Pseudolocal Mode Research Articles

Fine structure of another blue luminescence band in undoped GaN

A blue luminescence band, labeled BL3, has been found in undoped GaN samples grown by hydride vapor phase epitaxy. It has a maximum at 2.8 eV and a phonon-related fine structure at its high-energy side. The zero-phonon line of this band consists of a duplet with two sharp lines at 3.0071 and 3.0147 eV. Three phonon modes, including the LO mode with an energy of 91.3 meV and two pseudolocal phonon modes with energies of 39.6 and 68.2 meV, form the characteristic fine structure of the BL3 band. The BL3 band is attributed to internal transitions from excited states located near the conduction band to the 0/+ transition level of unknown defect. The defect is preliminarily identified as the RY3 center, which is also responsible for bright red-yellow luminescence bands in the studied samples.

Two yellow luminescence bands in undoped GaN

Two yellow luminescence bands related to different defects have been revealed in undoped GaN grown by hydride vapor phase epitaxy (HVPE). One of them, labeled YL1, has the zero-phonon line (ZPL) at 2.57 eV and the band maximum at 2.20 eV at low temperature. This luminescence band is the ubiquitous yellow band observed in GaN grown by metalorganic chemical vapor deposition, either undoped (but containing carbon with high concentration) or doped with Si. Another yellow band, labeled YL3, has the ZPL at 2.36 eV and the band maximum at 2.09 eV. Previously, the ZPL and fine structure of this band were erroneously attributed to the red luminescence band. Both the YL1 and YL3 bands show phonon-related fine structure at the high-energy side, which is caused by strong electron-phonon coupling involving the LO and pseudo-local phonon modes. The shapes of the bands are described with a one-dimensional configuration coordinate model, and the Huang-Rhys factors are found. Possible origins of the defect-related luminescence bands are discussed.

Nonadiabaticity in a Jahn-Teller system probed by absorption and resonance Raman scattering

A theory of absorption and resonance Raman scattering of impurity centers in crystals with E⊗e-type Jahn-Teller effect in the excited state is presented. The vibronic interaction with non-totally symmetric local or pseudolocal modes and with a continuum of bath modes (phonons) is considered. A number of specific quantum effects, such as the nonadiabaticity-induced enhancement of the Raman scattering at high-energy excitation, the size effect of the final state, the interference of different channels of scattering, the Fermi resonances in the conical intersection, and others, were shown to become apparent in the calculated spectra. The vibronic interaction with phonons essentially determines the structure of the spectra.

Temperature dependence of the R1 linewidth in Al 2O 3:Mn 4+: A spectral hole-burning and FLN study

The temperature dependence of the R 1 linewidth in Al 2O 3:Mn 4+ is reported. Transient holes broaden rapidly from 2.5 to 40 K due to the one-phonon process between the E ¯ and 2 A ¯ levels of the 2 E excited state. The linewidth varies from 3 MHz at 2.5 K to 2640 GHz at 294 K and the line shifts by −1440 GHz. Above 50 K the two-phonon Raman process becomes dominant. The quadratic electron–phonon coupling constant is larger for Al 2O 3:Mn 4+ compared to ruby, resulting in a stronger phonon sideband in Al 2O 3:Mn 4+. The best description of the linewidth data are yielded by a model using pseudo-local modes.

Vibrational properties of impurities in semiconductors

The most commonly used first-principles technique to predict the properties of impurities in semiconductors involves periodic supercells to represent the host crystal, classical molecular dynamics (MD) to describe the nuclear motion, with ab initio-type pseudopotentials and density-functional theory to treat the electronic problem. Calculating the entire dynamical matrix of the supercell is most useful. Indeed, the eigenvalues of this matrix give all the local, pseudolocal, and resonant vibrational modes associated with the impurity, and allow the calculation of the phonon density of states, from which the vibrational free energy can be obtained. Further, the eigenvectors of the dynamic matrix are used to quantify the ‘localization’ of specific vibrational modes and prepare the supercell in thermal equilibrium at a temperature T, up to a few hundred degrees kelvin. This supercell preparation allows non-equilibrium MD simulations to be performed. Applications include the calculation of vibrational lifetimes and of thermal conductivities. This paper describes the essential ingredients of such calculations.

Vibronic transitions between states with hard and soft phonon dynamics

Abstract The analytical theory of vibronic transitions between electronic states with hard and soft phonon dynamics is proposed. It is found that the low energy part of the spectrum is essentially enhanced due to appearance of the low-frequency pseudo-local mode in the final state. The Fourier transform of the corresponding spectrum, in proper units, has the universal shape (1 − it)−μ. The value of the exponent μ depends on the dimensionality of the system: in 3D, 2D and 1D lattices the values are 0.35, 0.23 and 0, respectively. The theory gives an analytical description of the lambda-shaped spectra observed experimentally.

Soft dynamics of the excited state: Lambda-shaped optical spectra

Anomalous optical spectra of centres with strongly reduced local elastic constants in the excited electronic state are studied. In this case, transitions take place to the vicinity of a flat minimum of the potential energy in the configurational coordinate space. The existence of a flat minimum results in the appearance of the resonant (pseudo-local) mode of a low frequency. This leads to a strong enhancement of the low-frequency part of the phonon wing, causing a formation of the possibly modulated lambda-shaped optical spectra; the modulation comes from the Airy oscillations of the quantum accelerated motion.

First-Principles Calculations of Vibrational Lifetimes and Decay Channels: Hydrogen-Related Modes in Si

The vibrational lifetimes and decay channels of local vibrational modes are calculated from first principles at various temperatures. Our method can be used to predict the temperature dependence of the lifetime of any normal mode in any crystal. We focus here on the stretch modes of H2*, H+(BC), and VH x HV in Si. The frequencies are almost identical, but the lifetimes vary from 4 to 295 ps. The calculations correctly predict the lifetimes for T > 50 K and illustrate the critical importance of pseudolocal modes in the decay processes of high-frequency local vibrational modes.

Cu0*: A metastable configuration of the{Cus,Cui}pair in Si

First-principles theory shows that the substitutional-interstitial copper pair in Si (Si-${\mathrm{Cu}}_{s}\ensuremath{\cdots}{\mathrm{Cu}}_{i}$) has a metastable state with ${\mathrm{Cu}}_{i}$ very near a tetrahedral interstitial site in a trigonal ${\mathrm{Cu}}_{s}\text{\ensuremath{-}}\mathrm{Si}\ensuremath{\cdots}{\mathrm{Cu}}_{i}$ configuration that exhibits three low-frequency pseudolocal vibrational modes. The lowest of them, at $40\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, has ${A}_{1}$ symmetry and is the likely source of the phonon sidebands observed at $52\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ in the photoluminescence band of a defect known as $^{*}\mathrm{Cu}_{0}$.

Multiphonon processes in impurity centres: nonperturbative theory

A nonperturbative theory of the multiphonon relaxation of a strongly excited local vibration is developed. It is found that for a high initial level, the relaxation first accelerates in time, and later starts to slow down. The experimental evidence of such a non-monotonous relaxation is given by the hot luminescence in solid Xe. A theory of optical transitions in a center with strongly reduced local springs in the final electronic state is also developed. In this case a resonant increase of the local density of states of low-frequency phonons takes place, and a low frequency pseudo-local mode emerges. Appearance of such a mode in the final state means that a strong mode mixing takes place at the transition. This results in strong increase of the mean number of created low-frequency phonons. As a consequence, the zero-phonon transition practically disappears and the long-wave part of the phonon sideband is strongly enhanced, resulting in formation of so-called lambda-shaped spectrum. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The role of defect‐induced phonon localization in quantum diffusion

A defect displacement to a nearest site in the crystal lattice is usually accompanied by breaking and reconstitution of fairly strong chemical bonds, which has a strong effect on quantum diffusion. In the present communication, we present a nonperturbative theory, which enables one to properly account for the effect mentioned. The theory is applied to the description of the diffusion of vacancies in cubic lattices. It is shown that the local softening of the lattice by a vacancy produces a low-frequency pseudolocal mode resulting in a strong enhancement of the contribution of the low-frequency phonons to the diffusion. As a consequence, at low temperatures the diffusion coefficient D of vacancies is strongly reduced and its temperature dependence is essentially weakened: instead of the D ∝ T–9 temperature dependence one gets D ∝ Tκ dependence with κ ∼ 1. The obtained results are in agreement with the experimental data for the diffusion of vacancies in solid helium at low temperatures. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Structural and vibrational properties of {N,N} pairs and {N,H} complexes in Si

First-principles molecular-dynamics simulations are used to predict the structures and binding energies of interstitial nitrogen ${\mathrm{N}}_{\mathrm{i}},$ substitutional nitrogen ${\mathrm{N}}_{\mathrm{s}},$ the ${\mathrm{N}}_{\mathrm{i}}$-self-interstitial complex, the ${{\mathrm{N}}_{\mathrm{i}},{\mathrm{N}}_{\mathrm{i}}},$ ${{\mathrm{N}}_{\mathrm{i}},{\mathrm{N}}_{\mathrm{s}}}={{\mathrm{N}}_{2},\mathrm{V}},$ and ${{\mathrm{N}}_{\mathrm{s}},{\mathrm{N}}_{\mathrm{s}}}={{\mathrm{N}}_{2},{\mathrm{V}}_{2}}$ pairs (V is the vacancy). The interactions of N with H in Si are studied and the properties of several ${\mathrm{N},\mathrm{H}}$ complexes are predicted. The dynamical matrices yield many new local and pseudolocal vibrational modes associated with the impurities and their Si nearest neighbors. The unidentified ${\mathrm{N},\mathrm{H}}$-related infrared absorption line reported by Pajot et al. is assigned to the ${{\mathrm{N}}_{\mathrm{s}},\mathrm{H}}$ complex.

Phase relaxation in the vicinity of the dynamic instability: anomalous temperature dependence of zero-phonon line

We study optical spectra of impurity centers in crystals in the case when in one or in both electronic states of the optical center the local elastic springs are strongly reduced, causing appearance of the pseudolocal mode of a very low or even imaginary frequency. In these cases, the optical transition takes place to the vicinity of a flat minimum or a flat potential barrier in the configurational coordinate space, where the density of states of low-frequency phonons is strongly enhanced. One example of systems of this type is the trigonal center with strong Jahn–Teller effect in the two-fold degenerate E-state, when the adiabatic surface has a shape of the so-called squeezed Mexican hat. We have found that in this case the usual T 7-dependence of the homogeneous width of the zero-phonon line (ZPL) at low temperatures is replaced by a dependence close to the T 3-one. Besides, the usual T 4-dependent red shift of the line is replaced by the T 2-dependent shift. Depending on the flatness of the adiabatic surface, the shift may be to the red or to the blue. The theory is applied to the ZPL 637 nm of the nitrogen-containing N− V center in diamond.

Analysis of f-element multiphonon vibronic spectra

Theoretical modeling of multi-phonon vibronic spectra is presented based on the Huang–Rhys theory of ion–phonon interaction in a single-mode lattice. The single-mode spectral function is modified for applications to vibronic spectra involving multiple vibrational modes. It is shown that, for lanthanide and actinide ions in crystals, f–d electronic transitions exhibit two types of vibronic couplings. One type of vibronic coupling to local and pseudo-local modes obeys Frank–Condon selection rules and has a sharp line width, whereas in the second type of vibronic coupling electronic transitions couple to lattice modes in which selectivity is absent, thus forming a broad vibronic band. The model calculation reproduces very well the experimental spectra of 5f–6d transitions of Pa 4+ in Cs 2ZrCl 6 and 4f–5d transitions of Ce 3+ in Cs 2NaYCl 6.

First-principles calculations of pseudolocal vibrational modes: the case of Cu and Cu pairs in Si.

Pseudolocal vibrational modes (pLVMs) are defect-related vibrational modes which are localized despite being below the phonon maximum. Such modes are sometimes seen as phonon replicas in photoluminescence spectra. The pLVMs associated with two copper-related defects are calculated from first-principles density-functional theory in periodic supercells. The localization of the pLVMs is quantified using the magnitude of the eigenvectors of the dynamical matrix.

Optical properties of the deep Mn acceptor in GaN:Mn

The optical and electrical properties of Mn-doped epitaxial GaN were studied. Low-temperature optical absorption measurements indicate the presence of a Mn-related band with a well-resolved fine structure. The zero-phonon line is at 1.418±0.002 eV with a full width at half maximum of 20±1 meV. Two pseudolocal vibrational modes associated with manganese were observed with energies of hv1=20 and hv2=73 meV. Deep-level optical spectroscopy measurements on lightly Mn-doped samples indicate that Mn forms a deep acceptor level at Ev+1.42 eV. Using the vacuum referred binding energy model for transition metals and the measured Mn energy level, the electron affinity of GaN is calculated to be 3.4 eV, which agrees well with experimental values.

Raman scattering and photoluminescence properties of MBE-grown GaN on sapphire

We have comprehensively investigated low temperature Raman and photoluminescence (PL) spectra of gas source MBE-grown GaN layers on sapphire. Strong and sharp Raman peaks are observed in the low frequency region which are enhanced by resonant excitation of yellow luminescence transitions. They are attributed to the electronic transitions related to shallow donor levels in hexagonal GaN. It is proposed that a low frequency Raman peak at 94 cm−1 may be caused by pseudo-local vibration modes related to defects involved in yellow luminescence transitions. The PL spectra are measured in dependence on temperature and excitation intensity. The correlation with residual impurities in GaN is discussed.

Temperature-dependent line broadening of chromophores in amorphous solids: Differences between single-molecule spectroscopy and photon echo results

Spectroscopic techniques exhibit different sensitivities for line broadening processes in amorphous solids. Photon echo and hole-burning spectroscopy yield averages over the chromophore ensemble. At low temperatures, the results can usually be fitted with a combination of a power-law term — corresponding to the relaxations of two-level systems- and of an exponentially activated contribution of pseudo-local phonon modes. Single-molecule spectroscopy (SMS). in contrast, can resolve the behavior of single dye molecules and yields a distribution of power laws as well as of activation energies. We compare photon echo results for tetra-tert-butylterrylene (TBT) in polyisobutylene (PIB) with SMS data for the same system. The latter were used to simulate numerically the data which would be obtained in an ensemble-averaging experiment. The results of the numerical calculation can be well fitted without assuming a distribution of parameters.

Single Molecule and Shpolskii Spectroscopy of Terrylene in a Series of N-Alkanes

Abstract We present a study of terrylene in a series of n-alkane matrices with increasing chain length, namely dodecane, tetradecane and hexadecane. Shpolskii absorption spectra provide the macroscopic characterization of the samples, such as site multiplicity, inhomogeneous line widths and positions. Based on this characterization the distributions of single molecule homogeneous line widths were measured in the maxima and in the wings of the inhomogeneous lines. The results indicate that in case of dodecane matrix the line broadening is caused by optical dephasing due to interaction with pseudolocal phonon modes. Exponential profile of temperature dependence of the line width gives the phonon energy of 23 cm−1. In cases of tetradecane and hexadecane matrices there is additional broadening present which we interpret as spectral diffusion. Further, we present a new method for collecting the single molecule fluorescence using a selfoc micro lens.

Picosecond absorbance difference spectra of the antenna of photosynthetic purple bacteria The influence of exciton interactions and librations

The influence of exciton interactions and pseudolocal librational modes on the relaxation of photo-induced absorption changes of the light-harvesting antenna of the photosynthetic purple bacterium, Rhodospirillum rubrum, was studied in the ps time domain. A hypothesis is put forward that the long-lived librational modes can occur in the circular aggregate of light-harvesting bacteriochlorophyll molecules of the core antenna. The model spectra obtained quantitatively fit the shape of the photo-induced picosecond absorbance difference spectra. The model predicts the decay of photo-induced spectra with the time constant within tens of picoseconds.