Impurity Wave Functions Research Articles

Impurity-related polarizability and photoionization-cross section in [formula omitted] double quantum wells under electric fields and hydrostatic pressure

Double quantum well heterostructures are quite important for the exploration of correlated electron states in two-dimensional systems. By using the variational procedure, within the effective-mass and parabolic-band approximations, the effects of both electric field and hydrostatic pressure on the shallow-donor-impurity related polarizability and photoionization cross-section in GaAs–Ga 1− x Al x As double asymmetric quantum wells are presented. The electric field is considered to be applied along the growth direction. It is found that the impurity binding energy and polarizability can be tuned by means of an applied external electric field or hydrostatic pressure in asymmetric double quantum wells, a behavior which could be used in the design and construction of semiconductor devices. The photoionization cross-section magnitude increases as the pressure and applied electric field are increased, except beyond the Γ – X crossover in the barrier material, where a decrease of the photoionization cross-section is expected due the smaller confinement of the impurity wave function.

Consistent hopping criterion in the Efros-Shklovskii regime

We address the variable-range hopping regime in the domain where the measuring temperature $T$ is of the order of the characteristic Efros-Shklovskii temperature ${T}_{\mathit{ES}}$. In such a range, current theories imply ${r}_{\mathit{hop}}∕\ensuremath{\xi}<1$, where ${r}_{\mathit{hop}}$ is the hopping length and $\ensuremath{\xi}$ is the localization length, clearly in contradiction with the standard criterion for hopping conduction. We consider impurity overlap wave functions of the form $\ensuremath{\psi}(r)\ensuremath{\propto}{r}^{\ensuremath{-}n}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}r∕\ensuremath{\xi})$ and include the preexponential factor of the hopping probability as a logarithmic correction in the Mott optimization procedure. From the general expressions derived, the standard Efros-Shklovskii law is recovered for $T⪡{T}_{\mathit{ES}}$, whereas an extended preexponential sensitive regime, consistent with ${r}_{\mathit{hop}}∕\ensuremath{\xi}>1$, is found for ${T}_{\mathit{ES}}\ensuremath{\gtrsim}T$. We argue that the expression resulting from an interplay between preexponential and exponential factors is a consistent extension of the classical Efros-Shklovskii argument. An additional parameter in the theory is directly related to the decay of the impurity wave functions and could be seen as a probe into their behavior. A fit of reference experimental data to the proposed theory yields consistent results.

Hydrogenic impurity in ridge quantum wire

The binding energies as well as wave functions of hydrogenic impurities located in V-groove GaAs/AlxGa1-xAs quantum wires are calculated for different positions of the impurity inside the wires. The variational method is used and the carrier ground states are analytically calculated by an effective potential scheme together with a suitable coordinate transformation that allows the decoupling of the two-dimensional Schrodinger equation. The results are in good agreement with experimental points and other previous investigations.

Ab initiocalculation of impurity effects in copper oxide materials

We describe a method for calculating, within density functional theory, the electronic structure associated with typical defects which substitute for Cu in the ${\mathrm{CuO}}_{2}$ planes of high-${T}_{c}$ superconducting materials. The focus is primarily on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$, the material on which most scanning tunnel microscopy (STM) measurements of impurity resonances in the superconducting state have been performed. The magnitudes of the effective potentials found for Zn, Ni, and vacancies on the in-plane Cu sites in this host material are remarkably consistent with phenomenological fits of potential scattering models to STM resonance energies. The effective potential ranges are quite short, of order 1 \AA{} with weak long-range tails, in contrast to some current models of extended potentials which attempt to fit STM data. For the case of Zn and Cu vacancies, the effective potentials are strongly repulsive, and states on the impurity site near the Fermi level are simply removed. The local density of states (LDOS) just above the impurity is nevertheless found to be a maximum in the case of Zn and a local minimum in the case of the vacancy, in agreement with experiment. The Zn and Cu vacancy patterns are explained as due to the long-range tails of the effective impurity potential at the sample surface. The case of Ni is richer due to the Ni atom's strong hybridization with states near the Fermi level; in particular, the short-range part of the potential is attractive, and the LDOS is found to vary rapidly with distance from the surface and from the impurity site. We propose that the current controversy surrounding the observed STM patterns can be resolved by properly accounting for the effective impurity potentials and wave functions near the cuprate surface. Other aspects of the impurity states for all three species are discussed.

Is High TC Possible in (Ga,Mn)N?: Monte Carlo Simulation vs. Mean Field Approximation

The magnetic properties of diluted magnetic semiconductors (DMSs) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. By using the Korringa–Kohn–Rostoker coherent potential approximation method within the local density approximation, the electronic structure of (Ga,Mn)N and (Ga,Mn)As is calculated. Effective exchange coupling constants J ij s are calculated by using the formula of Liechtenstein et al. (A.~I. Liechtenstein, M. I. Katsnelson, V. P. Antropov, and V. A. Gubanov, 1987, J.~Magn. Magn. Mater. Vol. 67, p. 65). It is found that the range of the exchange interaction in (Ga,Mn)N is very short due to the exponential decay of the impurity wave function in the gap. On the other hand, in (Ga,Mn)As, the interaction is weaker but long ranged because the extended valence hole states mediate the ferromagnetic interaction. Monte Carlo simulations show that the TC values of (Ga,Mn)N are very low since percolation is difficult to achieve for small concentrations and the mean field approximation strongly overestimates TC. Even in (Ga,Mn)As the percolation effect is still important.

Low-temperature ferromagnetism in (Ga, Mn)N: Ab initiocalculations

The magnetic properties of dilute magnetic semiconductors (DMSs) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. By using the Korringa--Kohn--Rostoker coherent-potential approximation (KKR-CPA) method within the local-density approximation, the electronic structure of (Ga, Mn)N and (Ga, Mn)As is calculated. Effective exchange coupling constants ${J}_{ij}$'s are determined by embedding two Mn impurities at sites $i$ and $j$ in the CPA medium and using the ${J}_{ij}$ formula of Liechtenstein et al. [J. Magn. Magn. Mater. 67, 65 (1987)]. It is found that the range of the exchange interaction in (Ga, Mn)N, being dominated by the double exchange mechanism, is very short ranged due to the exponential decay of the impurity wave function in the gap. On the other hand, in (Ga, Mn)As, where $p\text{\ensuremath{-}}d$ exchange mechanism dominates, the interaction range is weaker but long ranged, because the extended valence hole states mediate the ferromagnetic interaction. Curie temperatures (${T}_{\mathrm{C}}$'s) of DMSs are calculated by using the mean-field approximation (MFA), the random-phase approximation, and the, in principle exact, Monte Carlo method. It is found that the ${T}_{\mathrm{C}}$ values of (Ga, Mn)N are very low since, due to the short-ranged interaction, percolation of the ferromagnetic coupling is difficult to achieve for small concentrations. The MFA strongly overestimates ${T}_{\mathrm{C}}$. Even in (Ga, Mn)As, where the exchange interaction is longer ranged, the percolation effect is still important and the MFA overestimates ${T}_{\mathrm{C}}$ by about 50%--100%.

First principles calculations of ZnS:Te energy levels

A comprehensive density-functional calculation for the ZnS:Te isoelectronic impurity state is presented. We deploy a charge patching method that enables us to calculate systems containing thousands of atoms. We found that the impurity state is only weakly localized, and previous calculations using 64-atom cells were severely unconverged. Our calculated impurity binding energy agrees with experimental photoluminescence excitation spectrum. We have analyzed the impurity wave function in both real space and the reciprocal space, and in terms of the host bulk valence bands. We have also calculated the Stokes shifts and Jahn-Teller effects. We found small Stokes shift compared to the experimental results, which might indicate the limitations of the current method. We also calculated the ${\mathrm{Te}}_{n}$ clusters and their impurity states. We found six (counting spin) bound states inside the band gap of ZnS for all $1<~n<~4.$ We obtained pressure coefficients for ${\mathrm{Te}}_{n},$ all close to the value of bulk ZnS. This is consistent with the fact that the impurity states of ${\mathrm{Te}}_{n}$ consist almost entirely of the bulk valence bands of ZnS. Finally, we have calculated the effects of spin-orbit coupling for the impurity state eigenenergies.

Anisotropy of the hopping magnetoresistance of antiferromagnetic La2CuO4+δ single crystals

The anisotropy of the hopping conductivity of antiferromagnetic La2CuO4+δ single crystals with TN≈188 K is investigated in the temperature range 5–295 K and the anisotropy of their magnetoresistance, in the temperature range 5–55 K. The resistance is measured by the Montgomery method for different combinations of directions of the transport current and magnetic field relative to the crystallographic axes. For the case when the field and transport current are directed parallel to the CuO2 layers, a transition from negative to positive magnetoresistance is observed when the temperature is raised to T≈20 K. For fields perpendicular to the CuO2 layers, only negative magnetoresistance is observed. The nature of the positive magnetoresistance is discussed. It is shown that the effect is most likely due not to the interaction of the spin of the charge carriers with the surrounding magnetic medium but to the orbital motion of these carriers. The corresponding values of the positive magnetoresistance and its behavior as a function of magnetic field and temperature are found using the well-known model of Shklovskii and Efros, which is based on taking into account the compression of the impurity wave functions of the charge carriers in the magnetic field.

Microwave magnetoresistance of compensated p-Ge:Ga in the region of the insulator-metal phase transition

The microwave magnetoresistance (MR) of neutron transmutation doped (moderately compensated) Ge:Ga in the insulator-metal transition region was studied using ESR technique. As the hole concentration increases, the MR mechanism changes in the insulator state near the phase transition point: the hopping conductivity that is characterized by the impurity wave-function contraction by the magnetic field is replaced by the state of weak localization. In the latter case, the temperature dependence of the diffusion coefficient is of great importance near the transition point (1.2×1017 cm−3). This dependence decreases in the metallic state. In the metallic state, the diffusion coefficient is independent of temperature and the MR temperature dependence is described by the dephasing mechanism due to phonon scattering. The electron-electron interaction contribution to the dephasing time should be considered for heavier doping.

Shallow impurities in V-groove quantum wires

We calculate the binding energies for shallow impurities in V-groove $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wires using a variational technique. The carrier ground states are calculated by an effective potential method together with a suitable coordinate transformation that allows the decoupling of the two-dimensional wave function. This method enables a detailed calculation of binding energies, providing an efficient tool for the study of impurity-related properties in V-groove wires. We show that the lateral confinement of the V-groove potential localizes the impurity wave function very effectively in the central region of the quantum wire.

Electron spin resonance investigation of electronic states in hydrogenated microcrystalline silicon

Phosphorus-doped microcrystalline silicon with high-crystalline volume fraction was prepared by very high-frequency plasma enhanced chemical vapor deposition. The material is studied by electron spin resonance and transport measurements as a function of doping and temperature. In all samples a resonance at $g=1.998$ is found with spin densities very similar to the phosphorus dopant density and also the carrier density at high doping levels. This resonance is related to doping-induced excess electrons. Its spin density is largely temperature independent, and the corresponding electrons occupy dopant or conduction band tail states at low temperatures, while they are excited into the conduction band at high T. This gradual transition is accompanied by changes in linewidth, g value and spin-lattice relaxation time. Hyperfine interaction with P nuclei is only observed for intermediate doping levels and has very small intensity. From the value of the hyperfine splitting, the effective Bohr radius of the impurity wave function is estimated to 12 \AA{}. Transport at low temperatures $(T<20\mathrm{K})$ proceeds via hopping between donor states and/or conduction-band tail states. A thermal activation energy of 3.5 meV and similar localization lengths as from the hyperfine data are found for this process. At temperatures above 20 K electronic transport is governed by a wide distribution of activation energies.

Shallow donor states in GaAs-(Ga, Al)As quantum dots with different potential shapes

Energies of the ground and some excited states of on-centre donors in spherical quantum dots are calculated, within the effective mass approximation, as functions of the R dot radius and for different potential shapes. We propose an exact numerical solution for the radial Schrödinger equation in a quantum dot with any arbitrary spherical potential by using a trigonometric sweep method. An evident increase in the binding energy is found as the soft-edge-barrier potential model is considered. It is found that the binding energy increases as the dot size decreases up to a dot radius critical value and then, for R slightly smaller than , the impurity wave function spreads to the barrier region and the 3D character is rapidly restored. The properties of the shallow donors in a quantum dot with a double-step potential barrier and multiple barriers are analysed, and two peaks in the binding energy are found. Our results for the spherical-rectangular potential are in good agreement with previous calculations obtained using other methods.

Effects of a Diffuse Potential on Shallow-Donor States in GaAs-(Ga,Al)As Quantum Dots

The energies for the ground and excited states of a D° impurity located at the center of a GaAs/ Ga 1-x Al x As spherical quantum dot are calculated, in the effective-mass approximation, as functions of the dot radius R and spatial size. We use a variational procedure and take linear combinations of Gaussian and Slater orbitals for the impurity-envelope wave functions. A model barrier potential is proposed to study changes in the potential introduced by diffusion effects. The binding energy of a 1s 2- -like D - impurity is also studied by considering a parabolic correlation factor. It is found that the D° and D- binding energies increase as the dot size decreases up to a critical dot radius R = R c and then, for R slightly smaller than R c , the impurity wave function spreads to the barrier region and the 3D character is rapidly restored. The critical dot radius R = R c is estimated by using the uncertainty relations.

Quantum Interference and Spin Effects in the Variable Range Hopping Magnetoresistance of Heavily Doped Semiconductors: Comparison between Si, Ge, CdTe and GaAs

The negative hopping magnetoresistance (NHM) due to quantum interference, as well as the positive hopping magnetoresistance (PHM) due to the reduced overlap between the impurity wave functions should both only increase as the temperature decreases. For the first time in GaAs, CdTe and Ge we observed with decreasing temperatures a more complicated dependence on temperature and magnetic field. The NHM initially increases with decreasing temperature but then decreases sharply, and disappears at the lowest temperature. We relate this effect to the spin alignment of the impurity atoms in the magnetic field for gμ*B ≫ kBT. Experimentally this new spin contribution depends strongly on the impurity concentration which, together with the critical concentration of the MIT, increases in the sequence of GaAs, CdTe, Ge, Si from 2×1016 to 3.5×1018 cm—3. The small NHM in Ge and its absence in Si may be due to dominating spin effects.

Theoretical calculation of the miniband-to-acceptor magnetoluminescence of semiconductor superlattices

The acceptor-related photoluminescence of a GaAs–(Ga,Al)As superlattice, under the influence of a magnetic field applied parallel to the interfaces, is theoretically studied following a variational procedure within the effective-mass approximation. Electron and hole magnetic Landau levels and envelope wave functions were obtained by an expansion in terms of sine functions, whereas for the impurity levels the envelope functions were taken as products of sine and hydrogenic-like variational functions. Impurity binding energies and wave functions are obtained for acceptors at a general position in the superlattice and for different in-plane magnetic fields. Theoretical results corresponding to transitions from the conduction subband to states of acceptors (miniband-to-acceptor e−A0 transitions) at the edge and center positions of the GaAs quantum well compare well with available experimental data by Skromme et al. [Phys. Rev. Lett. 65, 2050 (1990)] on the magnetic-field dependence of the photoluminescence peak position of conduction miniband-to-acceptor transitions for different temperatures and values of the superlattice period.

ESTIMATION OF THE EFFECTIVE DIELECTRIC RESPONSE FROM HOPPING ACTIVATION ENERGY IN THE VICINITY OF INSULATOR-METAL TRANSITION IN SEMICONDUCTORS

The effect of the energy overlap integral, due to the partial overlap of the adjacent wave functions of impurities, on the dielectric response ε of n-type semiconductor is examined. The proposed model suggests that ε diverges as the overlap increases, i.e. as the impurity concentration n is increased and essentially goes to a non-vanishing value as n approaches a critical value nc, defining the insulator-metal transition. It also predicts that ε→k (the host material dielectric constant) when n becomes low enough such that the impurity contribution to ε is negligibly small.

Two-channel resonant tunneling.

We study the conductance of a tunneling junction with two resonant impurities. We show that when the distance between the impurities is of the order of the de Broglie wavelength of an electron in the contacts, the coupling of the impurity states via the continuum of states in the contacts becomes important. If two identical impurities are located in the middle of the barrier, the resonant peak in the conductance, as a function of the Fermi energy, is dramatically narrowed. The resonant peak transforms into a deep minimum if impurity states have different energies or if impurities are shifted from the middle of the barrier. With nonvanishing overlap of the impurity wave functions, the position of the minimum is shifted from the resonance. We also study two-channel resonant tunneling between the edge states in the quantum Hall geometry. We show that for perfect resonance the coupling between the edge states is nonzero only within a narrow interval of magnetic fields.

Test for the Impurity Wavefunction Modelling from the Alloy Broadening of the Impurity-Related Luminescence

Test for the Impurity Wavefunction Modelling from the Alloy Broadening of the Impurity-Related Luminescence

Impurity Wave Function and Alloy Broadening of Impurity-Related Luminescence

By performing state-of-art ckputations of the acceptor wave func- tions in GaAs we show that the linewidth of the conduction band to ac- ceptor luminescence increases more than qu^adratically with the increase in the binding energy. This proves that study of the fluctuation broadening of the impurity-related emission in semiconductor alloys may provide a critical test for theories claiming realistic impurity wave function computation. The theoretical results are compared with the experimental data for high purity p-type AlGaAs alloys.

Single-scattering-path approach to the negative magnetoresistance in the variable-range-hopping regime for two-dimensional electron systems.

An alternative approach to the calculation of the scattering-induced magnetoresistance in the regime of variable-range-hopping conductivity is developed. Under the assumption that the direct tunneling and the various single-scattering tunneling paths give the main contribution to the amplitude of a hop, the exact averaging over the positions and energies of scatterers of the logarithm of the resistance is performed. It is shown that in the strong-scattering limit the magnetoresistance is universal in the sense that it does not depend on the scattering strength. The transition from negative magnetoresistance in low magnetic fields, caused by the suppression of the destructive interference, to positive magnetoresistance in strong enough fields, caused by the orbital shrinkage of the impurity wave functions, is traced. The theory developed is applied to the system of two parallel impurity planes in a magnetic field parallel to the planes. The oscillations of the hopping resistance with magnetic field in such a system are studied quantitatively.