Urbach Focus Research Articles

Study of energy gaps and their temperature-dependent modulation in LaCrO3: A theoretical and experimental approach

In the present study, the origin of three energy gaps of lanthanum chromium oxide, one arises due to the charge-transfer gap between O-2p and Cr-3d and two arises from the d–d transitions, is analyzed in detail using the diffuse reflectance spectroscopy technique. The spin allowed transitions, such as 4T1(P)→4A2, 4T1(F)→4A2, and 4T2→4A2, and the spin and parity forbidden 2E →4A2 transitions are depicted using a Tanabe–Sugano (T–S) diagram and an absorption spectrum. The high crystal field strength of 3.27 obtained from the T–S diagram provides high directional emission and makes the system suitable for near infrared lasing applications. Moreover, the investigations into the variation of a charge-transfer gap with temperature will provide insights into the modification of numerous optical properties toward development of optoelectronic devices. Using this temperature-dependent diffuse reflectance spectroscopy studies, we have obtained the important optical parameters, such as Urbach energy (Eu) and Urbach focus. Furthermore, first-principles calculations are carried out in order to validate the experimental findings on LaCrO3. The experimental results are in consonance with the charge-transfer gap obtained from the theoretical calculations. Furthermore, the bandgap variation with temperature is fitted using Varshni's relation, and the Debye temperature is calculated.

Carrier thermalization and zero-point bandgap renormalization in halide perovskites from the Urbach tails of the emission spectrum

We develop techniques to study the temperature dependent localization, thermalization, and the effects of phonon scattering on the excitons in halide perovskites from the analysis of the emission spectra. The excitonic Urbach edge, when inferred from the low energy tails of the temperature dependent luminescence spectra, is shown to be sensitive to the electron distribution and thermalization. A method to observe the Urbach focus is devised for halide perovskites where the temperature dependence of the excitonic gap is anomalous. The value of the zero-point bandgap renormalization is inferred to be about 33 meV. This small value of the bandgap renormalization rules out the formation of small polarons and points to weak electron–phonon coupling. The experiments are performed on the nanosheets of the archetypal halide perovskite, CsPbBr3.

Experimental determination of the bare energy gap of GaAs without the zero-point renormalization

The energy gap of simple band insulators like GaAs is a strong function of temperature due to the electron–phonon interactions. Interestingly, the perturbation from zero-point phonons is also predicted to cause significant (a few percent) renormalization of the energy gap at absolute zero temperature but its value has been difficult to estimate both theoretically and, of course, experimentally. Given the experimental evidence (Bhattacharya et al 2015 Phys. Rev. Lett. 114 047402) that strongly supports that the exponential broadening (Urbach tail) of the excitonic absorption edge at low temperatures is the manifestation of this zero temperature electron–phonon scattering, we argue that the location of the Urbach focus is the zero temperature unrenormalized gap. Experiments on GaAs yield the zero temperature bare energy gap to be 1.581 eV and thus the renormalization is estimated to be 66 meV.

Comparative structural and optical studies on pellet and powder samples of BaTiO3 near phase transition temperature

In order to investigate the possible effect of inter-granular strain on the physical properties of Barium titanate (BaTiO3), comparative studies have been carried out on the polycrystalline pellet and its corresponding powder samples. For this purpose, the polycrystalline pellet sample of BaTiO3 has been prepared via conventional solid-state reaction route and powder is obtained by crushing the part of the prepared BaTiO3 pellet. The comparative room temperature structural studies, temperature dependent optical and Raman spectroscopy measurements have been carried out on the prepared pellet and powder samples. Room temperature X-ray diffraction and Raman analysis confirms the presence of extra amount of strain in pellet sample compared with that of the powder sample. Temperature dependent Raman analysis also suggests the difference in the high temperature tetragonal to cubic transition temperature in both cases. Temperature dependent optical absorption properties measured in terms of Urbach energy (EU), Urbach focus (E0) and Urbach relaxation clearly indicates the significant change in these quantities for both types of samples on BaTiO3. Present results strongly reveal the difference in structural, optical and vibrational properties of BaTiO3 especially across phase transition in pellet and its corresponding powder which clearly shows the importance of inter-granular strain at the grain boundaries.

Investigation of temperature-dependent optical properties of TiO2 using diffuse reflectance spectroscopy

Temperature-dependent diffuse reflectance spectroscopy (DRS) measurements have been carried out on the polycrystalline sample TiO2. Important values from optical parameters such as band gap (Eg), Urbach energy (EU), and Urbach focus (E0) have been estimated in the range of 300–450 K. In order to understand the experimental value of band gap (Eg) of TiO2, i.e., obtained from DRS, a first-principle calculation has been performed. The dependency of EU and the slope of exponential tails (β1, β2) of the density of states has also been studied which determines the distribution of exponential tails near the valence and conduction bands in semiconducting oxides. The behavior of optical band gap and EU has also been investigated with the influence of temperature using Cody model. From the temperature dependence of band gap measurements, the value of thermodynamical parameter such as Debye temperature (θD) has also been estimated. Thus it appears that the temperature-dependent optical absorption spectroscopy is very powerful and economical tool to probe the electronic structure near band edge and also to estimate the important thermodynamical parameter.

Strontium Bismuthates Sr<sub>2</sub>Bi<sub>2</sub>O<sub>5</sub> and Sr<sub>6</sub>Bi<sub>2</sub>O<sub>11</sub>: Temperature Dependencies of Urbach Energy and Location of «Urbach Focus»

We present information about temperature dependence of optical properties of two different strontium bismuthates. We demonstrate that temperature dependencies of Urbach energy of two strontium bismuthates differ radically. Abnormal behavior of Urbach focus of strontium bismuthate Sr2Bi2O5 is observed. We assume existence of phase transit in strontium bismuthate Sr2Bi2O5 at the temperature around 305 K.

Electronic and optical properties of BaTiO3 across tetragonal to cubic phase transition: An experimental and theoretical investigation

Temperature dependent diffuse reflectance spectroscopy measurements were carried out on polycrystalline samples of BaTiO3 across the tetragonal to cubic structural phase transition temperature (TP). The values of various optical parameters such as band gap (Eg), Urbach energy (Eu), and Urbach focus (E0) were estimated in the temperature range of 300 K to 480 K. It was observed that with increasing temperature, Eg decreases and shows a sharp anomaly at TP. First principle studies were employed in order to understand the observed change in Eg due to the structural phase transition. Near TP, there exist two values of E0, suggesting the presence of electronic heterogeneity. Further, near TP, Eu shows metastability, i.e., the value of Eu at temperature T is not constant but is a function of time (t). Interestingly, it is observed that the ratio of Eu (t=0)/Eu (t = tm), almost remains constant at 300 K (pure tetragonal phase) and at 450 K (pure cubic phase), whereas this ratio decreases close to the transition temperature, which confirms the presence of electronic metastability in the pure BaTiO3. The time dependence of Eu, which also shows an influence of the observed metastability can be fitted with the stretched exponential function, suggesting the presence of a dynamic heterogeneous electronic disorder in the sample across TP. First principle studies suggest that the observed phase coexistence may be due to a very small difference between the total cohesive energy of the tetragonal and the cubic structure of BaTiO3. The present work implies that the optical studies may be a sensitive probe of disorder/heterogeneity in the sample.

The Urbach focus and optical properties of amorphous hydrogenated SiC thin films

We report on the optical bandgap engineering of sputtered hydrogenated amorphous silicon carbide (a-SiC:H) thin films under different hydrogen dilution conditions during the deposition process and after post-deposition annealing treatments. The Tauc-gap and Urbach energy are calculated from ultraviolet-visible optical transmittance measurements. Additionally, the effect of the thermal annealing temperature on the hydrogen out-diffusion is assessed through infra-red absorption spectroscopy. A new model for the optical absorption of amorphous semiconductors is presented and employed to determine the bandgap as well as the Urbach energy from a single fit of the absorption coefficient. This model allowed the discrimination of the Urbach tail from the Tauc region without any external bias. Finally, the effect of the hydrogen dilution on the band-edge and the Urbach focus is discussed.

High temperature optical absorption edge of CdTe single crystal

The optical absorption edge of bulk CdTe single crystal was measured by infrared transmission under saturated Cd pressure in the temperature interval 295–1223 K. The absorption coefficient was directly determined up to the value of 100 cm−1. For higher values, it was estimated by extrapolating the spectra according to the Urbach exponential rule. It was observed that the common temperature-independent intersection of extrapolated Urbach absorption edge, the “Urbach focus,” does not exist in CdTe. The temperature dependence of band-gap energy Eg defined by Eg(300 K) = 1.518 eV and dEg/dT = − 4.4 × 10−4 eV/K was established, postulating linear temperature dependence of Eg by fitting the temperature dependent absorption coefficient at the band edge αg(T) = 6600 – 4T (K) (cm−1).

On the Origin of the Urbach Rule and the Urbach Focus

ABSTRACTA simple derivation of sub-bandgap exponential tails and fundamental absorption equations ruling the optical absorption of amorphous semiconductors are presented following the frozen phonon model. We use the Kubo-Greenwood formula to describe the average transition rate for the optical absorption process. Asymptotic analysis leads to the commonly observed exponential tail as well as the Tauc expression for the fundamental absorption. We test our theoretical results with experimental absorption coefficients of amorphous Si:H, SiC:H, AlN and SiN. The validity of the Urbach focus concept is evaluated.

Determination of the optical bandgap and disorder energies of thin amorphous SiC and AlN films produced by radio frequency magnetron sputtering

Amorphous aluminum nitrite and silicon carbide (a-AlN and a-SiC) thin films were prepared by radio frequency magnetron sputtering. Due to the deposition method and production conditions the deposited films grown in amorphous state. We systematically measure the optical bandgap through optical transmission spectroscopy and its change with a cumulative thermal annealing. The results show a linear relation between the Tauc-gap and the Tauc-slope for both AlN and SiC films, which can be explained analytically from the existence of an Urbach focus, and therefore can be used to determine the Urbach focus or to ensure the correct usage of the bandgap determination methods.

The Urbach focus and hydrogenated amorphous silicon

We critically examine the validity of the Urbach “focus” concept for the case of hydrogenated amorphous silicon. Our approach involves an analysis of a broad assortment of hydrogenated amorphous silicon experimental optical absorption data from many different sources. We find that these experimental data are consistent with the notion of the Urbach focus concept. The implications of this conclusion are explored.

Influence of temperature on the optical absorption edge in amorphous Zn–P thin films

The effect of temperature (in the range 8 to 300 K) on the fundamental absorption edge of amorphous Zn32P68 thin films have been determined from transmission and reflectivity measurements. Both the Tauc gap, EG, and the Urbach energy, EU, describing the absorption edge, have been shown to follow the Einstein expression for the total energy of a solid. Below 150 K, these two parameters are almost independent of temperature, while in the range 150 to 300 K, they change approximately linearly, but in opposite directions (EG decreases from 1.43 to 1.28 eV, while EU increases from 109 to 145 meV). The coordinates of the temperature independent Urbach focus and a linear dependence between the Tauc gap and the Urbach edge have been found. The observed changes of the optical gap and Urbach energy are discussed and compared with the structural study of the amorphous Zn–P films.

Optical-absorption edge and disorder effects in hydrogenated amorphous diamondlike carbon films.

Optical absorption (\ensuremath{\sim}1--5 eV) in rf-deposited hydrogenated (20--40 at. %) amorphous ``diamondlike'' carbon films has been studied as a function of heat treatment. For E\ensuremath{\gtrsim}2.5 eV a Tauc behavior is exhibited. Optical band gaps ${E}_{g}$ are \ensuremath{\lesssim}2.4 eV. At lower energies, band tailing with an Urbach focus is found. ${E}_{0}$, the width of the tail, is quantitatively explained in terms of the annealing temperature ${T}_{H}$. Increasing ${T}_{H}$ (<700 K) reduces the hydrogen content, lowers ${E}_{g}$, and appears to harden the films. ${E}_{g}$ is determined to be a linear function of ${E}_{0}$. Additional analysis was performed in terms of a divergence temperature, ${T}_{0}$; the results of this analysis are comparable to those observed in a-Si:H.

Temperature dependence of the Urbach optical absorption edge: A theory of multiple phonon absorption and emission sidebands.

The optical absorption coefficient for subgap electronic transitions in crystalline and disordered semiconductors is calculated by first-principles means with use of a variational principle based on the Feynman path-integral representation of the transition amplitude. This incorporates the synergetic interplay of static disorder and the nonadiabatic quantum dynamics of the coupled electron-phonon system. Over photon-energy ranges of experimental interest, this method predicts accurate linear exponential Urbach behavior of the absorption coefficient. At finite temperatures the nonlinear electron-phonon interaction gives rise to multiple phonon emission and absorption sidebands which accompany the optically induced electronic transition. These sidebands dominate the absorption in the Urbach regime and account for the temperature dependence of the Urbach slope and energy gap. The physical picture which emerges is that the phonons absorbed from the heat bath are then reemitted into a dynamical polaronlike potential well which localizes the electron. At zero temperature we recover the usual polaron theory. At high temperatures the calculated tail is qualitatively similar to that of a static Gaussian random potential. This leads to a linear relationship between the Urbach slope and the downshift of the extrapolated continuum band edge as well as a temperature-independent Urbach focus. At very low temperatures, deviations from these rules are predicted arising from the true quantum dynamics of the lattice. Excellent agreement is found with experimental data on c-Si, a-Si:H, a-${\mathrm{As}}_{2}$${\mathrm{Se}}_{3}$, and a-${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$. Results are compared with a simple physical argument based on the most-probable--potential-well method.

Faraday rotation in a-Si:H: A contribution to the study of optical transitions

Faraday rotation (FR) was measured in a 6 μm thick glow discharge a-Si:H film as a function of photon energy (1–1.9 eV) and temperature (10–295 K). The FR may be analyzed with a formula based on the assumption of a constant-dipole-matrix element and an absortion, at higher photon energies, of the form ϵ 2 ∼ ( h ̵ ω−E g ) 1 2 . The FR in the region of measurement is associated with transitions at photon energies higher than 2.2 eV (the FR energy gap). This value and its temperature coefficient indicate that the involved transitions are different from those determining the optical gap (1.7 eV) at lower energies. The obtained FR gap is further compared with characteristic energy parameters of optical absorption at higher energies and of the index of refraction, and also with the Urbach focus where a strinking resemblance is found.