Urbach Martienssen Research Articles

Investigation of Optical functions, sub-bandgap transitions, and Urbach tail in the absorption spectra of Ga2O3 thin films deposited using mist-CVD

We report on the investigation of optical properties of epitaxial Ga2O3 thin films deposited at different temperatures using mist-Chemical Vapor Deposition on c-plane sapphire. The deposited films were of highly crystalline quality, with measured full width at half maxima (FWHM) of on-axis rocking curve scans as low as 62 arcsec for α-Ga2O3 sample grown at 500 °C. Pure phase κ-Ga2O3 was found to get stabilized as temperature increased to 650 °C. The optical properties of the as-deposited films were studied using absorbance, reflectance, and transmittance spectra. Various optical functions have been calculated, such as refractive index (n), extinction coefficient (k), real part of dielectric function (ϵreal), imaginary part of dielectric function (ϵimaginary) and high-frequency dielectric constant (ϵ∞). Furthermore, absorption spectra were modeled for sub-bandgap transitions and exponential onset near band-edge using Elliott–Toyozawa and Urbach–Martienssen models, respectively. Codi’s rule was used to estimate the value of the structural disorder parameter (χ) associated with Urbach’s tail. Variation of the extracted parameters, for instance, Urbach’s Energy (EU), phonon energy (hνp), steepness parameter (σ), electron–phonon interaction strength (Ee−phonon), Codi’s structural disorder parameter (χ), bandgap (Eg) and excitonic binding energy (Eexc) were studied against deposition temperature; these parameters were found to correlate with deposition temperature and hence the crystalline quality of the film. In light of the results, it was inferred that the exponential tail is inevitable at finite temperature because of the dominant Eg phonon mode present at ∼430cm−1 in α- or α- dominated Ga2O3 phase.

Urbach–Martienssen tail as the origin of the two-peak structure in the photoluminescence spectra for the near-band-edge emission of a freestanding GaN crystal observed by omnidirectional photoluminescence spectroscopy

Omnidirectional photoluminescence (ODPL) and standard photoluminescence (SPL) spectroscopy measurements were carried out on a freestanding GaN crystal at various temperatures (T) between 12 K and 300 K. The intensity ratio (ρ) of the ODPL to SPL spectra for the near-band edge (NBE) emission of the crystal showed a linearly decreasing slope with respect to photon energy (E) below the fundamental absorption edge energy (Eabs), and the slope became steeper at lower T. The linear extrapolations of the slopes at various T converged at a common point (E, ρ) = (3.539 eV, −6.306). This fact implies that the slope obtained for ρ corresponds to the Urbach–Martienssen (U–M) tail of the optical absorption spectra. Numerical simulations under the assumption, where a part of photoluminescence traveled inside the crystal and the scattering occurred at a backside of the crystal, substantially reproduced the ODPL spectra. Accordingly, the origin of the two-peak structure in the ODPL spectra around the NBE emission of the GaN crystal is attributed to the existence of the U–M tail. The Eabs value gives the photon energy at which the absorption coefficient becomes approximately 16.7 cm−1, which corresponds to an inverse of a doubled value of the crystal thickness (0.03 cm).

Europium incorporation dynamics and some physical investigations within ZnO sprayed thin films

Europium doped ZnO thin films were deposited on glass substrates using a simple mini spray technique at 460°C. The structural properties of as-prepared thin films were characterized by X-ray diffraction (XRD). Both undoped and Eu-doped films show strong preferred c-axis orientation. The maximum value of the volume cells was obtained at 1% doping level. The texture coefficient (TC) of the films along (002) direction changes with the doping level due to Eu incorporation.The optical band gap calculated from transmittance and reflectance spectra show the effect of concentration on this energy. They equally outlined the direct gap absorption of these materials. Analysis of Urbach–Martienssen model parameters allows nano-scale explanations of the doping-related divergence of Urbach tailing evolution.

Thickness effect on the structural and optical constants of stibnite thin films prepared by sulfidation annealing of antimony films

This paper deals with some physical properties of antimony sulphide Sb2S3 thin films obtained by an annealing process in sulphur vapors at 300°C of Sb thermal evaporated thin films deposited on glass substrate. The crystal structure and surface morphology were investigated by both XRD and AFM techniques. This structural study shows that Sb2S3 thin films were well crystallized in orthorhombic structure and some parameters such as the lattice parameter, crystallite size, microstrain and degree of preferred orientation have been reported and correlated with the effect of crystallite size. On the other hand, the refractive index and the extinction coefficient were discussed in terms of the Forouhi–Bloomer model. The optical band gap was found to range from 1.75 to 2.23eV. Finally, the analysis of the optical parameters extracted from the Urbach–Martienssen and Forouhi–Bloomer models lead to some explanations of the correlations between the structural properties in terms of the crystallite size and optical ones.

The Urbach–Martienssen absorption tails in the optical spectra of semiconducting variable-sized zinc selenide and cadmium selenide quantum dots in thin film form

The sub-bandgap exponential absorption tails of Urbach–Martienssen type in chemically deposited variable-sized ZnSe and CdSe quantum dots in thin film form were studied. The Urbach energy, characterizing the steepness of the exponential absorption tails, was found to decrease upon particle size enlargement due to thermal annealing of the as-deposited ZnSe and CdSe quantum dots in thin film form. Such decrease of the Urbach energy was attributed to the decrease of the degree of structural disorder upon annealing of the semiconducting quantum dot thin films, manifested through lattice strain relaxation, average crystal size and lattice constant increase and dislocation density decrease. This behavior is in line with the predictions of the Cody model, relating the Urbach energy to the degree of structural disorder for a given material. In this way, it is shown that semiconducting quantum dots deposited in thin film form have a certain non-thermal component to the exponential absorption tails of the Urbach–Martienssen type. This non-thermal component is due to the inherent nanocrystalline character of the semiconducting quantum dots, characterized with a rather pronounced structural disorder, manifested through a certain degree of lattice strain and the rather large values for the dislocation densities.

Spectroscopic properties of the mixed J-aggregate of unsymmetric merocyanine dyes in wide temperature range

The monolayer assemblies incorporating two kinds of unsymmetric merocyanine dye aggregates (MC(X)/MC(Y), X = O, S, Se) have been fabricated by the Langmuir–Blodgett technique. The absorption spectra of the Langmuir–Blodgett films were measured in wide temperature range of T = 6.0–293 K. The absorption spectra of the MC(O)/MC(S) and the MC(O)/MC(Se) assemblies bear two absorption bands which are assigned to the MC(O) aggregate and the MC(S) J-aggregate or the MC(Se) J-aggregate, respectively. In contrast, the absorption spectrum of the MC(S)/MC(Se) assembly shows a single absorption band of the mixed J-aggregate. From detailed considerations of the low-energy tail of absorption spectra based on the Urbach–Martienssen rule, together with other spectroscopic properties, it is concluded that the MC(O)/MC(S) or the MC(O)/MC(Se) assembly forms a mosaic aggregate. The MC(S)/MC(Se) assembly can form high-quality homogeneous aggregate of amalgamation type.

Spectroscopic properties of persistence-type dye aggregate in wide temperature range

Spectroscopic properties of the monolayer assemblies, S9(J) + S11(J), which incorporate the mixed J-aggregate (JA) of oxacyanine dye; N, N′-dioctadecyl-oxacyanine perchlorate (S9) and thiacyanine dye; N, N′-dioctadecyl-thiacyanine perchlorate (S11), have been studied in the wide temperature range of T = 6.0–293 K. The mole fraction X of S11, X = [S11]/([S9] + [S11]), in the S9(J) + S11(J) assemblies has been varied from 0 to 1. At room temperature, absorption and fluorescence spectra of the monolayer assemblies incorporating the individual dye aggregate, S9 J-aggregate (S9(J)) or S11 J-aggregate (S11(J)), are characterized by a distinct J-band and resonance fluorescence. The S9(J) + S11(J) assemblies with X = 0.1–0.9 display two absorption bands; shorter-wavelength (SW) band and longer-wavelength (LW) band and a single fluorescence band (LW-fluorescence). With lowering temperature, the blue shift and narrowing of the absorption bands are observed. The low-energy tails of the J-band of the S9(J) ( X = 0) and the S11(J) ( X = 1) assemblies, as well as the LW-band of the S9(J) + S11(J) assemblies obey the Urbach–Martienssen (U–M) rule. The steepness parameter σ versus T curves show characteristic changes caused by mutual mixing of S9 and S11, which would supply us with a supporting evidence for the formation of the homogeneous aggregate of persistence-type (HP-aggregate) in the S9(J) + S11(J) assemblies.

Spectroscopic properties of merocyanine mixed J-aggregate in wide temperature range

The monolayer assemblies incorporating merocyanine J-aggregates, MC(S), MC(Se), 6-Me-MC(S), and their combinations have been fabricated by the Langmuir–Blodgett (LB) technique. At room temperature, absorption and fluorescence spectra of the monolayer assemblies: MC(S), MC(Se), 6-Me-MC(S), are characterized by a sharp J-band and resonance fluorescence. The monolayer assemblies incorporating two dyes: MC(S)/MC(Se), 6-Me-MC(S)/MC(S), 6-Me-MC(S)/MC(Se), bear a single absorption band and accompanying fluorescence band, which are assigned to the homogeneous aggregate of amalgamation type (HA-aggregate). Detailed spectroscopic measurements: absorption spectra in wide temperature range and the fluorescence decay curves, of the MC(S)/MC(Se) assembly have been carried out as a prototype of the HA-aggregate. The continuous shift of the absorption and fluorescence peak positions with increasing x, from x = 0 (MC(S) assembly) to x = 1 (MC(Se) assembly), would indicate that the doping of MC(Se) molecules into the MC(S) J-aggregate does not induce serious structure change. An observation that the fluorescence lifetime of the MC(S)/MC(Se) assembly lies between those of the MC(S) assembly and the MC(Se) assembly implies that the inclusion of MC(Se) molecules does not result in the formation of defect states which may promote non-radiative decay of molecular excitons. The usefulness of the Urbach–Martienssen (UM) rule for the analysis of the low energy tail of absorption spectra of the MC(S)/MC(Se) assembly has been examined.

Absorption measurement and Urbach’s rule in InSe and InSe:Ho0.0025, InSe:Ho0.025 single crystals

Abstract InSe and InSe:Ho single crystals were grown by the Bridgman–Stockberger method. Ho rare earth element are added to the InSe crystal as rate of 0.0025 and 0.025 g. Absorption measurements have been investigated as a function of temperature and Ho concentration. The high Ho concentration caused an increasing of intensity in absorption spectra and shifted towards to longer wavelengths. On the other hand low Ho concentration caused a decreasing of intensity in absorption spectra and shifted towards to longer wavelengths too. At 10 K and 320 K, the first exciton energies were calculated as 1.35 and 1.308 eV for InSe, 1.327 and 1.243 eV for InSe:Ho 0.0025 , 1.333 and 1.245 eV for InSe:Ho 0.025 , respectively. The exponentially increasing of absorption tail are explained as an Urbach–Martienssen’s (U–M’s) tail for InSe, InSe:Ho 0.0025 and InSe:Ho 0.025 samples in the 10–320 K temperature range. The Urbach’s energy ( E u ) are increased in both InSe:Ho 0.0025 and InSe:Ho 0.025 samples. But increasing rate is higher in InSe:Ho 0.0025 than InSe:Ho 0.025 sample.

Effects of zero-point phonons and atomic correlations on the electronic properties of crystalline MgO at finite temperatures

Utilizing the harmonic approximation, we introduce a simple technique for the generation of ensembles of thermally disordered atomic structures, and calculate for the MgO crystal electron densities of states (DOS) and the on-site potential probability distributions for the ensembles generated within the classical and quasi-classical harmonic approximations, molecular dynamics and uncorrelated Gaussian atomic disorder models. An account of the zero-energy vibrations even at room temperature results in a significant increase in the mean square atomic displacements and, thus, in the probability distributions of the electrostatic potential and ultimately in the extent of the band tails in the electron DOS. We also demonstrate that the correlations in atomic positions affect the electronic structure. We have evaluated directly the on-site potential autocorrelation function (PAF) for all disorder models, as well as the temperature dependence of the PAF. The correlation length, L, is shown to be less than the second nearest neighbour at low temperature and decreasing to below the nearest neighbour distance at T = 500 K. The short correlation length obtained in the direct modelling is in agreement with the Urbach–Martienssen rule for the optical absorption edge observed experimentally.

Urbach-Martienssen Tails in the Absorption Spectra of Layered Ternary Semiconductor TlGaS2

The dependence of the absorption coefficient on the photon energy and sample temperature near the fundamental absorption edge (AE) was investigated for TlGaS 2 layered semiconductor crystals. The exponential absorption tails observed in the 10-340 K temperature range were interpreted as Urbach-Martienssen (U-M) tails. From the analysis of these tails, characteristic Urbach parameters were determined. The results lead to the conclusion that the temperature dependence of the absorption tails near the fundamental AE of TlGaS 2 is the result of thermal disorder.

Temperature dependence of the optical energy gap and Urbach–Martienssen’s tail in the absorption spectra of the layered semiconductor Tl 2GaInSe 4

The effect of temperature on the optical energy gap for Tl 2GaInSe 4 layered crystals were investigated in the temperature range of 10–330 K. The variation of the optical absorption coefficient with energy near the band edge was analysed by Elliot’s model. From the analysis of the temperature dependent band gap with Manoogian and Woolley’s semi-empirical model, the Debye temperature, the dielectric constant and the effective masses of free excitons, electrons and holes were estimated as (373±13) K, 9.2±0.3, (0.31±0.06) m 0, (0.42±0.08) m 0 and (1.16±0.22) m 0, respectively. Effective phonon energy was obtained as hν p=56±1 meV from the temperature dependence of the Urbach’s energy. This relatively large hν p value was associated with the electronic distortion in addition to the influence of electron/exciton–phonon interaction. The electronic distortion results from the existence of multiple structural defects associated with two dimensional dislocations or stacking faults, presumably originated from voids and precipitates of the component elements, in the Tl 2GaInSe 4 lattice.

Urbach–Martienssen's tails in layered semiconductor GaSe

The dependence of the absorption coefficient on photon energy and temperature near the fundamental absorption edge was measured for layered single crystal, Gallium selenide (GaSe). The exponentially increasing absorption tail was explained as an Urbach–Martienssen's (U–M's) tails in the 10–340 K temperature range. Temperature dependence of the characteristic Urbach's parameters such as steepness parameter σ( T) and Urbach's energy ( E U=k B T/ σ) indicate that absorption is predominantly influenced by the phonon-induced microelectric fields and not compositional or structural potential fluctuations. The evaluated effective phonon energy hν p =17 meV is in good agreement with the A′ 1 (1) homopolar phonon mode obtained from Raman spectra and infrared (IR) measurement for this compound. The absorption process can be considered as an internal Franz–Keldysh effect, caused by the phonon-generated microelectric fields related with charged impurities or defects associated with bulk two-dimensional stacking faults, interstitial atoms, or vacancies in the GaSe lattice and can be described in the framework of the Dow and Redfield (DR) theory.

Urbach–Martienssen’s tail in the absorption spectra of the ordered vacancy compound CuIn3Se5

The presence of Urbach–Martienssen’s tail in the absorption coefficient spectra just below the fundamental absorption edge is observed in several samples of the ordered vacancy compound CuIn3Se5 at different temperatures below 300 K. An empirical relation that takes into account the effect of structural disorder and modification in the contribution of the thermal term, caused due to the deviation from the ideal stoichiometry 1:3:5, is proposed to explain the change of Urbach’s energy KT/σ with temperature. The phonon energy involved in the electron–phonon interaction, in the absence of structural disorder, is estimated to be around 23 meV.

Urbach–Martienssen tails in Er-doped and undoped n-type InSe

Optical absorption spectra of InSe : Er and InSe single crystals were investigated. The exponentially increasing absorption tail was explained as an Urbach–Martienssen (U–M) tail for both InSe : Er and InSe samples in the temperature range 100–340 K. Characteristic Urbach's parameters such as steepness parameter σ( T), Urbach's energy ( E u= k B T/ σ) and effective phonon energy ( hν p ) were obtained as a function of temperature. The Urbach's energy of the Er-doped sample decreased as a function of temperature in the investigated temperature region. Such a decrease of the Urbach's energy can be explained to be due to the reduction of the electronic distortion caused by the compositional disorder associated with the planar defects in the crystal lattice in InSe by the Er doping procedure.

Urbach–Martienssen tails in a wurtzite GaN epilayer

Effects of an interaction between the electronic and lattice systems on the optical spectra of a wurtzite GaN epilayer were investigated. The exponentially increasing absorption tail was well explained as an Urbach–Martienssen tail, giving the characteristic phonon energy of 30 meV. The result indicates that few longitudinal optical phonons contribute to the exciton-phonon coupling even at room temperature.

Exciton–lattice interaction and the line shape of exciton absorption in molecular crystals

The exciton–lattice interaction cannot be treated adiabatically in many molecular crystals where the exciton bandwidth is at most comparable to lattice-vibration energies. It cannot also be treated perturbationally at about room temperatures where the absorption line width of excitons is comparable to the larger of the exciton bandwidth and lattice-vibration energies in most molecular crystals. A simple model which describes excitons in molecular crystals from a unified viewpoint is proposed. The model has three characteristic energies: the half-width B of the exciton band, the average amplitude of the scattering potential for excitons produced by lattice vibrations D, and the inverse of the correlation time of the potential fluctuation γ on the order of lattice-vibration energies in units of C=1. It describes singlet excitons when B≳γ and triplet excitons when B≪γ. The dynamical-coherent-potential approximation applied to this model bridges reasonably the following two limits: the strong-scattering limit for D≫B and D≫γ in which the exciton absorption has a Gaussian line shape, and the weak-scattering limit for D≪B or D≪γ in which the exciton absorption has a motionally narrowed Lorentzian line shape. The exponentially decreasing low-energy absorption tail, obeying the Urbach–Martienssen rule, grows up as B/γ increases towards the adiabatic limit of B/γ ≫1. The model is consistently applied to observed exciton spectra in various molecular crystals.

Urbach-Martienseen Rule and Exciton Trapped Momentarily by Lattice Vibrations

Theory for the Urbach-Martienssen (U-M) rule on the low energy tail of the fundamental absorption edge of insulators is proposed. The exciton propagator solved for an adiabatic lattice is averaged for lattice vibrations at finite temperature, and the self-energy of exciton is obtained. It describes two characters of exciton in the lattice; the one is the mobile nature of exciton in the undeformed lattice, and the other is the localized nature of exciton trapped momentarily by the lattice deformation due to thermal vibrations. The interplay of the two natures results in the U-M tail below the exciton absorption peak. The result can be interpreted in terms of the Franck-Condon principle where the mobile nature is incorporated in the giant oscillator strength of the momentarily trapped exciton. Emission from this trapped state is discussed in connection with the U-M rule.