Features of interband absorption in the dielectric function of narrow-gap semiconductors

Abstract

For semiconductors and semimetals possessing a narrow gap between bands with different parity, the dispersion of the dielectric function is explicitly evaluated in the infrared region. The imaginary part of the dielectric function has a plateau above the absorption threshold for the interband electron transitions. The real part of the dielectric function has a logarithmic singularity at the threshold. This results in the large contribution into the dielectric constant for pure semiconductors at low frequencies. For samples with degenerate carriers, the real part of the dielectric function is divergent at the absorption threshold. This divergence is smeared with the temperature or the collision rate. PACS numbers: 71.20.Nr, 78.20.Ci, 78.20.Bh Usually experiments and theories describe 1,2,3,4 the direct allowed transitions in terms of the Fermi golden rule which provides the imaginary part of the dielectric function (or the real conductivity)giving the square root dependence ǫ ′′ (ω) ∼ hω − 2ε g near the band edge absorption for the case when the conduction band is empty and the valence band is filled. The electron-hole Coulomb interaction smears this squareroot singularity. For doped semiconductors, the threshold of absorption is determined by the carrier concentration, i.e., the chemical potential µ if the temperature is low enough. The interband transitions of carriers give also a contribution into the real part ǫ ′ (ω) which can be calculated with the help of the Kramers-Kronig relations. In reality, these numerical calculations involve the pseudopotential form-factor and do not present an evident result (see, for instance, Ref. 1,2 ). It is more productive to use an explicit expression for the complex optical conductivity which can be derived using the Kubo formula or the RPA approach.Here, we present calculations of the dielectric function for an important case when the gap ε g between the conduction and valence bands is much smaller than the distance ε at (on the atomic scale) to other bands. The model is applicable to the IV-VI semiconductors (as PbTe, PbSe, and PbS), i.e., such narrow-gap semiconductors and semimetals, where the narrow gap appears as a result of intersections of two bands with different parity. We evaluate the dispersion of the real part of the dielectric function and the reflectance along with the behavior of the imaginary part around the absorption threshold. We find that the contribution of the electron transitions into the real part has the logarithmic singularity at the threshold and can be more essential for optical properties than absorption given by the imaginary part of the dielectric function.The effective Hamiltonian of the problem can be writ-ten as a 4×4 matrix 5

InN dielectric function from the midinfrared to the visible range

“…The plateau noticed also in the paper [12] and for the A 4 B 6 semiconductors in [14] is a consequence of the linearity of the electron dispersion at the energy larger in comparison with the energy gap. The real part of the DF contains the following contributions.…”

“…We find, that the real part of the DF has at the absorption edge the kink-like singularity in the case (i) and the logarithmic divergence in the case (ii). Such singularities have been previously obtained for graphene [13] and for IV-VI semiconductors [14]. The singularities are smeared with temperatures or carrier relaxation.…”

“…For small relaxation rate ν in comparison with the photon frequency ω, we have in Eqs. (10), (13), (14) to substitute…”

Morphology-Controlled Synthesis of Au/Cu2FeSnS4 Core–Shell Nanostructures for Plasmon-Enhanced Photocatalytic Hydrogen Generation

“…The SPR absorption peak of Au in Au sp /CITS NPs exhibits a red shift from its normal position of 525 to 750 nm. The formation of a CITS shell surrounding Au core introduced a high dielectric constant of low band gap CITS to the composite materials . The SPR effect is obvious when the UV–vis spectra of CITS and Au/CITS NPs are compared.…”