–Dirac-Weizsäcker model in the warm dense matter regime

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