Possible nature of unusual behavior of lead chalcogenide absorption coefficient at the edge of the fundamental band

Abstract

In [1] it has been established that the absorption coefficient α for Pb1–xSnxTe (x = 0, 0.1, and 0.2) with ħω ≥ 2Eg (Eg is the optical gap width) increases much faster than it follows from the Kane nonparabolicity model. Dryabkin et al. [1] explained the observed effect by the deviation of the law of electron and hole dispersion from the Kane law toward a greater degree of nonparabolicity. However, in the experimental investigations of the effective electron mass m* for n-PbTe based on the Faraday effect [2] it was established that the dependence m*(n) can be described by the Kane model for free electron concentrations up to NTL = 1·10 cm (the corresponding Fermi energy EF ≈ 0.26 eV). The obvious contradiction between conclusions of [1] and [2] can be eliminated if we take into account that the valence band of lead chalcogenides consists of two subbands of light (L6) and heavy holes (Σ5) separated by the energy gap ∆Ev. Proceeding from this, it is possible to assume that the lead chalcogenide absorption coefficient at the edge of the intrinsic absorption band is a sum of two components, namely, α1 with the threshold Eg and α2 with the threshold Ei caused by optical electron transitions from the subbands of light (L6) and heavy holes (Σ5), respectively, to the conduction band. It is obvious that for nondegenerate samples, the difference Ei – Eg will correspond to ∆Ev. We note that the experimental observation of this effect is possible due to a significant difference between the effective masses of state densities in light and heavy hole subbands exceeding an order of magnitude (for example, see [3]). To verify the above assumption, the results of the most accurate measurements of α for Pb1–xSnxTe [1, 4] and PbS [5] at T = 300 K were analyzed together with the data obtained in the present work for the n-PbTe and p-Pb0.94Sn0.06Te films (with concentration of free current carriers n, p ≈ 1·10 cm) put on mica substrates (see Fig. 1). A comparison of the data shown in Fig. 1 with the results presented in [1, 4, 5] demonstrates that they are qualitatively similar. The abnormally fast increase in α, well noticeable already at ħω ≈ 2Eg, is observed for all spectra. This is indicative of the existence of additional component of the fundamental absorption. To separate this component, experimental dependences α(ħω) were drawn in α2– ħω coordinates, which corresponds to the simple formula α ~ (ħω – Eg). The applicability of this formula for a description of direct allowed transitions in lead chalcogenides was proved in [1]. As expected (Fig. 2), all examined dependences in these coordinates were rectified for ħω ≤ Eg + ∆Ev (in this spectral range, α ≡ α1). This allowed us to separate the components α2(ħω) from the experimental dependences by subtraction of α1 values obtained by linear extrapolation of straight lines α2(ħω) to the short-wavelength range of the spectrum. Our analysis demonstrated that the dependences α2(ħω) were rectified in the α2–ħω coordinates, which was typical of the indirect allowed transitions in lead chalcogenides (Eqs. (2)–(17а) from [6]). The parameters Eg and Ei determined from the points of intersection of the straight lines α2(ħω) and α2(ħω) with the abscissa and the parameter ∆Ev known from the literature are tabulated in Table 1. Insignificant deviations of Eg and Ei values from the literature data for films [6] was due to the film tension because of different thermal expansion coefficients of films and substrates [7]. It can be seen that for all samples, the difference Ei – Eg is equal to ∆Ev within the limits of experimental errors. However, ∆Ev values for Pb1–xSnxTe, as follows from the table, poorly agree among themselves. This contradicts conclusions of [8, 10] about the invariance of ∆Ev values for Pb1–xSnxTe with x ≤ 0.2. The ∆Ev value for PbTe obtained in [8] (0.15 eV at T = 300 K) was refined in [3]. This suggests that ∆Ev values presented in [8] for the Pb1–xSnxTe alloys can also be overestimated.