High-energy Optical Phonons Research Articles

Exceptionally high hole mobilities in monolayer group-IV monochalcogenides GeTe and SnTe

Two-dimensional semiconductors are considered as promising channel materials for next-generation nanoelectronics devices, while their practical applications are typically limited by their low mobilities. In this work, using first-principles calculations combined with the Boltzmann transport formalism involving electron–phonon coupling, we study the transport properties of monolayer group-IV monochalcogenides (MX, M = Ge, Sn; X = S, Se, and Te). We find that the GeTe and SnTe possess exceptionally high hole mobilities, which even reach 835 and 1383 cm2/V s, respectively, at room temperature. More interestingly, the hole mobilities increase with the increase in the atomic number of “X” in MXs when “M” remains the same. Such a trend is mainly due to the increased group velocity and decreased density of states, and the latter plays a significant role in determining the carrier scattering space and relaxation time. Meanwhile, different from the acoustic deformation potential theory, we find that the high-energy optical phonons contribute a lot to the scattering. Our work shows that the monolayer GeTe and SnTe are promising p-type semiconductors in nanoelectronics and reveals the intrinsic connection between phonons, charge density of states, and mobility, which would shed light on exploring the two-dimensional materials with high mobility.

General rules and applications for screening high phonon-limited mobility in two-dimensional semiconductors

Two-dimensional (2D) semiconductors with high mobility comparable to three-dimensional (3D) Si or GaAs are still lacking, hindering the development of high-performance 2D devices. In this work, based on the phonon-energy resolved matching function between the electronic band structure and the phonon spectrum recently proposed in our group, we provide some general rules for screening possible high-mobility 2D semiconductors. In general, a 2D semiconductor with high sound velocity, small effective mass, large atomic mass, high-energy optical phonons, small Born effective charge, large effective in-plane dielectric constant, and large effective layer thickness, is likely to have high phonon-limited mobility. Additionally, if the semiconductor has multiple valleys, the mobility-limiting factor due to intervalley scattering can be weak if the valleys are far apart in reciprocal space and have out-of-plane orbitals. Guided by these rules, we have systematically explored the mobility of traditional semiconductors at the 2D limit (2DTSs), which have been theoretically predicted and experimentally realized recently. Seven 2DTSs are found to have mobilities close to or exceeding 1000 $\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Most notably, BSb reaches record-high values of several thousand $\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ at room temperature and the experimentally synthesized 2D AlSb has an electron mobility of 921.9 $\mathrm{c}{\mathrm{m}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Using BSb, InN, and AlSb as examples, we reveal that, although the high mobilities of these systems are attributed to different underlying scattering mechanisms, they can all be understood from our proposed general rules. The present work demonstrates that 2DTSs can achieve comparable carrier mobility to 3D, thus opening possible doors to 2D high-performance electronic devices.

Joule heating in bad and slow metals

Heat supplied to a metal is absorbed by the electrons and then transferred to the lattice. In conventional metals energy is released to the lattice by phonons emitted from the Lindhard continuum. However in a 'bad' metal, with short mean free path, the low energy Lindhard continuum is destroyed. To describe energy transfer to the lattice in these cases we obtain a general Kubo formula for the energy relaxation rate in terms of the electronic density spectral weight \text{lm} \, G^R_{nn}(\omega_{k},k)lmGnnR(ωk,k) evaluated on the phonon dispersion \omega_kωk. We apply our Kubo formula to the high temperature Hubbard model, using recent data from quantum Monte Carlo and experiments in ultracold atoms to characterize \text{lm} \, G^R_{nn}(\omega_{k},k)lmGnnR(ωk,k). We furthermore use recent data from electron energy-loss spectroscopy to estimate the energy relaxation rate of the cuprate strange metal to a high energy optical phonon. As a second, distinct, application of our formalism we consider 'slow' metals. These are defined to have Fermi velocity less than the sound velocity, so that particle-hole pairs are kinematically unable to emit phonons. We obtain an expression for the energy relaxation rate of a slow metal in terms of the optical conductivity.

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.

Flat phonon modes driven ultralow thermal conductivities in Sr3AlSb3 and Ba3AlSb3 Zintl compounds

Searching for compounds with intrinsic low lattice thermal conductivity has been proven a successful strategy for achieving high thermoelectric performance. Herein, employing density functional theory calculations combined with electron and phonon Boltzmann transport theories, we report that Sr3AlSb3 and Ba3AlSb3 within the Zintl 3–1–3 compositional family exhibit record low thermal conductivities of 0.78 and 0.55 W/mK at room temperature, respectively. These low thermal conductivities are rooted in low-energy optical phonon modes with strong anharmonicity and the emergence of high-energy flat optical phonon modes with zero contribution to the lattice thermal conductivity. Heavier cationic atoms are found to soften low-lying optical phonon modes, which enhance phonon scattering and, therefore, favor a lower thermal conductivity. These combined characteristics lead to high and balanced figure of merit values around 2.3 for Zintl Ba3AlSb3 at both optimal p-type and n-type doping and high temperature. Our work highlights the important role of flat optical phonon modes on designing promising thermoelectric materials with intrinsic low thermal conductivity.

Strong anharmonicity in tin monosulfide evidenced by local distortion, high-energy optical phonons, and anharmonic potential

Recently, SnSe has been found to possess a remarkable thermoelectric performance. As an isostructural compound to SnSe, SnS contains a more environmentally compatible and earth abundant element, which enables SnS a promising thermoelectric material for commercial application. In this work, we have performed systematic studies of the crystal structures and the lattice vibrations by means of neutron total scattering, Raman scattering measurements, and first-principle calculations. A structural transition has been observed by both temperature dependent neutron diffraction and pressure dependent Raman scattering. The lattice anharmonicity has been revealed by the local distortion induced by the Sn $5{s}^{2}$ lone pair and is also evidenced from the temperature dependent atomic displacement parameter of the Sn atom. By separating the intrinsic anharmonicity and lattice thermal expansion effects, we found that the former plays the primary role in the softening of the Raman active modes. Such anharmonicity has also been observed experimentally by the linewidth broadening of the high-energy optical modes and confirmed by frozen phonon calculations. Furthermore, our frozen phonon calculation reveals the presence of the quartic anharmonicity potential of those high-energy optical modes vibrating along the $b$ axis. Our data will contribute to a better understanding of the thermal conduction in SnS, which will be beneficial for the enhancement of the thermoelectric performance of this material.

Strong lattice anharmonicity exhibited by the high-energy optical phonons in thermoelectric material

Thermoelectric material SnSe has aroused world-wide interests in the past years, and its inherent strong lattice anharmonicity is regarded as a crucial factor for its outstanding thermoelectric performance. However, the understanding of lattice anharmonicity in SnSe system remains inadequate, especially regarding how phonon dynamics are affected by this behavior. In this work, we present a comprehensive study of lattice dynamics on Na0.003Sn0.997Se0.9S0.1 by means of neutron total scattering, inelastic neutron scattering, Raman spectroscopy as well as frozen-phonon calculations. Lattice anharmonicity is evidenced by pair distribution function, inelastic neutron scattering and Raman measurements. By separating the effects of thermal expansion and multi-phonon scattering, we found that the latter is very significant in high-energy optical phonon modes. The strong temperature-dependence of these phonon modes indicate the anharmonicity in this system. Moreover, our data reveals that the linewidths of high-energy optical phonons become broadened with mild doping of sulfur. Our studies suggest that the thermoelectric performance of SnSe could be further enhanced by reducing the contributions of high-energy optical phonon modes to the lattice thermal conductivity via phonon engineering.

Phonon localization in single wall carbon nanotube: Combined effect of 13C isotope and vacancies

The combined effect of 13C isotope doping and vacancies on the phonon properties of a single-wall carbon nanotube is theoretically investigated using the forced oscillation method. The phonon density of states (PDOS) is calculated for all (0%–100%) 13C isotope contents and wide (0%–30%) vacancy concentrations. We found a redshift of the Raman active E2g peak in the PDOS with increasing isotope contents, while the disappearance of the E2g peak and the appearance of a new sharp peak in the low-energy region with increasing combined defects. Both 13C isotope and combined defects cause the localization of the high-energy optical phonons. We calculated the typical mode patterns for the in-plane longitudinal optical phonon to visualize the localization phenomena elaborately at the presence of isotope and vacancies. The calculated average localization length shows an asymmetric behavior with increasing 13C isotope concentrations which is in good agreement with the 13C isotope dependence localization length of single-layer graphene. We noticed that a typical localization length is on the order of ∼1 nm at 70% isotope concentrations. The combined effect of 13C isotope and vacancies shows an abruptly decreasing localization length with increasing defect densities. These results are important to understand the heat conduction as well as nanoscopic vibrational studies such as tip-enhanced Raman spectra in carbon nanotubes where the local phonon energies may be mapped.

MgB4 trilayer film: A four-gap superconductor

Since the discovery of two-gap superconductivity in bulk ${\mathrm{MgB}}_{2}$, many efforts have been devoted to searching for multigap superconductors. Recently, a monolayer of ${\mathrm{MgB}}_{2}$ and a trilayer film of ${\mathrm{AlB}}_{4}$ were predicted to be robust three-gap superconductors. Here we investigate using the fully anisotropic Migdal-Eliashberg theory the superconducting behaviors in a series of boron-based monolayers and trilayer films that are dynamically stable but not synthesized experimentally heretofore. Remarkably, we find that the trilayer film of ${\mathrm{MgB}}_{4}$ has an exciting four-gap superconducting nature with a high transition temperature ${T}_{c}\ensuremath{\sim}52$ K. We demonstrate that this high-${T}_{c}$ four-gap superconductivity is closely related to the Fermi surface exhibiting an unusually strong electron-phonon coupling with evident four-region distribution characteristics. The electron-lattice coupling is dominated by the acoustic modes of a softening kink and the high-energy optical phonons around the Brillouin-zone center, of which the former ones place the system on the verge of a latent charge density wave state. To our knowledge, no material with more than three superconducting gaps has been reported. At the same time, we also show that the ${\mathrm{GaB}}_{4}$ trilayer film has a robust three-gap nature with ${T}_{c}\ensuremath{\sim}51$ K, and the trilayer films of ${\mathrm{BeB}}_{4}$ and ${\mathrm{LiB}}_{4}$ are two-gap superconductors with ${T}_{c}$'s of $\ensuremath{\sim}39$ and 32 K, respectively.

Excited-state band mapping and momentum-resolved ultrafast population dynamics in In/Si(111) nanowires investigated with XUV-based time- and angle-resolved photoemission spectroscopy

We investigate the excited state electronic structure of the model phase transition system In/Si(111) using femtosecond time- and angle-resolved photoemission spectroscopy (trARPES) with an XUV laser source at 500 kHz . Excited state band mapping is used to characterize the normally unoccupied electronic structure above the Fermi level in both structural phases of indium nanowires on Si(111): the metallic (4x1) and the gapped (8x2) phases. The extracted band positions are compared with the band structure calculated using density functional theory (DFT) within both the LDA and GW approximations. While good overall agreement is found between the GW calculated band structure and experiment, deviations in specific momentum regions may indicate the importance of excitonic effects not accounted for at this level of approximation. To probe the dynamics of these excited states, their momentum-resolved transient population dynamics are extracted. The transient intensities are then simulated by a spectral function determined by a state population employing a transient elevated electronic temperature as determined experimentally. This allows the momentum-resolved population dynamics to be quantitatively reproduced, revealing important insights into the transfer of energy from the electronic system to the lattice. In particular, a comparison between the magnitude and relaxation time of the transient electronic temperature observed by trARPES with those of the lattice as probed in previous ultrafast electron diffraction studies imply a highly non-thermal phonon distribution at the surface following photo-excitation. This suggests the energy from the excited electronic system is initially transferred to high energy optical phonon modes followed by cooling and thermalization of the photo-excited system by much slower phonon-phonon coupling.

Phonon-induced linewidths of graphene electronic states

The linewidths of the electronic bands originating from the electron-phonon coupling in graphene are analyzed based on model tight-binding calculations and experimental angle-resolved photoemission spectroscopy (ARPES) data. Our calculations confirm the prediction that the high-energy optical phonons provide the most essential contribution to the phonon-induced linewidth of the two upper occupied $\sigma$ bands near the $\bar{\Gamma}$-point. For larger binding energies of these bands, as well as for the $\pi$ band, we find evidence for a substantial lifetime broadening from interband scattering $\pi \rightarrow \sigma$ and $\sigma \rightarrow \pi$, respectively, driven by the out-of-plane ZA acoustic phonons. The essential features of the calculated $\sigma$ band linewidths are in agreement with recent published ARPES data [F. Mazzola et al., Phys.~Rev.~B. 95, 075430 (2017)] and of the $\pi$ band linewidth with ARPES data presented here.

The ac conductivity of binary chalcogenide glasses $${\text {Se}}_{100-x}{\text {X}}_{x}$$ Se 100 - x X x (X = Ge, In, Te)

The random free energy barrier hopping model is used to investigate the temperature and frequency dependent ac conductivity $$\sigma _{ac}(\omega )$$ of binary chalcogenide glasses $${\text {Se}}_{100-x}{\text {X}}_{x}$$ (X = Ge, In, Te). The temperature dependent barrier height leads to Meyer–Neldel (MN) rule. The calculated MN energy $$E_{MN}$$ is in good agreement with the experimental estimates. The $$\sigma _{ac}(\omega )$$ is taken as the sum of bipolaron and single polaron hopping conductivities $$\sigma _{b}(\omega )$$ and $$\sigma _{s}(\omega ),$$ respectively. The calculated results are in close agreement with the experimental data. It is found that $$\sigma _{s}$$ is smaller by orders of magnitude than $$\sigma _{b}$$ in $${\text {Se}}_{100-x}{\text {Ge}}_{x}$$ alloys in the temperature range 250–400 K, while in $${\text {Se}}_{100-x}{\text {Te}}_{x}$$ alloys $$\sigma _{ac}(\omega )$$ is mainly due to $$\sigma _{b}$$ in the temperature range 150–250 K and $$\sigma _{s}$$ becomes significant above 250 K. However in $${\text {Se}}_{100-x}{\text {In}}_{x}$$ alloys in the temperature range 303–333 K, $$\sigma _{b}$$ is nearly temperature independent and $$\sigma _{ac}(\omega )$$ is mainly due to $$\sigma _{s}.$$ It is found that acoustic phonons assist hopping process in $${\text {Se}}_{100-x}{\text {Ge}}_{x}$$ and $${\text {Se}}_{100-x}{\text {Te}}_{x}$$ alloys, while both high energy acoustic and low energy optical phonons assist hopping process in $${\text {Se}}_{100-x}{\text {In}}_{x}$$ alloys.

Role of Biasing and Device Size on Phonon Scattering in Graphene Nanoribbon Transistors

We study the noncoherent transport due to electron–phonon (e-ph) interaction in graphene nanoribbon (GNR) field-effect transistors (GNRFETs) using nonequilibrium Green’s function method in mode space. Phonon dispersion calculations in conjunction with the e-ph interaction computations show that in an armchair GNR, only a small number of phonon modes are coupled to the carriers. Our simulation shows that under a threshold gate voltage, the drain–source current is diminished by the low-energy phonons such as acoustic phonon modes and radial-breathing-like phonon modes, while at great biases of the gate, the current drop is essentially due to high-energy optical phonon modes. The effect of drain voltage on scattering process is discussed, which shows that at higher drain voltages, the ballisticity decreases. We also explore the phonon scattering dependence on the dimensions of GNRFET channel. In larger width ribbon, the impact of phonon scattering decreases. The channel with a length of 30 nm is ballistic up to 90%, and only when its length is increased to approximately 180 nm, transport becomes semiballistic, which infers to an effective mean free path of ~200 nm.

Lattice-mediated magnetic order melting in TbMnO3

Recent ultrafast magnetic-sensitive measurements [Phys. Rev. B 92, 184429 (2015) and Phys. Rev. B 96, 184414 (2017)] have revealed a delayed melting of the long-range cycloid spin-order in TbMnO$_3$ following photoexcitation across the fundamental Mott-Hubbard gap. The microscopic mechanism behind this slow transfer of energy from the photoexcited carriers to the spin degrees of freedom is still elusive and not understood. Here, we address this problem by combining spectroscopic ellipsometry, ultrafast broadband optical spectroscopy and ab initio calculations. Upon photoexcitation, we observe the emergence of a complex collective response, which is due to high-energy coherent optical phonons coupled to the out-of-equilibrium charge density. This response precedes the magnetic order melting and is interpreted as the fingerprint of the formation of anti-Jahn Teller polarons. We propose that the charge localization in a long-lived self-trapped state hinders the emission of magnons and other spin-flip mechanisms, causing the energy transfer from the charge to the spin system to be mediated by the reorganization of the lattice. Furthermore, we provide evidence for the coherent excitation of a phonon mode associated with the ferroelectric phase transition.

Interface defect-assisted phonon scattering of hot carriers in graphene

The broadband and ultrafast photoresponse of graphene has been extensively studied in recent years, although the photoexcited carrier dynamics is still far from being completely understood. Different experimental approaches imply either one of two fundamentally different scattering mechanisms for hot electrons. One is high-energy optical phonons, while the other is disorder-driven supercollisions with acoustic phonons. However, the concurrent relaxation via both optical and acoustic phonons has not been considered so far, hindering the interpretation of different experiments within a unified framework. Here we expand the optical phonon-mediated cooling model, to include electron scattering with the acoustic phonons. By assuming the enhancement of electron-acoustic phonon supercollisions from the localized defect at the photothermoelectric current-generating interface, we provide a broader perspective to the ultrafast photoresponse of graphene, highlighting the previously overlooked effect of the interface for cooling dynamics. We show that the transient photothermoelectric response, which has been attributed exclusively to supercollisions, can be successfully explained without rejecting the established optical phonon relaxation pathway, demonstrating that the two cooling mechanisms are not mutually exclusive but complement each other.

Molecular dynamics study of phonon transport in graphyne nanotubes

We determine the thermal conductivities of α, β, and γ graphyne nanotubes (GNTs) as well as of carbon nanotubes (CNTs) using molecular dynamics simulations and the Green-Kubo relationship over the temperature range 50–400 K. We find that GNTs demonstrate considerably lower thermal conductivity than CNTs with the same diameter and length. Among α, β, and γ-GNTs, γ-GNT has the highest thermal conductivity at all temperatures. By comparing the phonon transport properties of GNTs with CNTs, we find that as the fraction of acetylene bonds in the atomic network increases, the population of high-energy optical phonons increases. This enhances phonon-phonon scattering, and reduces the mean free path, adversely affecting the thermal conductivity of GNTs relative to CNTs. Also reducing the thermal conductivity of GNTs relative to CNTs is the considerably lower acoustic phonon group velocities for the former as well as the lower volumetric heat capacity of GNTs. Optical phonons in α-GNT are high in energy (0.26 eV) with a high population number, making them more energetic than the electronic direct band gap and significantly more energetic than the thermal energy at room temperature. Therefore, we suggest α-GNT as a potential candidate for phonovoltaic energy conversion applications.

Superconductivity in the two-dimensional electron gas induced by high-energy optical phonon mode and large polarization of theSrTiO3substrate

Theory of superconductivity generated in one atomic layer thick two dimensional electron gas by a single flat band of high energy longitudinal optical phonons is considered. The polar dielectric $SrTiO_{3}$ (STO) exhibits such an energetic phonon mode and the 2DEG is created both when one unit cell $FeSe$ layer is grown on its $\left( 100\right) $ surface and on the interface with another dielectric like $LaAlO_{3}$ (LAO). We obtain a quantitative description of both systems solving the gap equation for $T_{c}$ without making use of approximations like the Kirzhnits Ansatz for arbitrary chemical potential $\mu $, electron-phonon coupling $\lambda $ and the phonon frequency $\Omega $, and direct (RPA) electron-electron repulsion strength $\alpha $. The high temperature superconductivity in 1UC$FeSe$/STO is possible due to a combination of three factors: high LO phonon frequency, large electron-phonon coupling $\lambda \sim 0.5$ and huge dielectric constant of the substrate suppression the Coulomb repulsion. It is shown that very low density electron gas in the interfaces is still capable of generating superconductivity of the order of $0.1$ K in LAO/STO. Superconductivity persists even on the band edge $\mu =0$.

Phonocatalysis. An ab initio simulation experiment

Using simulations, we postulate and show that heterocatalysis on large-bandgap semiconductors can be controlled by substrate phonons, i.e., phonocatalysis. With ab initio calculations, including molecular dynamic simulations, the chemisorbed dissociation of XeF6 on h-BN surface leads to formation of XeF4 and two surface F/h-BN bonds. The reaction pathway and energies are evaluated, and the sorption and reaction emitted/absorbed phonons are identified through spectral analysis of the surface atomic motion. Due to large bandgap, the atomic vibration (phonon) energy transfer channels dominate and among them is the match between the F/h-BN covalent bond stretching and the optical phonons. We show that the chemisorbed dissociation (the pathway activation ascent) requires absorption of large-energy optical phonons. Then using progressively heavier isotopes of B and N atoms, we show that limiting these high-energy optical phonons inhibits the chemisorbed dissociation, i.e., controllable phonocatalysis.

Crystal dynamics and thermal properties of neptunium dioxide

We report an experimental and theoretical investigation of the lattice dynamics and thermal properties of the actinide dioxide NpO$_2$. The energy-wavevector dispersion relation for normal modes of vibration propagating along the $[001]$, $[110]$, and $[111]$ high-symmetry lines in NpO$_2$ at room temperature has been determined by measuring the coherent one-phonon scattering of X-rays from a $\sim$1.2 mg single-crystal specimen, the largest available single crystal for this compound. The results are compared against ab initio phonon dispersions computed within the first-principles density functional theory in the generalized gradient approximation plus Hubbard $U$ correlation (GGA+$U$) approach, taking into account third-order anharmonicity effects in the quasiharmonic approximation. Good agreement with the experiment is obtained for calculations with an on-site Coulomb parameter $U = 4$ eV and Hund's exchange $J= 0.6$ eV in line with previous electronic structure calculations. We further compute the thermal expansion, heat capacity, thermal conductivity, phonon linewidth, and thermal phonon softening, and compare with available experiments. The theoretical and measured heat capacities are in close agreement with another. About 27% of the calculated thermal conductivity is due to phonons with energy higher than 25 meV ($\sim$ 6 THz ), suggesting an important role of high-energy optical phonons in the heat transport. The simulated thermal expansion reproduces well the experimental data up to about 1000 K, indicating a failure of the quasiharmonic approximation above this limit.

Random free energy barrier hopping model for ac conduction in chalcogenide glasses

The random free energy barrier hopping model is proposed to explain the ac conductivity (σac) of chalcogenide glasses. The Coulomb correlation is consistently accounted for in the polarizability and defect distribution functions and the relaxation time is augmented to include the overlapping of hopping particle wave functions. It is observed that ac and dc conduction in chalcogenides are due to same mechanism and Meyer-Neldel (MN) rule is the consequence of temperature dependence of hopping barriers. The exponential parameter s is calculated and it is found that s is subjected to sample preparation and measurement conditions and its value can be less than or greater than one. The calculated results for a − Se, As2S3, As2Se3 and As2Te3 are found in close agreement with the experimental data. The bipolaron and single polaron hopping contributions dominates at lower and higher temperatures respectively and in addition to high energy optical phonons, low energy optical and high energy acoustic phonons also contribute to the hopping process. The variations of hopping distance with temperature is also studied. The estimated defect number density and static barrier heights are compared with other existing calculations.