Thomas Fermi Screening Function Research Articles

Mott criterion for metal–insulator transition in doped semiconductors in intense magnetic fields

Metal–insulator transition in doped semiconductors in strong magnetic fields is a topic of recent interest as metal–insulator transition is a precursor to superconductivity. It is shown that the original Mott criterion is modified to = 0.36 (1 + γ), where is the number of conduction band valleys in the semiconductor and γ is a dimensional parameter, γ = ħωc /2R*. The new criterion is arrived at after solving the donor problem variationally within the effective mass approximation using the Thomas–Fermi screening function.

A thomas-fermi-like analytic independent particle model for atoms and ions

The applicability of an independent particle model which was initiated with a particular two-parameter analytic fit to the Thomas–Fermi screening function is further extended. Here, using the ab initio procedure of Bass, Green, and Wood, the two parameters d and K of the model are determined for all atoms and ions with Z ≦ 36, thus extending the determination of Szydlik and Green. The calculated total energies are in excellent agreement with Hartree Fock results. To a good accuracy K and 1/d may be represented as linear functions of Z — N where N is the total number of electrons and Z the nuclear charge. The slopes and intercepts of the K lines vary fairly smoothly with N, while those of the 1/d lines vary with N in a manner which reflects atomic shell structure.

MAGNETIC STUDIES OF METAL–INSULATOR TRANSITION IN A QUANTUM WELL SYSTEM

Metal–insulator transition in doped semiconductors is investigated in the presence of intense magnetic fields. A variational procedure within the effective mass approximation is employed using the Thomas–Fermi screening function and the exact quasi-Q2D Lindhard dielectric function. The Hubbard model results are justified using an effective mass that depends on interimpurity separation. The nonparabolicity of the subband is included using an energy-dependent effective mass. Though an increase of ionization energy with a magnetic field is observed for isolated donor models, the metallization occurs with an intense magnetic field at a higher concentration for a particular well width. The diamagnetic susceptibility of a hydrogenic donor impurity in GaAs / Ga 1 - x Al x As quantum well systems is discovered in the observation of metal–insulator transition. It is shown that the diamagnetic susceptibility diverges for all critical concentrations for a given well width. The large diamagnetic susceptibility (> 6) is observed at the transition. All the calculations are carried out for infinite and finite barriers, and the results are compared with the existing literature.

EFFECT OF MOTT TRANSITION WITH DIFFERENT DIELECTRIC FUNCTIONS IN LOW-DIMENSIONAL SEMICONDUCTOR SYSTEMS

Ionization energies of a GaAs/Ga 1-x Al x As superlattice system with finite and infinite barriers are investigated with different dielectric screening functions within the effective mass approximation. Within the one-electron approximation the occurrence of Mott transition is seen when the binding energy of a donor vanishes. While the Thomas–Fermi screening function does not admit the Mott transition below a well-width around 60 Å,1,2 the Hartree–Fock screening function with exchange and correlation effects included pushes the critical well-width to a value around 20 Å. The Lindhard screening function also gives the same results. The effects of Anderson localization and exchange and correlation in the Hubbard model are included in our model. It is found that the ionization energy (i) decreases as well-width increases, (ii) decreases when well-width increases and (iii) the critical concentration at which the metal-insulator transition occurs is lowered when well dimensions are reduced. All the calculations have been carried out with finite and infinite barriers and the results are compared with available data in the literature.

Magnetic field induced metal–insulator transition in semiconductors

Metal–insulator transition in doped semiconductors is investigated in the presence of intense magnetic fields. Using Thomas–Fermi screening function and a screened coulomb potential in the Hamiltonian, a two-parameter varitional calculation leads to metallization. The correlation effect among the electrons is considered through an effectivemass that depends on the spatial seperation between impurities. Results are provided for a many valley semiconductor (Si) and two single valley semiconductors (GaAs and CdTe). Our results show that in a magnetic field the critical concentration at which metallization occurs increases. The correlation effects bring out one order change in the critical concentration values, in intense magnetic fields.

Semiconductor–metal transition in quantum well systems. II

Semiconductor–metal transition in GaAs/GaAlAs quantum well systems with finite barriers is investigated with a more realistic screening function within the effective mass approximation. While the Thomas–Fermi screening function does not admit phase transition below a well width around 60 A ̊ , the Hartree–Fock screening function with exchange and correlation effects included pushes the critical well width to a value around 20 A ̊ . For all other well dimensions the results obtained with the two screening functions are otherwise similar, except for narrow wells (L⩽200 A ̊ ) for which the use of Hartree–Fock function yields values of critical concentration which are one order higher in all the three cases (Q0D, Q1D and Q2D) investigated. In the finite barrier cases when the confining dimension approaches zero (e.g. L→0 in a quantum well) the systems behave as in the bulk due to tunnelling and a phase transition is possible. Our calculations have been performed taking into account Anderson localization and Hubbard model results. Our results support the scaling theory of localization.

Angular distribution of ions axially channeled in a very thin crystal: Experimental and theoretical results.

We have studied the angular distributions for 6--30-MeV C[sup [ital q]+] ([ital q]=4--6) and 2--9-MeV H[sup +] ions axially channeled in the [001] direction of a thin silicon crystal (1792 and 1900 A). We report highly structured two-dimensional angular distributions that depend sensitively on the projectile's velocity and incident charge state and the target's thickness and azimuthal orientation. Some structure in the angular contour maps is the result of a rainbow effect in axial channeling (i.e., extrema in the classical deflection function). State-to-state charge-state distributions, which are required to interpret the data accurately, have also been measured. All measured angular distributions have been explained via Monte Carlo trajectory calculations using Moliere's approximation to the Thomas-Fermi screening function and a screening length given by target electrons alone. The calculations indicate that all projectile velocity and charge-state effects and the target-thickness effects observed are the result of the projectile's transverse oscillatory motion in the channel. Using this information, we show that swift heavy-ion and proton angular distributions are simply related using a scaling law that depends only on the projectile's velocity and charge-to-mass ratio and on the crystal thickness.

Effect of screening on the long-wavelength optical phonons in La1.85Sr0.15CuO4

The lattice dynamics of La1.85Sr0.15CuO4 are studied with a rigid-ion model that takes into account the anisotropic screening of the Coulomb field by the charge carriers. The coupling coefficients for the screened potential are obtained using a generalized Ewald transformation that incorporates the Thomas–Fermi screening function. From the calculated phonons in the long-wavelength region it can be seen that the screening considerably reduces the longitudinal optical–transverse optical splitting of the polar modes. The nonpolar modes do not exhibit any changes in their behaviour with respect to that in the unscreened Coulomb potential.

Comparison of experimental and theoretical Fermi screening of charged impurities in degenerate semiconductors

Optical measurements on semiconductor thin films can be used to derive their complex dielectric function. In a log-log graph, the imaginary part near the plasma frequency tends to have two linear segments, one slope denoting the Drude and the other the quantum region. The quantum region is represented by a von Baltz and Escher asymptotic expression. An empirical screening function for the charged impurities is derived by matching the Drude and quantum expressions at the relatively narrow transition frequency band between Drude and quantum regions. This empirical expression and the corresponding theoretical Thomas-Fermi screening function are applied to a series of In 2O 3 and CdIn 2O 4 films to show that the theory systematically underestimates the screening by a factor of 2–3.

The simplified thomas-fermi-dirac equation and approximation of its calculation for an atomic potential

Abstract A simple analytical formula χ(x) = Sh2βa/Sh2β(a + x) of the Thomas-Fermi screening function is presented, where β = 0.4/Z1/3, a = 1.8, x = 1.13 Z1/3 r, r - is the distance from atomic nucleus, e = m = phi; = 1, φ(r) = Z χ(x)/r is the atomic potential, Z - is the atomic number (the atomic units are used). The Thomas-Fermi function χτφ (x) is formally valid only for φ ≥ 10, or for r<0.2 Z 1/3, mainly due to neglect of the exchange effects. The proposed function χ(x) is valid for φ ≥ 1, and for r—about two times larger, because the exchange effects were considered. The proposed function χ(x) agrees with the Thomas-Fermi-Dirac function χTFD and Hartree-Fock function within 2% in the region of validity. With the help of this screening function one can easily obtain a simple analytical formula for the Born scattering amplitude at zero angle, which agrees within 30% with the expression calculated according to Hartree-Fock. The mean potential of a substance is expressed by means of this value (in the add...

Interpretation of Channeled-Ion Energy-Loss Spectra

The energy-loss spectra produced in beams of energetic He and I ions transmitted through planar channels in thin Au monocrystals have been explained by a simple model in which the ions execute transverse anharmonic oscillations in the channel between a pair of adjacent planes of target atoms and in which the stopping power of the medium is a function of the distance of the ion from the crystal planes. A quantitative comparison of this model with recent experiments is made using a plane-averaged potential based on Moliere's approximation to the Thomas-Fermi screening function to describe the oscillatory motion. The stopping power is found to obey the same functional dependence on the coordinates, but with a doubled screening length. The parameters of the model may be deduced directly from the experimental data. For He in Au, these parameters agree well with those expected from Firsov's treatment of the interaction potential between neutral atoms. For I in Au, the high charge of the ion leads to parameters which differ significantly from Firsov's theory. The data also suggest that the energy dependence of the stopping power for channeled ions may be somewhat different from that for randomly directed ones.

A simple analytical form of the Thomas-Fermi screening function and of Firsov's atomic interaction potential

The Thomas-Fermi screening function ∅(x) is shown to be accurately described by the expression 317 × exp(-6.62x1/4) in the range 0.3 < x < 16. The consequent form of the Thomas-Fermi electron density distribution is derived, and Firsov's atomic interaction potential is shown to have the form E = B exp(-αr1/4), where B and α are constants of known Z dependence and r is the internuclear distance. It is also suggested that a potential of the type E' = A' exp(-k'r1/3) gives a better representation of the interaction potential over a wider range of energies and distances, and explicit values of A' and k' are given for copper-copper interactions. However, the Z dependence of A' and k' is not obvious.