Multiphonon Processes Research Articles

Semi-analytic theory of multiphonon effects on the static structure factors of warm solids.

A semi-analytic formula for the temperature-dependent static structure factor S(k) of polycrystalline and amorphous solids applicable to the entire wavenumber (k) range is derived. The formula describes thermal diffuse scattering due to multiphonon processes entirely by a single kernel function without resorting to the standard perturbation expansion. It is analytically proven that S(k → 0) is determined from the one-phonon term, whereas the asymptotic limit S(k → ∞) = 1 can be reproduced through a Gaussian integral of the multiphonon term. The formula also reveals that an enhancement of the one-phonon scattering intensity at each Bragg point is expressed as a logarithmic singularity. Numerical examples for a face-centred cubic polycrystal near the melting point are shown. The present formula is computationally more efficient than other theoretical models, requiring only a one-dimensional integration to obtain S(k) once the elastic part of the structure factor and the Debye-Waller factor are given.

Phonon-Limited Valley Polarization in Transition-Metal Dichalcogenides.

The ability to selectively photoexcite at different Brillouin zone valleys forms the basis of valleytronics and other valley-related physics. Symmetry arguments combined with static lattice first-principles calculations suggest an ideal 100% valley polarization in transition-metal dichalcogenides under circularly polarized light. However, experimental reports of the valley polarization range from 32% to almost 100%. Possible explanations for this discrepancy include phonon-mediated transitions, which would place a fundamental limit to valley polarization, and defect-mediated transitions, which could, in principle, be reduced with cleaner samples. We explore the phonon-mediated fundamental limit by performing calculations of phonon-mediated optical absorption for circularly polarized light entirely from the first principles. We also use group theory to reveal the microscopic mechanisms behind the phonon-mediated excitations, discovering contributions from several individual phonon modes and from multiphonon processes. Overall, our calculations show that the phonon-limited valley polarization is around 70% at room temperature for state-of-the-art valleytronic materials including MoSe_{2}, MoS_{2}, WS_{2}, WSe_{2}, and MoTe_{2}. This fundamental limit implies that sufficiently pure transition-metal dichalcogenides are ideal candidates for valleytronics applications.

Multiphonon Process in Mn-Doped ZnO Nanowires.

The multiphonon process plays an essential role in understanding electron-phonon coupling, which significantly influences the optical and transport properties of solids. Multiphonon processes have been observed in many materials, but how to distinguish them directly by their spectral characteristics remains controversial. Here, we report high-order Raman scattering up to 10 orders and hot luminescence involving 11 orders of phonons in Mn-doped ZnO nanowires by selecting the excitation energy. Our results show that the intensity distribution of high-order Raman scattering obeys an exponential decrease as the order number increases, while hot luminescence is fitted with a Poisson distribution with a resonance factor. Their linewidth and frequency can be well explained by two different transition models. Our work provides a paradigm for understanding the multiphonon-involved decay process of an excited state and may inspire studies of the statistical characteristics of excited state decay.

Design of coherent wideband radiation process in a Nd3+-doped high entropy glass system

We discover that the spatially coherent radiation within a certain frequency range can be obtained without a common nonlinear optical process. Conventionally, the emission spectra were obtained by de-exciting excited centers from real excited energy levels to the ground state. Our findings are achieved by deploying a high-entropy glass system (HEGS) doped with neodymium ions. The HEGS exhibits a much broader infrared absorption than common glass systems, which can be attributed to be high-frequency optical branch phonons or allowable multi-phonon processes caused by phonon broadening in the system. A broadened phonon-assisted wideband radiation (BPAWR) is induced if the pump laser is absorbed by the system. The subsequent low-threshold self-absorption coherence modulation (SACM) can be controlled by changing excitation wavelengths, sample size, and doping concentrations. The SACM can be red-shifted through the emission of phonons of the excited species and be blue-shifted by absorbing phonons before they are de-excited. There is a time delay up to 1.66 ns between the pump pulse and the BPAWR when measured after traveling through a 35 mm long sample, which is much longer than the Raman process. The BPAWR-SACM can amplify the centered non-absorption band with a gain up to 26.02 dB. These results reveal that the shift of the novel radiation is determined by the frequency of the non-absorption band near the absorption region, and therefore the emission shifts can be modulated by changing the absorption spectrum. When used in fiber lasers, the BPAWR-SACM process may help to achieve tunability.

Ligand Fluorination to Mitigate the Raman Relaxation of DyIII Single-Molecule Magnets: A Combined Terahertz, Far-IR and Vibronic Barrier Model Study.

The fast Raman relaxation process via a virtual energy level has become a puzzle for how to chemically engineer single-molecule magnets (SMMs) with better performance. Here, we use the trifluoromethyl group to systematically substitute the methyl groups in the axial position of the parent bis-butoxide pentapyridyl dysprosium(III) SMM. The resulting complexes-[Dy(OLA )2 py5 ][BPh4 ] (LA =CH(CF3 )2 - 1, CH2 CF3 - 2, CMe2 CF3 - 3)-show progressively enhanced TB hys (@100 Oe s-1 ) from 17 K (for 3), 20 K (for 2) to 23 K (for 1). By experimentally identifying the varied under barrier relaxation energy in the 5-500 cm-1 regime, we are able to identify that the C-F bond related vibration energy of the axial ligand ranging from 200 to 350 cm-1 is the key variant for this improvement. Thus, this finding not only reveals a correlation between the structure and the Raman process but also provides a paradigm for how to apply the vibronic barrier model to analyze multi-phonon relaxation processes in lanthanide SMMs.

First‐principle investigation of defect‐associated LVM and structural parameter dependency in response to the ground state on‐site Hubbard correction of w‐ZnO

AbstractWe report a combined experimental (at 81 K, room temperature) and theoretical Raman study of plasma synthesized ZnO nanoparticles. The linear response method calculates the on‐site Coulomb interaction (Hubbard correction) energies Ud = 12.65 eV and Up = 7.65 eV. The structural changes and hybridization mechanism of the d‐p orbital of Zn and O have shown a significant role in bandgap discrepancies. Density of state (DOS) calculations under the influence of Hubbard correction explains the d‐band energy shift mechanism. Over underestimation of bandgap energies phenomena turns out to be highly sensitive to the choice of pseudopotential, and a series of calculations have been reported to converse to greater accuracy. The theoretical calculation was made possible using generalized gradient approximation (GGA)‐based basis set Perdew, Burke, and Ernzerh (PBE); B3LYP; and local density approximation (LDA). Estimates improve accuracy by including the Hubbard correction energy to the ground state energy calculation using the LDA. We have provided approximations methods suitable for the defect complex study based on our systematic analysis among PBE, B3LYP, and LDA. For the correlated system, the choice of pseudopotential is primarily essential; therefore, the present article also discusses the application of Hubbard correction energy only to a specific orbital and consequences. Experimentally observed fundamental and multiphonon decay processes are explained. The defect trapped hydrogen and defect complex configuration state , m = 1, …, 4, local vibrational mode is observed. Systematic molecular design and simulation support the experimentally reported results. The VZn, in association with a single 1s electron of hydrogen, compromises state followed by silent, and second‐order features are presented.

Multiphonon quantum dynamics in cavity optomechanical systems

The multiphonon quantum dynamics in laser-pumped cavity optomechanical samples containing a vibrating mirror is investigated. Especially, we focus on dispersive interaction regimes where the externally applied coherent field frequency detuning from the optical resonator frequency is not equal to the mirror's oscillating frequency or to its multiples. As a result, for moderately strong couplings among the involved subsystems, the quantum dynamics of this complex system is described by multiphonon absorption or emission processes, respectively. Particularly, we demonstrate efficient ways to monitor the phonon quantum dynamics via photon detection. The possibility to extract the relevant sample parameters, for instance, the coupling strength between the mechanical mirror and the electromagnetic field, is also discussed.

Manipulating the singular red emission in GdOF:Yb/Er nanosheets via defect engineering

Efficient tailoring of red emission in a selectively emitting Yb 3+ /Er 3+ up-conversion (UC) system is of great significance for optical applications. In this study, we adopted a facile and effective method to obtain a pure red emission by defect engineering in GdOF:Yb 3+ /Er 3+ (6/x mol%) nanosheets. It was observed that the defect engineering was realized by NaF etching of the precursors in a low-temperature water bath reaction. As a result, the probability of multi-phonon relaxation processes was increased, resulting in a red to green (R/G) ratio higher than 19 for all samples. The products perfectly inherited the sheet-like morphology of the precursors. Furthermore, the effect of calcination temperature on the UC emission selectivity was demonstrated in GdOF:Yb 3+ /Er 3+ nanocrystals. The R/G ratio of the samples obtained at 500 °C was increased by about 3–4 times compared with the samples obtained at different calcination temperatures. By combining the results with the outcomes of spectroscopic analyses, we simulated the role of defects in improving the R/G ratio of GdOF:Yb 3+ /Er 3+ samples using a model. The exciting discovery of the ability of defect engineering to modulate UC emission selectivity not only provides a general method to tailor red emission in a Yb 3+ /Er 3+ UC system, but also facilitates multicolor displays, anti-counterfeiting, and tissue bioimaging. Schematic diagram of Er 3+ up-conversion red emission enhanced via defect engineering. • The anion-exchange reaction of the layered structure materials was accomplished by low temperature water bath method. • During the anion-exchange reaction, the corrosion effect of NaF on the surface of the nanosheets produced defects. • The R/G ratio of the unmodified GdOF:Yb 3+ /Er 3+ nanosheets prepared by defect engineering were above 19. • The R/G ratio of the GdOF:Yb 3+ /Er 3+ nanosheets increased rapidly to 19.36 by controlling calcination temperature.

Europium-doped Zn-Al-LDH intercalated with 4-biphenylcarboxylate anion and undoped Zn-Al-LDH intercalated with its anionic Eu(III) complex: Structural and UV or X-ray excited luminescence properties

Undoped and doped layered double hydroxides (LDH) were obtained by coprecipitation and the bca (biphenyl-4-carboxylate) anion or [Eu(bca)4]- intercalation by solvothermal post treatment. The three systems, (i) [Zn2Al1-xEux]NO3-LDH x = 0.1 at.%, (ii) [Zn2Al1-xEux]bca-LDH x = 0.1 at.% and (iii) [Zn2Al][Eu(bca)4]-LDH are compared by XRD, FTIR, Zeta Potential, PLS and XEOL characterizations. The luminescent properties are exciting. The bca intercalation/coordination increases the luminescence intensity of the doped LDH because decreases the –OH groups, luminescence suppressors by multi-phonon process, and increases the ligand to Eu3+ energy transfer processes. The luminescence in the (iii) system is less intense than the (ii) system but more intense than (i) system and the Eu3+ symmetry in the intercalated complex is different from the free one. X-ray excited optical luminescence occurs on all systems with different radiation damage. The intense luminescence remarks the Eu3+ as an excellent spectroscopic probe, as dopant in the brucite-like layers and in the interlayer space as anion complex. Finally, the LDH host structure acts as a protective environment for the luminescence properties of intercalated species. Thus, LDH systems become potential candidates combining the inorganic and organic properties for promising emission materials.

Multiphonon processes of the inelastic electron transfer in olfaction.

Inelastic electron transfer, regarded as one of the potential mechanisms to explain odorant recognition in atomic-scale processes, is still a matter of intense debate. Here, we study multiphonon processes of electron transfer using the Markvart model and calculate their lifetimes with the values of key parameters widely adopted in olfactory systems. We find that these multiphonon processes are as quick as the single phonon process, which suggests that contributions from different phonon modes of an odorant molecule should be included for electron transfer in olfaction. Meanwhile, the temperature dependence of electron transfer could be analyzed effectively based on the reorganization energy which is expanded into the linewidth of multiphonon processes. Our theoretical results not only enrich the knowledge of the mechanism of olfaction recognition, but also provide insights into quantum processes in biological systems.

Optical properties of Praseodymium (Pr3+) doped bismuth boro-tellurite glasses containing CdSe nanoparticles

Adding TeO2 and growing nanoparticles of CdSe can significantly affect the optical properties of Pr3+ ions doped in bismuth borate glasses. We used a modified Judd-Ofelt analysis to obtain the intensity parameters from the optical absorption spectra. Adding TeO2 leads to an increase in the covalency of the Pr-O bond. However, the presence of CdSe nanoparticles makes Pr-O bond less covalent. Optical band gap shows a considerable decrease when nanoparticles are present. Phonon side band analysis suggests that energy levels of Pr3+ responsible for the intense red emission are populated through a cross-relaxation mechanism instead of multiphonon decay process. The blue transition of Pr3+ shows significant enhancement for the stimulated emission cross-section when CdSe nanoparticles are present. Chromaticity analysis identifies the overall light emissions from different glass samples with various standard sources. Our glass samples also possess high spectroscopic quality factors compared to similar systems doped with Pr3+ ions.

Energy Resonance Transfer between Quantum Defects in Metal Halide Perovskites.

Quantum defects have been shown to play an essential role in nonradiative recombination in metal halide perovskites (MHPs). Nonetheless, the processes of charge transfer assisted by defects are still ambiguous. Herein, we theoretically study the nonradiative multiphonon processes among different types of quantum defects in MHPs using Markvart's model for the induced mechanisms of electron-electron and electron-phonon interactions. We find that the charge carrier can transfer between the neighboring levels of the same type of shallow defects by multiphonon processes, but it will be distinctly suppressed with an increase in the defect depth. For the nonradiation multiphonon transitions between donor- and acceptor-like defects, the processes are very fast and not sensitive to the defect depth, which provides a possible explanation for the phenomenon of blinking of photoluminescence spectra. We also discuss the temperature dependence of these multiphonon processes and find that their variational trends depend on the comparison of the Huang-Rhys factor with the emitted phonon number. These theoretical results not only fill some of the gaps in defect-assisted nonradiative processes in the perovskite materials but also provide deeper physical insights into producing higher-performance perovskite-based devices.

Efficient First-Principles Methodology for the Calculation of the All-Phonon Inelastic Scattering in Solids

Inelastic scattering experiments are key methods for mapping the full dispersion of fundamental excitations of solids in the ground as well as nonequilibrium states. A quantitative analysis of inelastic scattering in terms of phonon excitations requires identifying the role of multiphonon processes. Here, we develop an efficient first-principles methodology for calculating the all-phonon quantum mechanical structure factor of solids. We demonstrate our method by obtaining excellent agreement between measurements and calculations of the diffuse scattering patterns of black phosphorus, showing that multiphonon processes play a substantial role. The present approach constitutes a step towards the interpretation of static and time-resolved electron, x-ray, and neutron inelastic scattering data.

Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials

Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal non-equilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multi-phonon excitations. In Ref. [{\it arXiv:2103.10108}] we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multi-phonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide (MoS$_2$), bulk MoS$_2$, and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multi-phonon excitations dominate in bP across multiple Brillouin zones, while in MoS$_2$ they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffuse scattering signals. We further demonstrate the high-throughput capability of our approach by reporting all-phonon scattering maps of 2D MoSe2, WSe2, WS2, graphene, and CdI2, rationalizing in each case the effect of multi-phonon processes. As a side point, we show that the special displacement method reproduces the thermally distorted configuration that generates precisely the all-phonon diffuse pattern.

Efficient near-infrared luminescence and energy transfer mechanism in Ca3Al2O6: Ce3+, Yb3+ phosphors

Solar cells have been extensively studied as a means of green energy converters in recent decades, especially the silicon solar cells. However, the energy efficiency of crystalline solar cells is very low, which is due to the reason that they have a good absorption in 800–1100 nm region but a bad absorption in 300–500 nm region. Based on this, a series of Ce3+-Yb3+ codoped Ca3Al2O6 samples are synthesized by the conventional solid state method in reduced atmosphere. Energy transfer process from Ce3+ to Yb3+ is affirmed by the characterizations of photoluminescence, photoluminescence excitation spectra and decay curves in different temperatures. The photoluminescence intensity and lifetime of Ce3+ decrease with the increase of Yb3+ content. And as the temperature increases, the energy transfer efficiency increases. These results demonstrated that the near-infrared luminescence from 2F5/2 to 2F7/2 transition of Yb3+ is implemented via a multi-phonon assisted energy transfer process in the Ce3+-Yb3+ ions pair. These phosphors exhibit broadband absorption in the ultraviolet region with efficient near-infrared emission (centering at 976 nm), which has better spectral response for crystalline Si solar cells. The obtained results illustrated that the phosphors have potential applications as spectral conversion materials to enhance the performance of crystalline Si solar cells.

Predicting the impact of temperature dependent multi-phonon relaxation processes on the photon avalanche behavior in Tm3+: NaYF4 nanoparticles

Photon avalanche (PA) is an anti-Stokes process in which lanthanide-doped materials can emit upconverted luminescence in a highly non-linear manner. PA was recently demonstrated in thulium (III)-doped NaYF4 colloidal nanoparticles at room temperature, with reported nonlinearities (power factors) exceeding 30. Importantly, good rate-equations model agreement with experimental data was achieved, which enabled the derivation of the rates of energy transfer processes, providing a foundation for further developments and optimization of similar materials and their new applications. In order to apply PA to, for example, luminescent (nano)thermometry, we need to have a better understanding of the susceptibility of photon avalanche phenomenon to temperature variation. For this purpose, we study how the temperature and energy-gap-dependent multiphonon relaxation and inter-ionic energy transfer processes affect the photon avalanche behavior. As a result of these simulations, high susceptibility to temperature changes with relative sensitivity over 40 %⋅K−1 above 400 K (up to 15 %⋅K−1at room temperature) was noted. Moreover, by knocking-out the temperature dependences of the individual processes involved in the PA, we found the temperature dependence of the multiphonon relaxation of the intermediate F34 state to the ground state to be the primary one responsible for the simulated temperature dependence of PA emission. This process is observed to be more significant than temperature dependencies of energy looping and phonon assisted ground state non-resonant absorption. Although there are challenges with a single band technique, these results still show the great potential, especially when used ratiometrically with different excitation wavelengths.

Yb3+ influence on NIR emission from Pr3+-doped spherical yttria nanoparticles for advances in NIR I and NIR II biological windows

Highly intense NIR emissions in the first and second biological windows and a remarkable UV–Vis and NIR to NIR energy conversion were observed for Pr3+, Yb3+ co-doped yttria nanoparticles, synthesized via the homogeneous precipitation method. A single-phase body center cubic Y2O3 structure was formed for all the samples after annealing 900 °C for 2 h. Increasing the dopants content, from 0.5 to 5.0 mol %, the replacement of Y3+ by Pr3+ and Yb3+ ions lead to a lattice expansion, which could be calculated. Spherical monodispersed nanoparticles, constituted of several crystallites, were observed by TEM and SEM images. The particles size ranged from 143 to 272 nm for the as-prepared samples and from 88 to 202 nm for the samples annealed at 900 °C. The crystallite size was estimated by Debye-Scherrer and Williamson-Hall methods and ranged from 6 to 27 nm with an average of 13 nm. Photoluminescent studies evidenced pronounced Pr3+ and Yb3+ near infrared (NIR) emission under ultraviolet, visible, and NIR excitation. How the Yb3+ ions co-doping, as well as, the total rare earth content, affected the luminescence properties, were evaluated, along with the energy transfer process involving UV–Vis and NIR to NIR energy conversion between the doping ions and the host. The energy was transferred between the Y2O3 host and Pr3+, Yb3+ upon CT band excitation at 290 nm. NIR emission at 948, 1080, 1115 nm, and 1.5 μm attributed to the Pr3+ transitions 3P0,1→1G4, 1D2→3F3, 1D2→3F4, and 1D2→1G4, denoting the 1D2 population through a multiphonon relaxation process (3P0+3H4→3H6+1D2). A concentration quenching process was ascertained in the highest concentration of dopants (5.0 mol % in total), which indicated that cross-relaxation took place. Both the Yb3+-doped and Pr3+, Yb3+ co-doped samples presented the Yb3+ emission 2F5/2→2F7/2 at 976 nm. All the structural, morphological, and spectroscopic properties of the materials make these spherical yttria nanoparticles potential NIR emitting probes candidates for advances in biophotonics, especially for deep-tissue imaging using NIR I and NIR II biological windows.

Excitons in CsPbBr3 Halide Perovskite.

Excitons in Bridgman grown halide perovskite CsPbBr3 single crystals were examined using photoluminescence (PL) spectroscopy to determine the nature of the electronic states. The photoluminescence intensity was strongly temperature-dependent and depended upon the specific exciton band. At low temperatures intrinsic disorder and its related shallow below bandgap tail states determine the emission properties. Photoluminescence at low temperature revealed the presence of several strong bands at the band edge that is attributed to free or trapped/bound excitons. This PL emission results from strong electron-phonon coupling with an average phonon energy Eph of 6.5 and 27.4 meV for the emissions, comparable to that observed in other perovskites. The Huang-Rhys parameter S was calculated to be 3.81 and 1.51, indicating strong electron-phonon coupling. The interactions between electrons and phonons produce small polarons that tend to bind charge carriers and result in trapped/bound excitons. The transient photoluminescence response of each specific band was studied, and the results indicated a multiphonon recombination process. Average PL lifetimes of ∼17 ns for free excitons and ∼38 ns for trapped/bound excitons were determined. The observed edge states could be associated with native defects such as vacancies and interstitials, as well as twinning due to the cubic-to-tetragonal phase transition in CsPbBr3. Elimination of the trapping sites for binding excitons could lead to improved charge transport mobilities, carrier lifetimes, and detector properties in this system.

Influence of aluminum doping on structural, morphological, vibrational, and optical properties of CdS thin films obtained by chemical bath deposition

Thin films of CdS and Al-doped CdS have been successfully deposited on glass substrates by using a CBD technique and their properties were investigated. The structural analysis confirmed the hexagonal structure of CdS with preferential orientation along (002) planes. Crystallite sizes decreases with Al content. The AFM images of the films show changes in morphology with increase the dopant concentration. Raman scattering were composed of fundamental longitudinal optical (LO) modes and their multi-phonon process. Transmittance, reflectance, refraction index and extinction coefficient were studied to extract the optical properties variation upon Al doping. The increase of the lattice strain due to Al doping modifies the optical properties of the films. The energy band gap was found to increase from 2.3 to 2.6 eV with increase in Al content. The doping also affects the photoluminescence properties of CdS crystal structure, causing a shift towards shorter wavelengths of the peaks of Al-doped films.

First-principles identification of deep energy levels of sulfur impurities in silicon and their carrier capture cross sections

Studies of the deep energy levels and nonradiative carrier capture induced by sulfur doping in silicon were initiated 60 years ago; however, the defect configurations, their deep energy levels, and the carrier capture cross sections are still not well understood. In this study, we focus on SSi substitution, and perform a first-principles study of its defect configurations and the deep energy levels using hybrid exchange-correlation functional. We discover a new distortive configuration for SSi + besides the previously obtained structure with higher symmetry. For both SSi + configurations, the deep transition levels (0/+) and (+/2+) are determined as 0.35 eV and 0.68 eV below the conduction band minimum, respectively. As a benchmark calculation, the hole-capture cross sections for neutral and +1 charged states are obtained based on the distortive structure. The cross section for SSi + agrees with the experiment, demonstrating the multi-phonon process for SSi + capturing a hole, whereas the cross section of SSi 0 is significantly lower than the experimental data because hole capture by SSi 0 is an Auger-type process. Our calculations provide a benchmark for the evaluation of the cross section of carrier capture in semiconductors using multi-phonon nonradiative recombination theory.