Phonon Peak Research Articles

Double Gold/Nitrogen Nanosecond-Laser-Doping of Gold-Coated Silicon Wafer Surfaces in Liquid Nitrogen

A novel double-impurity doping process for silicon (Si) surfaces was developed, utilizing nanosecond-laser melting of an 11 nm thick gold (Au) top film and a Si wafer substrate in a laser plasma-activated liquid nitrogen (LN) environment. Scanning electron microscopy revealed a fluence- and exposure-independent surface micro-spike topography, while energy-dispersive X-ray spectroscopy identified minor Au (~0.05 at. %) and major N (~1–2 at. %) dopants localized within a 0.5 μm thick surface layer and the slight surface post-oxidation of the micro-relief (oxygen (O), ~1.5–2.5 at. %). X-ray photoelectron spectroscopy was used to identify the bound surface (SiNx) and bulk doping chemical states of the introduced nitrogen (~10 at. %) and the metallic (<0.01 at. %) and cluster (<0.1 at. %) forms of the gold dopant, and it was used to evaluate their depth distributions, which were strongly affected by the competition between gold dopants due to their marginal local concentrations and the other more abundant dopants (N, O). In this study, 532 nm Raman microspectroscopy indicated a slight reduction in the crystalline order revealed in the second-order Si phonon band; the tensile stresses or nanoscale dimensions of the resolidified Si nano-crystallites envisioned by the main Si optical–phonon peak; a negligible a-Si abundance; and a low-wavenumber peak of the Si3N4 structure. In contrast, Fourier transform infrared (FT-IR) reflectance and transmittance studies exhibited only broad structureless absorption bands in the range of 600–5500 cm−1 related to dopant absorption and light trapping in the surface micro-relief. The room-temperature electrical characteristics of the laser double-doped Si layer—a high carrier mobility of 1050 cm2/Vs and background carrier sheet concentration of ~2 × 1010 cm−2 (bulk concentration ~1014–1015 cm−3)—are superior to previously reported parameters of similar nitrogen-implanted/annealed Si samples. This novel facile double-element laser-doping procedure paves the way to local maskless on-demand introductions of multiple intra-gap intermediate donor and acceptor bands in Si, providing related multi-wavelength IR photoconductivity for optoelectronic applications.

Electronic structure investigation and anisotropic phonon anharmonicity in ternary ZrGeTe4 single crystals

Ternary two-dimensional (2D) transition metal chalcogenides have gained immense attention because of their ability to overcome the intrinsic limitations of their binary counterparts. Layered 2D materials are important for future electronic and photonic devices owing to their low structural symmetry and in-plane anisotropy with tunable bandgap. Herein, the electronic structure and detailed vibrational properties of bulk ZrGeTe4 layered single crystals were investigated using angle-resolved photoemission spectroscopy (ARPES) and Raman scattering (RS). The ARPES results revealed an anisotropic Fermi surface of different momentum along kx and ky from the zone center and an anisotropic band structure with varying band curvatures along the high-symmetry directions. Furthermore, the RS of ZrGeTe4 was investigated under different polarizations and varying temperatures. The polarized RS exhibited twofold and fourfold symmetry orientations in different configurations, revealing the anisotropic phonon dispersions for bulk ZrGeTe4. The observed softening of Raman modes was corroborated with the anharmonic phonon dispersion, which was further supported by our third-order force constant calculations of thermal transport using density functional theory. Low lattice thermal conductivity with increasing temperature is linked with enhanced phonon–phonon scattering, which is evident from the decreased phonon lifetime and peak linewidth. In addition to these fundamental aspects, the anisotropic nature and unique layered structure of such materials reveal their bright future for next-generation nanoelectronic applications.

Suppressed thermal transport in silicon nanoribbons by inhomogeneous strain.

Nanoscale structures can produce extreme strain that enables unprecedented material properties, such as tailored electronic bandgap1-5, elevated superconducting temperature6,7 and enhanced electrocatalytic activity8,9. While uniform strains are known to elicit limited effects on heat flow10-15, the impact of inhomogeneous strains has remained elusive owing to the coexistence of interfaces16-20 and defects21-23. Here we address this gap by introducing inhomogeneous strain through bending individual silicon nanoribbons on a custom-fabricated microdevice and measuring its effect on thermal transport while characterizing the strain-dependent vibrational spectra with sub-nanometre resolution. Our results show that a strain gradient of 0.112% per nanometre could lead to a drastic thermal conductivity reduction of 34 ± 5%, in clear contrast to the nearly constant values measured under uniform strains10,12,14,15. We further map the local lattice vibrational spectra using electron energy-loss spectroscopy, which reveals phonon peak shifts of several millielectron-volts along the strain gradient. This unique phonon spectra broadening effect intensifies phonon scattering and substantially impedes thermal transport, as evidenced by first-principles calculations. Our work uncovers a crucial piece of the long-standing puzzle of lattice dynamics under inhomogeneous strain, which is absent under uniform strain and eludes conventional understanding.

Effect of water-based electrolyte on surface, mechanical and tribological properties of ZrO2 nanotube arrays produced on zirconium

In this work, highly ordered ZrO2 nanotube arrays were fabricated on commercial pure Zr substrates through anodic oxidation in the water-based electrolyte at various voltages (30 V, 40 V and 50 V) for 1 h. The monoclinic- and tetragonal-ZrO2 phases were obtained on ZrO2 nanotubes through anodic oxidation. 13 vibration modes have been observed for the samples grown at low voltages (30 V and 40 V), which are assigned to monoclinic symmetry (7Ag + 6Bg), while—with the increasing growth voltage, the dominant phonon peak intensities associated with the monoclinic symmetry 6 times are decreased, and Eg (268 and 645 cm − 1) mode corresponding to tetragonal symmetry is observed. The nanotube array surfaces exhibited hydrophilic and super-hydrophilic behavior compared to the bare Zr surface. The elastic modulus values of ZrO2 nanotube surfaces (14.41 GPa) were highly similar to those of bone structure (10–30 GPa) compared to bare Zr substrate (120.5 GPa). Moreover, hardness values of ZrO2 nanotube surfaces were measured between ∼76.1 MPa and ∼ 283.0 MPa. The critical load values required to separate the nanotubes from the metal surface were measured between ∼1.6 N and ∼26.3 N. The wear resistance of the ZrO2 nanotube arrays was improved compared to that of plain Zr substrate.

Acoustic and optical phonons in quasi-two-dimensional MPS3 antiferromagnetic semiconductors

We report the results of the investigation of the acoustic and optical phonons in quasi-two-dimensional antiferromagnetic semiconductors of the transition metal phosphorus trisulfide family with Mn, Fe, Co, Ni, and Cd as metal atoms. The Brillouin–Mandelstam and Raman light scattering spectroscopies were conducted at room temperature to measure the acoustic and optical phonon frequencies close to the Brillouin zone center and the Γ−A high symmetry direction. The absorption and index of refraction were measured in the visible and infrared ranges using the reflectometry technique. We found an intriguing large variation, over ∼28%, in the acoustic phonon group velocities in this group of materials with similar crystal structures. Our data indicate that the full-width-at-half-maximum of the acoustic phonon peaks is strongly affected by the optical properties and the electronic bandgap. The acoustic phonon lifetime extracted for some of the materials was correlated with their thermal properties. The results are important for understanding the layered van der Waals semiconductors and assessing their potential for optoelectronic and spintronic device applications.

Raman Spectroscopy Analysis for Precise Channel Temperature Estimation in AlGaN/GaN HEMT Devices

In recent years, high-electron-mobility GaN HEMTs have demonstrated significant advancements in applications such as power converters and RF amplifiers. Nevertheless, their thermal reliability poses a notable challenge, placing constraints on their power-handling capacities. This study employs micro-Raman spectroscopy to evaluate the localized self-heating-induced channel temperature. The channel temperature, determined using the single phonon modes of GaN HEMT (E2(H) & A1(LO)), exhibits discrepancies and does not align with device temperature values calculated using the SiC phonon peak near the GaN channel. However, by employing both phonon modes of GaN to decouple the combined effects of joule heating and the thermoelastic effect, accurate channel temperature values are obtained, matching well with those obtained from the SiC phonon peak. The agreement between calculated temperatures from phonon modes and those obtained by heating the device from the back side enhances the credibility of the proposed method.

Effect of Metal Nanoparticles in the Field Emission of Silicon Nanowires

In this work, an efficient method is reported for creating a metal nanoparticle (silver) / Si composite structure consisting of a vertical array of silicon nanowires (SiNWs) decorated with silver metal nanoparticles. A two-stage metal-assisted etching method is employed to obtain SiNWs and Silver (Ag) metal nanoparticles are decorated on the SiNWs using the electroless deposition method. It allows the good coverage of silver metal nanoparticles over SiNWs. Scanning Electron Microscopy (SEM) analysis revealed that Ag was covered with SiNWs. High-work function metal nanoparticles such as Ag nanoparticles on SiNWs have been utilized in different applications such as photovoltaics and sensors. The size of SiNWs is determined through the Raman shift. The silicon optical phonon peak showed an increase in redshift and a decrease of full-width at half maxima with a decrease in diameter due to the quantum confinement. The Electron Field Emission (EFE) characteristics of the Agdecorated SiNW films were studied based on the current-voltage measurements and analyzed using the Fowler-Nordheim (F-N) equation. The low turn-on field is obtained through the Ag metal nanoparticles which have wider applications in lowpower operational devices.

Anisotropic structural, vibrational, electronic, optical, and elastic properties of single-layer hafnium pentatelluride: an ab initio study.

Motivated by the highly anisotropic nature of bulk hafnium pentatelluride (HfTe5), the structural, vibrational, electronic, optical, and elastic properties of single-layer two-dimensional (2D) HfTe5 were investigated by performing density functional theory (DFT)-based first-principles calculations. Total energy and geometry optimizations reveal that the 2D single-layer form of HfTe5 exhibits in-plane anisotropy. The phonon band structure shows dynamic stability of the free-standing layer and the predicted Raman spectrum displays seven characteristic Raman-active phonon peaks. In addition to its dynamic stability, HfTe5 is shown to exhibit thermal stability at room temperature, as confirmed by quantum molecular dynamics simulations. Moreover, the obtained elastic stiffness tensor elements indicate the mechanical stability of HfTe5 with its orientation-dependent soft nature. The electronic band structure calculations show the indirect-gap semiconducting behavior of HfTe5 with a narrow electronic band gap energy. The optical properties of HfTe5, in terms of its imaginary dielectric function, absorption coefficient, reflectance, and transmittance, are shown to exhibit strong in-plane anisotropy. Furthermore, structural analysis of several point defects and their oxidized structures was performed by means of simulated STM images. Among the considered vacancy defects, namely , , VTeout, VTein, , and VHf, the formation of VTeout is revealed to be the most favorable defect. While and VHf defects lead to local magnetism, only the oxygen-substituted VHf structure possesses magnetism among the oxidized defects. Moreover, it is found that all the bare and oxidized vacant sites can be distinguished from each other through the STM images. Overall, our study indicates not only the fundamental anisotropic features of single-layer HfTe5, but also shows the signatures of feasible point defects and their oxidized structures, which may be useful for future experiments on 2D HfTe5.

Scalable nano-integration strategy: Controllable three-dimensional monocrystalline GaN nanostructures from nanobelts to nanonetwork

The effective and scalable assembly of 1D nano-units into ordered 3D monocrystalline networks remains a challenge. Based on the crystal structure and growth characteristics of GaN, we have designed a specific epitaxy strategy and successfully achieved large area self-networking of 3D monocrystalline nanostructure on Au-coated β-LiGaO2 (100) substrate formed by the interconnection of GaN nanobelts grown along three equivalent directions of the m-axis [011̅0], [101̅0] and [11̅00]. This well-aligned 3D GaN nanostructure grown by simple CVD method has good reproducibility and the yield of cross-linked junctions are quite high. The mono-crystallinity of this structure were proved by X-ray diffraction (XRD) and transmission electron microscope (TEM) results, especially at the crosslinked junctions. The overall epitaxial relationships between GaN and LiGaO2 was analyzed and the defect-mediated anisotropic VS growth mechanism was deduced from thorough characterization of individual nanobelts. Besides, the morphology of 3D GaN nanostructure including length, width and height was found to be controllable. The E2 (high) phonon peak at 567.4 cm−1 in the Raman spectrum and the strong ultraviolet emission peak centered at 363.3 nm (3.41 eV) in the photoluminescence (PL) spectrum indicate that the 3D GaN nanostructures are nearly strain-less and have high crystalline quality. This large-scale 3D monocrystalline network not only retains the advantage of 1D nanomaterials, but also become easier to operate compared with individual nanowire. The epitaxy assembly strategy is expected to ensure the property homogeneity of chip-scale devices for their real applications and provide a reference for further growth of tunable 3D structures of other materials.

Effects of anisotropy and disorder on the superconducting properties of niobium

We report results for the superconducting transition temperature and anisotropic energy gap for pure niobium based on Eliashberg’s equations and electron and phonon band structures computed from density functional theory. The electronic band structure is used to construct the Fermi surface and calculate the Fermi velocity at each point on the Fermi surface. The phonon bands are in excellent agreement with inelastic neutron scattering data. The corresponding phonon density of states and electron–phonon coupling define the electron–phonon spectral function, α2F(p, p′; ω), and the corresponding electron–phonon pairing interaction, which is the basis for computing the superconducting properties. The electron–phonon spectral function is in good agreement with existing tunneling spectroscopy data except for the spectral weight of the longitudinal phonon peak at ℏωLO = 23 meV. We obtain an electron–phonon coupling constant of λ = 1.057, renormalized Coulomb interaction μ⋆ = 0.218, and transition temperature Tc = 9.33 K. The corresponding strong-coupling gap at T = 0 is modestly enhanced, Δ0 = 1.55 meV, compared to the weak-coupling BCS value Δ0wc=1.78kBTc=1.43meV. The superconducting gap function exhibits substantial anisotropy on the Fermi surface. We analyze the distribution of gap anisotropy and compute the suppression of the superconducting transition temperature using a self-consistent T-matrix theory for quasiparticle-impurity scattering to describe niobium doped with non-magnetic impurities. We compare these results with experimental results on niobium SRF cavities doped with nitrogen impurities.

In Situ Monitoring of Drug Precipitation from Digesting Lipid Formulations Using Low-Frequency Raman Scattering Spectroscopy.

Low-frequency Raman spectroscopy (LFRS) is a valuable tool to detect the solid state of amorphous and crystalline drugs in solid dosage forms and the transformation of drugs between different polymorphic forms. It has also been applied to track the solubilisation of solid drugs as suspensions in milk and infant formula during in vitro digestion. This study reports the use of LFRS as an approach to probe drug precipitation from a lipid-based drug delivery system (medium-chain self-nanoemulsifying drug delivery system, MC-SNEDDS) during in vitro digestion. Upon lipolysis of the digestible components in MC-SNEDDS containing fenofibrate as a model drug, sharp phonon peaks appeared at the low-frequency Raman spectral region (<200 cm-1), indicating the precipitation of fenofibrate in a crystalline form from the formulation. Two multivariate data analysis approaches (principal component analysis and partial least squares discriminant analysis) and one univariate analysis approach (band ratios) were explored to track these spectral changes over time. The low-frequency Raman data produces results in good agreement with in situ small angle X-ray scattering (SAXS) measurements with all data analysis approaches used, whereas the mid-frequency Raman requires the use of PLS-DA to gain similar results. This suggests that LFRS can be used as a complementary, and potentially more accessible, technique to SAXS to determine the kinetics of drug precipitation from lipid-based formulations.

Nanoscale Electric Field Probing in a Single Nanowire with Raman Spectroscopy and Elastic Strain.

In this work we investigate the Raman response of extremely strained gallium phosphide nanowires. We analyze new strain-induced spectral phenomena such as 2-fold and 3-fold phonon peak splitting which arise due to nontrivial internal electric field distribution coupled with inhomogeneous strain. We show that high bending strain acts as a probe allowing us to define the electric field distribution with deep subwavelength resolution using the corresponding changes of the Raman spectra. We investigate the nature of the localization with respect to nanowire diameter, excitation spot position, and light polarization, supporting the experiment with 3D numerical modeling. Based on our findings we propose a research tool allowing to precisely localize the electric field in a certain subwavelength region of the nanophotonic resonator.

Improved photoconductive gain and high responsivity in LT-GaAs on UHV annealing without arsenic overpressure

The study reports peculiar light absorption in LT-GaAs due to the prominence of arsenic vacancies (VAs), interstitials (Asi), and neutral arsenic anti-sites (AsGa0) after UHV annealing under no Arsenic vapour pressure. We compared unannealed and annealed samples’ transient absorption behaviour and vibrational modes through ultrafast transient absorption spectroscopy (UFTS) (over 2.75 eV–0.775 eV spectral range) and RAMAN spectroscopy, respectively. We found that the UHV heating of LT-GaAs has augmented the tensile strain in the film by incorporating split Asi. However, there is overall defect mitigation, as evident from the reduced TO phonon peak (RAMAN) and ∼59 meV reduction in Fermi level (UFTS). Even with reduced defects, the UFTS data for the annealed sample shows a higher switching speed and responsivity (1.75 ps faster) in the NIR range and a higher photoconductive gain in the visible region.

Symmetrical Linkage in Porphyrin Nanoring Suppressed the Electron–Hole Recombination Demonstrated by Nonadiabatic Molecular Dynamics

Macromolecular porphyrin nanorings are receiving significant attention because of their excellent optoelectronic properties. However, their efficiencies as potential solar materials are significantly affected by nonradiative charge recombination. To understand the recombination mechanism by alternating structural parameters and using tight-binding nonadiabatic molecular dynamics, we demonstrate that charge recombination depends strongly on the mode of the linker in the porphyrin nanoring. The nanoring having all-butadiyne-linkage (pristine-P8) inhibits carrier relaxation. In contrast, a partially fused nanoring (fused-P8) expedites the rate of quantum transition. An extension of the lifetime by a factor of 4 is due to the larger optical gap in pristine-P8 that reduces the NA coupling by decreasing the overlap between band edge states. Additionally, an intense phonon peak in the low-frequency region and rapid coherence loss within the electronic subsystem favors prolonging the carrier lifetime. This study provides an atomistic realization for the design of macromolecular porphyrin nanorings for the potential use in photovoltaic materials.

Localization of the Optical Phonon Modes in Boron Nitride Nanotubes: Mixing Effect of 10B Isotopes and Vacancies.

We explored the mixing effect of 10B isotopes and boron (B) or nitrogen (N) vacancies on the atomic vibrational properties of (10,0) single-wall boron nitride nanotubes (BNNTs). The forced oscillation technique was employed to evaluate the phonon modes for the entire range (0–100%) of 10B isotopes and atomic vacancy densities ranging from 0 to 30%. With increasing isotope densities, we noticed a blue shift of the Raman-active A1 phonon peak, whereas an increased density of mixed or independent B and N vacancies resulted in the emergence of a new low-frequency peak and the annihilation of the A1 peak in the phonon density of states. High-energy optical phonons were localized as a result of both 10B isotopes and the presence of mixing defects. We found an asymmetrical nature of the localization length with increasing 10B isotope content, which corresponds well to the isotope-inherited localization length of carbon nanotubes and monolayer graphene. The localization length falls abruptly with the increase in concentration of both atomic vacancies (B or N) and mixing defects (10B isotope and vacancies). These findings are critical for understanding heat conduction and nanoscopic vibrational investigations such as tip-enhanced Raman spectra in BNNTs, which can map local phonon energies.

Microwave N2 plasma nitridation of H-diamond (111) surface studied by ex situ XPS, HREELS, UPS, TPD, LEED and DFT

We report on an experimental investigation and density functional theory (DFT) modeling of the physico-chemical properties of nitrided diamond (111) surface prepared by exposing a hydrogenated diamond (111) surface to high purity nitrogen microwave plasma (MW(N2)). Ex-situ X-ray photoelectron spectroscopic analysis showed that the maximum nitrogen coverage is ∼1/4 monolayer alongside coadsorbed hydrogen, as corroborated by high-resolution electron energy loss spectroscopy (HREELS). The observed broad peak at ∼630 °C in the N2 temperature programmed desorption spectrum suggests that nitrogen desorption substantially occurs below 700 °C. As nitride surface exhibits an increase in electron affinity/work function compared to the hydrogenated surface. Low energy electron diffraction of the nitride surface exhibits a 1×1 pattern, which confirms that the MW(N2) exposure results in low-level damage to the diamond (111) surface; these results complement well with the presence of 1st order optical phonon peak (∼300 meV), the characteristic signature of a highly ordered diamond surface, on the HREEL spectrum. DFT simulations reveal that it is facile for nitrogen to insert into the CH bond on H-diamond (111), forming NH(ad) species adsorbed over C(111), which dimerizes into NH-NH(ad) at increasing coverages. The computed modes of vibration are in qualitative agreement with the HREELS data.

Nano polycrystalline structured ZnSe synthesized by the hydrothermal elemental-direct-reaction method: Structures, Raman and photoluminescence properties

Nano polycrystalline ZnSe (np-ZnSe) have been synthesized by a hydrothermal elemental direct reaction of metal Zn with Se in ethylenediamine at 180 °C for 6 h, which shows an irregular structure and is characterized with nanobelts and nanowires. A broad Raman spectrum with a strong TO phonon peak has been observed, which can be decomposed into six peaks located at ∼143 cm−1, ∼175 cm−1, ∼207 cm−1, ∼233 cm−1, ∼253 cm−1 and ∼275 cm−1, respectively, are assigned to 2 TA mode, the interaction of two-phonon with disorder, TO mode, the scattering from the simple substance Se, LO mode and the interface of ZnSe–ZnO. The A band, B band and C band from photoluminescence (PL) at 300 K are attributed to bandgap, transition from Zn interstitials to the valence band and the nano polycrystalline structure, respectively. Compared with PL at 16 K, the emissions from bandgap show blueshift with the decreasing temperature. Redshift of B bands and C bands is due to the carrier scattering with LO phonon of np-ZnSe. From PL at 16 K, the emission of ∼701 nm is attributed to the recombination from oxygen-related states. It is believed that understanding of the structures, Raman and PL properties are beneficial to the application of np-ZnSe in the optoelectronic field.

First-principles investigation of CZTS Raman spectra

${\mathrm{Cu}}_{2}{\mathrm{ZnSnS}}_{4}$ (CZTS) is an earth-abundant photovoltaic absorber material predicted to provide a sustainable solution for commercial solar applications. However, the efficiency of such solar cells is rather limited, cation disorder being often designated as the culprit. Raman spectroscopy has been widely used to characterize CZTS. Nonetheless, the interpretation of the spectra in terms of the atomic-scale disorder is precluded by the lack of consensus between theoretical and experimental results. In particular, there is a strong discrepancy in the relative intensities of the two prominent $A$ phonon peaks of the spectra. In the present study, we demonstrate that the internal parameters characterizing the position of the S atoms strongly influence these intensities. We show that agreement with experiments can be completely recovered when adopting the geometry computed using a hybrid exchange-correlation functional. Finally, using special quasirandom structures, we demonstrate that the disorder only leads to a change of the shape of the Raman peaks (tailing or leading edges, shouldering and splitting). This could be exploited to assess the quality of the sample in terms of how ordered they are.

Localized Phonon Densities of States at Grain Boundaries in Silicon.

Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope, it is of interest to explore whether extended defects in crystals such as dislocations or grain boundaries will result in measurable changes of the phonon densities of states (dos) that are reflected in the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. The boundaries are modeled by supercells with up to 160 atoms, and the vibrational densities of states were calculated by taking the Fourier transform of the velocity–velocity autocorrelation function from molecular dynamics simulations with larger supercells doubled in all three directions. In selected cases, the results were checked on the original supercells by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary, the height of the optic phonon peak in the dos at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths.

Anomalous transverse optical phonons in SnTe and PbTe

We present a study of the soft transverse optic phonon mode in SnTe in comparison to the corresponding mode in PbTe using inelastic neutron scattering and ab-initio lattice dynamical calculations. In contrast to previous reports our calculations predict that the soft mode in SnTe features a strongly asymmetric spectral weight distribution qualitatively similar to that found in PbTe. Experimentally, we find that the overall width in energy of the phonon peaks is comparable in our neutron scattering spectra for SnTe and PbTe. We observe the well-known double-peak-like signature of the TO mode in PbTe even down to $T$ = 5 K questioning its proposed origin purely based on phonon-phonon scattering. The proximity to the incipient ferroelectric transition in PbTe likely plays an important role not included in current models.