A confinement model for many-electron atoms enclosed by a spherical boundary with finite-barrier potential height is presented. The model is based on the Thomas–Fermi–Dirac–Weizsacker (TFDλW) functional formalism using known properties of the orbital electron densities and constitutes a natural extension of a previously published report for the case of infinitely hard walls [Cruz et al., Int J Quantum Chem, 2005, 102, 897]. The confining barrier potential is considered as a step-like function of finite height V0. This assumption demands of the appropriate description of the TFDλW energy functional for both the interior and exterior regions together with corresponding ansatz orbital density representations, subject to continuity boundary conditions at the wall. For a given cage radius R and confining barrier height V0, the total ground-state energy is variationally optimized with respect to the characteristic parameters defining the interior and exterior orbital densities. The total ground-state energy and corresponding electronic density are obtained as function of barrier height and cage radius for many-electron atoms and ions. The model is explicitly applied to He, Li, C, and Ne and various ionic species for barrier heights (atomic units) V0 = 0, 5, and ∞. Given a barrier height V0, the results are presented for the critical cage size to produce one or more unbound electrons—yet, confined by the box—until reaching threshold size values for which electron escape from the confinement region take place. © 2008 Wiley Periodicals, Inc. Int. J. Quantum Chem, 2008

Many-electron atom confinement by a penetrable spherical box

An assessment of the use of statistical atomic models for the study of many-electron atom confinement is presented. The Thomas–Fermi–Dirac- λ -Weizsacker TFDλW functional formalism based on known properties of the orbital electron density is shown to be an appropriate tool for the description of the ground-state energy evolution of many-electron atoms spatially limited by closed and open boundaries. A brief review of the strategy followed in the TFDλW method for the study of atoms enclosed in hard and soft spherical cavities is presented along with more refined quantitative calculations as compared with previous results. Also, detailed quantitative results are shown–for the first time–in the case of confinement by a hard prolate spheroidal box for nuclear positions located at one of the foci and for an atom located at a distance D from a hard plane. A discussion is presented on the physical consequences of different confinement geometries and the adequacy of the TFDλW formalism to explore many-electron atom confinement by open and closed boundaries.

Thomas–Fermi–Dirac–Weizsäcker Density Functional Formalism Applied to the Study of Many-electron Atom Confinement by Open and Closed Boundaries

We calculate the effects of dielectric mismatch on shallow donors and acceptors in a spherical GaAs-Al1-xGaxAs quantum dot for both a finite barrier and an infinitely high barrier using the variational approach. The results have shown that the addition of dielectric mismatch enhances impurity binding energies considerably, especially when the radius of the quantum dot is small. The results also showed that the effects of dielectric mismatch on donors are comparable with those on acceptors, and the corresponding effects for an infinitely high barrier are larger than for a finite barrier.

Effects of dielectric mismatch on shallow donors and acceptors in a spherical GaAs-Ga1-xAlxAs quantum dot

The electronic and impurity states in the corner of well material surrounded by barrier material are investigated using the variational method. The results show that the binding energies of impurity ground states tend to the value of the third impurity excited states in the bulk when the impurity approaches the corner. The dependence of the ground-state electronic level and impurity binding energy on the dielectric mismatch between the well material and barrier material is also discussed.

Electronic and shallow impurity states in a corner

The ground state binding energies of hydrogenic impurities in strained wurtzite AlxGa1−xN/GaN/AlyGa1−yN quantum wells are calculated numerically by a variational method. The dependence of the binding energy on well width, impurity location and Al concentrations of the left and right barriers is discussed, including the effect of the built-in electric field induced by spontaneous and piezoelectric polarizations. The results show that the change in binding energy with well width is more sensitive to the impurity position and barrier heights than the barrier widths, especially in asymmetric well structures where the barrier widths and/or barrier heights differ. The binding energy as a function of the impurity position in symmetric and asymmetric structures behaves like a map of the spatial distribution of the ground state wave function of the electron. It is also found that the influence on the binding energy from the Al concentration of the left barrier is more obvious than that of the right barrier.

https://iopscience.iop.org/article/10.1088/1674-4926/32/4/042001/pdf

Binding energies of shallow impurities in asymmetric strained wurtzite AlxGa1 xN/ GaN/AlyGa1 yN quantum wells

The effect of image potential on the ground-state energy of a shallow-donor impurity near a sharp surface of a semi-infinite crystal is studied. A simple but realistic trial function is used in the confocal elliptic coordinate system with the foci at the hydrogenic donor impurity and its image point. The groundstate energy of this system is calculated as a function of the impurity position

Effect of an image potential on the ground-state energy of shallow-donor impurities near the surface of semi-infinite crystals.

On a Hilbert-type integral inequality in the whole plane with the equivalent forms

Using a variational technique, the change of ground-state energy and binding energy of an impurity atom with impurity position and well width in a GaAs-${\mathrm{Ga}}_{0.7}$${\mathrm{Al}}_{0.3}$As quantum well is calculated. In the calculation the electron--surface-optical-phonon interactions are taken into account. The result is discussed. It is found that the electron-phonon interaction energy depends not only on the width of the well but also on the position of the impurity atom in the well.

B. C. Yang

Papers

Effect of an image potential on the ground-state energy of shallow-donor impurities near the surface of semi-infinite crystals.

On a Hilbert-type integral inequality in the whole plane with the equivalent forms

Effect of the electron-surface-optical-phonon interaction on the impurity-state energies in a semiconductor quantum well.