The room temperature reflectance spectra in UV-VIS-NIR region (energy range of 0.6 to 6.2 eV) for glassy, partially crystalline and its fully crystalline superconducting ceramic phases of Bi_3.9Pb_0.1Sr₃Ca₃Cu₄O_x have been studied by Kramers-Kronig (KK) analysis. A comparative study of the energy loss function [− Im (1/ε)] and the absorption coefficient [α(E)] has been done. Excitions in the superconducting phase hitherto evidenced by the authors are located in the polarizable layers of the superconducting cuprate and their implications for superconductivity have been pointed out. An estimate of the optical band gap energy (E_g) has also been made from the linear fit ofα² vs.E curve for the superconducting phase. Jezierski’s method ofR-extrapolations in the higher energy has been used to show that both methods yield results that agree quantitatively and can be relied upon.

We provide the energy spectrum of an electron in a degenerately doped semiconductor of parabolic band. Knowing the energy spectrum, the density-of-states (DOS) functions are obtained, considering the Gaussian distribution of the potential energy of the impurity states, showing a band tail in them e.g., energy spectrum and density-of-states. Therefore, Fermi integrals (FIs) of DOS functions, having band tail, are developed by the exact theoretical calculations of the same. It is noticed that with heavy dopings in semiconductors, the total FI demonstrates complex functions, containing both real and imaginary terms of different FI functions. Their moduli possess an oscillatory function of $\eta$ (reduced Fermi energy = $E_{f}/k_{B}T, k_{B}$ is the Boltzmann constant and $T$ is the absolute temperature) and $\eta e$ (impurity screening potential), having a series solutions of confluent hypergeometric functions, $\Phi(a, b; z)$, superimposed with natural cosine functions of angle $\theta$. The variation of $\theta$ with respect to $\eta$ indicated resonance at $\eta$ = 1.5. The oscillatory behaviour of FIs show the existence of ‘band-gaps’, both in the real as well as in the forbidden bands as new band gaps in the semiconductor.

Optical band gap ($E_{g0}$) is a parameter of paramount importance in describing various transport and opto-electronic properties of the III–V-type low band-gap semiconductors. In the present communication, an attempt has been made to develop an energy–momentum ($E−\bar{k}$) dispersion relation for studying the density-of-state (DOS) and band-gap-related parameters. The external laser excitation has been treated as a perturbation. It has been shown theoretically that due to such excitation with different intensity ($I$) and wavelength ($\lambda$), the band edge of the conduction band (CB) of the III–V compound semiconductors moves vertically upward, indicating laser modulation (increase) of $E_{g0}$ and related parameters compared to those of the normal ones (unperturbed). Therefore, in the presence of light, the original CB edge forms a pseudo-CB edge above the unperturbed CB edge in the forbidden band (FB) zone. This new development of the ($E−\bar{k}$) relationship has also been extended for the estimation of exact optical effective mass (OPEM) of an electron in some III–V compound semiconductors. The OPEM variation with carrier concentration showed a continuous decreasing nature, while the corresponding variation of electron effective mass (EEM) (without laser excitation) exhibited an increasing trend. The present theoretical results would be important for the deeper understanding of the variation of OPEM with $I$ and $\lambda$. The observed new results will also be beneficial for studying laser-induced effects in semiconductor heterostructures with different applications in optoelectronic devices.