Bandgap Energies and Refractive Indices of Pb_1-xSr_xSe

Abstract

Optical transmission measurements were carried out on Pb_1-xSr_xSe samples with different Sr compositions (x ranging from 0 to 1) grown by molecular beam epitaxy (MBE). Refractive indices were calculated at room temperature and at 77K by fitting the transmittance data. The bandgap energies were determined by fitting the absorption curve with direct and indirect energy bandgap transitions. A distinct bandgap inversion from the direct to the indirect transition is observed at x ∼ 0.20 as the Sr composition increases. This is the first observation of such transition in the Pb_1-xSr_xSe material system. Both direct and indirect bandgap energies were determined by fitting the experimental results.

PbSe and lead-alkaline-earth-chalcogenide materials Pb_1-xSr_xSe have attracted considerable attention in optoelectronic applications especially in the mid-infrared (mid-IR) lasers and mid-IR/ultraviolet (UV) detectors.¹ The bandgap energies and the refractive indices of this material system vary widely with the change of Strontium composition. Such properties have been used to grow quantum wells and diffraction Bragg reflectors (DBR) for vertical cavity surface emitting lasers² (VCSELS) and detectors. Yet only a narrow range of the whole material system has been explored and the basic electronic and optical properties are widely unknown for Pb_1-xSr_xSe with high Sr compositions. The primary aim of this research is to determine, experimentally, the electronic and optical properties of these ternary compounds for different compositions. PbSe which is a narrow bandgap material, have been studied widely and are know to have a direct narrow bandgap of 0.3eV at L point.³ SrSe on the other hand is a wide bandgap material which have an indirect bandgap between X-Γ.⁴ As the Sr composition in the ternary compound Pb_1-xSr_xSe increases, its electronic structure changes from a narrow direct bandgap material to a wide indirect bandgap material. However, the composition at which the material becomes indirect was unknown, even though it is an important parameter in designing optoelectronics devices. The other properties of this material system on which we have investigated upon are the refractive index and absorption coefficient, which were largely unknown.

In this research, we have grown epitaxial layers of Pb_1-xSr_xSe by molecular-beam epitaxy (MBE), on <111> BaF₂ substrate, with nine different Sr compositions (x) ranging from zero to one. The crystal growth is characterized by high-resolution X-ray diffraction measurements and the Sr composition is determined by assuming that the material follows the Vegard's law. Transmissions, in the wavelength range mid-IR to UV, were measured at different temperatures. The refractive indices and absorption coefficients of Pb_1-xSr_xSe with different Strontium composition were determined. Bandgap energies of all different compositions are calculated by fitting the absorption coefficients to theoretical models of either direct or indirect bandgap. A distinct bandgap inversion from the direct to the indirect is observed at x ∼ 0.20. While the 3.81eV direct bandgap of SrSe calculated from our experiments agreed closely with that from reported photoluminescence measurements, the lowest bandgap of SrSe is observed to be ∼ 1.82 eV, contradicting previously published results.

Compound sources of PbSe and elemental sources of Sr and Se were used to grow epitaxial layer of Pb_1-xSr_xSe on freshly cleaved <111>BaF₂ on a custom made MBE chamber. The substrate temperature varied from 360°C to 450°C for growths with different Sr composition and the epitaxial layers were grown to a thickness in the range of 2μm to 4μm for different samples. Details of the growth are described elsewhere.⁵ X-ray diffraction measurements were performed on Philips high resolution X-ray diffraction spectrometer (HRXRD) having four crystal Ge (220) monochromator. The Sr composition was determined by considering that lattice constant of Pb_1-xSr_xSe increases linearly with increase in Sr composition. Figure 1 shows the composition vs lattice constant graph, and insert on it is a typical XRD curve of Pb_1-xSr_xSe grown on BaF₂<111>.

Optical transmittance of the epitaxial layers, were measured at different temperatures by Fourier transform infrared (FTIR) transmission spectroscopy, using deuterated triglycine sulfate (DTGS) detector and globar source for the mid-IR region, Silicon detector and Tungsten source for nearinfrared (NIR) and visible regions, and Xenon-arc source and Gallium-Phosphide (GaP) detector for the UV region of the spectrum. The transmission spectra are shown in figure 2. The refractive index and the absorption coefficient of the epitaxial layers have been calculated by the method described elsewhere.⁶ The approximate refractive index for each composition is calculated first from the odd interference peaks of the no absorption region of the transmission spectra (long wavelength regions that are well below the energy bandgap). The approximate values were then in turn used in the equation of transmittance⁶ and matched with the experimental curve by iterative method to calculate the true values of refractive index, absorption coefficient and thickness of the epilayer.

T(n₂, k₂, λ, d, n₁, n₃)– T_exp = 0,⁶

It may be noted that absorption coefficient and the refractive index of the substrate, whose thickness is in the range of 0.6 to 0.8mm, and which might affect the interference peak, have been measured and used in the calculation to eliminate the error introduced by the substrate. The refractive index at 4μm (non-absorbing region for all compositions of Pb_1-xSr_xSe) calculated from the samples at room temperature and at 77K is plotted in figure 3.