Impurities In Solids Research Articles

Interlevel nonradiative transitions of impurities in solids

The spin-orbit interaction in transition-metal ions induces fast nonradiative transitions among states of different spin; the transition rates can be directly measured by the homogeneous broadening of zero-phonon optical lines. The configuration-interaction formalism developed by Fano is well suited for the evaluation of the widths and shifts caused by these nonradiative processes. By taking the Jahn-Teller effect into account, we have shown that within the framework of Fano's formalism it is possible to reproduce the shape of the zero-phonon line of MgO: ${\mathrm{V}}^{2+}$ as regards both widths and splittings without making use of any fitting parameter. The model has also been applied to ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$: ${\mathrm{Cr}}^{3+}$, ${\mathrm{Cs}}_{2}$Si${\mathrm{F}}_{6}$: ${\mathrm{Mn}}^{4+}$, and MgO: ${\mathrm{Cr}}^{3+}$; its limits of validity have been discussed.

Relaxation dynamics of excited impurities in solids

We calculate classical trajectories of atomic displacements in a crystal that contains an excited impurity. The decay of the localised excitation by vibrational relaxation on an adiabatic potential energy surface emerges from the study. We obtain the dephasing and anharmonic parts of the rate of escape of excitation from the impurity centre and determine shapes of phonon-pulses emanating from the centre. Hot luminescence band-shapes are derived in terms of the classical trajectory. Several types of impurity-lattice interactions are used in the computations, but the stochasticity of the relaxat dynamics is not investigated.

Calorimetric absorption spectroscopy of nonradiative recombination processes in GaP

A new, simple and highly sensitive spectroscopic method, calorimetric absorption spectroscopy (CAS), for direct detection of phonons emitted via nonradiative recombination processes of charge carriers bound to defects or impurities in solids is demonstrated. Electronic levels of these centers are populated by resonant excitation with monochromatic light. The phonons emitted during recombination are detected with a low-temperature calorimeter with a sensitivity of ≊10−12 J. Thus absorption coefficients as low as ≊10−7 cm−1 and quantum efficiencies can be determined without using radiation detectors. CAS spectra of N- and S-doped GaP are presented, and the low-temperature internal quantum efficiency of the nitrogen bound exciton is found to be close to 100%.

The importance of static strains in studies of thermal phonon scattering by strongly coupled impurities

Most interpretations of the scattering of thermal phonons by strongly coupled impurities in solids make the assumption that static strains in the crystal can be neglected, so that the relevant transition energies and probabilities may be taken as those for unstrained sites. The authors present heat pulse evidence to show that, for MgO:Cr2+ at least, this assumption is not valid. Strong scattering is observed from sites corresponding to turning points of magnetic field anticrossings with static strain, which are not necessarily those at zero strain. Furthermore, one of the strongest scattering transitions A1 to A2 is actually forbidden for zero strain.

The slow approach to a semi-classical absorption band-shape in certain Jahn-Teller systems

Absorption band-shapes of impurities in solids are often calculated using a semi-classical approximation, which should give correct results in the limit of strong coupling. We have computed some band-shapes to compare with the semi-classical approximation and show that for E ⊗ ε Jahn-Teller systems this limit is only approached very slowly, and is not reached at realistic coupling strengths. Zero temperature is assumed.

Pressure Effects of Optical Spectra of Impurity Centers in Solids

Pressure dependences of absorption and emission spectra of impurities in solids are calculated with a one dimensional configuration-coordinate model considering pressure-dependent linear coupling coefficient and force constants which arise through anharmonic terms of the adiabatic potential energies. It is shown that the pressure-dependent force constants play an important role in the understanding of the pressure effects on the peak positions, band-widths and Huang-Rhys parameters.

Spin-dependent correlated atomic pseudopotentials

The previously developed first-principles density-functional (nonlocal) atomic pseudopotentials are extended to include explicit spin effects as well as electronic correlation effects beyond the local-spin-density (LSD) formalism. Such angular-momentum-and spin-dependent pseudopotentials enable the extension of pseudopotential applications to study magnetic problems (e.g., transition-metal and other open-shell impurities in solids, ferromagnetic surfaces, etc.). As the spurious electronic self-interaction terms characterizing the LSD energy functional are self-consistently removed, these pseudopotentials can also be used to calculate reliably localized electronic states (e.g., deep defect levels, surface and interface states, narrow-band states in solids, etc.). Applications to atoms show that this pseudopotential method removes many of the anomalies of the LSD approach, including the systematically high total energy, the failure to predict the stability of negative ions, the lack of correlation between orbital energies and observed ionization potentials, and the erroneous ordering of $s$ and $d$ levels of the $3d$ transition elements Sc to Fe in their ${d}^{n\ensuremath{-}1}{s}^{1}$ configuration.

Intermediate Hamiltonian and lower bounds to localised energy levels

The intermediate Hamiltonian method is applied to the calculation of lower bounds to localised energy levels due to impurities in solids. This technique, together with judicious application of the Koster-Slater method, giving upper bounds in favourable cases, allows the exact localised energy levels to be bracketed. An application to a one-dimensional Kronig-Penney potential with rectangular impurities is presented. The accuracy attained varies in the range of 2.43% of the deviation of the energy level from its band of origin.

A Modification of Förster's Deactivation Relation due to Inhomogeneous Spatial Distribution and Active Behavior of the Acceptors

AbstractThe deactivation behavior of excited molecules and impurities in solids is analyzed under consideration of a long‐range excitation energy transfer based on dipole‐dipole interaction between donors and acceptors. Under the condition of inhomogeneous spatial distribution and active behavior of the acceptors a time evolution formula is derived, which essentially differs from Förster's original relation [2]. The results are discussed for physically representative values of concentration and medium parameters.

Moments of semiclassical and classical absorption and emission band shapes of impurities in solids

General expressions for all moments are calculated for both semiclassical and classical approximations to absorption and emission band shapes due to impurities whose vibrational interactions with the surrounding lattice of a solid contain both linear and quadratic terms. The first five moments are presented and compared to the exact quantum-mechanical results. The semiclassical approximation is found to be most accurate for vibrational interactions having either linear or linear plus quadratic terms with strong coupling and/or high temperature. The semiclassical approximation is rarely, if ever, appropriate if only quadratic terms occur. The classical approximation is a valid representation of the semiclassical approximation at high temperatures. These conclusions are shown to be consistent with the correspondence principle.

Entropy and volume of solution of substitutional impurities in solids

Entropy and volume of solution of substitutional impurities in solids

Moments of the Poisson distribution

An explicit expression is developed for the $n\mathrm{th}$ moment of the Poisson distribution that portrays optical absorption and emission band shapes of impurities in solids.

Theory of the effects of hydrostatic pressure on the radiative transitions of impurities in crystals

The effects of hydrostatic pressure on radiative electronic transitions of impurities in solids are analyzed in the adiabatic approximation. A procedure is established for including the effects of pressure on the adiabatic potential for each electronic state. From harmonic configuration coordinates the effects of pressure on peak energy and half-width are determined classically for broad-band, phonon-assisted, absorption and luminescent emission spectra. The conditions for linear dependence of the peaks on pressure are clarified. The impurity is then considered quantum mechanically, and the effects of pressure on vibronic transition energies and probabilities determined. The pressure at which the zero-phonon transition becomes most probable is predicted for some defects. Finally, the effect of anharmonicity on the pressure dependence of vibronic transition energies is evaluated. From this study it is concluded that impurities with vibronic structure can be understood in great detail from the application of the theory to experimental pressure-dependent spectra.

Activation volume for self-diffusion and for the diffusion of impurities in lead

A recently derived representation of the Gibbs free energy of a defect process in terms of the thermoelastic properties of the host crystal is shown to be applicable to the calculation of the activation volume for the diffusion of impurities in solids. The experimental data for the diffusion of several metals (Ag, Au, Cu, Hg, Zn, Sn, Tl, Ni, Pd) in lead and the self-diffusion are discussed showing a fair agreement with the theoretically determined activation volumina.

A resolvent technique for the simulated ab initio molecular orbital (SAMO) method

The purpose of this paper is twofold. Firstly, we show how the Koster-Slater equations for impurities in solids may be applied to the simulated ab initio molecular orbital (SAMO) method. The resulting equations are modified and a method of generating eigenvalues and eigenvectors of perturbed molecular systems is discussed in detail. The method is shown to be much quicker than normal eigenvalue techniques for problems of the type involving interactions between small systems and large ones. Secondly, we compare eigenvalues and first-order properties of SAMO wavefunctions of octane with SCF wave functions. The agreement is excellent in all properties studied.

Stochastic classical trajectory approach to relaxation phenomena. II. Vibrational relaxation of impurity molecules in Debye solids

The stochastic classical trajectory approach is extended through introduction of a systematic class of phonon mode densities. Convenient algorithms are presented for generating the required random forces and damping integrals corresponding to mode spectra which approach, as closely as desired, the Debye spectrum. Extension to realistic mode densities involving irregular and discontinuous features is discussed. Application to vibrational relaxation of impurities in solids demonstrates that rates can depend sensitively on the structure of the phonon density of states, particularly at low temperatures.

The effects of core structure on radiative and non-radiative recombinations at metal ion substituents in semiconductors and phosphors

Abstract Carrier binding and recombination processes at transition metal (TM) and post-transition metal impurities in solids are reviewed. The presence of low-lying empty core orbitals in these impurities introduces novel binding and recombination phenomena and leads naturally to a classification of impurity centres as ‘simple’ or ‘structured’. ‘Simple’ impurities, generally the main group elements, introduce only effective-mass-like states into the forbidden gap of the host lattice, whereas ‘structured’ impurities show localized atomic-like transitions below the lattice absorption edge. The fact that donor or acceptor centres generated by TM ions in semiconductors are usually deep is discussed with reference to a simple oxidationstate correlation diagram based on the variable chemical valency characteristic of these ions. Many metal ion impurities in solids generate iso-electronic centres however, and evidence is assembled to show how the normally accepted range of iso-electronic centres can be extended ...

Stochastic classical trajectory approach to relaxation phenomena. I. Vibrational relaxation of impurity molecules in solid matrices

We present a theory of impurity vibrational relaxation in condensed media based on computer simulation of the classical equations of motion of the impurity molecule and a small number of neighboring host atoms. The host atoms are in communication with the remainder of the lattice through the presence of stochastic forces and damping terms that are constructed from knowledge of the phonon spectrum of the solid. Temperature is introduced via the fluctuation–dissipation theorem. The method is applied here to a Cl2 impurity molecule imbedded in an argon matrix. The dependence of energy relaxation and dephasing times on interaction parameters is monitored, and comparison is made with recent spectroscopic measurements on this system.

Elastic interaction of tunneling impurities in solids

The tunneling model for dipolar impurities in solids is applied to a study the static collective behavior of systems with large impurity concentrations. A rigorous formal result for the elastic constants is derived predicting anomalous softening near the phase transition corresponding to orientational ferroelastic ordering of the impurities. The nature of the phase transition is studied within the mean field approximation and examples of second and first order transitions are given for typical cases of impurity equilibrium orientations. Application to mixed KCl1−xCNx crystals and to pure KCN is discussed in the light of recent experimental and theoretical work.

Moments of absorption- and emission-band shapes of impurities in solids

General expressions are reviewed and explicitly presented for determining all quantum-mechanical moments of absorption- and emission-band shapes that originate from electronic transitions in a defect whose vibrational interaction contains, in the Condon and adiabatic approximations, terms both linear and quadratic in a single configuration coordinate. The zeroth through fourth absorption and emission moments are presented, the fourth moments for the first time. The band shapes, proportional to transition probabilities, have moments that differ from those of experimentally measured absorption coefficients and emission rates.