Influence of nonparabolic-energy-band dispersion on the optical constants close to the fundamental absorption in PbSe andPb1−xMnx

Abstract

The absorption and refractive indices of IV-VI semiconductor PbSe and Pb 1Ϫx Mn x Se (xр0.013) epitaxial layers are strongly influenced by band nonparabolicity in the absorbing regime above the fundamental energy gap E g , as well as below in the transparent regime. This fact follows simply from causality since interband transitions far above the energy gap contribute remarkably to the optical constants near and below E g . The observation of multiple reflection and interference phenomena in the transmission spectrum of the epitaxial layers grown on BaF 2 substrates, which were taken with high photometric accuracy ͑0.1%͒, allowed us to probe the dispersion of the refractive index very precisely as well as to determine the energy gap of PbSe and Pb 1Ϫx Mn x Se with an uncertainty of Ϯ2 meV. A dielectric function is derived which contains the contributions from the interband transitions at the L point of the Brillouin zone and the residual dispersion from higher critical point oscillators at E 1 ϭ1.6 eV, E 2 ϭ2.73 eV, and E 3 ϭ4.2 eV. In contrast to previous studies, the dissipative and dispersive parts of the dielectric function strictly obey the Kramers-Kronig causality relations. Also, in this sense all level broadenings do not only appear in the imaginary part of the dielectric function, but cause corresponding energy shifts in its real part. An analytic formula of the complex dielectric function for the nonparabolic energy-momentum dispersion was derived within the framework of the six-band many-valley k• p model, and compared with the results of a corresponding parabolic model, keeping the oscillator strength and energy-level broadening identical. Only the dielectric function based on the nonparabolic band model correctly explains the observed transmission in the transparent regime below E g and its steep decrease above the gap. It turns out that both the extinction coefficient as well as the refractive index of PbSe have considerably higher values than previously published.

Temperature-dependent optical properties of Pb1−xMnxSe films epitaxially grown on Zn0.04Cd0.96Te substrates

“…Note that the Fabry-Perot oscillations on the transmission spectra in Fig. 1 are apparently weaker than those of the films grown on BaF 2 [4,9]. We perform a leastsquare fit to the experimental transmission data in Fig.…”

“…Thus, the nonlinearity is likely due to the error in fitting the data. In the framework of the six-band k·p model, the parameter A for Pb 0.962 Mn 0.038 Se has the form of [9] A = 4.8…”

“…Theoretically, the complex dielectric function based on a nonparabolic band model takes the form of [9] ε…”

“…For magnetic semiconductor Pb 1−x Mn x Se with x ≤ 0.02, band parameters below 77 K has been studied by using magneto-optical spectroscopy and coherent anti-Stokes Raman scattering [6]. Krenn et al [9] developed an analytical complex dielectric function based on a nonparabolic band model, and then analyzed the transmission data of Pb 1−x Mn x Se with x ≤ 0.013 at room temperature. Recently, Qing-Lei Wang et al [10] have studied optical transmission spectra of Pb 1−x Mn x Se at room temperature.…”

Spectroscopy on Vertical Microcavities for the Mid-Infrared

“…In order to determine the exact values of the dispersion of the refractive indices of the layer materials, transmission measurements were performed for single reference layers. The measured data were then fitted to calculations using a model for the dielectric function of lead salts [14], which gives an analytic Kramers-Kronig conform expression of the optical constants including the non-parabolicity of the band structure near the energy gap and the manyvalley band structure of the lead salt compounds. To describe the cavity sample containing a superlattice of correlated, self organized PbSe quantum dots, the dielectric function was modified in order to take into account the two-dimensional and zero-dimensional joint density of states present in the wetting layers and the quantum dots.…”