Mott Variable Range Hopping Model Research Articles

Modulating the conductivity of free-standing, flexible composite films of poly(vinylidene fluoride)/poly(3,4 ethyelenedioxythiophene):poly(styrelenesulfonate)

Free-standing, flexible, composite films of poly(vinylidene fluoride)/poly(3,4 ethyelenedioxythiophene):poly(styrelenesulfonate) (PVDF/PEDOT:PSS) were deposited. The films were characterized using Field Emission Scanning Electron Microscopy, X-Ray Diffraction, Raman, and Fourier-transformed infrared spectroscopic studies. Enhancement in the conductivity with an increase in the concentration of the additives was observed. The electrical conductivity of the high resistive PVDF films increased to ∼10−3Scm−1 with the addition of a maximum of 1.7 mL of a 1.3 wt.% aqueous dispersion of PEDOT:PSS. An increase in the conductivity of the films with temperature was observed, indicating semiconducting nature. At room temperature, the conductivity of the composite films was found to be in the range of ∼1.3 × 10−4Scm−1 to ∼7.3 × 10−3 Scm−1. The conductivity of the composite films was found to follow the Mott Variable Range Hopping model of conduction.

Enhancement of conductivity and transmittance of graphene oxide/PEDOT:PSS electrodes and the evaluation of charge transfer dynamics

Poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate), PEDOT:PSS, is a polymeric composite that can substitute indium tin oxide (ITO), enabling ITO-free organic devices. However, PEDOT:PSS films have conductivities two orders of magnitude lower than ITO due to the presence of PSS, an insulator polymer added to provide water dispersion to PEDOT. To enhance the electrical performance of the films and overcome the insulator limitations, we prepared thin films of graphene oxide (GO) and PEDOT:PSS composites. The dried films were then treated with ethylene glycol (EG). An increment of two orders of magnitude in conductivity values was observed, as well as an increase in transmittance at the visible region. Also, GO:PEDOT:PSS thin films became more hydrophobic due to the partial removal of PSS. The mass ratio that is equal to 0.058 of GO/PEDOT provides higher electrical conductivity due to higher chain orientation of PEDOT as seen in the near edge X-ray absorption fine structure and resonant Auger spectroscopy measurements. The electrical transport follows the Mott Variable Range Hopping model for low temperature, showing that the conduction occurs in three dimensions. The solvent treatment increases the characteristic conductivity and decreases the activation hopping energy, with the characteristic temperature remaining almost unchanged. It indicates that the EG treatment promotes a decrease in charge transfer time and resistivity.

Charge transport mechanism and thermoelectric behavior in Te:(PEDOT:PSS) polymer composites

Polymer thermoelectics are an emerging class of materials for realizing flexible thermoelectric devices due to its low cost, solution processability and bio-compatibility. We report a systematic investigation of the charge transport and thermoelectric properties of polymer composites comprising of tellurium (Te) nanorods and poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) spanning over a temperature range from 10 K up to 320 K. The temperature dependence of electrical resistivity for Te:(PEDOT:PSS) composites is dominated by the thermal assisted hopping following Mott’s and Efros-Shklovskii (ES) variable range hopping (VRH) mechanism. A cross-over from ES to Mott VRH model is observed near 105 K. The Seebeck coefficient and the electrical resistivity values for Te:(PEDOT:PSS) composites are found to decrease with the increase in PEDOT:PSS concentration at 300 K. Moreover, the thermal conductivity of the polymer composites is found to decrease due to enhanced phonon-phonon scattering ascribed to the acoustical mismatch between the Te-nanorods and PEDOT:PSS interface. The maximum thermoelectric figure of merit, ZT, of the polymer composites is estimated to be 0.013 ± 0.001 for Te:(PEDOT:PSS) (1:5) weight percentage. The bending test done on the polymer composite film and mechanical properties investigated using nanoindentation technique suggest the flexible nature of the composite sample which is promising for room temperature flexible thermoelectric application.

High-pressure synthesis of A-site ordered perovskite CaMn3(Fe3Mn)O12 and sequential long-range antiferromagnetic ordering and spin glass transition

An AA’3B4O12-type perovskite oxide CaMn3(Fe3Mn)O12 was synthesized at 8 GPa and 1473 K. X-ray diffraction shows a cubic crystal structure with space group Im-3. The charge states are verified by soft x-ray absorption spectroscopy to be CaMn3+3(Fe3+3Mn4+)O12, where the Ca2+ and Mn3+ are 1:3 ordered respectively at A and A′ sites, while the Mn4+ and Fe3+ are disorderly distributed at B site. The spin interaction of A′-site Mn3+ ions causes a long-range antiferromagnetic phase transition at about 39 K. Subsequently, a spin glass transition is found to occur around 14 K due to the randomly distributed Fe3+ and Mn4+ at B site. Moreover, the spin glass behavior follows a dynamic scaling power law. The temperature dependent resistivity can be well fitted by a 3D Mott variable-range hopping model, indicating the insulating nature of CaMn3(Fe3Mn)O12 due to the strong electron correlation effects.

Growth of high quality Sr2IrO4 epitaxial thin films on conductive substrates**Project supported by the National Natural Science Foundation of China (Grant Nos. 51627901 and 11574287), the National Key Research and Development Program of China (Grant No. 2016YFA0401004), and Hefei Science Center-Chinese Academy of Sciences (Grant No. 2016HSC-IU004). X. Z. acknowledges the support of the Youth Innovation Promotion Association of Chinese

Ruddlesden–Popper iridium oxides have attracted considerable interest because of the many proposed novel quantum states that arise from the large spin–orbit coupling of the heavy iridium atoms in them. A prominent example is the single layer Sr2IrO4, in which superconductivity has been proposed under electron doping. However, the synthesis of Sr2IrO4 high quality thin films has been a huge challenge due to the easy formation of impurities associated with different numbers of SrO layers. Thus techniques to optimize the growth of pure phase Sr2IrO4 are urgently required. Here we report the deposition of high quality Sr2IrO4 thin films on both insulating SrTiO3 and conducting SrTiO3:Nb substrates using pulsed laser deposition assisted with reflective high-energy electron diffraction. The optimal deposition temperature of Sr2IrO4 epitaxial films on SrTiO3:Nb substrates is about 90 °C lower than that on SrTiO3 substrates. The electrical transports of high quality Sr2IrO4 films are measured, which follow the three-dimensional Mott variable-range hopping model. The film magnetizations are measured, which show weak ferromagnetism below ∼240 K with a saturation magnetization of /Ir at 5 K. This study provides applicable methods to prepare high quality 5d Sr2IrO4 epitaxial films, which could be extended to other Ruddlesden–Popper phases and potentially help the future study of exotic quantum phenomena in them.

Electrical conduction in 70V2O5·30TeO2 (mol%) pelletized glasses annealed in an H2 gas atmosphere

The direct-current electrical conductivities (σ) of 70V2O5∙30TeO2 (mol%) pelletized glasses annealed in an H2 gas atmosphere at 473 K were determined in the temperature (T) range of 322–473 K. Based on the log(σT)–T−1 relation in the considered temperature range, the electrical conduction is discussed in detail. The conduction of each glass sample at high temperatures (T > ~460 K) was attributed to nonadiabatic small polaron hopping. At T < ~353 K, the slopes of the curves were the smallest. The smallest slopes at temperatures below ~353 K are discussed based on the Mott's and Greaves' variable-range hopping (VRH) conduction models. The tunneling factors α and densities of states at the Fermi level N(EF) estimated using the Mott's VRH model confirmed that this model was not suitable. On the other hand, the α and N(EF) values estimated by the Greaves' VRH model indicated that the conduction was attributed to the Greaves VRH. The values of WD (0.0765 ± 0.0006 to 0.108 ± 0.0006 eV) calculated using the Greaves' model were on the same order as those of the reported vanadate binary glasses. These parameters demonstrated that the Greaves' VRH model was applicable for the considered glasses and could be used to explain the conductivity data at temperatures below ~354 K.

Direct Synthesis of Graphene with Tunable Work Function on Insulators via In Situ Boron Doping by Nickel-Assisted Growth

Work function engineering, a precise tuning of the work function, is essential to achieve devices with the best performance. In this study, we demonstrate a simple technique to deposit graphene on insulators with in situ controlled boron doping to tune the work function. At a temperature higher than 1000 °C, the boron atoms substitute carbon sites in the graphene lattice with neighboring carbon atoms, leading to the graphene with a p-type doping behavior. Interestingly, the involvement of boron vapor into the system can effectively accelerate the reaction between nickel vapor and methane, achieving a fast graphene deposition. The changes in surface potential and work function at different doping levels were verified by Kelvin probe force microscopy, for which the work function at different doping levels was shifted between 20 and 180 meV. Finally, the transport mechanism followed by the Mott variable-range hopping model was found due to the strong disorder nature of the system with localized charge-carrie...

Crossover from Efros-Shklovskii to Mott Variable Range Hopping in Amorphous Thin NixSi(subscript 1-x) Films

The temperature dependence of the electrical conductivity of insulating amorphous Ni(subscript x)Si(subscript 1-x) alloys is studied in the temperature range 1-160 K. At low temperatures, Efros-Shklovskii (ES) variable range hopping (VRH) is observed. This is assumed to occur because of the creation of the Coulomb gap (CG) in the vicinity of the Fermi level. With increasing temperature, the CG vanishes and the measured conductivity can be described by the Mott VRH model, where the density of states is constant. The criterion of the crossover ES from to Mott VRH is assessed by extracting the related parameters.

Erratum to: Study of Structural, Electrical, and Magnetic Properties of Layered Perovskite Oxides LnSr2TiFeO7 (Ln = Nd, Gd)

We report here the synthesis and results of electrical resistivity and magnetic susceptibility measurements in the low temperature range of the rare-earth-doped bilayered system LnSr2TiFeO7 (Ln = Nd, Gd). Both phases crystallize with a tetragonal unit cell in space group I4/mmm. The phases exhibit insulating behavior, and the electrical transport mechanism agrees with the Mott variable-range hopping model. The decrease in electrical resistivity with decreasing ionic size of the rare-earth ion could be attributed to enhancement of the three-dimensional (3D) character along the c-axis because of the proximity of the (Ti/Fe)O2 and (Ln,Sr)O layers along the c-axis. The magnetic studies suggest that the phases are antiferromagnetic and the antiferromagnetic behavior could be due to the Fe3+-O–Fe3+ exchange interaction.

Effect of thermal annealing on some electrical properties and optical band gap of vacuum evaporated Se65Ga30In5 thin films

Electrical properties and optical band gap of amorphous Se65Ga30In5 thin films, which were thermally evaporated onto chemically cleaned glass substrates, have been studied before and after thermal annealing at temperatures above the glass transition temperature and below the crystallization temperature. The I–V characteristics, which were recorded in the temperature range (200–300 K), were obtained at different voltages and exhibit an ohmic and non-ohmic behavior at low (0–5 V) and high (5–18 V) voltages, respectively, for annealed and as-prepared films. Analysis of the experimental data in the high voltage range confirms the presence of space charge limited conduction (SCLC) for annealed and as-prepared films. The dependence of DC conductivity on temperature in the low voltage region shows two types of conduction channels: The first is in the range 270–300 K and the other at the lower temperature range (200–270 K). The conduction in the first region is due to thermally activated process, while in the other is due variable range hopping (VRH) of charge carriers in the band tails of the localized states. After annealing, the conductivity has been found to increase but the activation energy decreases. This is attributed to rupturing of Se–In weak bonds and formation of Se–Ga strong bonds. This process changes the concentration of defects in the films which in turn decreases the density of states N(EF) as predicted by Mott's VRH model. Analysis of the absorption coefficient of annealed and as-prepared films, in the wavelength range 300–700 nm, reveals the presence of parabolic densities of states at the edges of both valence and conduction bands in the studied films. The optical band gap (Eg) was obtained through the use of Tauc's relation and is found to decrease with annealing temperature.

Diffusivity in one-dimensional generalized Mott variable-range hopping models

We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variable-range hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We prove various estimates on the low-temperature behavior which confirm and extend previous work by physicists.

Thermal and electrical properties of some single and mixed transition-metal ions-doped tellurite glasses

Two sets of tellurium-based glasses doped with vanadium and vanadium-cobalt oxides have been prepared by melt quench method and investigated for density, glass-transition temperature, specific-heat capacity and dc electrical conductivity in the temperature range 300–500 K. Thermal stability, fragility and glass-forming tendency in these systems have been estimated. Thermal stability of these glasses was found to be larger than for similar systems. The dc electrical conductivity has been analyzed in the light of Mott's small polaron hopping (SPH) and Mott's and Greave's variable range hopping (VRH) models. The electrical conduction was confirmed to be due to non-adiabatic SPH. The conductivity behavior at temperatures above TD (=θD/2) (where θD is Debye's temperature) was found to be in agreement with Mott's SPH model and at low temperatures behaved in accordance with Mott's VRH model. The temperature regions in which Mott's SPH and VRH models hold for the present systems are found to be different from similar systems already reported. Various physical parameters in these models such as, activation energy, polaron hopping energy, etc., were determined. It is for the first time that the above-mentioned properties have been investigated for the present mixed transition-metal ions-doped glasses.

High-pressure low-temperature electrical properties of template-synthesized polypyrrole at low synthesis temperature: dimensional crossover under pressure

We have measured the pressure and temperature dependence of the electrical conductivity of thin films composed of doped polypyrrole microtubules with a diameter of 400 nm. The microtubules have been synthesized at 0°C in a host membrane. The wall thickness of these microtubules can be controlled by a variation of the synthesis time. The results of these measurements are interpreted using the Mott Variable Range Hopping model. Samples composed of thin wall microtubules show a higher characteristic dimension of the conduction process than samples composed of thick wall microtubules. Under pressure, the dimension of the hopping process increases and three-dimensional behavior prevails for all investigated wall thicknesses of the microtubules. Under pressure samples composed of thin wall microtubules show also a change of the temperature dependence of the pre-exponential factor in the Mott law. The results suggest that the microtubules are not homogeneous but are composed of layers with different electrical conductivity behavior.

Colossal magnetoresistance of the variable range hopping regime in the manganites

Evidence for variable range hopping (VRH) is presented in resistivity measurements in thin films and bulk samples of different substituted x=0.3 manganese perovskites. The necessity to modify the Mott VRH model is shown and we have developed a model based on magnetic localization hopping, which is used to reproduce temperature and field dependence of resistivity in these mixed-valence compounds.

Physical properties of polypyrrole films containing tetracyanonickelate(II) anions, PPy–Ni(CN)4

Polypyrrole–tetracyanonickelate, PPy–Ni(CN)4, has been synthesized in thin-film form by electrochemical oxidation of pyrrole in aqueous or non-aqueous media. The room-temperature electrical conductivity of one of the films (122 S cm–1) is the highest reported to date for any PPy–metal anion system. The temperature dependence of the conductivity is consistent with the Mott variable-range hopping model. Some of the films show good stability in air at room temperature, their conductivity decreasing by less than 7% over 50 days.

Electrical conductivity and thermoelectric power of polypyrrole with different doping levels

The electrical conductivity and absolute thermoelectric power of the conducting polymer polypyrrole have been measured between approximately 4 K and 350 K. Normally-doped films had a conductivity of 26 Ω −1 cm −1, whilst lightly-doped films had a conductivity of 8 Ω −1 cm −1. The Mott variable-range hopping model for electrical conductivity is obeyed at higher temperatures for both types. The thermoelectric power is approximately linear in temperature, reaching about 5 μV K −1 at 200 K, but is sublinear at higher temperatures and becomes constant above about 300 K. The Kuivalainen model, which explains the reported anomaly between optical and d.c. electrical conductivity, gives a good fit to the experimental data.

Interaction effects and thermoelectric power in low-temperature hopping

The effect of electron-electron interactions on the thermoelectric power for hopping transport in two and three dimensions is calculated in the low-temperature limit. While the conductivity requires a very precise measurement to extract a temperature exponent with enough precision to determine the role of the interactions, it is shown that the thermopower behaviour will reflect the presence of interactions in an unambiguous manner. In contrast to a Mott variable-range hopping model where the thermopower decreases to zero as the temperature decreases (S=0 at T=0), the thermopower in an Efros interaction mode, should approach a non-zero constant as T to 0.

Anomalous magnetoresistance in rf-sputtered hydrogenated amorphous silicon

Magnetoresistance (MR) measurements for magnetic fields up to 10 T have been made on amorphous-silicon---hydrogen ($a$-Si: H) thin films prepared by reactive rf sputtering. The effect of a systematic decrease of the gap state and spin densities due to the hydrogenation on MR has been investigated. Electron-spin-resonance (ESR) and dark dc conductivity measurements, which give supporting information on the electrical behavior of $a$-Si: H, have also been made in the temperature range 30-500 K. The Movaghar-Schweitzer-Osaka hopping model, in which MR is a result of the magnetic field dependence of the spin-flip relaxation time of the charge-carrier spin, accounts well for the results at temperatures $Tg150$ K. With the fitting of this model to the MR results, values of the positive Hubbard-type repulsion energy ${U}_{\mathrm{eff}}$ for doubly occupied gap states near the Fermi level are obtained, ${U}_{\mathrm{eff}}=0.21$ eV for the $a$-Si films and ${U}_{\mathrm{eff}}=0.31\ensuremath{-}0.32$ eV for the $a$-Si: H films. It is concluded that the change of sign in MR at low fields with decreasing spin density is due merely to a narrowing in the distribution of the hopping relaxation times. Some of the parameters needed in the analysis of the MR results are determined by the fitting of Mott's variable range-hopping model to the conductivity data of the films with ${N}_{s}\ifmmode\times\else\texttimes\fi{}{10}^{18}$ spins ${\mathrm{cm}}^{\ensuremath{-}3}$. Quite reasonable values of Mott's parameters are obtained if high values for jump-rate prefactors ${\ensuremath{\nu}}_{0}={10}^{19} \mathrm{to} {10}^{20}$ ${\mathrm{s}}^{\ensuremath{-}1}$ are accepted, which values are also needed to account for the magnitudes of the MR effect and the ESR linewidth.