Variable-range Hopping Conduction Research Articles

High-field hopping magnetotransport in kesterites

Transport properties of the kesterite-like single crystals of Cu2ZnSnS4, Cu2ZnSnxGe1−xSe4 and Cu2ZnGeS4 are investigated in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping (VRH) conduction is established by investigations of the resistivity, ρ (T), in all the materials mentioned above within broad temperature intervals of ΔTv4 ∼ 50–150 K, 50–250 K and 100–200 K, respectively. In addition, the Shklovskii-Efros VRH conductivity below Tv2 ∼ 3–4 K, the nearest-neighbour hopping (NNH) charge transfer between T ∼ 250–320 K and the conductivity by activation of holes on the mobility threshold at temperatures outside ΔTv4, respectively, are observed in these materials. In Cu2ZnSnS4, magnetoresistance (MR) contains only a positive contribution, connected mainly to a shrinkage of impurity wave functions by the magnetic field. At the same time, a negative contribution to MR, attributable to interference effects in VRH, is observed in Cu2ZnSnxGe1−xSe4 and, especially, in Cu2ZnGeS4. The joint analysis of the MR and ρ (T) data has yielded important electronic parameters of the materials. This includes widths of the acceptor band W and of the Coulomb gap Δ, the NNH activation energy En, the localization radius a, the acceptor concentration NA and the density of the localized states at the Fermi level, g (μ). A dramatic increase of a in Cu2ZnSnS4 with decreasing T is observed, whereas in Cu2ZnSnxGe1−xSe4 all the parameter W, En, g (μ), a and NA are non-monotonic functions of x. Finally, in Cu2ZnGeS4 the Hall coefficient RH (T) is negative (despite of the p-type conduction), exhibiting the dependence close to that of ρ (T) in the Mott VRH interval.

Electrical and thermoelectric transport by variable range hopping in reduced graphene oxide

This study investigated the transport properties of single-layer reduced graphene oxides (rGOs). The rGOs were prepared by the bubble deposition method followed by thermal reduction. The crossover of the transport mechanism from Efros-Shklovskii (ES) variable range hopping (VRH) between the localized states to Mott-VRH was observed near 70 K using the temperature-dependent conductance. The ES-VRH conduction below 70 K is apparent in the electric field dependence of the field-driven hopping transport in the high-electric field regime. We also figure out that the thermoelectric power is consistent with the 2D Mott VRH above 70 K. We argue that the VRH conduction results from the topological disorders of rGO as confirmed by Raman spectroscopy. This infers that the average distance between defects is approximately 2.0 nm.

Mechanisms of charge transfer and electronic properties of Cu2ZnGeS4 from investigations of the high-field magnetotransport

Recent development of the thin film solar cells, based on quaternary compounds, has been focused on the Ge contain compounds and their solid solutions. However, for effective utilization of Cu2ZnGeS4, deeper investigations of its transport properties are required. In the present manuscript, we investigate resistivity, ρ (T), magnetoresistance and Hall effect in p-type Cu2ZnGeS4 single crystals in pulsed magnetic fields up to 20 T. The dependence of ρ (T) in zero magnetic field is described by the Mott type of the variable-range hopping (VRH) charge transfer mechanism within a broad temperature interval of ~100–200 K. Magnetoresistance contains the positive and negative components, which are interpreted by the common reasons of doped semiconductors. On the other hand, a joint analysis of the resistivity and magnetoresistance data has yielded series of important electronic parameters and permitted specification of the Cu2ZnGeS4 conductivity mechanisms outside the temperature intervals of the Mott VRH conduction. The Hall coefficient is negative, exhibiting an exponential dependence on temperature, which is quite close to that of ρ(T). This is typical of the Hall effect in the domain of the VRH charge transfer.

Low temperature resistivity studies of [formula omitted]: Observation of two-dimensional variable-range hopping conductivity

We studied electrical resistance of a single-crystalline SmB6 sample with a focus on the region of the “low-temperature resistivity plateau”. Our observations did not show any true saturation of the electrical resistance at temperatures below 3K down to 70mK. According to our findings, temperature dependence of the electrical conduction in a certain temperature interval above 70mK can be decomposed into a temperature-independent term and a temperature-activated term that can be described by variable-range hopping formula for two-dimensional systems, exp[−(T0/T)1/3]. Thus, our results indicate importance of hopping type of electrical transport in the near-surface region of SmB6.

Optical and electrical characteristics of thermally evaporated Cu0.5Ag0.5InSe2 thin films

In this study, optical and electrical characteristics of the Cu0.5Ag0.5InSe2 (CAIS) polycrystalline thin films were investigated. They were deposited on soda lime glass substrates with the evaporation of pure elemental sources by using physical thermal evaporation technique at 200°C substrate temperature. The thin films were characterized firstly in as-grown form, and then annealed under the nitrogen environment to deduce the effects of annealing on the optical and electrical properties of the deposited thin films related to their structural changes. In fact, these material properties of the CAIS thin films were studied by carrying out transmission, Hall Effect, and temperature dependent dark- and photo-conductivity measurements as a function of annealing temperature. From the optical analysis, the band gap energies were found between 1.44 and 1.51eV for the as-grown and annealed films, respectively. The analysis of electrical conductivity showed that electrical properties of the films were dependent on the variable range hopping and thermionic emission conduction mechanisms at low temperature region and above the room temperature, respectively. Under different illumination intensities, the photo-conductivity properties of CAIS film samples were analyzed under the consideration of two-center model.

Copper-silicon dioxide nanocomposites: Structure and electron transport

We investigated correlation between structure and electron transport properties of composite films synthesized by the ion-beam sputtering of Cu + SiO2 target. Photoluminescence (PL) spectra testify to an oxygen deficiency in the silicon dioxide matrix in agreement with the Raman spectroscopy, which reveals the presence of Cu2O phase along with elemental copper. For the nanocomposites with copper atomic fraction x < 0.64, the temperature dependence of conductivity obeys ln(σ) ∼ T−0.5 law at low temperatures (electron tunneling between size distributed copper nanoparticles) replacing with the Mott Variable Range Hopping (VRH) with the temperature increase. Electron transport properties of the studied nanocomposites are significantly affected by matrix defectiveness, which increases with metallic phase content according to PL study. The increasing matrix defectiveness results in decrease of crossover temperature from tunneling to VRH conductivity, as well as growth of matrix permittivity due to an enhanced contribution of electrons localized at defects.

Specific features of the transport properties of the Lu0.1Bi1.9Te3 compound

The temperature and electric- and magnetic-field dependences of the resistivity of the R0.1Bi1.9Te3 compound are investigated. It is shown that, in the low-temperature region, variable-range hopping conductivity is realized in this compound. In the temperature range of hopping conductivity, the electrical resistivity decreases with increasing electric-field strength in the sample, which is typical of charge-carrier tunneling from one localized state in the impurity band to another. Investigation of the transverse magnetoresistance revealed the crossover from the parabolic dependence of the magnetoresistance in low fields to the linear dependence in high fields. The established features of the transport properties of the R0.1Bi1.9Te3 compound are characteristic of inhomogeneous and disordered semiconductors.

Temperature-Dependent Electrical Characterization of Amorphous Indium Zinc Oxide Thin-Film Transistors

In this study, N-type amorphous indium zinc oxide thin-film transistors are fabricated and temperature-dependent electrical characteristics in the range of 170–295 K are analyzed through experimental measurements and using an equivalent-circuit model. In this model, thermionic field emission for reverse bias and a thermionic emission mechanism for forward bias are applied. The barrier height coefficient of a contact region between the channel and the Ti/Au electrode is 1.26 meV/K, and the resistance of the channel material decreases at a rate of $- 0.39 \Omega \cdot {\mathrm{ K}}^{-1}$ at various temperatures. The obtained energy level is experimentally confirmed through a Kelvin probe measurement. In addition, the simulation results of the channel resistance successfully describe the Arrhenius behavior of the drain current and the Mott variable-range hopping conduction mechanism in a low-temperature regime below 230 K.

Structural, magnetic and magnetocaloric properties of Co-doped nanocrystalline La0.7Te0.3Mn0.7Co0.3O3

Structural, magnetic and magnetocaloric properties of the nanocrystalline La0.7Te0.3Mn0.7Co0.3O3 perovskite manganite were investigated. X-ray diffraction pattern indicated that the nanocrystalline sample crystallized in orthorhombic crystal structure with Pbnm space group. The average particle size was calculated using scanning electron microscope and it was found to be ∼150nm. Temperature dependence magnetization measurements revealed ferromagnetic–paramagnetic phase transition and the Curie temperature (TC) was found to be ∼201K. Field dependence magnetization showed the hysteresis at low temperature with a coercive field of ∼0.34T and linear dependence at high temperature corresponds to paramagnetic region. Based on the magnetic field dependence magnetization data, the maximum entropy change and relative cooling power (RCP) were estimated and the values were 1.002Jkg−1K−1 and 90Jkg−1 for a field change of 5T respectively. Temperature dependent resistivity ρ(T) data exhibited semiconducting-like behavior at high temperature and the electrical transport was well explained by Mott’s variable-range hopping (VRH) conduction mechanism in the temperature range of 250K–300K. Using the VRH fit, the calculated hoping distance (Rh) at 300K was 54.4Å and density of states N(EF) at room temperature was 7.04×1018eV−1cm−3. These values were comparable to other semiconducting oxides.

Magnetocaloric as a sensitive tool to study magnetic phase in [formula omitted

We report here magnetic properties of non-stoichiometric Ca4Mn3O10-δ. We have measured magnetization, electrical resistance, magnetoresistance, specific heat and thermo remanent magnetization (TRM) relaxation measurements. We find that at temperatures above 75K the electrical transport can be explained in terms of activated hopping of magnetic polarons. These polarons are formed due to oxygen vacancy inducing Mn3+ sites. Below 50K the polarons begins to strongly localize causing loss of moment and the electrical transport is governed by variable range hopping (VRH) conduction. The system shows glassy spin relaxation below 50K, which presumably evolves into cluster spin glass at 12K due to short range ordering of the canted moments. All these aspect could be well correlated with characteristics signature from magnetocaloric effect indicating magnetocaloric is a sensitive tool to study magnetic phase.

Mott type variable range hopping conduction and magnetoresistance in p-type CuIn3Te5 semiconductor compound

Variable range hopping (VRH) conduction of Mott type for a constant and non-vanishing density of states at the Fermi level is observed over a wide range of temperature between 45 and 210 K in the ordered defect compound CuIn3Te5 (CIT135). For this type of electrical conduction at a very high temperature, not reported before in elemental, II-VI, and I-III-VI2 compound semiconductors, we employed three different methods to analyze the data and to confirm this behavior. The occurrence of VRH at very high temperatures is explained as due to the presence of the electrically inactive (InCu+2 + 2 VCu−1) donor-acceptor defect pairs in CIT135. This defect-pair partially annihilates the shallow acceptor defect state Cu vacancy, which is responsible for the activated electrical conductivity observed in p-type ternary I-III-VI2 chalcopyrite compounds in the temperature range of liquid nitrogen. In such conditions, the only acceptor level available for electrical conduction in CIT135 is a deep acceptor state whose activation energy is about 200 meV and cannot be activated below about 200 K. Hence, the VRH conduction mechanism dominates the electrical properties of this material up to about 200 K. The study of the temperature and magnetic field dependence of the magnetoresistance (MR) up to 27 T is made by taking into consideration different theoretical models. To explain the negative MR at lower fields, the theory based on quantum interference is used. At higher magnetic fields, the MR becomes positive and is explained with the model based on the shrinkage of the wave function.

Fabrication and characterizations of nitrogen-doped BaSi2 epitaxial films grown by molecular beam epitaxy

Nitrogen doped BaSi2 layers are grown on high-resistivity n-Si (111) substrates by molecular beam epitaxy using a radio-frequency nitrogen plasma. The nitrogen concentration measured by secondary ion mass spectrometry is homogeneous throughout the grown layers. The carrier concentration is measured by Hall measurement using the van der Pauw method. Nitrogen-doped BaSi2 shows n- or p-type conductivity, depending on the intensity of nitrogen plasma. The hole concentration is of the order of 1016–1017cm−3 at room temperature. The acceptor level is estimated to be approximately 64meV from the temperature dependence of hole concentration. The temperature dependence of resistivity is explained by variable-range hopping conduction in p-BaSi2. First-principle calculation suggests that the nitrogen atoms are most likely to occupy the interstitial site in BaSi2.

Crystal structure, electrical, and optical properties of Cu3In7Te12 ordered defect semiconducting compound

CuInTe2 chalcopyrite semiconductor and the ordered defect compounds of the Cu2Te–In2Te3 pseudo‐binary system have recently emerged as suitable candidates for thermoelectric applications. In this article, the crystal structure, optical, and electrical properties of Cu3In7Te12, a member of this ternary system, have been studied. It was established that this material crystallizes in a tetragonal structure with space group P. The analysis of the optical absorption spectrum near the fundamental absorption edge shows that the energy gap is direct and the band gap varies from 1.030 to 0.952 eV between 10 and 300 K. From the analysis of electrical data, it was found that above 160 K, the electrical conduction is due to the activation of a shallow acceptor level of about 10 meV, and the value of the hole‐effective mass is mh = (1.18 ± 0.35) me. In the temperature range from 160 to 130 K, variable range hopping (VRH) mechanism of Mott‐type in the impurity band is observed. At high temperatures, the mobility is explained by taking into account the scattering mechanism of the charge carriers by donor–acceptor defect pairs, ionized and neutral impurities, acoustic and non‐polar optical phonons. In the low temperature region, the mobility data can be explained by an expression related to Mott law for VRH conductivity.

Hopping Transport and Spin-Polarized Tunneling Mechanism in Cr-Doped Gd0.7Ca0.3Mn1−x Cr x O3 (x = 0.0–0.5)

Temperature-dependent DC electrical resistivity of polycrystalline samples with orthorhombic perovskite structure Gd0.7Ca0.3Mn1−x Cr x O3 (x = 0.0–0.5) has been reported. The samples were prepared by the solid-state reaction method. The resistivity of all the samples indicates a semiconducting nature. In the high-temperature region, the electrical conduction process follows the small polaron hopping (SPH) mechanism showing exponential variation of resistivity with temperature. The activation energy increases with Cr concentration. The low-temperature resistivity data follows Mott’s ln(ρT −1/2)∼T −1/4 law of variable-range hopping (VRH) conduction mechanism. The estimated values of hopping distances (R) and hopping energies (W) of the samples start to increase with increasing Cr concentrations from and above x = 0.5 and satisfy essential conditions of the Mott VRH, i.e., αR>> 1 (α = inverse localization length) and W/ K B T>> 1. This signifies that evaluation of these parameters being logical and the effect can be attributed to high density of doping which introduces simultaneously potential disorder and localized states. The magnetic field-dependent magnetoresistance has been explained by a phenomenological model considering spin-polarized tunneling at grain boundaries in the samples.

Magnetotransport of Cu2ZnSnS4 single crystals in two regimes of variable–range hopping conduction

The resistivity, ρ(T), and the magnetoresistance (MR) of Cu2ZnSnS4 (CZTS) single crystals are investigated at temperatures T = 2–300 K in pulsed magnetic fields of B up to 20 T. The Mott variable–range hopping (VRH) conductivity over localized states of the defect acceptor band is observed between T ~ 50–150 K. The Shklovskii–Efros (SE) VRH conduction over the states of the Coulomb gap is found below T ~ 3–4 K. The positive MR is observed at all temperatures and magnetic fields, its value decreasing with T. In the Mott VRH conduction region, MR follows the law ln ρ(B) ∝ B 2 up to the highest applied fields. The joint analysis of the resistivity and MR data in this region has yielded values of the localization radius as well as a set of important microscopic parameters, including the mobility threshold in the acceptor band, the values of the density of localized states near the Fermi level and the critical concentration of the metal–insulator transition. In the SE region, the MR law above is observed only in much smaller fields, transformed into those of lnρ(B) ∝ B 2/3 or ∝ B 3/4 when B increases. Such transformation, accompanied by a strong increase of the localization radius, give evidence for an important role of scattering and interference phenomena in the VRH conduction at low temperatures.

Transition between Efros–Shklovskii and Mott variable-range hopping conduction in polycrystalline germanium thin films

We report on the electrical transport properties of polycrystalline germanium thin films which are grown by the DC magnetron sputtering method. The temperature dependent resistance of seven devices are measured from 290 K down to 10 K. The thermal excitation model dominating the transport properties at the high temperature regime (above ∼60 K) is demonstrated and the low temperature electron transport is governed by the variable-range hopping (VRH) mechanism. Moreover, we observed a transition from Efros–Shklovskii to Mott VRH at ∼25 K over the entire VRH conduction regime, which is well described by a universal scaling law.

Structural, Optical and Electrical Conductivity Properties of Stannite Cu2ZnSnS4

A precursor powder was obtained from drying the solutions of a mixture of different ratios of Cu, Zn and Sn chloride and thiourea. The Cu2ZnSnS4 (CZTS) samples were prepared from thermal decomposition of the corresponding precursors in vacuum, and were then characterized using scanning emission microscopy, energy dispersive x-ray analysis, x-ray powder diffraction and Raman scattering. According to x-ray diffraction analysis, all the synthesized samples had a tetragonal structure of space group \(I\overline{4} 2m\). The electrical properties of the CZTS samples were investigated in the temperature range of 10–325 K. The charge carrier concentration was measured to be about p = 1 × 1016 cm−3. A crossover from a nearest-neighbor hopping conduction mechanism at high temperatures (T > 150 K) to a Mott variable-range hopping conduction mechanism at low temperatures (T < 150 K) was observed. The activation energies of the CZTS samples were calculated for the low and high ranges of temperature. A thin film on quartz substrates was obtained using magnetron sputtering, for which a band gap of Eg = 1.3 eV was determined from transmittance measurements.

On the temperature dependent electrical resistivity of CNT layers in view of Variable Range Hopping models

Thin films of randomly dispersed carbon nanotubes make highly promising material for transparent electrode applications. Knowing and understanding the nature of the films conductivity is crucial for improvement of their electrical properties. In the paper we present our investigation of electrical conductivity of single wall and multiwalled carbon nanotube (SWCNT and MWCNT) thin films deposited on a polymeric substrate by Langmuir-Schaefer technique. The conductivity of the films is consistent with the Variable Range Hopping (VRH) model. Moreover, remarkable differences in SWCNT and MWCNT films conductivity are observed. A significant impact of the thin film annealing and its temperature history on the conductivity properties is shown. The study of the carbon nanotubes layers transferred on polymeric substrate was undertaken in view of the films possible applications in flexible transparent electrodes. The VRH conductivity in carbon nanotube Langmuir-Schaefer layer is reported for the first time.

AC Electrical Conduction of Cr-Doped SrTiO3 Thin Films with an Oxygen-Deficient Interface Layer

The ac electrical conduction of Cr-doped SrTiO3 thin films with an oxygen-deficient interface layer was investigated as a function of temperature and frequency. The Cr-doped SrTiO3 (Cr-STO) thin films with an ultra-thin (∼2 nm) oxygen-deficient layer inserted between the top electrode and the Cr-STO layer exhibited two ac conduction mechanisms, i.e., variable-range hopping and small-polaron hopping conduction, accompanied by a relaxation process. Since high oxygen deficiency induces large lattice distortion in the depletion layer, the first relaxation process occurs at low frequencies in the thin oxygen depletion layer Cr-SrTiO3−δ , and the corresponding conduction behavior follows the small-polaron tunneling model. In the high frequency range, an additional relaxation process is involved and is associated with the variable-range hopping between the localized states in the band gap of the thick Cr-SrTiO3 layer.

High positive magnetoresistance in Ge films at low temperatures

High positive magnetoresistance is found and investigated in p-Ge films on GaAs at low temperatures (1.4–4.2 K) and in magnetic fields up to 14 T. The film resistance grows exponentially with magnetic field. At a temperature of 1.4 K and in a magnetic field of 14 T, the film resistance is increased by a factor of 3.8. The magnetoresistance also grows exponentially as temperature is reduced. The Mott variable-range hopping conduction is observed in the films studied in the 1.4–21 K temperature range. It is shown that experimentally observed magnetoresistance agrees well with the theory of compression of wave functions of the localized states in the plane normal to magnetic field. This results in reduction of their overlapping, decrease of electron tunneling probability, and consequently, considerable growth of film resistance. Based on experimental resistance dependences on temperature and magnetic field, the parameters of hopping resistivity in Ge films on GaAs are determined. A possibility of transition to interference effects in conduction leading to localization of charge carriers and negative magnetoresistance at temperature decrease is also discussed.