Variable-range Hopping Conduction Research Articles

Charge transport mechanisms in inkjet-printed thin-film transistors based on two-dimensional materials

Printed electronics using inks based on graphene and other two-dimensional materials can be used to create large-scale, flexible and wearable devices. However, the complexity of ink formulations and the polycrystalline nature of the resulting thin films have made it difficult to examine charge transport in such devices. Here we report the charge transport mechanisms of surfactant- and solvent-free inkjet-printed thin-film devices based on few-layer graphene (semimetal), molybdenum disulfide (MoS2, semiconductor) and titanium carbide MXene (Ti3C2, metal) by investigating the temperature, gate and magnetic-field dependencies of their electrical conductivity. We find that charge transport in printed few-layer MXene and MoS2 devices is dominated by the intrinsic transport mechanism of the constituent flakes: MXene exhibits a weakly localized 2D metallic behaviour at any temperature, whereas MoS2 behaves as an insulator with a crossover from 3D Mott variable-range hopping to nearest-neighbour hopping around 200 K. Charge transport in printed few-layer graphene devices is dominated by the transport mechanism between different flakes, which exhibit 3D Mott variable-range hopping conduction at any temperature.

Surface-potential-based drain current model for two-dimensional organic TFTs using the multiple trapping and release conduction theory

A new analytical surface-potential-based drain current model is presented for the organic thin-film transistors (TFTs) when carriers are confined in two dimensions. Following the carrier multiple trapping and release (MTR) conduction theory, i.e., the assumption that the trapped carrier concentration is much higher than the free carrier concentration, the model is developed. The presented model can account for the linear regime and saturation regime by a single formulation. The calculated results of the presented model are verified by the available experimental drain current considering the temperature characteristics. Comparing with the previous model using the variable range hopping and percolation (VRH) conduction theory, although the presented model and the previous model are similar in mathematics, the presented model is more efficient to estimate the density of trap states for the organic TFTs.

Variable Range Hopping in SrTiO3-Ca10(PO4)6(OH)2 Bio-Ceramic Composites.

We investigate the electrical properties in ceramics, focusing primarily on the conductivity mechanisms crucial to bio-electrets’ service life. A biocompatible ceramic composite of varying concentrations of SrTiO3 (ST) and Ca10(PO4)6(OH)2 (HAP) is developed. By X-ray diffraction, we establish the microstructural and phase evolution of the bio-composites. The crystallite sizes are found to increase with the increasing concentration of ST in the composites. The composites’ micrograph reveals the presence of pores, and the grain sizes calculated from it are found to follow a trend similar to the crystallite size. The conduction mechanisms in the composites are studied to explore the composites’ electrical properties from the perspective of biological applications. The conductivity is very low (≃10–8 S/cm), and the porous structure of the composites revealed from the micrographs is one of the factors for such low conductivity. From a plethora of conduction mechanisms, Motts’ variable range hopping (VRH) conduction is projected as the most appropriate mechanism that appropriately describes the conduction process in the composites. Motts’ VRH is also related to the polarization mechanism associated with the development of electrets. Our study points toward the practical potential of applying the designed bio-composites in generating bio-electrets or understanding the electrical properties that are at the forefront of research in designing electro-active smart scaffolds for bone tissue engineering applications.

Electronic Transport Mechanisms Correlated to Structural Properties of a Reduced Graphene Oxide Sponge.

We report morpho-structural properties and charge conduction mechanisms of a foamy “graphene sponge”, having a density as low as ≈0.07 kg/m and a carbon to oxygen ratio C:O ≃ 13:1. The spongy texture analysed by scanning electron microscopy is made of irregularly-shaped millimetres-sized small flakes, containing small crystallites with a typical size of ≃16.3 nm. A defect density as high as ≃2.6 × 10 cm has been estimated by the Raman intensity of D and G peaks, dominating the spectrum from room temperature down to ≃153 K. Despite the high C:O ratio, the graphene sponge exhibits an insulating electrical behavior, with a raise of the resistance value at ≃6 K up to 5 orders of magnitude with respect to the room temperature value. A variable range hopping (VRH) conduction, with a strong 2D character, dominates the charge carriers transport, from 300 K down to 20 K. At T < 20 K, graphene sponge resistance tends to saturate, suggesting a temperature-independent quantum tunnelling. The 2D-VRH conduction originates from structural disorder and is consistent with hopping of charge carriers between defects in the plane, where clusters related to oxygen functional groups act as potential barriers.

Features in low-temperature electrical resistivity of amorphous Cd3As2 films due to hopping conductivity with changing activation energy

Amorphous Cd3As2 films were deposited on single-crystalline SrTiO3 substrate by high-frequency non-reactive magnetron sputtering. Electrical resistivity of the film, measured within 3-75 K range, increases at cooling. Below ∼70 K, negative transverse magnetoresistance observed. Features in electrical resistivity and magnertoresistance can be attributed to variable-range hopping conductivity of the Mott type with local activation energy, which is temperature-dependent. Two temperature ranges in the hopping conductivity observed. Appearing two ranges is in qualitative accordance with the Mott-Davis energy-band model developed for amorphous semiconductors. High temperature range of the hopping conductivity is attributed to electron hops between localized states, positioned inside band tails, whereas electron hops between localized states, positioned inside Fermi-peak, can be responsible for low-temperature range. At taking into account temperature dependences of local activation energy, universal expression for various mechanisms of the hopping conductivity could be successfully applied to analyze the experimental data.

Nd-doped ZnO films on (100) MgO substrate: From metal to semiconductor

We report a wide range of electric and magneto-transport properties of epitaxial Nd-doped ZnO thin films grown on (100) MgO single crystal substrate by pulsed-laser deposition under 10−2 mbar high oxygen pressure as a function of the growth temperature Tg. The classical (001) texture of the ZnO wurtzite phase is present in all films whatever the growth temperature, while for Tg lower than 500 °C an additional epitaxial (100) texture is observed. These structural changes are accompanied by drastic modifications of the charge transport mechanisms. For Tg = 300 °C, the films behave as a metal from 300 to 275 K, from which temperature a metal-insulator transition occurs. The electrical behaviour between 275 and 50 K is described by the quantum correction to conductivity theory in disordered systems and comforted by magneto-resistance data. For Tg = 500 °C, a semiconducting behavior with partial metallic character is evidenced, while for Tg = 700 °C, pure semiconductor characteristics are obtained with variable-range hopping conductivity at low temperatures. Magneto-resistance measurements indicate that Nd3+ ions act below 150 K as scattering centers for electrons only for films grown at 300 °C and 500 °C. These observations have to be related to the incorporation of Nd3+ into the ZnO films during growth. The evolution from a metallic film to a semiconducting one, while acting on the single growth temperature parameter, opens new perspective in the context of charge transport.

Impedance Spectroscopy and ac Conductivity in Ba0.5Sr0.5TiO3-Ca10(PO4)6(OH)2 Ceramic Composites: An Electrical Approach to Unveil Biocomposites.

We report bioceramic composites of varying concentrations of Ba0.5Sr0.5TiO3 (BST) and Ca10(PO4)6(OH)2 (HAP) for the analysis of electrical properties. The motivation is to predict the suitability of the composites for bio-electrets or the practical possibility in designing electro-active scaffolds. X-ray diffraction (XRD) and field-emission scanning electron microscopy (FESEM) are used to analyze the microstructural evolution of the composites. A systematic variation in the grain and crystallite sizes is noticed from the FESEM and XRD, along with the presence of Sr5(PO4)3(OH) (SAP). The temperature and frequency variations of the dielectric properties of the composites are studied. Modeling of the dielectric properties with the microstructural properties and at. % of the monolith BST is presented. Cole-Cole formalism is adopted to model the electrical behavior of the synthesized composites. Furthermore, the ac conductivity analysis reveals that Mott's variable range hopping (VRH) conduction is the most appropriate formalism that successfully describes the conduction process. The established Mott's VRH is also related to the polarization mechanisms active in the specimens. Our study projects a correlation between the electrical and biological properties by predicting the protein adsorption behavior from the perspective of impedance spectroscopy.

Electrical Conduction Properties of Hydrogenated Amorphous Carbon Films with Different Structures.

Hydrogenated amorphous carbon (a-C:H) films have optical and electrical properties that vary widely depending on deposition conditions; however, the electrical conduction mechanism, which is dependent on the film structure, has not yet been fully revealed. To understand the relationship between the film structure and electrical conduction mechanism, three types of a-C:H films were prepared and their film structures and electrical properties were evaluated. The sp2/(sp2 + sp3) ratios were measured by a near-edge X-ray absorption fine structure technique. From the conductivity–temperature relationship, variable-range hopping (VRH) conduction was shown to be the dominant conduction mechanism at low temperatures, and the electrical conduction mechanism changed at a transition temperature from VRH conduction to thermally activated band conduction. On the basis of structural analyses, a model of the microstructure of a-C:H that consists of sp2 and sp3-bonded carbon clusters, hydrogen atoms and dangling bonds was built. Furthermore, it is explained how several electrical conduction parameters are affected by the carrier transportation path among the clusters.

Dielectric relaxation and variable range hopping conduction in sol-gel auto combustion derived La0.7Bi0.3Fe0.5Mn0.5O3 manganite

In the present work, the polycrystalline La0.7Bi0.3Fe0.5Mn0.5O3 maganite was synthesized by sol-gel auto-combustion method. The room temperature X-ray powder diffraction pattern confirmed the orthorhombic phase of the sample with pbnm space group. Frequency and temperature dependent electric modulus and impedance spectroscopic analyses revealed two electro-active components of the material characterized by highly resistive grain boundaries and comparatively conducting grains, respectively. The normalized scaling behavior of modulus plots divulged the temperature independence of the dynamic process in electro-active regions. The fitting of impedance data by the equivalent circuit (RG||QG) + (RGB||QGB) was applied to explore the physical parameters associated with grains and grain boundaries. The dispersion in dielectric permittivity and loss factor at lower frequencies attributed to the space charge polarization were observed. The electrical conductivity obeyed Mott’s T1/4 law and the slope of frequency dependent AC conductivity spectra changed due to multiple activation barriers and active traps, consistent with the variable-range hopping conduction in the material.

Simple physical model for the sign of the Hall coefficient in variable-range hopping conduction in heavily Al-doped p-type 4H-SiC

We observe negative Hall coefficients (R H(T)) in the variable-range hopping (VRH) conduction region for heavily Al-doped p-type 4H-SiC. We have proposed a simple physical model in which the difference between the density of hopping sites for holes and the density of hopping sites for electrons under a magnetic field determines the sign of R H(T), and explained the negative R H(T) in nearest-neighbor hopping (NNH) conduction. Based on our proposed model for NNH conduction, here we propose a model in which R H(T) becomes positive when the density of localized states (g(E)) around the Fermi level (E F) increases with increasing energy (E), whereas R H(T) becomes negative when g(E) around E F decreases with increasing E. In heavily Al-doped p-type 4H-SiC where g(E) around E F is considered to decrease with increasing E, the proposed model can explain why R H(T) becomes negative in the VRH conduction region.

Polaronic Relaxation and Variable-Range-Hopping Conductivity in Fe3O4 Nanoparticles

We report the polaronic relaxation and Variable Range Hopping (VRH) conductivity in 100nm average particle size cold pressed Fe3O4 nanoparticles. The crystal structure was studied using XRD showing spinel structure with (311) intense peak. The AC transport in the cold pressed powder was studied from 10 K to room temperature and from 100 Hz to 5.5 MHz. It was observed that the solid couples capacitively with the perturbing electric field initially and as the frequency increases it becomes more inductive. The impedance data was modelled using modified Havriliak–Negami relaxation model. It was observed that the cold pressing introduces an asymmetric broadening in the relaxation process. The change in impedance with temperature showed a drastic drop at around 120 K due to Verwey transition in real as well as imaginary part. The change in DC resistance with temperature indicated VRH mechanism of charge transport in the solid with a metal insulator transition at around 120 K. The relaxation times calculated indicated that the hopping process has an attempt frequency of the order of 30 microseconds. The activation energy change across the phase transition with relaxation time and resistance indicated that the charge transport is coherent. The activation energy of ∼0.05eV above Varway transition indicated that the transport is small polaronic in nature.

Polaronic effect of a metal layer on variable range hopping

We investigate the effect of a metal plate on the variable range hopping (VRH) conductivity of a two dimensional electron-glass (EG) system. The VRH conductivity is known to have a stretched exponential dependence on temperature, with an exponent $p$ that depends on the shape of the EG's single particle density of states (DOS). For constant DOS $p=1/3$ and for linear DOS $p=1/2$, also known as Mott's and Efros-Shklovskii's VRH respectively. The presence of the plate causes two effects on the EG system, static and dynamic. The well known static effect accounts for the additional screening of the Coulomb repulsion in the EG and for the partial filling of the Coulomb gap in the DOS. This in turn causes an increase of the conductivity at very low temperatures. Here we investigate the complementary dynamical effect, which is related to the polaronic phenomena. Our main result is the dynamical suppression of the standard phonon assisted hopping and, thus, suppression of the conductivity in a much wider range of temperatures as compared to the low temperature static effect. The relation to experiments is discussed.

Non-adiabatic small polaron hopping transport above metal-like to insulator transition in the vacant 3d-orbital Tb2Ti2O7 pyrochlore oxide

We report the validity of Mott variable range hopping (VRH) conduction mechanism and small polaron hopping in Tb2Ti2O7 in the temperature range 603–803 K. The temperature-dependent resistivity data are in good agreement with Mott 3d VRH. The other parameters estimated such as hopping range, hopping energy and density of states near Fermi level are in good agreement with those of many semiconductor oxides. The Holstein’s condition for non-adiabatic conduction mechanism is also satisfied. The ac conductivity is governed by Jonscher’s power law as $$ {\sigma}_{a.c}^{\prime}\left(\upsilon, T\right)={\sigma}_{d.c}(T)+\alpha (T){\upsilon}^n $$ and the exponent n values in the range of 1.02–1.23 suggest that conduction takes place due to the small polaron hopping mechanism. The possible polaron formation and their mechanism are discussed systematically.

Effect of Mixed Transition Metal Ions in B2O3-V2O5-MoO3 Glass System

The effect of having two different transition metal oxides in a glass matrix is an interesting phenomenon to study, as this kind of composition leads to various anomalous effects in terms of electrical and other physical properties. The present series of glasses were explored for density and DC electrical conduction in borate glass systems containing molybdenum and vanadium oxides. The glasses were synthesized using the melt-quench method and their amorphous characteristics were established by XRD techniques. The glasses were explored for density and DC electronic conduction in a temperature range between 318 K and 473 K. The estimated density, molar volume and oxygen packing density (OPD) varied non-linearly with increasing MoO3 content. The DC conduction and activation energy attained maximum and minimum around 0.15 mole fraction of MoO3. This was attributed to the fact that with the addition of MoO3 up to x = 0.15 molar fraction, the V2+ transition metal ions and Mo5+ transition metal ions may create bond defects and non-bridging oxygen (NBO) by altering the bonds of boron-oxygen-boron, boron-oxygen-molybdenum, boron-oxygen-vanadium. As a result, at x = 0.15 mole fraction of MoO3, the glass linkage among the bonds becomes close or tightly packed. Consequently, the net movement of ions begins effortlessly over the pathways of the tightly packed glass system. The high-temperature conduction data were analysed following Mott’s small polaron hopping theory, and the low-temperature conduction data were analysed in terms of Mott’s and Greave’s variable-range hopping conduction models. Several polaron-related parameters were estimated and are discussed.

On the Intersecting Temperature in Presence of Several Normal State Conduction Mechanisms in High-Tc Superconductors

An intersection temperature of the normal state conduction and a state which follows the three-dimensional Aslamazov-Larkin (3DAL) has been studied in several high-temperature superconductors (HTS). Extraction of the coherence length by using the 3DAL equation depends on the existing normal state conduction mechanism. We have used bulk HTS having normal states of different types which can be explained either by using the metallic behavior or the variable range hopping (VRH) conduction. In presence of the several coherence lengths, the shifting of the intersecting point has been studied.

Scaling behavior and variable-range-hopping conduction of localized polarons in percolative BaTiO3-Ni0.5Zn0.5Fe2O4 ceramic composite with colossal apparent permittivity

The percolative BaTiO3-Ni0.5Zn0.5Fe2O4 (BTO-NZFO) ceramic composite represents a family of multifunctional materials exhibiting multiferroic properties and colossal apparent permittivity. It is of fundamental interest to investigate the conduction mechanism in such percolative composites from both macroscopic and microscopic perspectives. Herein, three representative systems with the NZFO content locating below the percolation threshold fc, near fc, and above fc, respectively, were investigated, using pure NZFO ceramic as a comparison. The conductivity of the composite as a function of NZFO content agrees well with the McLachlan model, which takes percolation into consideration and essentially equivalent to the Kirkpatrick model. The electrical conductivity of the composite conforms to Mott's variable-range-hopping (VRH) model in the temperature range of 303–573 K, suggesting that VRH conduction of localized polarons dominates the electrical behavior microscopically. Parameters including the most probable hopping range (R); the density of localized states at the Fermi level [N(EF)]; and the activation energies of VRH (W), dc conductivity (Edc), hopping (Eon), and relaxation (Er) were obtained and analyzed. Scaling behaviors of the conductivity and the imaginary part of complex impedance of the composite have been observed, implying that the distribution of relaxation times is temperature independent. The impedance data measured at different temperatures exhibit typical semiconducting behavior, which can be well fitted by an equivalent circuit model considering both grain and grain boundary responses. The correlation between conductivity and colossal apparent permittivity has also been revealed. The discoveries deepen the understanding of the conduction mechanism in such multifunctional composites composed of an insulating phase and a semiconducting phase.

Synthesis, Transfer, and Properties of Layered FeTe2 Nanocrystals.

Different from layered two-dimensional (2D) transition metal dichalcogenides (TMDs), iron dichalcogenides crystallize in the most common three-dimensional pyrite or marcasite structures. Layered iron dichalcogenides are rarely reported and little is known about their structures and properties. Here, layered hexagonal phase iron ditelluride FeTe2 (h-FeTe2) nanocrystals are grown on mica by atmospheric pressure chemical vapor deposition (APCVD) method and are fully characterized by various methods. Like other 2D layered TMD materials, the FeTe2 nanoflakes exhibit regular hexagon, half hexagon, or triangle shapes with a controllable thickness of 6-95 nm and lateral length from a few to tens of micrometers. A simple and effective method is used to transfer the FeTe2 nanoflakes from the mica substrate onto any other substrates without quality deterioration by using polystyrene (PS) as a support polymer, which can also be operated in ethanol or ethylene glycol in a glovebox to avoid contact with water and air. Temperature-dependent electrical transport demonstrates that the FeTe2 nanoflake is a semiconductor with a variable range hopping (VRH) conduction, and its nonsaturated linear magnetoresistance (MR) reaches up to 10.4% under magnetic field of 9 T at 2 K, both probably due to its structure disorders. No signature of magnetic ordering is observed down to 2 K. The CVD growth of this layered FeTe2 represents an addition to the extensive library of 2D materials, particularly iron chalcogenides or alloys. Synthesis, properties, and even doping of phase pure h-FeTe2 call for further study in the future.

Measuring current effect on low-temperature resistivity of n-type Bi1.9Lu0.1Te3 compound: Probing the changing in conductivity mechanism under weak electric field

The measuring current effect on low-temperature resistivity of Bi1.9Lu0.1Te3 has been analyzed. Values of currents correspond to weak electric fields with strength of several V·m−1. Temperature behavior of the resistivity is connected to two mechanisms. High-temperature mechanism (above 35 K) is due to acoustic phonon scattering. For this mechanism, the resistivity is growing with both increasing temperature and increasing current (positive current effect). Low-temperature mechanism (below 35 K) results in appearance of resistivity minimum at low temperatures. Below the minimum, the resistivity is growing with decreasing temperature. This feature is originated from contribution from variable-range hopping conductivity. With increasing current, the resistivity is falling (negative current effect). Crossover from positive to negative current effect on the resistivity occurs with decreasing temperature. Positive effect is originated from saturation of drift velocity of electrons under electric field. Negative effect is due to activation of hopping conductivity via electric field.

Influence of Substrates on Conductivity of Thin Carbon Films Deposited by Methane Plasma and Subsequent Annealed

The properties of thin carbon films obtained by the deposition of carbon in CH4 - plasma on the surface of various substrates (Si, SiO2 and quartz glass) and subsequent annealing at 650 to 800 °C were investigated. The sizes of graphene domains from 5 to 15 nm from Raman spectra were determined which increases with rising temperature on synthesis of carbon films. Also, sizes of graphene domains were estimated based on the electrical conductivities of obtained carbon films, and their values were equal ∼10.8 nm. The Efros-Shklovskii variable-range hopping (ES-VRH) conduction mechanism is replaced by percolation conductivity with increasing temperature from 650 to 800° C. When using Si substrates, the hopping mechanism was not observed at all temperatures.

Variable-range hopping conductivity in (x = 0.5; y = 0, 0.02, 0.1)

The temperature dependences of the resistivity ρ(T) of ceramic samples at x = 0.5, and y = 0, 0.02 and 0.10 are investigated in the temperature range of 5-300 K in magnetic field B up to 1 T. It was found that dependences ρ(T) with x = 0.5; y = 0.02, and 0.10 obey the Shklovskii–Efros-like variable-range hopping conductivity law This behavior is governed by generation of a soft Coulomb gap Δ ≈ 0.3 eV in the density of localized states, as well as a rigid gap ≈ 0.20 and 0.17 eV at y = 0.02 and y = 0.10, respectively. The obtained values of the rigid gap at y = 0.02 indicate the presence of charge ordering. It was shown that a decrease in the width of the rigid gap when y is increased, is accompanied by both a growing disorder attributed to the presence of Fe and a decrease in lattice distortions caused by charge ordering at y = 0.02. It is shown that the pre-exponential factor of resistivity follows the law where m changes from 9/2 at y = 0.02 to 5/2 at y = 0.10. This confirms that doping with Fe enhances microscopic disorder by introducing an additional fluctuating short-range potential. The calculated values of the carrier localization radius α ≈ 5.1 and 2.7 Å at y = 0.02 and y = 0.10, respectively, satisfy the condition for the formation of small polarons.