Varshni Equation Research Articles

High-Contrast Thermochromism in Room-Temperature Transparent Layered Perovskite PEA2PbBr4 with a High Temperature-Induced Bandgap Change Rate of 0.8 meV/K.

Two-dimensional organic-inorganic hybrid layered perovskites have emerged as a new generation of optoelectronic materials. However, the thermochromism in organic-inorganic hybrid layered perovskites has been rarely explored in depth. A further understanding of the mechanism is necessary and favorable for the application. Here, transparent centimeter-sized single crystals of the organic-inorganic hybrid layered perovskite (C6H5C2H4NH3)2PbBr4 (PEA2PbBr4) were synthesized using an improved evaporation method. As a typical organic-inorganic hybrid layered perovskite, the PEA2PbBr4 single crystal shows high-contrast and progressive thermochromism exhibiting a change from colorlessness and transparency to lemon yellow in a wide temperature range of 200-450 K. Based on the calculation through the Varshni equation, the temperature-induced bandgap change rate directly associated with the high-contrast thermochromism of PEA2PbBr4 reaching 0.8 meV/K. This value is higher than that of many three-dimensional perovskites and traditional IV-III semiconductors. Furthermore, the temperature-dependent 193 nm photoluminescence spectra suggest that this high temperature-induced bandgap change rate of PEA2PbBr4 is a result of the competitive interaction between lattice thermal expansion and electron-phonon coupling (Fröhlich coupling coefficient ΓLO = 2.215). Based on the characteristics introduced above, PEA2PbBr4 as an organic-inorganic hybrid layered perovskite has a better performance in achieving the balance between high-contrast and high room-temperature transmittance. Therefore, PEA2PbBr4 is a material with great potential in applications like temperature-indicating labels. This work provides valuable insights into the thermochromism of layered perovskites, offering a new material system and approach for developing thermochromic materials with higher sensitivity and efficiency.

Temperature and power-dependent photoluminescence spectroscopy in suspended WSe2 monolayer

This work, the photoluminescence (PL) of a suspended monolayer of WSe2 was investigated to avoid the substrate effect, and its evolution with temperature and excitation energy. Raman spectroscopy and PL demonstrated the monolayer characteristic of the sample due to the absence of the B1 2g peak along with a symmetric PL peak centered at approximately 1.65 eV. The PL spectrum exhibited two main emission bands attributed to a neutral exciton (X0) and a trion (X T ), where X0 showed a redshift with temperature variation from 10 K to 310 K, and the intensity ratio between the bands varied from 2.68 to 3.96 eV. The energy evolution of the bands as a function of temperature was analyzed using the modified Varshni equation, yielding an electron–phonon coupling constant with a value of 1.54 (2.11) for X0 (X T ). The intensity behavior was studied using the multi-level model, which provided activation energies of 58.0 meV for X0 and 94.6 meV for X T . The redshift of the mentioned bands is explained by the Urbach formalism, attributing this shift to an increase in phonon density in the material. Computational calculations demonstrated an increase in the material’s lattice parameter with rising temperature, resulting in an increase in the W–Se bond length and a decrease in the distance between Se atoms from different sublattices, causing the direct transition to decrease with temperature. In conclusion, this study showed that the observed evolution in the PL spectrum of the suspended WSe2 monolayer could be related to the increase of phonon density in the material which is important for the future applications of 2D materials in optoelectronics.

Remarkable Thermochromism in the Double Perovskite Cs2NaFeCl6

AbstractLead‐free halide double perovskites (HDPs) have emerged as a new generation of thermochromic materials. However, further materials development and mechanistic understanding are required. Here, a highly stable HDP Cs2NaFeCl6 single crystal is synthesized, and its remarkable and fully reversible thermochromism with a wide color variation from light‐yellow to black over a temperature range of 10 to 423 K is investigated. First‐principles, density functional theory (DFT)‐based calculations indicate that the thermochromism in Cs2NaFeCl6 is an effect of electron–phonon coupling. The temperature sensitivity of the bandgap in Cs2NaFeCl6 is up to 2.52 meVK−1 based on the Varshni equation, which is significantly higher than that of lead halide perovskites and many conventional group‐IV, III–V semiconductors. Meanwhile, this material shows excellent environmental, thermal, and thermochromic cycle stability. This work provides valuable insights into HDPs' thermochromism and sheds new light on developing efficient thermochromic materials.

Temperature dependence of luminescence characteristics from Eu doped Ga2O3 thin films excited by synchrotron radiation source

Ga2O3 thin film with Eu doping was prepared on p-Si substrate by pulsed laser deposition to investigate the temperature dependence of photoluminescence from Eu3+ and host. The obtained Ga2O3:Eu thin film has a polycrystalline monoclinic structure and smooth surface. The film exhibits multiple sharp emissions originating from Eu3+ dopants, as well as broad defect-related emissions in the UV-green region from Ga2O3 host. With increasing the temperature from 21 K to RT, the red emission from Eu3+ keeps unchanged in the wavelength, and remains ∼55% PL intensity. Meanwhile, Ga2O3 defect-related UV and blue emissions experience a strong thermal quenching and a distinct red shift following the Varshni equation and Bose–Einstein expression. These experimental data will provide reliable guide for fabricating efficient luminescent devices based on rare-Earth doped Ga2O3.

The properties of the valence band maximum in the as-rich InBixAs1-x alloy

The properties of the valence band maximum (VBM) in the As-rich InBixAs1-x alloy are investigated. It is found that the VBM depending on composition in the As-rich range is ascertained based on the peak location of the In-4d states in the low-energy region. It is also found that the weakened temperature sensitiveness of the bandgap for the dilute bismuth InBixAs1-x can be ascribed to the localized character of the Г VBM. In order to describe the localized character of the Г VBM quantitatively, the modified Varshni's equation including the localized energy parameter is used. The result demonstrates that the localized energy parameter enlarges with increasing bismuth fraction. For the sake of giving a quantitative depiction for the localized energy parameter depending on bismuth fraction, a model is developed though analogy with the bandgap narrowing depending on impurity concentration. It can be seen that the localized energy parameter for InBixAs1-x is proportional to the 1.5th power of the bismuth fraction in the dilute bismuth range.

Simulation of Emission Spectra of Transition Metal Dichalcogenide Monolayers with the Multimode Brownian Oscillator Model.

The multimode Brownian oscillator model is employed to simulate the emission spectra of transition metal dichalcogenide (TMD) monolayers. Good agreement is obtained between measured and simulated photoluminescence spectra of WSe2, WS2, MoSe2, and MoS2 at various temperatures. The Huang-Rhys factor extracted from the model can be associated with that from the modified semiempirical Varshni equation at high temperatures. Individual mechanisms leading to the unique temperature-dependent emission spectra of those TMDs are validated by the multimode Brownian oscillator (MBO) fitting, while it is, in turn, confirmed that the MBO analysis is an effective method for studying the optical properties of TMD monolayers. Parameters extracted from the MBO fitting can be used to explore exciton-photon-phonon dynamics of TMDs in a more comprehensive model.

The bandgap energy of the dilute bismuth GaBi x Sb1−x alloy depending on temperature

Abstract The bandgap energy of the dilute bismuth GaBi x Sb1−x alloy vs. temperature is investigated in this study. Its reduced temperature-sensitiveness is because of the localized character of the valence band states (VBS). In order to describe the reduced temperature-sensitiveness of the bandgap energy, a new term including localized energy is added to Varshni's equation. It is found that the localized energy exhibits an increasing trend as the bismuth fraction increases, which indicates that the localized character of the VBS becomes strong with the increasing bismuth fraction. It is also found that the influence of the bismuth fraction on the temperature dependence of the bandgap energy of GaBi x Sb1−x is smaller than that of GaBi x As1−x . In addition, the element indium is undoubtedly a good candidate to lessen the bismuth fraction to realize that the spin-orbit-splitting (SOP) energy surpasses the bandgap energy in GaBi x Sb1−x .

Photoluminescence characteristic of as-grown and thermally annealed n- and p-type modulation-doped Ga0.68In0.32NxAs1-x/GaAs quantum well structures

The electronic band structure of n- and p-type modulation-doped Ga0.68In0.32NyAs1-y/GaAs (y=0, 0.9, 1.2, 1.7) quantum well is calculated using the 10 band k•p model and the finite element method for valance band (VB) and band anti-crossing model for conduction band. Experimental characterization has been carried out temperature dependent photoluminescence (PL) measurements at room temperature. It is determined that optical transition occurs between the first quantized energy level in the conduction band (CB) and VB for n-type samples. While it occurs between localized level and VB, due to empty of the localized level closes CB for p-type samples. It is observed that the intensity of PL emission is higher for p-type samples and the effective bandgap energy redshifts with increasing Nitrogen (N) concentration. Rapid thermal annealing improves the optical quality and causes a blueshift effect. We have determined a similar amount of the blueshift for n-type N-free and N-containing samples, which may be the interdiffusion of the In/Ga atoms. The temperature dependency of the bandgap energies has been fitted using a semi-empirical Varshni equation. It has been observed that thermal Debye temperature and thermal expansion coefficient decreases with N. The redshift of the temperature dependence of the bandgap becomes larger as N concentration decreases. On the other hand, the annealing process causes a reduction in the temperature dependency of the bandgap for p-type samples

Thermal tuning of light-emitting diode wavelength as an implication of the Varshni equation

In this article, we show that the variation of the wavelength of a non-pumped light-emitting diode (LED) is practically linear with temperature, a novel consequence of Varshni's widely accepted empirical expression. This formula models the bandgap variation for most semiconductors from 0K to their high-temperature limits, subject to fitting parameters. Therefore, we suggest an external thermal mechanism that can be used to tune the wavelength of a constant-current biased LED and also to stabilize its wavelength. Furthermore, we demonstrate the approach on published AlN data and show that the fitting parameters follow trivially. In addition, we suggest a novel method to characterize semiconductors. Finally, we present the results of experimental measurements on several commercial LEDs.

Time-resolved spectroscopy of Fe3+d-d transition in bulk ZnSe polycrystal

We report temperature dependent time-resolved photoluminescence studies of Fe3+ in ZnSe polycrystals over 10–300 K temperature ranges fabricated by the post growth thermal diffusion technique. The d-d transitions of Fe3+ assigned to the 4T2(G)→6A1(S) and 4T1(G)→6A1(S) transitions are clearly identified at 528 and 627 nm, respectively, at 10 K. The observed emission peaks in the near bandgap region are red-shifted from 439 to 463 nm as the temperature increases, resulting in a temperature coefficient of 10.21×10−4 eV/K and Debye temperature = 336 K fitted by the Varshni equation. The radiative lifetime at 528 nm by time-resolved photoluminescence is evaluated as τrad = 774 ± 4 ps, activation energy (ΔEa) = 717.2 cm−1, and relaxation time rate (1/W0) = 3.1 ps.

Effects of growth temperature and thickness on structure and optical properties of Ga2O3 films grown by pulsed laser deposition

A series of Ga2O3 films grown on sapphire substrate by pulsed laser deposition with different growth temperature (400–1000 °C) and different thickness (69–332 nm) were studied by X-ray diffraction, optical transmittance and spectroscopic ellipsometry. The phase was transformed from amorphous to polycrystalline β-Ga2O3 structure with increasing growth temperature. Refractive indexes increase with increasing thickness or growth temperature of the films in the transparent area, where the effect of film thickness is much more significant than that of growth temperature. The Urbach tail observed in absorption edge by ellipsometry combined with the transmittance spectra and the XRD intensities illustrate that higher growth temperature or thicker thickness can improve the crystal quality of films. The band gap of Ga2O3 films decrease with increasing growth film thickness and elevated experimental temperature (25–600 °C), and the quantitative analysis of temperature-dependent band gap was conducted by using the Varshni equation.

Monocrystalline elastic constants and their temperature dependences for equi-atomic Cr-Mn-Fe-Co-Ni high-entropy alloy with the face-centered cubic structure

The temperature dependences of monocrystalline elastic constants of Cr-Mn-Fe-Co-Ni high entropy alloy with the face-centered cubic (fcc) structure have been experimentally determined using resonance ultrasound spectroscopy from liquid helium temperature to 1173 K. The values of three independent monocrystalline and estimated polycrystalline elastic constants are fitted using the Varshni equation so that one can obtain the values at any temperatures. The elastic anisotropy of the alloy is characterized by a relatively large value of anisotropy factor of shear modulus, which is closely related to a small value of stacking fault energy of this alloy. The monocrystalline elastic constants also indicate that a relatively strong directional interatomic bonding exists in the present high-entropy alloy.

On the origin of temperature dependence of the emission maxima of Eu2+and Ce3+- activated phosphors

In this paper, temperature dependence of the emission maxima of Eu2+ and Ce3+-activated phosphors and various explanations for the thermal red-shift or blue-shift proposed by different authors are reviewed. Depending on the host lattice, doping concentration of Eu2+ or Ce3+, or the temperature range at which the PL spectrum was monitored, both the way and magnitude of emission spectrum shifting were quite different. Various explanations for the thermal shifts of the emission maxima were proposed. Nonetheless, a close inspection of a collection of the data indicates that some popular explanations seemingly plausible for the thermal red/blue-shifts of the emission maxima of Eu2+ and Ce3+-activated phosphors are highly questionable, because they either misused the Varshni equation or discussed the energy of the 5d-4f transitions of Eu2+ and Ce3+ in isolation without considering simultaneous change of the host lattice. An explanation of lattice dynamic induced thermal shifts of the emission maxima of Eu2+ and Ce3+-activated phosphors is proposed in this paper. By considering the dominant contribution to the energy of the 5d-4f transitions either from a lattice dilatation or from the interactions between the 5d electrons and phonons, the complex temperature dependences of the emission maxima of various Eu2+ and Ce3+-activated phosphors experimentally observed in literature could be explained reasonably.

The localized effect of the Bi level on the valence band in the dilute bismuth GaBixAs1-x alloy

The research on the temperature dependence of the band gap energy of the dilute bismuth GaBixAs1-x alloy has been done. It is found that its temperature insensitiveness is due to the enhanced localized character of the valence band state and the small decrease of the temperature coefficient for the conduction band minimum (CBM). The enhanced localized character of the valence band state is the main factor. In order to describe the localized effect of the Bi levels on the valence band, the localized energy is introduced into the Varshni's equation. It is found that the effect of the localized Bi level on the valence band becomes strong with increasing Bi content. In addition, it is found that the pressure dependence of the band gap energy of GaBixAs1-x does not seem to be influenced by the localized Bi levels. It is due to two factors. One is that the pressure dependence of the band gap energy is mainly determined by the Г CBM of GaBixAs1-x. The Г CBM of GaBixAs1-x is not influenced by the localized Bi levels. The other is that the small variation of the pressure coefficient for the Г valence band maximum (VBM) state of GaBixAs1-x can be cancelled by the variation of the pressure coefficient for the Г CBM state of GaBixAs1-x.

Temperature dependence of the band gap of zinc nitride observed in photoluminescence measurements

We report the photoluminescence properties of DC sputtered zinc nitride thin films in the temperature range of 3.7–300 K. Zinc nitride samples grown at 150 °C exhibited a narrow photoluminescence band at 1.38 eV and a broad band at 0.90 eV, which were attributed to the recombination of free carriers with a bound state and deep-level defect states, respectively. The high-energy band followed the Varshni equation with temperature and became saturated at high excitation powers. These results indicate that the high-energy band originates from shallow defect states in a narrow bandgap. Furthermore, a red-shift of the observed features with increasing excitation power suggested the presence of inhomogeneities within the samples.

Temperature dependent energy gap shifts of single color center in diamond based on modified Varshni equation

Although the diamond has the similar structure (diamond cubic) and symmetry (Oh) as many other conventional semiconductor materials, the extraordinary large Debye temperature and small lattice expansion coefficient make the temperature dependence of energy gaps in diamond to be totally different from those in other semiconductors. Here we propose a modified Varshni formula to describe the temperature dependent zero field splitting and zero phonon line of the nitrogen vacancy center in diamond. The shift of energy gaps shows a T4 scaling at low temperature and a T2 scaling at high temperature. The crossover between these two regimes is determined by two positive parameters in the modified formula. This empirical formula can give an excellent prediction of the temperature dependent energy gaps up to 700K. We experimentally verify this temperature dependent behavior with single negatively charged nitrogen vacancy centers in diamond. These observations demonstrate the leading role of electron-acoustic phonon interaction in the temperature dependent shift of energy gaps in diamond. This empirical equation can benefit the diamond-based applications such as quantum sensing and computing.

Anomalous photoluminescence enhancement due to hot electron transfer in core–shell Au–CdS nanocrystals

At room temperature, an enhanced photoluminescence (PL) intensity of core–shell Au–CdS nanocrystals (NCs) with respect to that of CdS NCs is observed; that is weakly affected at low temperature. PL intensity as a function of temperature depicts three different regions in CdS and Au–CdS NCs; the difference in the nature of curves implicates hot electron transfer from Au to CdS. Even though, the Fermi level of Au is at lower energy than conduction level of CdS NCs, plasmon induced charge transfer from Au to CdS overcomes the potential barrier that enhances band edge emission intensity at room temperature. Moreover, at lower temperature, PL emission splits in narrow and sharp distinct features from free exciton and bound exciton levels along with the first and second order phonon replica. In case of core–shell Au–CdS NCs, emission from free exciton and bound exciton remains unaffected, while phonon replica are perturbed; measured energy values of narrow lines fit well with the empirical Varshni equation revealing an intrinsic nature of CdS. The present work demonstrates decay of plasmon by generating electron in semiconductor; the concept with great potential for energy harvesting.

Optical bandgap and dispersions of 0.24Pb(In1/2Nb1/2)O3-0.43Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 single crystal poled along [011]c direction

The ternary relaxor-based ferroelectric single crystal 0.24Pb(In1/2Nb1/2)O3-0.43Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 (0.24PIN-0.43PMN-0.33 PT) poled along [011]c has single domain state and remarkable optical properties. The temperature dependence of the optical direction energy bandgap for the single crystal coincides with dielectric constant curve at the phase transition points. The variation tendency of the bandgap energies in different phase structures coincide with Varshni equation. The parameters in Varshni equation were obtained from the approximate fitting of the optical bandgap energies, which were calculated at various temperatures from 300 to 540 K. The refractive indices and the extinction coefficients in the single-domain state were obtained. The parameters of room temperature monomial Sellmeier oscillator were also derived.

Observation of near-band-edge photoluminescence and UV photoresponse in near-stoichiometric Zn2SnO4 nanowires

Single-phase, near-stoichiometric zinc stannate (Zn2SnO4) nanowires were synthesized by a direct vapor transport process on c-Al2O3 substrates under optimized growth conditions. The optimal growth temperature for Zn2SnO4 nanowires is above 700 °C. Structural characterization indicates that the nanowires had the single crystal cubic spinel structure and diameters of ∼90 nm and they grew in the [1 direction. Low-temperature photoluminescence (PL) shows a strong emission peak at 3.7 eV, attributed to the near-band-edge-emission of Zn2SnO4 nanowires. Temperature-dependent PL results are consistent with the Varshni equation, and the band gap is redshifted by ∼170 meV as the temperature is increased from 11 to 300 K. The obtained direct gap of Zn2SnO4 nanowires is 3.546 eV at 300 K. A UV photodetector based on as-grown Zn2SnO4 nanowires was fabricated by a simple and cost-effective process. The Zn2SnO4 nanowires exhibited UV photoconductivity, and good selectivity and decent response to UV. The efficient fabrication method, high chemical and thermal stability of the Zn2SnO4 nanowire UV photodetector made it very suitable for use in harsh environments.

Strain-induced spatially indirect exciton recombination in zinc-blende/wurtzite CdS heterostructures

Strain engineering provides an effective mean of tuning the fundamental properties of semiconductors for electric and optoelectronic applications. Here we report on how the applied strain changes the emission properties of hetero-structures consisting of different crystalline phases in the same CdS nanobelts. The strained portion was found to produce an additional emission peak on the low-energy side that was blueshifted with increasing strain. Furthermore, the additional emission peak obeyed the Varshni equation with temperature and exhibited the band-filling effect at high excitation power. This new emission peak may be attributed to spatially indirect exciton recombination between different crystalline phases of CdS. First-principles calculations were performed based on the spatially indirect exciton recombination, and the calculated and experimental results agreed with one another. Strain proved to be capable of enhancing the anti-Stokes emission, suggesting that the efficiency of laser cooling may be improved by strain engineering.