Multiphonon Nonradiative Transitions Research Articles

Defect-related Auger excitation of erbium ions in amorphous silicon

A transition probability for defect-related Auger excitation (DRAE) of rare-earth ion inserted into amorphous matrix is calculated. The result is applied to excitation of an erbium ion in amorphous silicon occurring via capture of an electron by the dangling bond (D) defect. We have demonstrated high efficiency of the DRAE process which ensures photo- and electroluminescence of erbium ions in amorphous silicon matrix. It is shown that the temperature quenching of erbium luminescence in amorphous silicon is controlled by competition of the DRAE and the multiphonon nonradiative transitions.

Phonon bottleneck effect in multiphonon non-radiative transitions of rare-earth ions

Fluorescence transients of resonantly excited RE multiplets were recorded as function of excitation density in different glasses. Multiphonon relaxation rates are reduced at high excited state concentration for large energy gaps. Such behavior is analysed in a statistical approach and explained on the basis of a theoretical model for the microscopic process. We suggest a phonon bottleneck effect on radiationless relaxation rate related to an accepting modes saturation. At high excited state density, the accepting modes are simultaneously filled by several ions lying in a phonon diffusion volume. The phonon diffusion length I c in the host deduced from our model is compared with the phonon mean-free path independently derived.

Defect-related Auger excitation of erbium ions in amorphous silicon

The transition probability for defect-related Auger excitation (DRAE) of a rare-earth ion inserted into an amorphous matrix is calculated. The result is applied to excitation of an erbium ion in amorphous silicon occurring via capture of an electron by the dangling bond (D) defect. We have demonstrated high efficiency of the DRAE process which ensures strong photoluminescence and electroluminescence of erbium ions in an amorphous silicon matrix. It is shown that the temperature quenching of erbium luminescence in amorphous silicon is controlled by competition of the DRAE and the multiphonon nonradiative transitions.

Concentration and excitation effects in multiphonon non-radiative transitions of rare-earth ions

Non-radiative transitions in rare-earth ion doped systems are usually considered to be concentration and excitation intensity independent. Here we consider theoretically and experimentally a saturation in the capacity for the modes of the lattice to dissipate energy. Some first experimental results of this new effect in the case of Yb 3+ doped borate glasses are presented showing that at excited ion densities larger than 10 18 cm −3, non-radiative multiphonon transitions can be completely quenched well before amplification by stimulated emission is reached except when concentration rises above 8 × 10 20 cm −3. The experiment is well described at lower concentration by considering that the excited ions can share a common phnon density of states. At higher concentration, the common accepting modes diffusion length is reduced from 23 to 8 Å and a non-saturable radiative relaxation rate background of about 575 s −1 is observed which can be viewed as an increase in the effective accepting mode coupling strength by a factor 1.33.

Band-edge-related luminescence due to the energy backtransfer in Yb-doped InP

Band-edge-related photoluminescence in Yb-doped InP was investigated by solving rate equations. For InP:Yb, two characteristic properties have been observed in the band-edge-related luminescence. One is that the decay curve of the band-edge-related luminescence has a slowly decaying component above about 100 K, which has not been observed in undoped InP. The other is that the luminesce intensity shows an increase at around 120 K, although that for undoped InP monotonically decreases as temperature increases. These two properties were investigated based on a proposed model of energy transfer between the Yb 4f shell and the InP–host electrical state. In the model, it is assumed that a nonradiative multiphonon transition process assists the energy transfer. We have shown, in a previous article, that the temperature dependence of the decay time and of the intensity of the Yb 4f shell luminescence can be explained by using this assumption. In this article, we calculated the band-edge-related luminescence properties under the same assumption. Good agreement was obtained between the calculated and experimental results. Thus, the experimentally observed characteristic properties in the band-edge-related luminescence are explained by the energy backtransfer from the excited Yb 4f shell to the host electronic state.

Quantum efficiency and multiphonon nonradiative transition of Er 3+ ions in fluoride glass

Optical absorption, emission and excitation spectra, lifetimes of 4S3/2 state and 4F9/2 state from 10K to 500K, and Raman spectra were measured for Er3+ ions in fluoride glass. The radiative transition probabilities were calculated on the basis of Judd-Ofelt theory. The nonradiative transition probabilities and the quantum efficiencies were determined by calculating the difference between the measured lifetimes and the calculated radiative transition probabilities. The temperature dependence of nonradiative transition probability was investigated using the Huang-Rhys theory of multiphonon relaxation, in which two kinds of phonons as well as the parameter s were taken into consideration. A fairly good agreement of the theoretical calculation with the experimental results has been obtained. The value of s is estimated and the effect of s is discussed.

Molecular orbital method in the theory of multiphonon nonradiative transitions of impurity rare-earth ions

The overlap of the 4f-states of a rare-earth ion with the ligand orbitals is taken into account in the calculations of nonradiative relaxation probabilities and is shown to lead to a considerable increase of such probabilities when many phonons participate in the transition (the corresponding energies are ∼3000 cm -1).

Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation

Semiclassical versions of the static (diabatic) and adiabatic coupling schemes are applied to a two-level-one-mode system at total energies above the cross-over level. The corresponding rates of nonradiative multiphonon transitions reduce to alternativemonotonous dependences on the usual Landau-Zener parameterγ. Static coupling gives an increasing transition probability (per oscillation) of the familiar formPst(γ) = 4πγ. Adiabatic coupling associated with a sufficiently low mechanism-specific potential barrier of Born's type produces a decreasing transition probability of the formPad(γ) exp (−2πγ). The underlying “Beyond-Non-Condon” calculation procedure shows that (1) the weak dependence of the pre-exponential factorPad is a consequence of theγ-independent normalization of the electronic matrix element governing the non-adiabaticity operator and (2) the occurrence of the mechanism-specific tunnelling factor exp(−2πγ) is due to the avoided crossing of adiabatic oscillator potentials. Ranges of applicability of both alternative coupling schemes are limited by comparison with earlier non-perturbational results.

Quenching of the 4T1-6A1 transition of CsMnCl3:2H2O by OH stretching vibration

Multiphonon radiative and nonradiative transitions of CsMnCl3:2H2O(2D2O) have been investigated. We show that quenching of the 4T1-6A1 transition occurs through the coupling of OH stretching vibration to normal modes of the octahedron surrounding the Mn2+ ions. A two-configuration-coordinate model is proposed to explain the nonradiative relaxation.

Multiphonon Nonradiative Transition of RE3+ Ions in Ten Host Crystals11This work was partly supported by the National Natural Science Foundation of China

By using the formula of RE3+ multiphonon nonradiative transition (MPNRT) probability Wp0 derived on the basis of single-frequency model, the dependence of the Wp0 for the various RE ions in 10 hosts at the energy gap ΔE is analyzed and calculated systematically. The results agree well with a great deal of experimental data taken from the references and show clearly the characteristic of MPNRT under the condition of weak electron-phonon interaction: Wp0 decreases rapidly with the increase of order p which is the leading factor to determine Wp0; the values of K. HUANG-Rhys factor S progressively increase in the order of halide-oxide-fluoride, and the values of S for the various hosts in the same group are close.

Comparison between static and adiabatic coupling mechanisms for nonradiative multiphonon transitions in semiclassical approximation I. Tunnelling at small relaxation

Basic equations of the perturbational theory of nonradiative multiphonon transitions are reformulated in semiclassical approximation. They are specialized for the mechanisms of static (diabatic) and adiabatic coupling corresponding to the polar alternatives of crossing versus non-crossing oscillator potentials in a two-level-one-mode system. Tunnelling rates are calculated on the basis of contour integrals in the complex co-ordinate plane. These rates for static coupling are proportional to the square of the off-diagonal electron-oscillator interaction as commonly expected. For the alternative of adiabatic coupling we have obtained a non-monotonous (oscillating) pre-exponential transition rate factor. This unfamiliar result is based on a certain “beyondnon-Condon” procedure consisting in a consequent observation both of the familiarnon-Condon effect represented by the Lorentz function behaviour of the non-adiabaticity term and the associatedavoided- crossing (hyperbolic) behaviour of adiabatic potentials in the classical transition region. Present results confirm both the general non-equivalence of both alternative coupling mechanisms and a certain asymptotic approach between mechanism-specific tunnelling rates at small off-diagonal interactions.

Dynamics of the self-trapping process in cesium iodide

To describe the autolocalization at V k-centres in simple cubic alkali halides the adiabatic potentials are investigated. The barriers separating free and self-trapped excitonic states are analyzed for a wide range of the input parameters, and the rates of the respective multi-phonon non-radiative transitions are derived. The obtained results are consistent with the experimental data in CsI.

Radiative and non-radiative decay of excitons in solid xenon

Highly resolved luminescence spectra of high quality Xenon samples are presented. Lifetime-measurements yield self-trapping rates consistent with a theoretical description of the respective multiphonon non-radiative transitions.

Tunneling through the self-trapping barrier in rare gas solids

The adiabatic potential surfaces for atomic-type and molecular-type self-trapped excitons are explicitly determined for all rare gas solids. The resultant barrier separating the free exciton from atomic-type and molecular-type self-trapped states is analyzed, determining the barrier height and the tunneling path length for a wide range of parameter combinations. The tunneling through the barrier is then described by means of the theory of multi-phonon non-radiative transitions. Restricting the possible paths to one along a single interaction mode the tunneling rate is optimized. The results are consistent with experiments.

Numerical evaluation of non-radiative multi-phono transition rate from different electronic bases

Rigorous numerical calculations on the non-radiative multi-phonon transition probability based on the adiabatic approximation (AA) and the static approximation (SA) have been accomplished in a model of two electronic levels coupled to one-phonon mode. The numerical results indicate that both the diagonal non-adiabatic operator and the mixture and split of the potential sheets have a significant effect on the adiabatic vibrational states near or above the classical cross point and on the transition rates between these states. For strong electron-phonon coupling, the calculated transition rates based on AA are more reliable; on the other hand, for weak coupling the difference between transition rates near or beyond the crossing region based on different approximations can be beyond an order of magnitude. When the transition occurs far below the crossing point, both approximations give the same results. The relationship among the transition matrix element and the vibration level shift, the Huang-Rhys factor, the separation of the electronic levels and the electron-phonon coupling are analysed and discussed.

Multiphonon Nonradiative Transition of Rare-Earth Ions

Based on the general theory, the formula of multiphonon nonradiative transition probability is derived by adopting simplified approximations involving single-frequency model. Satisfactory agreement is obtained through the comparison of theory and experiment.The principal differences between the present paper and relevant literatures as well as the validity of simplified approximation are discussed.

Is the Barrier Height of Exciton Self-Trapping Evaluated So far Correct?–Quantum Mechanical Reevaluation–

The barrier height E B for self-trapping (ST) has been evaluated so far by analyzing the data on thermal quenching of free-exciton luminescence with the use of the classical formula (∝ exp [- E B / k B T ]) of the ST rate even at temperature T considerably lower than the Debye one. The rate of multiphonon nonradiative transition such as the ST rate cannot be described by the classical formula at such low temperatures. Analysis of the data of RbI below 30 K with the quantum mechanical formula gives E B ≃38–39 meV much larger than 17–18 meV obtained so far. The analysis shows simultaneously that concerning n =1 free excitons ST into a state of one-center type determines the rate in RbI while in KI it is overcome by ST into a state of two-center type with increasing temperature. This enables us to predict that the so called E x luminescence should be emitted from a still unknown self-trapped state of one-center type.

Static and adiabatic approaches to nonradiative multiphonon transitions: correct transition matrix elements of order Δ

The static base approach (SBA) and adiabatic base approach (ABA) are analysed for an electronic two-level system coupled to a single vibrational mode. In the ABA due account is taken of the non-adiabatic contribution to the oscillatory potential. This permits the introduction of a suitable model potential whose eigensolutions can be calculated exactly. It is proven that the calculation of the non-adiabatic transition matrix elements by means of these model eigenfunctions yields the correct first-order result in the promoting-mode coupling constant Delta and thus provides the same accuracy as the SBA calculation. The analysis evinces the importance of the diagonal non-adiabaticity operator, which has been neglected in earlier work. The transition matrix elements of the two approaches are compared. It is found that the absolute value of the SBA result is always larger than that of the ABA result and rises up to about a factor of two times the latter for higher Huang-Rhys factors. The authors finding resolves an old controversy.

The relation between various coupling schemes for calculating nonradiative multiphonon transition rates

In an earlier paper (see ibid., vol.15, p.L381, 1982) the author gave a simple proof that the static, adiabatic and intermediate coupling schemes give the same nonradiative multiphonon transition rates to leading order in the off-diagonal part of the electron-phonon interaction. In that proof, the time dependence in the interaction picture of the matrices describing the transformation from one representation to another was neglected using a heuristic argument. In this paper it is shown explicitly that this time dependence can be neglected, hence firmly establishing the earlier result. The equivalence between the various coupling schemes is also established for the time rate of change of a general observable; for example the charge density. The present work is discussed in relation to the recent papers by Peuker et al. (1982) and by Wagner (1982). In particular it is shown that there is no contradiction between the present work and that due to Wagner. It is also shown that Wagner's alternative adiabatic base is none other than the base defined by Condon electronic wavefunctions and displaced lattice oscillators and that this result holds independently of the strength of the off-diagonal part of the electron-phonon interaction.

ENERGY TRANSFER OF THE EXCITON IN THE QUASI-ONE-DIMENSIONAL ANTIFERROMAGNET CsMnCl3·2D2O

The dynamic processes, of energy transfer of the 4T1 exciton of Mn2+ ions have been studied in the temperature region 2-300 K in the pure and Mg2+-, Ni2+-, Co2+-doped quasi-one-dimensional antiferromagnet CsMnCl3·2D2O (CMC). It has been found that the fluorescent intensity and the lifetime of the exciton drops rapidly with increasing temperature in the region 2-10 K, with a further weakened fluorescence and shortened lifetime in the heavily doped crystals. These phenomena are presumed to be associated with the multiphonon nonradiative transition and energy transfer between donors and acceptors, both of which are related to the magnetic interactions and the spin ordering. At higher temperature, the rate of energy transfer increases. However, because of the persistence of spin short-range order and the Jahn-Teller effect, the energy transfer among donors is still limited to some extent, and nonexponential attenuation processes appear. The different impurities show different abilities of trapping and relaxing to a certain degree.