High Frequency Dielectric Constant Research Articles

Tailoring physical properties and electrochemical performance of polyaniline thin films via chemical bath deposition

This study focuses on the properties of polyaniline (PANI) thin deposited onto glass substrates using a chemical bath method. The films were prepared under the same conditions, except for the type of oxidant used. Three oxidants were utilized: potassium per-sulfate (KPS), sodium per-iodate (NAIO4), and ferric chloride di-hydrated (FeCl3·2H2O). X-ray diffraction (XRD) analysis confirmed that all deposited films had an amorphous structure. Fourier-transform infrared spectroscopy (FT-IR) confirmed the presence of PANI films, as indicated by the recorded peaks. Scanning electron microscopy (SEM) was employed to study the surface structure and morphologies of the films, revealing nano-structured grains with varying average grain sizes depending on the oxidant type. The elemental composition of the films was analyzed using X-ray photoelectron spectroscopy (XPS). The optical band gap values were determined to be 4.06 eV, 3.93 eV, and 3.96 eV for FeCl3·2H2O, NAIO4, and KPS oxidants, respectively. The refractive index and extinction coefficient were also calculated from optical data, showing significant variations with changes in the oxidant type. The high frequency dielectric constant of the films was estimated using the Spitzer-Fan model, resulting in values of 5.15, 3.24, and 474 for FeCl3, NAIO4, and KPS oxidants, respectively. Additionally, cyclic voltammetry studies revealed that PANI/glass films grown using NAIO4 exhibited the highest specific capacity. Further investigation of PANI/FTO/glass films showed a specific capacity estimated to be 100 Fg-1 for this particular film configuration.

Investigation of optical and dispersion parameters poly vinyl alcohol doped Safranin O dye (PVA/SO) thin film

Optical characteristics of polyvinyl alcohol/Safranin O dye (PVA/SO) thin films prepared by casting technique have been examined. Compositions and crystalline features of PVA/SO thin films are investigated with X-Ray Diffraction analyses. Ultraviolet–Visible spectroscopy has been utilized to measure the absorption and transmission optical properties of the thin films through the wavelength range 300-900 nm. Two regions can be recognized in absorption coefficient related to the direct band gaps, which are about 3.93 eV of the fundamental energy gap and 2.11eV of the onset gap. The theoretical WempleDiDomenico model has been performed to quantify the static refractive index n and the dispersion energy in addition to the oscillation energy (Eo). The results reveal that the data of the refractive index dispersion in this model obeyed the single oscillator, which is used to deduce the dispersion and the high frequency dielectric constant. In the examined wavelength range, it has been investigated the complex dielectric constant of PVA/SO dye thin films. The ratio of the carrier concentration to the effective mass has been estimated. Oscillation energy values have been examined in this study by describing the expression Eo ≈ Eg and checking the Wemple-DiDomenico model. PVA/SO thin films have interesting physical properties for solar cell applications.

Near IR light sensitization modulated to self-assembled CuO–CuxS nanorods thin films

An assembled CuO-CuxS nanorods heterostructure has been produced by liquid chemical conversion and wet etching of the Cu thin film. The chemical etching and anionic exchange modify and convert the Cu thin film to self-assembled CuO/CuxS random nanorods. The enhanced near infrared (NIR) light absorption capability and the effective separation of electron–hole pairs generated by the conjugated CuO-CuxS nanorods complement high visible (especially red) light driven photocatalytic activities as well as NIR photodetecting performances.The surface morphology, chemical content, crystalline analysis and structural vibrations of the CuO/CuxS nanorods were characterized using field emission scanning electron microscopy (FESEM), energy dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD) and Raman scattering, respectively. Diffuse reflectance spectroscopy was utilized to evaluate optical properties of the CuO-CuxS nanorods. The assembled CuO–CuxS nanorods thin film exhibits good crystallinity with superior reproducibility and high selectivity for NIR absorption. The CuxS coupling into CuO is also responsible to surface enhanced Raman scattering. The static and high frequency dielectric constant, Urbach tail, optical carrier density and nonlinear refractive index have been estimated. The bandgap energy and optical carrier density are estimated around 1.22 eV and 1027 m−3, respectively. The photoharvesting performance was characterized using under sunlight illumination, and green, red and NIR laser irradiation. The CuO–CuxS hetero-interface manipulate charge transferring of the photoinduced carriers, which promotes the photodegradation efficiency of Methylene blue (MB) and NIR photosensitization.

Structural modifications, low temperature magnetic behavior and optoelectronic trends in A-site substituted spinel ferrites

MnxZn1-xFe2O4nanoparticles having cubic spinel phase were synthesized through chemical sol–gel method. The results showed a linear increase in crystallite size, lattice constant, packing factor, and number of unit cells per sample with x, following Vegard's law. High specific surface area (20.34–34.35 m2/g) has been observed which shows suitability for energy storage applications. Magnetic propertieswere improved, likely due to the blocking state of tiny nanoparticles. Switching in direct (4.26–5.12 eV) and indirect (3.03–4.63 eV) bandgaps and Urbach energy was observed at x = 0.5. Refractive index showedtunable trend against incident wavelength making the system a potential candidate for hetero-lasers and non-linear optics. Nyquist plot revealed a non-Debye relaxation phenomenon and the contribution of grain boundaries and grains. Variations in dispersion energy (2.61–30.49 eV), excitation energy (8.44–10.25 eV), optical spectrum moments (M−1: 0.3047 to 2.9757, M−3: 0.0041 to 0.0283 eV−2), and high frequency dielectric constants (1.30–3.98)have been observed.

Structural, optical and dielectric properties of nanostructured La1−xSrxMnO3 perovskites

In this study, a series of nanocrystalline perovskites, La1−xSrxMnO3 (x = 0, 0.3, 0.5, 0.7), were synthesized via the combustion method, utilizing citric acid as fuel, which is an inexpensive synthesis method compared to the vacuum methods for growth. The powder X-ray diffraction study confirms the formation of the desired compositions. The XRD pattern shows that as the Sr doping concentration increases, crystallite size decreases from 30 nm to 14 nm. SEM micrographs reveal the spongy, porous structure of the prepared samples. A good optical absorbance is present in the UV and higher wavelength regions. The optical bandgap energy was increased from 1.4 eV to 2.5 eV. The concentration of Sr2+ ions can be correlated with the differences in refractive index, high frequency dielectric constant, and static dielectric constant. The BDS scrutiny of the specimens discloses that La0.3Sr0.7MnO3 harbours a prodigious dielectric constant at ambient temperature and subsonic frequencies. The dissemination of dielectric constants within the realm of low-frequency regions is elucidated in the context of the Maxwell-Wagner model. According to the results of the dielectric analysis, the dielectric constant exhibits a decrease as frequency increases, while it shows an increase with an increase in Sr doping concentration. The conductivity scrutiny lucidly expounds Johnscher's universal power law in the realm of the high-frequency region, and from the log σ – log f plot, the discernible effects of electrode polarization become manifest. Moreover, the presence of Sr ions enhances the ac conductivity.

Characterization of PbWO4 thin films formed by the pulsed laser welding technique

Herein thin films of PbWO4 were formed from bilayers of Pb/WO3 by the pulse laser welding technique (PLW) within couple of seconds in an argon atmosphere. Thin films of Pb (100 nm)/WO3 (500 nm) were deposited by the thermal evaporation technique under a vacuum pressure of 10−5 mbar. The films were then exposed to a pulse laser beam of fixed amplitude and variable pulse width (0.1–10 ms). The produced films were characterized by means of X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy and optical spectrophotometry techniques. An almost pure phase (∼90%) of tetragonal PbWO4 was achieved after the pulse width exceeds 5.0 ms. PbWO4 thin films produced by the PLW technique exhibited a direct and indirect energy band gaps of 2.27 eV and 3.52 eV, respectively. Energy band tails of widths of 1.35 eV were found dominant in these films. In addition fitting of the dielectric resonance spectra for Pb/WO3 and PbWO4 thin films indicated that the formation of PbWO4 was accompanied with a decrease in the high frequency dielectric constant, a decrease in the free hole concentration and an increase in the electronic friction in the films. The fast method of obtaining PbWO4 thin films and the formation of the direct band gap being 2.27 eV together with the nonlinear dielectric and optical properties make the PbWO4 films obtained by the PLW technique suitable for optoelectronic technology.

Spectroscopic ellipsometry and raman spectroscopy of Bi1-xSbxTeI solid solutions with x≤0.1

Spectroscopic ellipsometry supported by reflectivity measurements and Raman spectroscopy are applied at room temperature to n-type Rashba semiconductors BiTeI and Bi1-xSbxTeI with nominal compositions x = 0.05 and 0.1. Complementary four probe Hall measurements are made using standard ac technique and the concentration of free carriers is determined. The Raman spectra, including TO-LO resonances are found to occupy a frequency range below 250 cm−1 in the studied materials. The pseudodielectric function, retrieved at different angles of incidence is analyzed focusing on the free carrier absorption (intraband transitions) and the optical transitions between the Rashba-split branches of the conduction band (intersubband vertical transitions). The former transitions with screened plasma frequency anchored to the zero-crossing point of the real part of the pseudodielectric function are described within a simple Drude model and the important parameters such as electron effective mass, electron mobility and high frequency dielectric constant are obtained. Anchored to the Rashba energy, the intersubband transitions obtained for each material by refining the pseudodielectric function from Drude contribution, appear in the imaginary part as a broad peak in the photon energy range between 0.15 and 0.4 eV. A noticeable red shift of this peak for Bi0.9Sb0.1TeI as compared to BiTeI is proposed to be a manifestation of the reduction of the spin splitting after part of Bi atoms is replaced by lighter Sb atoms.

Mechanism of THz dielectric constant enhancement in multi-component oxide glasses investigated by infrared and THz spectroscopies

Dielectric properties of multi-component silicate oxide glasses are investigated with a focus on high dielectric constant oxyfluorosilicate (OFS) glasses by using the infrared reflection spectroscopy and terahertz (THz) time-domain spectroscopy. On the basis of multiple Lorentz oscillator model, vibrational parameters and most responsible ionic pairs are identified for major modes in OFS glasses. The lowest frequency mode is found to dominate the total THz dielectric strength. Among various glasses, the high frequency (optical) dielectric constant shows a superlinear dependence on the electronic polarizability of oxygens. In contrast, the low frequency (THz) mode contribution to the dielectric constant is enhanced by the ionicity (expressed by the polarization ionicity parameter) and exhibits an even steeper dependence on the electronic polarizability. This feature well explains the mechanism of attaining the highest THz dielectric constant in an OFS glass (e.g. ZNbKLSNd glass). Also, the oxygen ion effective charges bearing the lowest frequency modes of OFS glasses are evaluated and found to behave consistently with the polarization ionicity parameter, confirming the relevance of both of these parameters as good ionicity indicators.

The effect of fluorination on the low and high frequency dielectric constants of non-polymeric organic semiconductors – towards homojunction solar cells

Fluorination of a non-polymeric donor–acceptor–acceptor–donor organic semiconductor leads to an increase in the thin-film low frequency and decrease in the optical frequency dielectric constant relative to the protonated material.

Exploring the effect of dielectric screening on neutral and charged-exciton properties in monolayer and bilayer MoTe2

Dielectric engineering of heterostructures made from two-dimensional van der Waals semiconductors is a unique and powerful tool to tailor the electric and optical band gaps solely via the dielectric environment and the crystal thickness modulation. Here, we utilize high quality MoTe2 monolayer and bilayer crystals as a candidate for near-infrared photonic applications. The crystals are exfoliated on various technologically relevant carrier substrates: silicon/silicon dioxide, poly(methyl methacrylate), hexagonal boron nitride, silicon carbide, and silicon nitride. These substrates provide a large range of high frequency dielectric constants from 2.1 to 7.0 for MoTe2-containing heterostructures. We assess the relationship between the environmental dielectric function and Coulomb screening by combining detailed spectroscopic measurements, utilizing low-temperature and high-spatially resolved photoluminescence and contrast reflectivity, with microscopic many-body modeling, to explore the potential of this less-recognized material platform for applications in optoelectronics at photon wavelengths above 1 μm. We observe a redshift of the optical gap emission energy from the monolayer to bilayer regime on the order of 30 meV. Furthermore, the thickness controlled shift is slightly larger than the one induced by the local dielectric environment, which ranges on the order of 20 meV for the MoTe2 monolayers and on the order of 8 meV for the MoTe2 bilayers. We also show that the local dielectric screening barely affects the trion binding energy, which is captured by our microscopic model, accounting for the screened Coulomb potential for the heterostructures.

Investigation of the impact of iron amounts on optical and physical properties of coated TiO2 thin films used for PV solar cells

This paper displays the influence of iron (Fe) amounts on the physical properties of anatase titanium dioxide (TiO2) obtained by the spin coating technique. The effect on each film's structural, morphological, optical, and dielectric properties was studied. The X-ray diffraction spectra shows the anatase phase, and many vibrational modes were seen via a Raman analysis. A fourier transform infrared (FTIR) analysis indicated the formation of Ti–O–Fe bonds into the host lattice. The X-ray photoelectron spectroscopy (XPS) results revealed Fe was present in all doped films. A scanning electron microscope (SEM) demonstrated that the surface of the film's had a non-spherical agglomeration formation. Atomic force microscopy (AFM) was also used to assess surface roughness. An energy-dispersive X-ray spectroscopy (EDXS) analysis suggested the presence of Fe used for doping in the TiO2 structure. A maximum transmittance of 65% was found for 2g of Iron (III) nitrate nanohydrate added in TiO2. Optical studies obtained via a UV-VIS-NIR spectroscopy demonstrated that the band gap was effectively reduced with increased amounts of iron. The single oscillator energy (E0), the dispersion energy (Ed), as well as the high frequency dielectric constant, are calculated via the Wemple-DiDomenico model.

Optical and electrical properties of BaSnO3 and In2O3 mixed transparent conductive films deposited by filtered cathodic vacuum arc technique at room temperature

For the crystalline temperature of BaSnO3 (BTO) was above 650 °C, the transparent conductive BTO-based films were always deposited above this temperature on epitaxy substrates by pulsed laser deposition or molecular beam epitaxy till now which limited there application in low temperature device process. In the article, the microstructure, optical and electrical of BTO and In2O3 mixed transparent conductive BaInSnO x (BITO) film deposited by filtered cathodic vacuum arc technique (FCVA) on glass substrate at room temperature were firstly reported. The BITO film with thickness of 300 nm had mainly In2O3 polycrystalline phase, and minor polycrystalline BTO phase with (001), (011), (111), (002), (222) crystal faces which were first deposited at room temperature on amorphous glass. The transmittance was 70%–80% in the visible light region with linear refractive index of 1.94 and extinction coefficient of 0.004 at 550-nm wavelength. The basic optical properties included the real and imaginary parts, high frequency dielectric constants, the absorption coefficient, the Urbach energy, the indirect and direct band gaps, the oscillator and dispersion energies, the static refractive index and dielectric constant, the average oscillator wavelength, oscillator length strength, the linear and the third-order nonlinear optical susceptibilities, and the nonlinear refractive index were all calculated. The film was the n-type conductor with sheet resistance of 704.7 Ω/□, resistivity of 0.02 Ω ⋅cm, mobility of 18.9 cm2/V⋅s, and carrier electron concentration of 1.6 × 1019 cm−3 at room temperature. The results suggested that the BITO film deposited by FCVA had potential application in transparent conductive films-based low temperature device process.

Spectroscopic ellipsometry characterization of PbWO4 single crystals

Optical characterization of PbWO4 single crystals grown by Czochralski method was achieved in virtue of spectroscopic ellipsometry experiments carried out in the energy region of 1.0–5.6 eV at room temperature. Tetragonal scheelite structure with lattice parameters of a = b = 5.4619 Å and c = 12.0490 Å was determined for the bulk crystal utilizing from XRD analysis. Analyses of the ellipsometry data presented the photon energy dependencies of complex dielectric function of the crystal. The real part of the dielectric function exhibited increasing behavior with energy in the below 4.1 eV and then decreased immediately. Zero frequency refractive index and dielectric constant were determined to be 2.02 and 4.08, respectively, using Wemple and DiDomenico oscillator model. High frequency dielectric constant was calculated as 4.30 by Spitzer-Fan model. Optical band gap of PbWO4 was found to be 3.24 eV from the dielectric relaxation time spectrum. Moreover, existence of two critical points with energies of 3.70 and 4.58 eV was revealed from the analyses of extinction coefficient and second derivative of the dielectric function. These levels were considered to be due to creation of cation exciton (Pb2+ 6s2 − Pb2+ 6s6p) and transitions in the [WO4]2− group.

Investigation of optical characteristics of PbMoO4 single crystals by spectroscopic ellipsometry

In this study, we investigated the optical properties of PbMoO4 single crystals grown by Czochralski method. Spectroscopic ellipsometry measurements were carried out in the energy region between 1.0 and 5.5 eV at room temperature. X-ray diffraction measurements were achieved for structural characterization. The resulted pattern exhibited one peak belonging to (200) plane. Spectral variations of complex dielectric function, complex refractive index, absorption coefficient and dissipation function were obtained from the analyses of ellipsometry data. Real part of dielectric function increased up to 4.0 eV and then decreased suddenly at above this value. Zero frequency refractive index and dielectric constant were found to be 2.04 and 4.15, respectively. High frequency dielectric constant was determined to be 4.36. Optical band gap of PbMoO4 crystals was calculated as 3.09 eV. Two critical points with energies of 3.57 and 4.34 eV were estimated from the analyses of second-energy derivative spectra of real and imaginary parts of dielectric function. It was determined that [MoO4]2− complexes and charge transfer from Pb2+ ions into the neighboring Mo groups were responsible for these interband transitions. Dissipation function increased with increasing photon energy.

Electronic, optical, and mechanical properties of AlxIn1−xP alloys under temperature and pressure

In this work, the optoelectronic and mechanical properties of AlxIn1−xP combinations in the zinc-blende structure were studied for different Al concentrations. The energy band gaps left( {{text{E}}_{{text{g}}}^{{text{L}}} ,,{text{E}}_{{text{g}}}^{Gamma } ,,{text{E}}_{{text{g}}}^{{text{X}}} } right), refractive index (n), high frequency and static dielectric constants (ɛ∞, ɛo), elastic parameters (C11, C12, C44) were investigated. Other mechanical properties such as bulk (Bu), shear (Cs), Young’s (Y0) moduli, Poisson ratio (σ), linear compressibility (C_{o} ), Cauchy (C_{a} ) ratio, isotropy factor (A), bond stretching parameter (alpha ,), bond-bending force parameter (beta ,), internal-strain parameter (xi ), and the transverse effective charge (e_{T}^{*} ) were calculated. Also, the temperature and pressure dependences of these properties were studied. Our estimations were made with the empirical pseudo-potential method combined with the virtual crystal approximation incorporated the compositional disorder impact. There was a reasonable agreement between our determined outcomes and the accessible experimental values for the binary materials AlP and InP which give help for the consequences of the ternary combinations.

Effect of transparent Pb substrates on the structural, optical, dielectric and electrical properties of copper selenide thin films

Herein, copper selenide thin films are coated onto transparent lead substrates. Pb/CuSe stacked layers is fabricated by the thermal evaporation technique under a vacuum pressure of 10-5 mbar. They are structurally, morphologically, optically and electrically characterized. Lead substrates enhanced the crystallinity of CuSe through increasing the crystallite sizes, reducing the microstrain and lowering defect densities. In addition, a blue shift in the energy band gap associated with remarkable increase in the value of the high frequency dielectric constant resulted from replacement of glass by Pb substrates. Moreover, significant increase in the optical conductivity in the ultraviolet range of light is observed. Fitting the optical conductivity in accordance with Drude- Lorentz models allowed determining the effect of transparent Pb substrates on the plasmon frequency, scattering time at femtosecond level and drift mobility of CuSe. On the other hand, electrical measurements on the Pb/CuSe/C by imposing an ac signal of low amplitude in the frequency domain of 10-1000 MHz, have shown that the Pb/CuSe can perform as negative capacitance source employable for devices scaling and low power applications.

Innovative Green Chemistry Approach to Synthesis of Sn2+-Metal Complex and Design of Polymer Composites with Small Optical Band Gaps.

In this work, the green method was used to synthesize Sn2+-metal complex by polyphenols (PPHs) of black tea (BT). The formation of Sn2+-PPHs metal complex was confirmed through UV-Vis and FTIR methods. The FTIR method shows that BT contains NH and OH functional groups, conjugated double bonds, and PPHs which are important to create the Sn2+-metal complexes. The synthesized Sn2+-PPHs metal complex was used successfully to decrease the optical energy band gap of PVA polymer. XRD method showed that the amorphous phase increased with increasing the metal complexes. The FTIR and XRD analysis show the complex formation between Sn2+-PPHs metal complex and PVA polymer. The enhancement in the optical properties of PVA was evidenced via UV-visible spectroscopy method. When Sn2+-PPHs metal complex was loaded to PVA, the refractive index and dielectric constant were improved. In addition, the absorption edge was also decreased to lower photon. The optical energy band gap decreases from 6.4 to 1.8 eV for PVAloaded with 30% (v/v) Sn2+-PPHs metal complex. The variations of dielectric constant versus wavelength of photon are examined to measure localized charge density (N/m*) and high frequency dielectric constant. By increasing Sn2+-PPHs metal complex, the N/m* are improved from 3.65 × 1055 to 13.38 × 1055 m−3 Kg−1. The oscillator dispersion energy (Ed) and average oscillator energy (Eo) are measured. The electronic transition natures in composite films are determined based on the Tauc’s method, whereas close examinations of the dielectric loss parameter are also held to measure the energy band gap.

Elastic, lattice dynamical, thermal, electronic, and optical properties of nano-semiconductor CdTe under the effect of temperature

The energy band gaps of CdTe semiconductor material have been determined using the empirical pseudo-potential method (EPM). The refractive index (n), high frequency (ε∞) and static dielectric constants (εs) of the considered material have been studied. The elastic constants, as well as some associated factors like bulk, (Bu), shear (Cs), Young (Y0) moduli, isotropy factor (A), and Poisson ratio (σ), have been reported for CdTe in zinc blende structure. The longitudinal and transverse phonon frequencies (ωLO,ωTO), and Debye temperature (θD) have also been calculated. All of the variables studied have been investigated in terms of their temperature sensitivity. Generally, Our findings are in good agreement with those published in the literature. The studied material could be useful in the fabrication of optoelectronic devices under high temperatures.

Photoelectron Spectroscopy of Benzene in the Liquid Phase and Dissolved in Liquid Ammonia.

We report valence band photoelectron spectroscopy measurements of gas-phase and liquid-phase benzene as well as those of benzene dissolved in liquid ammonia, complemented by electronic structure calculations. The origins of the sizable gas-to-liquid-phase shifts in electron binding energies deduced from the benzene valence band spectral features are quantitatively characterized in terms of the Born-Haber solvation model. This model also allows to rationalize the observation of almost identical shifts in liquid ammonia and benzene despite the fact that the former solvent is polar while the latter is not. For neutral solutes like benzene, it is the electronic polarization response determined by the high frequency dielectric constant of the solvent, which is practically the same in the two liquids, that primarily determines the observed gas-to-liquid shifts.

Physical properties of rhodium retrieved from modeling its dielectric function by a simulated annealing approach

Optical, charge carriers transport, quantum mechanics, magnetic, thermal, and plasmonic properties of the transition metal rhodium are considered. An extended Drude-Lorentz (DL) model is applied to describe the dielectric function (DF) of rhodium in a spectral range going from the mid-infrared (12.4 μm) to the vacuum ultraviolet (32 nm). The Drude term of the DF includes, as optimization parameters, the inverse of the high frequency dielectric constant, the volume plasma frequency and scattering frequency of the electrons, the scattering frequency of holes relative to that of electrons, the ratio between the effective masses of electrons and holes, the number of holes per atom relative to that of electrons, and the renormalized times between grain boundary scattering events for electrons and holes. The Lorentz contribution to the DF includes the number of conduction electrons per atom, the oscillator strengths, the resonance energies, and the Lorentzian widths. Values of the parameters involved in the DF are optimized by an acceptance-probability-controlled simulated annealing method that minimizes spectral differences between the real and imaginary parts of the DF values obtained from the literature and those evaluated from the DL parametric formulation, accounting for the presence of electrons and holes as charge carriers. Once an optimized spectral description of the DF of rhodium is obtained, a large set of charge-transport, magnetic, thermal, plasmonic, and quantum mechanics derived quantities are evaluated: mobilities, relaxation times, Fermi velocities, effective masses, electrical and thermal conductivities, heat capacity coefficients, Hall coefficient, diamagnetic and paramagnetic susceptibilities, effective number of Bohr magnetons, Fermi energies and corresponding densities of states, energy loss functions, effective number of charge carriers participating in conduction, and effective number of electrons involved in inter-band transitions.