Impurity Wave Functions Research Articles

High magnetic field studies of resonant tunneling via shallow impurities in δ-doped quantum wells

We have observed a new sub-threshold peak in the I(V) characteristics of double-barrier resonant tunneling structures. By investigating a range of intentionally δ-doped and control layers we can relate this peak to resonant tunneling through the bound state of a shallow donor impurity in the quantum well. We have studied the dependence of the voltage position of this peak on the magnitude of a magnetic field applied either parallel or perpendicular to the plane of the quantum well. In the parallel orientation the donor peak shifts slightly to lower voltage whereas the threshold of the continuum resonance shows the usual large quadratic shift to higher voltage. The amplitude of the donor-related peak is reduced in the presence of a magnetic field. We present a theoretical model to explain this behaviour and show how the results can be used to probe the spatial form of the impurity wavefunction in the quantum well.

Donor-photoluminescence line shapes from GaAs-(Ga,Al)As quantum wells

The D\ifmmode^\circ\else\textdegree\fi{}-h impurity-related photoluminescence spectra of confined donors in GaAs-(Ga,Al)As quantum wells is theoretically investigated within the effective-mass approximation. The impurity wave functions and binding energies are evaluated via a variational procedure. Calculations are performed for different well widths, temperatures, and impurity doping profiles. Typical D\ifmmode^\circ\else\textdegree\fi{}-h theoretical photoluminescence line shapes show peaked structures corresponding to on-center and on-edge donors in good agreement with experimental results.

Nuclear electric quadrupole interaction of implanted ions in graphite

A number of isotopes have been implanted into thin foils of highly oriented pyrolytic graphite in order to investigate the possibility of using this material as a catcher for on-line LT-NO experiments to measure the quadrupole interaction of short-lived nuclei. Pure nuclear electric quadrupole interaction of nuclei of188,189Ir,203Hg,69mZn,182m,183Re and111In has been observed. Values for the electric field gradient along theC-axis are: +10.0(3) +8.2(9), +5.4(2.6) and +1.5(1)·1022 V/m2, respectively, for Ir, Hg, Re and In in graphite. A value ofQ=+0.79(6) b is deduced for the quadrupole moment of189Ir. Two theoretical models provide a better understanding of the origin of the electric field gradient in graphite. The first is based on induced electric polarization of graphite atoms, while in the second one hybridization of impurity and graphite electronic wave functions is calculated.

Nuclear electric-quadrupole interaction of ion-implanted 203Hg and 69mZn in graphite.

$^{203}\mathrm{Hg}$ and $^{69\mathit{m}}\mathrm{Zn}$ ions have been implanted into thin foils of highly oriented pyrolytic graphite at room temperature and at temperatures below 1 K. Low-temperature nuclear orientation due to strong electric-quadrupole interaction has been observed and the derived electric-field gradients are compared with two kinds of theoretical calculation. The first is based on the induced polarization of the graphite atoms, while in the second the hybridization of impurity and graphite electron wave functions is calculated. The results indicate that the fraction of nuclei that contribute to the macroscopic alignment is located in the layers of the C atoms. The experimental value of ${\mathit{V}}_{\mathit{z}\mathit{z}}$ at the nuclear site of Hg is +[8.2(9)]\ifmmode\times\else\texttimes\fi{}${10}^{22}$ V/${\mathrm{m}}^{2}$, parallel to the graphite c axis.

Impurity-related optical absorption from GaAs-(Ga,Al)As quantum wells under an applied electric field.

Impurity-related optical-absorption spectra for GaAs-(Ga,Al)As quantum wells under an externally applied longitudinal electric field are investigated. A variational procedure in the effective-mass approximation is used in the evaluation of the impurity binding energies and wave functions. Effects of the variation of both field intensity and well width on the donor- and acceptor-related absorption line shapes are analyzed in the cases of infinite- and finite-barrier potentials. The results show that the absorption spectra present an edge associated with the maximum value of the impurity binding energy and two van Hove--like singularities corresponding to impurities positioned at the two edges of the well. As the field intensity is increased, the absorption spectra are shifted towards lower energies, with their intensities reduced, and the relative importance of the van Hove--like singularities is changed. Such effects become more pronounced for larger widths of the quantum wells.

The incoherent mechanism of negative magnetoresistance for variable-range-hopping transport in two-dimensional electron systems

Abstract The experimental data on hopping magnetotransport in dilutely doped δ layers for both perpendicular and parallel orientations of magnetic field B are discussed. The temperature dependence of the resistance, InRαT −1/3, indicates that the variable-range-hopping mechanism applies. At strong enough fields (B > 2·5 T) the resistance for both orientations rises rapidly with increasing B because of the orbital shrinkage of the impurity wavefunctions. In the range of intermediate fields (1 T < B < 2T) the resistance in the perpendicular orientation appears to be several times less than in the parallel orientation. Such an ‘inverted’ relation cannot be accounted for by the mechanism proposed by Nguyen, Spivak and Shklovskii which is based on the interference of alternative tunnelling paths. To explain the experimental results the effect of magnetic field on the energy positions of the impurity levels is taken into account. By reducing the overlap between the neighbouring sites, a magnetic field pushes th...

First-principles supercell studies of the nitrogen impurity in diamond.

We have used a first-principles, local-orbital computational scheme to study the electronic structure of a substitutional N donor impurity in cubic diamond. The calculations were carried out in a supercell framework, using three different supercells with increasing impurity-impurity separation. Comparison of the results from all three supercells allows a reliable extrapolation to the isolated-impurity limit; we find that the N impurity level falls at ${\mathit{E}}_{\mathit{c}}$-0.8 eV, where ${\mathit{E}}_{\mathit{c}}$ is the conduction-band edge. Analysis of the impurity wave function for the three supercells shows that, while the calculated energies indicate a deep donor level, the impurity wave function is nonetheless surprisingly long ranged. The implications of this for the interpretation of recent findings on magnetic multilayers are briefly discussed.

Theory of Auger core-valence-valence processes in simple metals. I. Total yields and core-level lifetime widths.

There is a considerable disagreement in the literature on the description of lifetime effects arising from core-valence transitions in solids. We calculate here Auger and radiative widths of shallow core levels in Li, Be, Na, Mg, and Al with use of principles consistent with dynamical theories of secondary-emission processes developed earlier. The lifetime has no simple relation to the usual self-energy but is instead directly related to emission yields. The problem of choosing reliable approximations for Auger rates and matrix elements is analyzed theoretically and computationally. We also comment on some earlier approaches. Much of our discussion pertains also to calculations of Auger line shapes from first principles. For long hole lifetimes the total and partial level widths obey an initial-state rule and follow from wave functions perturbed by a static core hole. To obtain these impurity wave functions we perform self-consistent supercell calculations. The core-hole screening increases the Auger rates by factors of the order 2–4 compared with results from ground-state orbitals but has never been properly included before. The width of the 1s level in Li is rather accurately known because it monitors large effects of incomplete lattice relaxation. For Li we obtain here a width 17 meV in excellent agreement with the value 16 meV deduced earlier from measurements by Callcott et al. (Less)

Auger recombination at double donors

Double donors are deep impurities which are favourable for Auger recombination. The cross section of this recombination process and its temperature dependence are calculated for double donors in indirect-band-gap semiconductors (for instance S, Se and Te in Si). Because of the uncertainty of the impurity wavefunction, the cross section covers a wide range (10-14-10-19 cm2). The temperature dependence is only in agreement with experiments if the influence of lattice relaxation is taken into account. A remarkable point is the independence of this process with respect to the carrier density which is also observed in other cases. The analogous problem of a double acceptor (Zn in Si) is discussed.

Persistent photoconductivity in Si-doped AlxGa

Persistent photoconductivity in Si-doped molecular-beam epitaxial ${\mathrm{Al}}_{0.28}$${\mathrm{Ga}}_{0.72}$As was studied. The carrier concentration decreases with time according to a simple power law. The decay is explained semiquantitatively by an effective-mass-like model of the impurity with a wave packet centered near but not at the $\ensuremath{\Gamma}$ point in the Brillouin zone. The shift of the impurity wave function in k space may be explained in terms of long-range composition ordering in the AlAs-GaAs system. Other physical properties may also be influenced by periodic composition fluctuations observed in many semiconducting alloys.

Binding energies of hydrogenic impurities in parabolic quantum wells.

We have calculated binding energies of simple, hydrogenic-type impurities in parabolic quantum wells as functions of the displacement of the impurity from the well center and the strength of the well potential. The calculation method is based on an expansion of the impurity wave function in a series of hydrogenic-type functions. Our results for the impurity at the well center are in excellent agreement with those obtained by a different method elsewhere.

Electron-nuclear double resonance of interstitial chromium in silicon.

The positively charged state of interstitial chromium in silicon was investigated using electron-nuclear double resonance. We have found the hyperfine interaction of the impurity electrons with nine shells of surrounding silicon neighbors containing 102 atoms. The well-resolved fine structure due to the cubic-field splitting for chromium made it possible to determine the absolute signs of the measured hyperfine interaction parameters. The results are analyzed using a linear combination of atomic orbitals treatment that takes into account the spin S=(5/2 of the impurity and the symmetry of the atomic orbitals centered at the ligands for the different shells. This analysis results in a spin density that is transferred from the impurity to the host crystal of at least 22%. The apparent contradiction between the reduced core polarization (indicating a delocalization of some 52% of the impurity wave function) and the absence of large hyperfine interactions with the silicon ligands is hereby resolved. Our results are compared with those obtained for the positively charged state of interstitial titanium and neutral interstitial iron. It appears that the electronic structure of chromium is similar to that of titanium.

Scattered impurity states in transition metals. II. Approximate solutions using phase shifts.

To solve the problem of a transition metal with an impurity, the one-electron linear-combination-of-atomic-orbitals wave functions are constructed in terms of spherical harmonics multiplied by spherical Bessel or spherical Neumann functions. These solutions are approximated afterwards by the standing-wave-like projected-coefficient (SWLPC) functions, calculated in the preceding paper, and their modifications. At large distances from the impurity area the impurity wave function has the form of a scattered wave. Any solution for an imperfect crystal differs from that obtained for a perfect crystal by the presence of a phase shift. In each case the electron states can be quantized according to the requirement that their wave functions vanish at the crystal boundary, which is assumed to be spherical. This makes the analysis of the impurity problem in a crystal very similar to that done by Friedel in the free-electron case. However, any present phase shift depends on the symmetry index of the SWLPC function, the branch of the solution of the secular problem, and the wave vector belonging to the irreducible part of the Brillouin zone. The phase shifts, which can be expressed in terms of the perturbation matrix, are proportional to corresponding components of the density of states of the unperturbed metal. An expression for the change in the number of metal electrons due to scattering is obtained. In its derivation the phase shifts found in the present paper enter into a modified Friedel's formula given originally for the free-electron case.

Bound magnetic polarons in semimagnetic quantum wells.

We examine the position dependence of the binding energy of a hydrogenic impurity in a semimagnetic quantum well. We consider in particular, a CdTe well confined by (Cd,Mn)Te potential barriers. We show that, due to the penetration of the impurity wave function inside the barrier, at low temperatures, the exchange interaction with the Mn local spins may lead to the formation of a bound magnetic polaron. In such a case, the impurity is more strongly bound at the interface than at the center of the well, in contrast to the situation in nonmagnetic quantum wells.

Optical autoionization resonance theory as an approach to electron transfer via adsorbed atoms at metal—solution interfaces

Electron transfer between an ion in solution and an impurity atom adsorbed at a metal electrode is sometimes faster than direct electron transfer between an ion and a metal. This process displays close analogies to Fano autoionization resonances in atoms excited to formally bound states broadened by coupling to continuum states. On the basis of this analogy we have derived current—voltage relationships for electron transfer via adsorbed impurity atoms. The most striking effect is that the current passes through a maximum at overvoltages approximately coinciding with the nuclear reorganization enery, then drops, and rises again at still higher voltages. This pattern is quite different from that of direct electron transfer and is caused by the “interference” of metal and impurity wave functions in certain energy ranges. The effect is generally expected only for activationless process, i.e. for large overvoltages, where the current variation directly reflects the behaviour of the pre-exponential factor in the current expressions. The impurity level also modifies the Gibbs energy of nuclear activation due to the solvent configuration dependence of the electron density at the adatoms. This effect is commonly small and in contrast to the electronic structural effects, leads to smooth current-voltage relations.

Model for phonon-assisted indirect recombination at impurity sites in semiconductors: A test of impurity wave-function theories.

A new method for studying the wave functions associated with defect levels is presented. The method is based on a model that includes the role of intrinsic lattice phonons in indirect electron-hole recombination at impurity sites in semiconductors; the model contains information about the impurity-phonon matrix elements and the intrinsic phonon dispersion relations as well. In particular, it can be used in conjunction with experimental data as a test of the accuracy of impurity wave-function models. As an illustration, an application to the acoustic-phonon sidebands in the low-temperature luminescence spectrum of the N-bound excition in GaP is described wherein the method is used to test the Koster-Slater one-band one-site approximation for the electron wave function.

Comment on "Optical-transition cross sections involving impurities in semiconductors"

It is shown how, in contrast with matrix elements of the momentum operator, matrix elements of the position operator between shallow impurity levels in semiconductors associated with one band and states in a band of opposite parity are very sensitive to slight variations of assumptions made about impurity wave functions. Since recent results of Chaudhuri for absorption due to transitions between acceptor levels and conduction bands based on a formulation involving matrix elements of the position operator are in disagreement with those published by other authors using a formulation in terms of momentum matrix elements, it is inferred that Chaudhuri's results are in error due to a small departure of the wave functions used from true energy eigenfunctions. When small improvements, deducible from published work of Bowlden, are made to impurity wave functions, it is shown that consistency between matrix elements of position and momentum operators is obtained, and it is the matrix elements of the position operator which are altered by the small changes in wave functions.

Effect of impurity scattering of a tunneling electron on variable-range hopping conduction

Variable-range hopping conduction in semiconductors is determined by the asymptotic behavior of impurity wave functions on distances much larger than mean interimpurity separation. Scattering of an impurity electron by the other impurities situated near its tunneling path is shown to result in a correction Δa to electron localization lengtha. This correction depends on the impurity scattering length and impurity concentrationN and may be of the order ofa(Na3) ora(Na3)1/2.

DEEP LEVELS OF TRANSITION IMPURITIES IN SILICON

A simple model about transition impurities in semiconductors is proposed, and the impurity energy levels and wave functions produced by substitutional and interstitial atoms in silicon are calculated by Green's function method. It is shown that the properties of these two kinds of impurities are remarkably different. The substitutional atom can produce impurity energy level only when Vd, the atomic level of d state, is below the top of valence band. It's wave function is mainly dangling bond state, and gradually turns into bond state when the energy level approaehs the edge of conduction band. The interstitial atom can produce impurity energy level only when Vd is above the top of valence band. It's wave function is mainly d state of central atom and gradually turns into weak antibond state. Finally, the chemical trend and some experimental facts of transition impurity energy levels are qualitatively explained.

Complex band structure and deep impurities. II. Γ15and Γ12states

For pt.I see ibid., vol.15, p.3711 (1982). The authors apply a model described in their paper I to Gamma 15 and Gamma 12 (p- and d-like) impurity states in zincblende structure semiconductors. The complex band structure for these symmetries is obtained and this is then related through the matching conditions, which are different for each irreducible representation, to the impurity wavefunction. These wave functions are then used to calculate the optical cross section and elucidate its dependence on the symmetry of the impurity.