Analytic form of Thomas-Fermi-Dirac dielectric function for Si, Ge and diamond by variational method

1990 ◽  
Vol 79 (2) ◽  
pp. 181-184 ◽  
Author(s):  
D. Chandramohan ◽  
S. Balasubramanian
Keyword(s):  
Variational Method ◽  
Dielectric Function ◽  
Analytic Form ◽  
Thomas Fermi

Angular terms in the electron density for the phosphine molecule

1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March
Keyword(s):  
Variational Method ◽  
Charge Density ◽  
Electron Density ◽  
Legendre Polynomials ◽  
Molecular Axis ◽  
Thomas Fermi ◽  
Line Charge ◽  
Density Map ◽  
Circular Line

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.

Optical properties of the massive Vanadium dioxide

2015 ◽  
Vol 8 (3) ◽  
pp. 2222-2230
Author(s):  
Abderrahim Benchaib ◽  
Abdesselam Mdaa ◽  
Izeddine Zorkani ◽  
Anouar Jorio
Keyword(s):  
Optical Properties ◽  
Variational Method ◽  
Band Gap ◽  
Effective Mass ◽  
Dielectric Function ◽  
Vanadium Dioxide ◽  
Normal Incidence ◽  
Index Of Refraction ◽  
The Real

 We can easily extract the optical properties from a material starting from its permittivity complexes ԑ; . The real part of this dielectric function clearly takes its place in the Colombian interaction of an exciton. We are interested in exciton 1S in the case of the massive vanadium dioxide. We will solve Schrödinger’s equation for this exciton by variational method and we obtain  according to energy E of the same exciton. We make a simulation by means of the Maple software of   and of the index of refraction n according to energy E of the exciton 1S, around and far from the band gap of this material while being based on the approximation of the effective mass. We will extract the reflectivity R and transmittivity T of the massive vanadium dioxide for the normal incidence of the incidental photons by considering a slightly absorbent semiconductor state. 

Effect of Quantum Inhomogeneity Corrections in Semi-Statistical Thomas–Fermi Calculations for Atoms

1974 ◽  
Vol 52 (19) ◽  
pp. 1926-1932 ◽  
Author(s):  
J. A. Stauffer ◽  
J. W. Darewych
Keyword(s):  
Dirac Equation ◽  
Variational Method ◽  
Quantum Correction ◽  
Correction Term ◽  
Approximate Solutions ◽  
The Other ◽  
Gradient Term ◽  
Gradient Expansion ◽  
Thomas Fermi ◽  
Correction Terms

Approximate solutions to the Thomas–Fermi equation with so-called 'quantum correction terms' have been obtained by the use of a variational method. The results for krypton support the conclusions of Tomishima and Yonei that the coefficient of the gradient term should be 9/5 of the value derived by Kirzhnits. On the other hand, when the use of these equations is restricted to a region of the atom where the gradient expansion of Kirzhnits might be expected to be valid, the Kirzhnits value of the constant gives the better results, but the best results are obtained with no correction term at all (i.e. with the Thomas–Fermi–Dirac equation).

Nonlinear Thomas-Fermi Dielectric Function in Semiconductors

1985 ◽  
Vol 128 (2) ◽  
pp. 723-729
Author(s):  
Kaiyi Zhang ◽  
K. A. Chao
Keyword(s):  
Dielectric Function ◽  
Thomas Fermi

Thomas-Fermi-Dirac dielectric function for GaAs and GaP

1987 ◽  
Vol 35 (6) ◽  
pp. 2750-2754 ◽  
Author(s):  
D. Chandramohan ◽  
S. Balasubramanian
Keyword(s):  
Dielectric Function ◽  
Thomas Fermi

Electrons in a box: Thomas–Fermi solution

2006 ◽  
Vol 84 (9) ◽  
pp. 833-844 ◽  
Author(s):  
J Sañudo ◽  
A F Pacheco
Keyword(s):  
Quantum Dots ◽  
Density Distribution ◽  
Dimensionless Parameter ◽  
Three Dimensional ◽  
Analytic Form ◽  
Semiconductor Technology ◽  
Electron Number ◽  
Artificial Atoms ◽  
Perturbative Series ◽  
Thomas Fermi

The Thomas-Fermi density distribution of N electrons located inside a box is obtained. This system models some aspects of the structure of the new artificial atoms or quantum dots fabricated using present semiconductor technology. The three-dimensional solutions are obtained by means of a perturbative series, using a convenient dimensionless parameter characteristic of the size of the box and the electron number. The explicit analytic form for the first two terms of the series is derived. PACS No.: 71.10.Ca

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