Temperature Dependence Of Band Gap Research Articles

Contribution of individual phonon to the band gap renormalization in semiconductors

Understanding the origin of temperature-dependent bandgap in semiconductors is essential for their applications in photovoltaics, optoelectronic and space applications. In this regard the electron–phonon coupling is known to play a crucial role in the temperature dependence of the bandgap of semiconductors. Several models have also been proposed in this regard which are also found experimentally compatible; however, these models need to account for more information about the contribution of individual modes in band gap renormalization. The present report is an analytical attempt to do so by utilizing the Bose–Einstein oscillator model, thereby discussing a method for finding the individual renormalization term contributed by respective phonon modes to the overall bandgap. This study contributes to the fundamental understanding of the temperature variation of optical properties of semiconductors that correlates with the role of electron–phonon interaction.

Temperature-dependent optical bandgap of TiO2 under the Anatase and Rutile phases

A crucial step in developing new and/or more efficient devices relies on the detailed knowledge of the properties of their main (elemental or combined) parts. The same applies to titanium dioxide TiO2 that forms the basis of today numerous applications whose performances are determined by the presence or relative amount of the Anatase (A-) and Rutile (R-) most common phases of TiO2. Whereas the basic structural characteristics of these two polymorphs are very well-established, some of their optical aspects still deserve attention. With these ideas in mind this work presents a comprehensive investigation of the optical bandgap Egap of TiO2 under the Anatase and Rutile phases. The study considered pure A-TiO2 and R-TiO2 samples in the form of powder, and optical reflectance and Raman spectroscopy in the 83–823 K temperature range. In addition to reliable Egap values the study explores their temperature-dependent Egap(T) behavior that is expected to assist future advancements in the field of TiO2-based materials and devices (thin films, interfaces, low-dimensional systems, and photocatalytic and solar cells, for example).

Influence of temperature on bandgap shifts, optical properties and photovoltaic parameters of GaAs/AlAs and GaAs/AlSb p–n heterojunctions: insights from ab-initio DFT + NEGF studies

The III–V group semiconductors are highly promising absorbers for heterojunctions based solar cell devices due to their high conversion efficiency. In this work, we explore the solar cell properties and the role of electron–phonon coupling (EPC) on the solar cell parameters of GaAs/AlSb and GaAs/AlAs p–n heterojunctions using non-equilibrium Green function method (NEGF) in combination of ab-initio density functional theory (DFT). In addition, the band offsets at the heterointerfaces, optical absorption and bandgap shifts (BGSs) due to temperature are estimated using DFT + NEGF approach. The interface band gaps in heterostructures are found to be lower than bulk band gaps leading to a shift in optical absorption coefficient towards lower energy side that results in stronger photocurrent. The temperature dependent electronic BGS is significantly influenced by the phonon density and phonon energy via EPC. The phonon influenced BGS is found to change the optical absorption, photocurrent density and open-circuit voltage. In case of GaAs/AlSb junction, the interface phonons are found to have significantly higher energies as compared to the bulk phonons and thereby may have important implications for photovoltaic (PV) properties. Overall, the present study reveals the influence of EPC on the optical absorption and PV properties of GaAs/AlSb and GaAs/AlSb p–n heterojunctions. Furthermore, the study shows that the DFT + NEGF method can be successfully used to obtain the reasonable quantitative estimates of temperature dependent BGSs, optical absorption and PV properties of p–n heterojunctions.

Dielectric, electrical and optical properties of a Ni-substituted double perovskite ceramic

In this report, iron based double perovskite oxide Ca2Fe0.85Ni0.15NbO6 was successfully synthesized adopting the solid state reaction method. The structure and microstructure along with the purity, frequency and temperature dependent dielectric properties, energy storage and band gap modulation properties of the ceramic is also discussed. The ceramic shows a small band gap with a high remnant polarization which aligns it toward ferroelectric photovoltaic device applications. The temperature stable dielectric constant of the material up to a high temperature range is useful for MLCC applications. The energy storage density of the material is calculated from room temperature hysteresis loop. The frequency variation of ac conductivity refers Jonscher’s law. The temperature variation of frequency exponent term n indicates CBH (correlated barrier hopping), model of the conduction mechanism in the sample. The presence of room temperature M-H loop with negligible magnetization and coercive value indicates the soft ferromagnetic behavior of the ceramic.

High-performance CsSnBr<sub>3</sub>/Si PN heterojunction photodetectors prepared by pulsed laser deposition epitaxy

Halide perovskite semiconductors have outstanding physical properties such as high light absorption coefficient, large carrier diffusion length, and high photoluminescence quantum efficiency, and demonstrate significant potential applications in optoelectronic devices such as photodetectors and solar cells. However, the toxicity and environmental instability associated with lead-based perovskites significantly limit their applications. An attractive solution is substituting tin for lead in perovskites and growing high-quality tin-based perovskite films. In this study, we adopt the pulsed laser deposition method to achieve the epitaxial growth of CsSnBr<sub>3</sub> films on silicon substrates. The morphologies, optical and electrical properties of the CsSnBr<sub>3</sub> films, as well as the CsSnBr<sub>3</sub>/Si heterojunction detectors, are comprehensively investigated with various characterization techniques, including XRD <i>2θ</i>-<i>ω</i> and <i>φ</i> scans, atomic force microscope, scanning electron microscope, photoluminescence and time-resolved photoluminescence spectroscopy, and Hall electrical measurements. The results indicate that such a CsSnBr<sub>3</sub> film grows epitaxially onto the silicon substrate via a face-to-face mode. Interestingly, an unusual temperature-dependent bandgap increase is found to be due to the high electron effective mass of CsSnBr<sub>3</sub>. The CsSnBr<sub>3</sub> film shows the P-type semiconductor behavior with a high mobility of 122 cm²/(V·s), enabling the formation of an ideal Type-II heterojunction with the silicon substrate. The CsSnBr<sub>3</sub>/Si semiconductor heterojunction detector exhibits distinctive heterojunction PN diode characteristics in the dark and a pronounced photoresponse under illumination. At zero bias, the detector displays a switch ratio exceeding 10<sup>4</sup>, responsivity of 0.125 mA/W, external quantum efficiency of 0.0238 %, detectivity (D*) of 2.1×10<sup>9</sup> Jones, response time 3.23 ms, and recovery time of 4.87 ms. Under a small bias of –1 V, the switch ratio decreases to 50, but responsivity and external quantum efficiency increase by 568 times. The detectors can maintain self-powered operation state with a high switch ratio of 10<sup>4</sup>, millisecond-level response time and millisecond-level recovery time. In conclusion, this work presents a self-powering, high-performance photodetector based on CsSnBr<sub>3</sub> epitaxial films integrated with silicon substrates.

Cu2ZnGeSe4 single crystals: Growth, structure and temperature dependence of band gap

This work describes the production of single crystals of the semiconducting quaternary compound Cu2ZnGeSe4 using a gas chemical method in which iodine was used as a transporter. For all the synthesized samples, their phase state, crystal structure syngony and lattice constants were refined. The unit cell of the studied compound is characterized by tetragonal symmetry. The transmission spectrum was applied to calculate the band gap, which is depicted as temperature function in 20–300 K range. It was fixed that the band gap increases by 12% with decreasing temperature.

Studies on temperature-dependent bandgap and gap-to-midgap ratio in diamond lattice photonic crystal with biosensing applications

The present study examines the temperature dependence of the photonic bandgap, the corresponding wavelength and the gap-to-midgap ratio in a three-dimensional diamond lattice photonic crystal. The bandgap calculations establish that the structure shows a complete photonic bandgap centered around 1550 nm at 300 K. The thermo-optic effect, observed in silicon, is employed to compute the photonic bandgap, band-edge wavelengths and mid-bandgap wavelength at various temperatures in the range of 300 K–400 K. The gap-to-midgap ratio, for the proposed structure, is also evaluated at different temperatures. It is seen that the upper and lower band-edge wavelengths and the mid-bandgap wavelength show a linear temperature dependence. The sensitivity of the structure is observed to be 0.0518 nm/K, thus supporting temperature sensing applications. It is found that the gap-to-midgap ratio, for the proposed diamond lattice structure, shows linear variation with temperature. The effect of variation of the dielectric constant and the fill factor on the gap-to-midgap ratio for the diamond structure has also been analyzed. The proposed design has also been analyzed as a refractive index sensor with a sensitivity of 254.9 nm/RIU for sensing the different components of blood.

Optical, structural and dielectric properties of solvothermally grown molybdenum sulfide nanosheets

MoS2 nanosheets have been synthesized by simple and conventional solvothermal methods. FEG-TEM images reveal that the produced MoS2 sample has a hexagonal crystal structure with large (2μm) nanosheets. The XRD and Raman spectra of the samples also confirm the hexagonal crystal phase. The schematic refined unit cell with electron density mapping is visualized after Rietveld refinement. The optical properties such as absorbance, PL, refractive index, extinction coefficient, dielectric constant, optical conductivity, etc. have been investigated in the wavelength range of 330nm to 1000nm. The normal dispersion (ND) and the anomalous dispersion (AD) regions have been observed in the refractive index spectrum. The estimated carrier concentration has been found to be 5×104cm−3. The temperature-dependent indirect bandgap of MoS2 has been simulated using a semi-empirical formula based on electron-phonon coupling and it decreases with increasing temperature. The calculated average lifetime of carriers is 1.17 ns. The grown MoS2 shows large dielectric constant and low tangent loss in the frequency range of 5–500 kHz. The Nyquist plot of the sample gives the NTCR (negative temperature coefficient of resistance) behaviour like a semiconductor. The activation energy (EA) has been estimated from temperature dependence AC conductivity.

Understanding the temperature sensitivity of the photovoltaic parameters of perovskite solar cells

Perovskite solar cells (PSCs) have promised high-efficiency and low-cost solar-to-electrical conversion that now go outdoors for practical applications; however, the elevated outdoor temperature remarkably affects the photovoltaic efficiency. To date, there has been little work about understanding the temperature sensitivity of PSCs. Here, we build an analytical model to understand the temperature sensitivity and the limiting factors of temperature coefficient (TC) in PSCs. Our model is based on diffusion-drift numerical method by involving the temperature-dependent bandgap and band edge of perovskite layers, which quantitively describe the effect of many physical factors, including carrier recombination channels, trap density, band alignment and band variation of transport layers. It was found that the built-in electrical field and minority carrier concentration at interface are closely corrected with temperature, that is responsible for the temperature sensitivity of device performance. We show that this model can be used to explain the disparate temperature sensitivity of a series of reported real PSCs, and also gives potential pathways for the design and fabrication of temperature-insensitive photovoltaics towards practical applications.

Temperature dependence of band gap of CeO2 nanoparticle photocatalysts

Temperature dependence of band gap of CeO2 nanoparticle photocatalysts

Nonmonotonic temperature-dependent bandgap change of CsPbCl3 films induced by optical phonon scattering

The CsPbCl3 perovskite films are successfully grown on quartz substrates by radio frequency (RF)-magnetron sputtering method and their detailed photoluminescence properties are studied over the temperatures from 10 K to 300 K. There exists one near bandgap emission peak (∼410 nm) in the violet region with typical lifetime of few nanoseconds at room temperature. To our surprise, with temperature increasing, this band shows nonmonotonic shift, which is different to the traditional semiconductor like silicon or the same group of perovskites like MAPbI3 or CsPbBr3. The origin of this band and its temperature-dependent shift can be well described with the Bose-Einstein two-oscillator model that takes into account the interaction between electrons and phonons including acoustic phonons and optical phonons. Due to the anisotropic optical properties of the perovskite crystal, the (001)-orientated films have stronger electron phonon coupling and weaker exciton binding energy.

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fr\"ohlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $\mathrm{\ensuremath{\Gamma}}$ point. We also incorporate SOC into a generalized Fr\"ohlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fr\"ohlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fr\"ohlich model, within the physically relevant energy range of the Fr\"ohlich interaction for materials with high phonon frequencies treated with SOC.

Temperature dependence of the band gap of Si28 :P at very low temperatures measured via time-resolved optical spectroscopy

We measure the temperature dependence of the indirect band gap of isotopically purified $^{28}\mathrm{Si}$:P in the regime from 0.1 K to 3 K by high-resolution absorption spectroscopy of the donor bound exciton transition. The measurements increase the up-to-date precision of the temperature-dependent band gap change by more than one order of magnitude and reveal a ${\mathrm{T}}^{4}$ dependence which is about a factor of two less than observed in previous measurements. Such a ${\mathrm{T}}^{4}$ dependence is predicted by theory, but the absolute values differ between our experiment and the most up-to-date calculations by a factor of 30, corroborating that the electron-phonon interaction at low temperatures is still not correctly included into theory. What is more, the ability of such very high-precision band-gap measurements facilitates the use of time- and spatially resolved $^{28}\mathrm{Si}$:P absorption as a contactless, local thermometer and electric field sensor with a demonstrated time resolution of milliseconds.

Optical properties of AgxCu1–xI alloy thin films

We report on the excitonic transition energy E0 and spin–orbit split-off energy Δ0 of γ-AgxCu1–xI alloy thin films studied by using reflectivity measurements at temperatures between 20 K and 290 K. The observed bowing behavior of the E0 transition as a function of the alloy composition is explained based on first-principles band structure calculations in terms of different physical and chemical contributions within the description of ordered alloys. The spin–orbit coupling is found to increase from a value of 640 meV for CuI to approximately 790 meV for AgI. Furthermore, we show that the temperature-dependent bandgap shift between 20 K and 290 K decreases with increasing Ag-content from 25 meV for CuI to 6 meV for AgI. We attribute this behavior mostly to changes in the contribution of thermal lattice expansion to the bandgap shift.

Temperature dependence of the energy band gap in ZrTe5 : Implications for the topological phase

Using Landau level spectroscopy, we determine the temperature dependence of the energy band gap in zirconium pentatelluride (ZrTe$_5$). We find that the band gap reaches $E_g=(5 \pm 1)$ meV at low temperatures and increases monotonously when the temperature is raised. This implies that ZrTe$_5$ is a weak topological insulator, with non-inverted ordering of electronic bands in the center of the Brillouin zone. Our magneto-transport experiments performed in parallel show that the resistivity anomaly in ZrTe$_5$ is not connected with the temperature dependence of the band gap.

Temperature dependence of width band gap in Inxga1-Xasquantum well in presence of transverse strong magnetic field

This article investigated the temperature dependence of the width band gap in InxGa1-xAs quantum well in the presence of a transverse strong magnetic field. A new method was proposed for determining the width band gap of GaAs/InxGa1-xAs heterostructures based on a InxGa1-xAs quantum well in the presence of a magnetic field and temperature. An analytical expression is obtained for calculating the width band gap of a rectangular quantum well at various magnetic fields and temperatures.

Temperature Dependent Band Gap Correction Model Using Tight-Binding Approach for UTB Device Simulations

In order to accurately determine the electrostatics of Ultra-Thin-Body (UTB) devices, the semi-empirical tight-binding (TB) approach is widely used for calculating the channel thickness dependent band structure of any material at those temperatures where TB parameters are available (generally defined at 0 K and 300 K). In this work, we analyze the variation of band structure for Si, Ge, and GaAs over different channel thicknesses at 0 K and 300 K, and show that the band curvature at the band minima remains unchanged with temperature, while the band gap changes significantly and affects the channel electrostatics. Based on this finding, we propose an approach to simulate the electrostatics of UTB devices, at any temperature between 0 K and 300 K, using the band structure obtained at 0 K, along with a suitable channel thickness and temperature-dependent band gap correction. From the results obtained for the channel charge density, we show good agreement with band structure based simulation results, at 300 K, over a wide range of channel thicknesses, for Si, Ge, and GaAs, while also showing good agreement with TCAD simulation results, at a typical intermediate temperature of 150 K, thus highlighting the accuracy, simplicity and wide applicability of the proposed approach.

Electron–phonon effects and temperature-dependence of the electronic structure of monoclinic β-Ga2O3

Gallium oxide (Ga2O3) is a promising semiconductor for next-generation high-power electronics due to its ultra-wide bandgap and high critical breakdown field. To utilize its unique electrical properties for real-world applications, an accurate description of its electronic structure under device-operating conditions is required. Although the majority of first-principles models focus on the ground state, temperature effects govern the key properties of all semiconductors, including carrier mobility, band edge positions, and optical absorption in indirect gap materials. We report on the temperature-dependent electronic band structure of β-Ga2O3 in a wide temperature range from T = 0 to 900 K using first-principles simulations and optical measurements. Band edge shifts from lattice thermal expansion and phonon-induced lattice vibrations known as electron–phonon renormalization are evaluated by utilizing the quasi-harmonic approximation and the recently developed “one-shot” frozen phonon method, respectively. Electron–phonon effects and thermal expansion together induce a substantial temperature-dependence on the bandgap, reducing it by more than 0.5 eV between T = 0 and 900 K, larger than that observed in other wide bandgap materials. Key implications, including an increase in carrier concentrations, a reduction in carrier mobilities due to localization of band edge states, and an ∼20% reduction in the critical breakdown field, are discussed. Our prediction of temperature-dependent bandgap matches very well with experimental measurements and highlights the importance of accounting for such effects in first-principles simulations of wide bandgap semiconductors.

Determination of band tail widths in MOCVD grown InGaN single layer within GaN based p-i-n LED structure through photo-induced measurements

Within a p-i-n LED structure, energy band gaps of MOCVD grown %10 In content InGaN and GaN layers were obtained through traditional UV–Visible transmission-absorption measurements and utilizing surface photovoltage (SPV) and spectral photoconductivity (SPC) measurements. Moreover, all applied techniques determined that the total band offset between InGaN and GaN layers were around 0.3–0.4 eV. Furthermore, the temperature dependence of band gaps of each InGaN and GaN layer was analyzed through a modified Varshni relation where both Varshni coefficients and band tail energy width were explored. Band tails in a modified Varshni relation, SPV and SPC measurements were in agreement with each other and originated Franz-Keldysh Effect attributed to the presence of photon assisted tunneling.

Tailoring the Electron-Phonon Interaction in Au25(SR)18 Nanoclusters via Ligand Engineering and Insight into Luminescence.

Understanding the electron-phonon interaction in Au nanoclusters (NCs) is essential for enhancing and tuning their photoluminescence (PL) properties. Among all the methods, ligand engineering is the most straightforward and facile one to design Au NCs with the desired PL properties. However, a systematic understanding of the ligand effects toward electron-phonon interactions in Au NCs is still missing. Herein, we synthesized four Au25(SR)18- NCs protected by different -SR ligands and carefully examined their temperature-dependent band-gap renormalization behavior. Data analysis by a Bose-Einstein two-oscillator model revealed a suppression of high-frequency optical phonons in aromatic-ligand-protected Au25 NCs. Meanwhile, a low-frequency breathing mode and a quadrupolar mode are attributed as the main contributors to the phonon-assisted nonradiative relaxation pathway in aromatic-ligand-protected Au25 NCs, which is in contrast with non-aromatic-ligand-protected Au25 NCs, in which tangential and radial modes play the key roles. The PL measurements of the four Au25 NCs showed that the suppression of optical phonons led to higher quantum yields in aromatic-ligand-protected Au25 NCs. Cryogenic PL measurements provide insights into the nonradiative energy relaxation, which should be further investigated for a full understanding of the PL mechanism in Au25 NCs.