Indirect Transitions Research Articles

Photoluminiscence and absorption of emission by phonons of indirect transitions in layered GaS single crystals

Absorption in E||b and E⊥c polarizations and photoluminescence at the absorption edge were studied at temperatures range 10 - 300 K. It was found that the smallest indirect transitions take place from the minimum of conduction band C1 (point M) to the maximum of valence band V1 in the Brillouin zone center (point Γ or nearby). A distance between these extrema is 2.4484 eV at 10 K. In addition, the magnitude of indirect transitions from the second band C2 (point M) to valence band V1 (Brillouin zone center) is 2.4912 eV at 10 K. The splitting of C1-C2 bands in M point of the Brillouin zone is equal to ∼ 43 meV. The indirect transitions from third conduction band C3 (point K) to valence band V1 in the nearby of Γ point are equal to 2.7683 eV at 10 K. The splitting of conduction bands C2 (point M) and C3 (point K) is higher than one for the splitting C1-C2. It was observed bands associated with self-absorption of photoluminescence emission by phonons with symmetries E1g1+A1g2, A1g2+A1g1 and A1g2+E2g2 involved in indirect transitions.

Supramolecular architectures, Hirshfeld surfaces analysis, spectroscopic, computational and photovoltaic properties of nickel(II) binary and ternary complexes of N-phenethyl-iminodiacetate (2-) chelate

The bluish-green color nickel(II) binary and/or ternary compounds have been isolated from the solution of stoichiometric reaction between Ni(II) hydroxy-carbonate and N-phenethyl-iminodiacetic acid (H2pheida) chelating ligand in aqueous media with compound (2); [Ni(pheida)(Him)3]·4H2O and without imidazole compound (1); [Ni(pheida)(H2O)3]. The crystal pattern of binary compound [Ni(pheida)(H2O)3] (1) differs from the related tetra-hydrated ternary complex of [Ni(pheida)(Him)3]·4H2O (2) can be attributed to the presence of stronger N-(Him) spacer of imidazole ligand. The compounds reported herein, have been characterized by means of elemental analysis, FTIR, UV–vis, TGA and X-ray crystallography. Moreover, the distinctive inter-molecular forces particularly H-bonding interactions, 2D fingerprint plots and supramolecular architecture have been studied using Hirshfeld surface analysis. The nickel(II) binary and ternary complexes (1) and (2) show distorted octahedral geometry around the Ni(II) ion of the type 1 + 2 + 2 + 1 imposed by 3d8 electronic configuration with degenerate fully and half occupied t2g6 and eg2 orbitals respectively. The higher John-Teller distortion has been observed for complex (2) than that of complex (1). The IDA arm of chelate adopted fac-NO2 conformation in both complexes (1) and (2). Moreover, the photovoltaic properties as semiconducting nature for ligand and their corresponding Ni(II) complexes were estimated using Tauc’s equation, αhν = A(hν-Eg)r, where r = ½ for indirect and 2 for direct electronic transitions through UV–vis absorption data. The indirect and direct electronic transition bandgap (Eg) calculated for complex (1) is 2.0 and 3.07 eV respectively. Similarly, 2.55 and 4.39 eV respectively measured for complex (2).

Structural, optical, and shielding investigation of PVA/Te composite for technological applications

Using the casting process, polymeric films made of polyvinyl alcohol (PVA) including varying percentages of Te were created to form PVA/Te composite at doping concentrations of Te (0, 4.76, 13.04, 20 wt %), which denoted as PT1, PT2, PT3 and PT4 respectively. XRD results show semicrystalline nature in PT1 and PT2 however with further increasing of Te contents, a nano-crystallite Te appeared in PT3 and PT4. The absorption spectrum confirms that PT3 film is a good option to be used in UV-shielding. PT4 film shows an abrupt rise in absorption coefficient at 0.5 eV, 1.5 eV and UV regions, hence this qualifies this sample for various optical applications. The optical energy gap of the films varies between 4.94 eV and 3.32 eV for the indirect transitions and between 5.3 eV and 4.5 eV for the direct transitions, the PT4 film has the lowest values of both direct and indirect energy gaps. Several methods were used to measure the average refractive index nav value. Furthermore, the nonlinear refractive index (n2) was estimated. PT4 possesses the highest value of both nav and n2. Furthermore, the radiation shielding coefficients have been estimated according to the Phy-X/PSD online software. The sample with the highest Te concentration, PT4, has the best radiation shielding between the films under investigation. The investigated polymer with high Te weight percentage is an optical system that can be used for solar cells, optoelectronics, electronics, nonlinear optics, optical filters and for radiation shielding.

The Annealing Temperature Effect Enhances the Structural and Optical Parameters of Bi2Te3 Thermally Evaporated Thin Films

The current work investigates the influence of the annealing temperature (373, 473 K) on the structural and optical properties of Bi2Te3 thin films produced by the thermal evaporation technique. The crystal structure of samples is examined using an X-ray diffraction, indicating that Bi2Te3 thin films have a Rhombohedral structure with space group R-3m. The crystallite size (D) increased from 10.85 to 14.46 nm by increasing the annealing temperature. Additionally, increasing the annealing temperature reduces the micro-strain and the dislocation density from (3.33 × 10−3 to 2.5 × 10−3) and (8.49 × 1015 to 4.78 × 1015) Lines / m 2 , respectively. These micro-strain and dislocation density reductions refer to the crystallinity enhancement of sample Bi2Te3 thin films. The transmittance and reflectance spectra were measured using an Fourier transform infrared spectrometer. All samples reveal direct and indirect transition types and both direct and indirect optical energy gap decreased with increased annealing temperature from (0.325 to 0.29 eV) and (0.24 to 0.274 eV), respectively. From transmittance and reflectance data, the refractive index is calculated. These results reveal the refractive index decreasing as temperature annealing increased from (2.45–1.79) at 3250 nm. Other optical parameters such as absorption index, dielectric constant, energy loss function, and optical conductivity were estimated.

Correlation of interface structure and optical properties of Ga(N,As) and Ga(As,Bi) based type-II hetero structures

The type-II band alignment of particular III/V heterostructures is a promising route towards achieving certain wavelengths on specific substrates, which would not be possible with type-I structures. One example is telecommunication lasers on GaAs substrates. This study reports on the progress in combining dilute nitrides and dilute bismides in W-type hetero structures to improve the luminescence intensity, which is a fundamental prerequisite for future incorporation in a laser structure. Increasing the emission wavelength of these structures is challenging and the interface formation is critical, especially as two metastable materials are combined. Here, we investigate the impact of different interface configurations by growing Ga(N,As)/Ga(As,Bi) and Ga(As,Bi)/Ga(N,As) type-II structures. We employ metal–organic vapor phase epitaxy (MOVPE) to grow Ga(N,As) and Ga(As,Bi) layers and investigate the effects of interlayer thicknesses on the structural and optical properties of the hetero structures. The results indicate that − while the introduction of a GaAs interlayer can affect the direct and indirect transitions intensities − it does not significantly improve the interface quality. However, this is strongly influenced by the order in which the materials are grown. The growth of Ga(N,As) on Ga(As,Bi) shows no peculiarities, while the type II transition energy is shifted to lower energies when Ga(As,Bi) is grown on Ga(N,As). High-resolution X-ray diffraction (HR-XRD), photoluminescence (PL) spectroscopy, atomic force microscopy (AFM), and scanning transmission electron microscopy (STEM) were used to characterize the samples.

Enhancing optical properties of Ba-Ni ferrite through nonmagnetic ion doping for sustainable green technologies and renewable energy applications

Barium ferrite powder was produced using a standard ceramic procedure, and its structure and optical properties were investigated. X-ray diffraction analysis (XRD) showed that the powder had a w-type hexagonal structure. The crystallite size was at approximately 35–36 nm, with bulk density and lattice constants increasing as zinc concentration rose. Conversely, X-ray density and porosity decreased with the increasing zinc concentration. This material has useful optical properties, as well as the standard ferrimagnetic properties of barium ferrite, which make it suitable for use in recording media. Ferrimagnetic behavior, which is useful for recording media, occurs because the powder's crystallites have their unit cell axes aligned. Up to the near-infrared part of the spectrum, the powder was found to have a very low absorption coefficient. Both of these properties—an arrangement that gives rise to ferrimagnetism and a corresponding low optical density—make barium ferrite very attractive for high-density recording and microwave applications. Fourier transform infrared spectra of the samples were recorded in the wavenumber range of 400–4000 cm−1 and supported the X-ray diffraction findings by confirming the idea of the formation of W-type hexagonal ferrite by the presence of two prominent peaks at 454 and 591 cm−1 in the FTIR spectra. Zinc addition was also found to enhance the optical properties of the material. The UV–VIS analysis confirms that the band gap energy of Ba-Ni ferrite was indeed reduced by zinc doping. Values decrease from 3.34 eV to 3.20 eV for direct transitions and from 2.96 eV to 2.79 eV for indirect transitions, using Tauc equation. That means that zinc doping enhances the optical properties of Ba ferrite without affecting the hexagonal structure of Ba-Ni ferrite. Moreover, key parameters of optical performance such as the dielectric constant, the extinction coefficient, the penetration depth, and the refractive index show a dramatic increase with a rise in zinc concentration. These attributes make zinc-doped Ba-Ni ferrite a promising optoelectronic material. The material also showed high absorbance in the wavelengths ranging from 334 to 338 nm, which makes it good for the solar cell applications. Overall, zinc-doped Ba-Ni ferrite is a good candidate for sustainable and renewable energy applications. Our study of the optical properties of barium ferrite up to the near-infrared part of the spectrum demonstrated that the powdered material has a very low absorption coefficient. Indeed, the combination of ferrimagnetism and low optical density makes barium ferrite particularly appealing for use in high-density recording and microwave technology applications.

Q-switched Nd: YAG Fundamental and Second Harmonic Wavelengths Impact on Preparing Nb2O5 Thin Films by a PLD Technique: A Comparative study

We aim to study and investigate the structural, optical, topographical, and morphological properties of Nb2O5 thin films deposited under vacuum Q-switched Nd: YAG pulsed laser for the first time to the best of our knowledge. The obtained results of this study can contribute in different fields of applications including the optoelectronic and biomedical fields. The fundamental (1064 nm) and the visible second harmonic (532 nm) wavelengths were utilized for this purpose. The laser energy was fixed at 657 mJ. The number of pulses and the substrate temperatures were 200 laser shots and 450 ºC, respectively. The observed X-ray diffraction patterns were assigned for T-Nb2O5 that refers to the orthorhombic and H-Nb2O5 which is related to the monoclinic phases supported by Raman spectra analyses. Nb2O5 thin film deposited by Nd: YAG fundamental wavelength (1064 nm) showed a thicker film, a higher surface roughness and, on average, a larger particles size It also provided better matching of the lattice d-spacing with the standard d-spacing obtained by JPCDs cards 00-030-0873 and 00-009-0372. The optical properties including the band gap values for both direct and indirect transitions were estimated with the lower gap was reported for the thin film prepared at the fundamental wavelength. The photoluminescence analyses supported that the transitions of both prepared films were indirect. FE-SEM clarified the surface morphology of each prepared film. The EDX analyses provided the elemental compositions and the purity of the Nb2O5 prepared films.

Abnormal Response of Indirect Excitons to Non‐Uniform Elastic Strain in MoS2 Flakes

AbstractRegulating the electronic structures and carrier dynamics in 2D materials via elastic strain is a fascinating avenue for tailoring their optoelectronic properties at atomic scale. Here, the abnormal response of indirect excitons to non‐uniform elastic strain in MoS2 flakes is reported. The non‐uniform elastic strain in the MoS2 flakes is introduced by transferring them to pre‐prepared convex cross structures on a SiO2/Si substrate, where the topography and strain distribution are determined by atomic force microscopy and Raman spectroscopy, respectively. It is observed that the emission energy of the indirect excitons shows an unexpected blue‐shift followed by a red‐shift with increasing the local tensile strain, which is in sharp contrast to the linear red‐shift of the direct excitons. Density functional theory calculations reveal that the abnormal energy shift of the indirect excitons in the MoS2 flakes arises from the strain‐induced competition between two indirect bandgap transitions and the spatial exciton funnel effect in the non‐uniform strain field. This work provides new insights into the elastic strain effect on the indirect excitons in 2D semiconductors, which possesses potential applications in flexible optoelectronic devices.

Structural and Optical Properties of SnS2:Cu Thin films prepared by chemical Spbay Pyrolysis

Thin filis have been prepared from the tin disulphide (SnS2 ), the pure and the doped with copper (SnS2:Cu) with a percentages (1,2,3,4)% by using ahemical spray pyrolysis techniqee on substrate of glass heated up to(603K)and sith thicknesses (0.7±0.02)?m ,after that the films were treated thermally with a low pressure (10-3mb) and at a temperature of (473K) for one hour. The influence of both doping with copper and the thermal treatment on some of the physical characteristics of the prepared films(structural and optical) was studied. The X-ray analysis showed that the prepared films were polycrystalline Hexagonal type. The optical study that included the absorptance and transmitance spectra in the weavelength range (300-900)nm demonstrated that the value of absorption coefficient (?) was greater than (104 cm-1) for the pure and doped films and that the electronic transitions at the fundamental absorption edge were of the indirect kind whether allowed or forbidden and the value of the optical energy gap in the case of the indirect transition, the allowed decreased from (2 eV) to (1.8,1.7,1.5,1.2)eV at the doping percentages (1,2,3,4)% respectively, also it was found that the value of energy gap for the pure and doped films increased after annealing. Tthe absorption and transmission spectra were used to find the optical constant including refractive index(n), extinction coefficient (k), imaginary and real part of dielectric constant (?1 &?2) , and it was found that all the optical constant was affected by changing the doping percentages; in addition to being affected after treating the films thermally

Photon Momentum Enabled Light Absorption in Silicon.

Photons do not carry sufficient momentum to induce indirect optical transitions in semiconducting materials, such as silicon, necessitating the assistance of lattice phonons to conserve momentum. Compared to direct bandgap semiconductors, this renders silicon a less attractive material for a wide variety of optoelectronic applications. In this work, we introduce an alternative strategy to fulfill the momentum-matching requirement in indirect optical transitions. We demonstrate that when confined to scales below ∼3 nm, photons acquire sufficient momentum to allow electronic transitions at the band edge of Si without the assistance of a phonon. Confined photons allow simultaneous energy and momentum conservation in two-body photon-electron scattering; in effect, converting silicon into a direct bandgap semiconductor. We show that this less-explored concept of light-matter interaction leads to a marked increase in the absorptivity of Si from the UV to the near-IR. The strategy provides opportunities for more efficient use of indirect semiconductors in photovoltaics, energy conversion, light detection, and emission.

A Comparative Study of the Linear/Nonlinear Optical, and Dielectric Properties of PVA/CMC/(1−x)ZnWO4−xPbS Blended Polymers for Optoelectronic Applications

An analysis was conducted on the optical, structural, and dielectric characteristics of PVA/CMC/(1−x)ZnWO4/xPbS blends. The structures of the filler samples, undoped, and doped blends were examined using X-ray diffraction. The crystallite sizes of the various phases in the filler samples are affected by the amount of PbS in the nanocomposite. The morphologies of different blends were explored using scanning electron microscopy. The doped blend exhibited superior absorption of Ultraviolet A (UVA) and Ultraviolet B (UVB) types in addition to the visible spectrum. The optical band gaps were minimized to (5.37, 5.56, 4.11) and (4.76, 3.14, 2.92) eV for direct and indirect optical transitions, respectively, when the PVP/CMC doped with nanocomposite had 10% PbS. The highest refractive index, optical dielectric constant,and nonlinear optical parameter values were achieved when the blend was loaded with ZnWO4 only while the highest optical conductivity was obtained as the blend contained 15% PbS. The highest fluorescence intensity was observed when the fillers did not contain PbS, and it decreased as the concentration of PbS in the filler increased.

Modulation of photoluminescence properties of transition metal dichalcogenides through temperature and Au/Ag nanoparticles

Abstract Transition metal dichalcogenides (TMDCs) attract significant attention because of their remarkable optical properties. Nowadays, the light emission efficiency of TMDCs is still inferior. Temperature and plasma resonance effects can be important approaches in the modulation of their luminescence performance. Here, multilayer WSe2 and monolayer MoSe2 were synthesized. Under the temperature control system, two photoluminescence (PL) peaks are observed from multilayer WSe2. The higher-energy PL peak results from K-Γ indirect band gap transition, which is then demonstrated by the first principle calculation. Otherwise, PL enhancement is realized on monolayer MoSe2 decorated with Au nanoparticles. The PL of WS2 is inhibited by hybridization with Ag nanoparticles.

Layer stacking effect on structural, vibrational, and electronic properties of Janus-Ga2SeTe crystals

The van der Waals stacking of Janus Ga2SeTe quadruple-atomic layers leads to the formation of polytype bulk crystals, where the stacking order plays a critical yet elusive role in their fundamental properties. Here, we perform first-principles density functional theory calculations to investigate the stacking-dependent structural, electronic, and vibrational properties of four Ga2SeTe polytypes. Our results indicate that the γ polytype has two sub-phases of γ [ABC] and γ [ACB]. Lattice vibration studies manifest that symmetry operations depend on the stacking orders, in which the irreducible representations of optically active modes at Γ for the β, ε, γ, and δ phases are Γ = 3A1 + 4B1 + 4E2 + 3E1, Γ = 7E+7A1, Γ = 11A1 + 11E, and Γ = 8E2 + 7E1 + 8B1 + 7A1, respectively. Moreover, taking spin–orbit coupling into account, the estimated indirect bandgaps are 0.967, 0.926, 0.879, 0.925, and 0.950 eV for β, ε, γ [ABC], γ [ACB], and δ polytypes, respectively, in which the bandgap differences between indirect and direct transitions are within 10 meV. The Bader charge analysis indicates that the stacking order modulates the charge distribution among the compositional layers. These findings provide valuable insights for the development of optoelectronic devices based on Janus structures.

Elastin-like polypeptide-functionalized nanobody for column-free immunoaffinity purification of aflatoxin B1.

A column-free immunoaffinity purification (CFIP) technique for sample preparation of aflatoxin B1 (AFB1) was developed using an AFB1-specific nanobody (named G8) and an elastin-like polypeptide (ELP). The reversible phase transition between liquid and solid in response to temperature changes was exhibited by the ELP which was derived from human elastin. The G8 was tagged with ELPs of various lengths (20, 40, 60, and 80 repeat units) at the C-terminus using recursive directional ligation (RDL). Coding sequences were then subcloned into pET30a at the multiple cloning sites. Bioactive recombinant proteins were produced by expressing them as inclusion bodies in Escherichia coli BL21 (DE3), then dissolved and refolded. Analysis by indirect competitive enzyme-linked immunosorbent assay (icELISA) and transition temperature (Tt) measurement confirmed that the refolded G8-ELPs preserved the ability to recognize AFB1 as well as phase transition when the temperature rose above Tt. To establish the optimal conditions for cleaning AFB1, the effects of various parameters on recovery were investigated. The recovery in ELISA tests was 95 ± 3.67% under the optimized CFIP workflow. Furthermore, the CFIP-prepared samples were applied for high-performance liquid chromatography (HPLC) detection. The recovery in the CFIP-HPLC test ranged from 54 ± 1.86% to 98 ± 3.58% for maize, rice, soy sauce, and vegetable oil samples. To the best of our knowledge, this is the first report combining the function of both nanobody and ELP to develop a cleanup technique for small molecules in a complex matrix. The CFIP for the sample pretreatment was easy to use and inexpensive. In contrast to conventional immunosensitivity materials, the reagent utilized in the CFIP was entirely biosynthesized without any chemical coupling reactions. This suggests that the nanobody-ELP may serve as a useful dual-functional reagent for the development of sample cleaning or purification methods.

Influence of doping soda-lime-silica glasses with Gd2O3, In2O3, and La2O3 on the enhancing of their physical, opto-mechanical and radiation shielding properties

A series of soda-lime-silicate glasses doped Gd2O3, In2O3, and La2O3 rare earth ions was prepared using the melt-quenching technique. The prepared glass samples are designed depending on a chemical composition of (15-X)Na2O – 30CaO – 55SiO2 –XM2O3, where X = 1.0 mol% and M = Ga (NCSG), In (NCSI), and La (NCSL). The amorphous state of the synthesized samples confirmed by XRD analysis, and structural changes were studied via density (ρg), molar volume (Vm), Oxygen molar volume (Vo), and Oxygen packing density (OPD). The mechanical and shielding attenuation parameters of the produced glasses were also projected. The ρg of prepared glasses increased from 2.742 to 2.829 g/cm3 as a result of M2O3-dopant with high molecular weight rare earth oxides. Whereas, the physical parameters Vm, Vo, and OPD were behave in the same trend. Elastic moduli were improved when Na2O replaced with M2O3. The M2O3/Na2O replacement led to increase stiffer and rigidity of the prepared glasses. The NCSL sample was possessed the lowest optical energy band (Eopt.) values (3.45 eV and 2.63 eV for direct and indirect transitions). The NCSL glass sample possessed the highest mass (MAC) and linear (LAC) absorption capacity. In addition, the same glass sample verified the lowest values of half-value layer (HVL) and mean free path (MFP). Thus, the sample coded as NCSL sample including La2O3 is a superior for optical and radiation shielding capacities among all studied glasses. Therefore, the studied glasses can be applied for several optical and radiation shielding applications.

Nonreciprocal conversion based on line trajectory near exceptional points

Spatio-temporal permittivity modulation can simultaneously impart wave vector and frequency shifts during an indirect photonic transition process where nonreciprocal responses are accomplished. Here, we combine the nonreciprocity with exceptional points (EPs) by employing line parameter trajectory to a spatio-temporally modulated waveguide. The instantaneous state evolutions on direction-dependent Riemann sheets are thus different in forward and backward directions. Light propagates through the structure is nonreciprocal. Forwardly, an arbitrary incident wave will convert to a combination of the two waveguide modes with same intensity. Backwardly, the waves almost entirely convert to one specific mode. The conversion efficiency is more than 80% and robust to the line design. The operating wavelength is in the telecommunications band, conducive to integration with other chips. Compared to the widely used loop path, the line path has the merit of easy preparation in experiments as only one parameter is changed. The research sheds light on the optical devices such as isolator and amplifier.

Impact of different rinsing temperatures on SnS thin films created using the SILAR technique

The (SnS) thin films were prepared by Successive Ionic Layer Adsorption and Reaction (SILAR), a versatile and simple method. The cationic and anionic solutions SnCl2.2H2O and Na2S.9H2O respectively were used as precursor materials, which will be deposited on glass substrates to study the effect of rinsing temperature on the properties of our thin films. The structural, morphological, and optical properties were investigated by using X-ray diffraction, Energy Dispersive X-ray analysis (EDX), Scanning Electron Microscopy (SEM) and spectrophotometer. X-ray Diffraction (XRD) patterns indicated that the deposited SnS thin films have an orthorhombic crystal structure. Uniform deposition of the material over the entire glass substrate was shown by Scanning Electron Microscopy (SEM). The optical band gap energy ranged from 1.5 to 1.82eV for direct transitions and from 0.6 to 0.95eV for indirect transitions.

Atomic layer deposition, mechanical, wear resistance, and optical properties of (Cr1-xAlx)2O3 films on Si (100)

This study presents the comparison of microstructure, mechanical, tribological, and optical properties of the ternary chromium-aluminum oxide films ((Cr1-xAlx)2O3) with binary Cr2O3 and Al2O3 films, deposited by atomic layer deposition at 275 °C. The atomic growth per cycle of the Al atoms increased from 3.1 to 8.5 atoms/nm2 on chromium oxide film. The Al2O3 films were X-ray amorphous. The Cr2O3 films contained crystallites of the eskolaite phase. Nano-size (diameter from 3 to 5 nm) crystallites with cubic symmetry and matching with that of cubic γ-Al2O3 or η-Al2O3 phases were observed in (Cr1-xAlx)2O3 films. The ternary film with Al/(Al + Cr) of 0.40 showed the highest hardness (18.4 GPa) and elastic modulus (169.4 GPa), whereas the wear rate of this film decreased by ∼80 % compared with Cr2O3 films. Optical band gap energy values corresponding to the indirect transition model decreased from 2.93 eV for the Cr2O3 film to 2.58 eV for the Cr-Al-O films.

A Markovian description of the multi-level source function and its application to the Lyman series in the Sun

Aims. We introduce a new method to calculate and interpret indirect transition rates populating atomic levels using Markov chain theory. Indirect transition rates are essential to evaluate interlocking in a multi-level source function, which quantifies all the processes that add and remove photons from a spectral line. A better understanding of the multi-level source function is central to interpret optically thick spectral line formation in stellar atmospheres, especially outside local thermodynamical equilibrium (LTE). Methods. We compute the level populations from a hydrogen model atom in statistical equilibrium, using the solar FALC model, a 1D static atmosphere. From the transition rates, we reconstruct the multi-level source function using our new method and compare it with existing methods to build the source function. We focus on the Lyman series lines and analyze the different contributions to the source functions and synthetic spectra. Results. Absorbing Markov chains can represent the level-ratio solution of the statistical equilibrium equation and can therefore be used to calculate the indirect transition rates between the upper and lower levels of an atomic transition. Our description of the multi-level source function allows a more physical interpretation of its individual terms, particularly a quantitative view of interlocking. For the Lyman lines in the FALC atmosphere, we find that interlocking becomes increasingly important with order in the series, with Ly-α showing very little, but Ly-β nearly 50% and Ly-γ about 60% contribution coming from interlocking. In some cases, this view seems opposed to the conventional wisdom that these lines are mostly scattering, and we discuss the reasons why. Conclusions. Our formalism to describe the multi-level source function is general and can provide more physical insight into the processes that set the line source function in a multi-level atom. The effects of interlocking for lines formed in the solar chromosphere can be more important than previously thought, and our method provides the basis for further exploration.

Cr-induced structural phase transformation in sputter deposited poly-AlN thin film from wurtzite to rocksalt structure and their effect on the optical properties

We report Cr doping-induced structural phase transformation (PT) in sputter-deposited polycrystalline-AlN thin film from wurtzite (w) to rocksalt (r) structure. Rietveld analysis shows that the steady substitution of Al ions by Cr ions in the w-AlN lattice distorts and compresses the wurtzite lattice along the c-axis. The chemical pressure exerted in the w-AlN lattice by the compression from the doped Cr ions causes the PT, similar to the high-pressure-induced PT in AlN. Post the PT, the r-Al1-xCrxN thin film continues to exhibit compressive residual stress, indicating that such sustained stress may also play a role in stabilizing the metastable r-Al1-xCrxN phase. The structural distortion and the PT also affected the optical absorption characteristics of the w-Al1-xCrxN thin films. The w-Al1-xCrxN exhibit a direct inter-band transition and the band gap (Eg) decreases from ∼ 6.06 eV for pure w-AlN to ∼ 4.15 eV for w-Al0.73Cr0.27N. After the PT, the r-Al0.61Cr0.39N thin film, on the other hand, exhibits an indirect inter-band transition with an Eg of ∼ 1.84 eV. In addition to the change in Eg, a prominent defect band appears at ∼ 4 eV at low Cr% and another band appears at ∼ 0.98 eV at higher Cr%.