Efros-Shklovskii Variable Range Hopping Research Articles

Transitions of electrical conduction mechanism in graphene flake van der Waals thin film

The electrical conduction mechanism in 2D van der Waals (vdW) thin film made of graphene flakes can be characterized by the variable range hopping (VRH) over a wide range of temperature, followed by a transition into an Arrhenius type conduction at the higher temperature. Regarding the nature of the subsequent Arrhenius type conduction, a lack of consensus exists between the nearest neighbor hopping (NNH) and the band conduction (BC). We discuss how to assess the transition in conduction mechanism based on the transient behavior of the reduced activation energy (W) and the structure of electronic density of states (DOS) of the sample. With a multi-channel conduction model, we show that the transition from VRH to BC always accompany an increase in W, which is absent in the transition from VRH to NNH. Also discussed are the peculiarities of VRH in vdW thin film and what they imply towards the properties of defects. In most vdW flake thin films, the spread of defect band in DOS is governed by the intrinsic defect energy not by the Coulomb interaction between defects. It can further be deduced that the gap in DOS near Fermi level associated with Efros-Shklovskii VRH observed in vdW film is not a Coulomb gap as found in weakly doped crystalline semiconductor, but inherent in the distribution of defect intrinsic energy. For the graphene flake thin film we synthesized, Mott VRH and BC are identified.

Investigating structural, optical, and electron-transport properties of lithium intercalated few-layer MoS2 films: Unraveling the influence of disorder

Molybdenum disulfide is a promising candidate for various applications in electronics, optoelectronics, or alkali-ion batteries. The natural presence of the van der Waals gap allows intercalating alkali ions, such as lithium, into MoS2 films. Intercalation can modify the electronic structure as well as the electrical and optical properties. Here, we present a structural, optical, and electrical characterization of Li-intercalated few-layer MoS2 films. The intercalation was carried out by annealing MoS2 film in the presence of Li2S powder, serving as a lithium source. The initial MoS2 layers were prepared by pulsed laser deposition (PLD) and by sulfurization of 1 nm thick Mo film (TAC). The presence of lithium was confirmed by synchrotron-based x-ray Photoelectron Spectroscopy. The Raman spectroscopy, x-ray diffraction, and optical absorption measurements confirmed semiconducting behavior for all samples. All samples exhibited the thermally activated dependence of the electrical resistance, R, typical for the Efros–Shklovskii variable range hopping in a disordered semiconductor, ln R(T) ∝ (TES/T)1/2, where kBTES is the hopping activation energy. The PLD-grown MoS2 samples exhibited a relatively mild initial disorder primarily caused by grain boundaries. Lithium intercalation led to an increase in disorder, evident in the increase in kBTES and a substantial rise in electrical resistance. The TAC-grown undoped MoS2 sample already exhibited significant resistance, and the impact of Li intercalation on resistance was minimal. This observation was attributed to the fact that the TAC-grown MoS2 samples exhibit a perturbed stoichiometry (the S:Mo ratio ∼ 2.20), causing strong disorder even before Li intercalation. The electron doping caused by lithium, if any, was completely obscured by the effect of disorder.

Engineering lattice oxygen defects and polaronic transport in vanadium pentoxide via isovalent phosphorus doping

Oxygen vacancies are equilibrium defects in the vanadium pentoxide system that give rise to polaronic hopping transport via V4+ charge compensating defect. In this paper, we report the tunability of polaron formation, the hopping process, and their magnetic signature by substitution of isovalent (5+) phosphorus ions in the V5+ site. The powder x-ray diffraction data show a monotonous shift in lattice parameters with progressive P-doping, confirming the presence of a substitutional dopant. The polaron hopping energy reduced from 0.307 to 0.290 eV depicting a lower defect concentration in P-doping in V2O5. At low temperatures, it is found to obey the Efros–Shklovskii variable range hopping mechanism. The estimated hopping range increased to 1.6 ± 0.1 nm in doped V2O5 in contrast to ∼1.3 nm in the undoped one. The electron spin resonance measurements show a diminishing broad ferromagnetic signal and rising paramagnetic signal (g = 1.97) with progressive P-doping depicting predominant isolated electronic spins in the doped sample. The same is corroborated in room temperature M–H with a distinct hysteresis that diminishes with P-doping and a rise of a paramagnetic slope. Moreover, the reduced oxygen defects and lower V4+ relative occupancy together with fermi level fall toward intrinsic position are substantiated by photoelectron emission studies.

Low-temperature electron transport of rutile-type GexSn1−xO2

Rutile-type wide and ultrawide band-gap oxide semiconductors are emerging materials for high-power electronics and deep ultraviolet optoelectronics applications. A rutile-type GeO2-SnO2 alloy (r-GexSn1–xO2) recently found is one of such materials. Herein, we report low-temperature electron transport properties of r-GexSn1−xO2 thin films with x = 0.28 and 0.41. Based on resistivity and magnetoresistance measurements, along with the theory of quantum interference, it is suggested that Efros–Shklovskii variable-range hopping, i.e., hopping over the states within the Coulomb gap, is dominant at lower temperatures (T ≤ 10 and 15 K) in both r-Ge0.41Sn0.59O2 and r-Ge0.28Sn0.72O2. The negative and positive magnetoresistances observed at low temperatures are attributable to the quantum interference and field-induced spin alignment, respectively. The magnetoresistance measurements at higher temperatures suggest that both Mott variable–range hopping and thermally activated band conduction occur at T < 100 K and that almost pure thermally activated band conduction takes place at T ≥ 150 K.

Low-frequency electrical response related to oxygen vacancies in Al3+ substituted M-type hexaferrite

The presence of oxygen vacancies is unavoidable in many complex metal oxide materials such as hexaferrites. This article investigates the role of crystal defects, such as oxygen vacancies, and different oxidation states of Fe ions, on the electrical conduction behaviors of Al3+ substituted Ba0.4La0.1Sr0.5Al x Fe12−x O19 hexaferrites by analyzing the temperature dependent AC impedance and AC conductivity. The optimal substitution of La3+ ions and high-temperature sintering is responsible for forming oxygen vacancies while reducing Fe from Fe3+ to Fe2+ cations, as observed in structural and XPS analysis, which affects electrical conduction behaviors. The departure from ideal Debye-type relaxation behavior is also one of the effects of crystal defects. Temperature variation of relaxation time shows a sharp change at around 403 K. This may be due to different electrical entities influencing the mode of electron hopping with temperature. The activation energy calculated from the temperature dependent relaxation time confirmed the presence of electron hopping through the bridging effects of the first ionization of oxygen vacancies Fe2+––Fe3+ below a temperature of 403 K. Above 403 K, electron hopping through different oxidation states of Fe3+ + e− → Fe2+ and migration of oxygen vacancies toward the bulk surface are responsible for the conduction mechanism. The DC resistivity and AC conductivity show that the bridging effects of oxygen defects can also induce Coulomb interaction between the defect sites resulting in Efros–Shklovskii variable range hopping and correlation barrier hopping below 403 K. Above 403 K, polaron-assisted electron hopping is more desirable, as confirmed by the non-overlapping small polaron tunneling model.

Insulating Nature of Iridium Oxide Ca5Ir3O12 Probed by Synchrotron-Radiation-Based Infrared Spectroscopy

Ca5Ir3O12 shows semiconducting behavior, although it is expected to have metallic conduction because of its 1/6-filled band. To investigate the insulating nature of Ca5Ir3O12, synchrotron-radiation-based infrared spectroscopy and electrical resistivity measurements were performed. Optical conductivity obtained using Kramers–Krönig transformation is compared with ab initio calculations based on density-functional and random-phase-approximation calculations, and their differences are carefully discussed. A detailed analysis of the temperature dependence of electrical resistivity along the c-axis reveals that ln ρ ∝ T−2/3. This temperature dependence indicates that the electrical conduction of Ca5Ir3O12 along the c-axis follows Efros–Shklovskii variable-range hopping. The optical conductivity with polarization parallel to the c-axis shows no clear onset at 1,300 cm−1 (0.16 eV) of the energy gap obtained by assuming the Arrhenius law. This feature of the optical conductivity is consistent with the fact that Ca5Ir3O12 follows Efros–Shklovskii variable-range hopping.

Electronic transport mechanisms in a thin crystal of the Kitaev candidateα-RuCl3 probed through guarded high impedance measurements

α-RuCl3 is considered to be the top candidate material for the experimental realization of the celebrated Kitaev model, where ground states are quantum spin liquids with interesting fractionalized excitations. It is, however, known that additional interactions beyond the Kitaev model trigger in α-RuCl3 a long-range zigzag antiferromagnetic ground state. In this work, we investigate a nanoflake of α-RuCl3 through guarded high impedance measurements aimed at reaching the regime where the system turns into a zigzag antiferromagnet. We investigated a variety of temperatures (1.45–175 K) and out-of-plane magnetic fields (up to 11 T), finding a clear signature of a structural phase transition at ≈160 K as reported for thin crystals of α-RuCl3, as well as a thermally activated behavior at temperatures above ≈30 K, with a characteristic activation energy significantly smaller than the energy gap that we observe for α-RuCl3 bulk crystals through our angle resolved photoemission spectroscopy (ARPES) experiments. Additionally, we found that below ≈30 K, transport is ruled by Efros–Shklovskii variable range hopping (VRH). Most importantly, our data show that below the magnetic ordering transition known for bulk α-RuCl3 in the frame of the Kitaev–Heisenberg model (≈7 K), there is a clear deviation from VRH or thermal activation transport mechanisms. Our work demonstrates the possibility of reaching, through specialized high impedance measurements, the thrilling ground states predicted for α-RuCl3 at low temperatures in the frame of the Kitaev–Heisenberg model and informs about the transport mechanisms in this material in a wide temperature range.

Exchange bias effect and inhomogeneous magnetism in 6H Ba3CoFeRuO9: Role of structural site disorder

Structural, magnetic, electrical and thermal investigations on ternary barium ruthenate Ba3CoFeRuO9 (BCFRO) reveal the role of the two different octahedral B-site in creating locally varying competing antiferromagnetic and ferromagnetic interactions. BCFRO forms in 6H hexagonal structure in the P63/mmc space group. Neutron diffraction and specific heat capacity measurements affirmed the absence of any long-range ordering and structural transition in the compound. DC thermomagnetic studies evidences spin glass magnetism with Tg ∼ 50 K. A large exchange bias (EB) field of 3.48 kOe is obtained at 3 K under a cooling field of 50 kOe. Careful analysis indicates, EB in our system stems from inhomogeneous magnetism owing to spatially varying chemical composition. Competing ferromagnetic and antiferromagnetic phases giving rise to spin glass behaviour is the manifestation of site disorder induced by mixed valences of magnetic ions. The exchange bias training effect in our system follows spin relaxation model of rotatable and frozen spins which are exchange coupled at the interface. Strong electron localisation occurs by virtue of the specific 6H structure with corner shared octahedral 2a site and face shared octahedral 4f site. The electrical and thermal transport in BCFRO follows Efros-Shklovskii variable range hopping (ES VRH) model below 150 K. The high resistivity of BCFRO at low temperatures is also reflected in the low thermal conductivity and huge Seebeck coefficient.

Metal-to-insulator transition in an Anderson insulator with Kondo impurities

We report a voltage-controlled critical behavior observed in a GaAs epitaxial structure containing a dense array of ErAs nanoparticles. When fabricated with metal electrodes, the structure displays a voltage- and temperature-dependent metal-to-insulator transition and strong hysteresis in the current versus voltage and versus temperature characteristics, with critical temperatures as high as 77 K. Furthermore, we observed a diverging rms deviation of the electrical conductance with respect to the critical bias voltage, which further supports the existence of a phase transition. The insulating phase is governed by Efros-Shklovskii variable range hopping, and the conductance reduces beyond instrument limits as the temperature drops toward zero; supporting it is an Anderson insulator. The metallic phase displays a conductance minimum at a critical temperature behaving similarly to that of single quantum dot due to Kondo resonance, and then the conductance increases as the temperature continues to drop. Furthermore, the metallic phase displays a colossal magnetoresistance under a weak magnetic field at 77 K while the insulating phase does not. And the metal-to-insulator phase transition can be induced by the magnetic field showing a critical discontinuity, similar to that versus temperature and voltage. We propose that the metal-to-insulator phase transition can be explained by the concept of an Anderson insulator with Kondo impurities.

Temperature-dependent transition of charge transport in core/shell structured colloidal quantum dot thin films: From Poole–Frenkel emission to variable-range hopping

Solution-processed core/shell quantum dot films are of great significance for light-emitting diodes. It is well known that the operation of core/shell quantum dot-based light-emitting diodes largely relies on charge transport. However, the charge transport mechanism in quantum dot films is still under debate and inconclusive. Herein, the temperature-dependent charge transport properties of light-emitting core/shell colloidal quantum dot thin films are characterized and analyzed across a wide temperature range, and the charge transport mechanism is studied. The results reveal that Poole–Frenkel emission conduction is applicable in the high-temperature range. With the decrease in the temperature, the measured current can be described by the Efros–Shklovskii variable-range hopping model. It is worth noting that, in both cases, trap states and disorders in the quantum dot film play a very important role in charge transport. These findings are of great importance for optimizing quantum dot light-emitting diodes and understanding the effects of charge transport on the device performance.

Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder

In the ideal disorder-free situation, a two-dimensional band-gap insulator has an activation energy for conductivity equal to half the band gap $\mathrm{\ensuremath{\Delta}}$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $\mathrm{\ensuremath{\Delta}}$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional insulator on a substrate containing Coulomb impurities, with random potential amplitude $\mathrm{\ensuremath{\Gamma}}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$. We show that the conductivity generically exhibits three regimes of conductivity, and only the highest-temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through activated hopping or Efros-Shklovskii variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We also arrive at a similar steep disorder driven insulator-metal transition in thin films of three-dimensional topological insulators with large dielectric constant, for which Coulomb impurities inside the film create a large disorder potential due to confinement of their electric field inside the film.

Electrical Conduction Mechanism of β‐MnTe Thin Film with Wurtzite‐Type Structure Using Radiofrequency Magnetron Sputtering

Manganese telluride (MnTe) compound is known to be a polymorphic chalcogenide. Recently, it has been reported that the MnTe shows nonvolatile memory properties with a significant change in resistance via a polymorphic transition between NiAs‐type (NC) structure (low resistance) and wurtzite‐type (WZ) structure (high resistance). This crystalline polymorphic MnTe is expected to realize a phase‐change memory with fast operation speed and ultralow operation energy. While the NC‐MnTe, generally designated as α‐MnTe, is intensively studied, WZ‐MnTe is still poorly understood. Herein this study, electrical conduction mechanism of a β‐MnTe film with a WZ‐type structure is studied. A resistivity, Hall mobility, and Seebeck coefficient of the WZ‐MnTe film are measured at various temperatures. The temperature dependence of resistivity in the temperature range 120–300 K clearly indicates that the WZ‐MnTe film shows a variable‐range hopping (VRH) conduction. In this temperature region, with decreasing temperature, the conduction mechanism changes from Mott–VRH conduction to Efros–Shklovskii VRH conduction at about 210 K. Furthermore, the low thermally activated Hall mobility, occurrence of Hall‐effect sign anomaly, and relatively low activation energy for thermopower, which are the observed results, suggest that the small polaron hopping conduction is dominant above 310 K.

Mott and Efros–Shklovskii Variable-Range Hopping Conduction in Films Formed by Silicon Nanoparticles Doped with Phosphorus and Boron

Mott and Efros–Shklovskii Variable-Range Hopping Conduction in Films Formed by Silicon Nanoparticles Doped with Phosphorus and Boron

Investigation of charge transport of monolayer polymeric films with field effect tuning and molecular doping for chemiresistive sensing application

Semiconducting and conducting 2D conjugated polymers have been widely investigated due to their merits such as mechanical flexibility, solution processability, and large-area fabrication. Nevertheless, the transport characteristics of field-effect tuning and molecule doping ultra-thin even monolayer conjugated polymers haven't been understood thoroughly. Moreover, a general and facile method for the direct synthesis of large-area conjugated polymer monolayer films with good uniformity and high coverage on the SiO2/Si substrates is highly desirable and still remains challenging. Here, we have used the simple drop-casting method to successfully fabricate high-coverage and homogeneous poly(2,5-bis(3-hexadecylthiophen-2-yl)thieno [3], [2-b]thiophene) (PBTTT) monolayer films directly on the surface of SiO2/Si substrate. The electrical transport behaviors were investigated systematically in both field effect doping and molecular doping the systems. 2D hopping transport was observed dominating the conductance of the field effect tuned monolayer PBTTT. While Efros-Shklovskii variable range hopping (ES-VRH) contributed the main transport at higher carrier concentration system doped with 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4-TCNQ). And the onset interlayer transport should effectively reduce the energetic disorder revealed in bi- or tri-layer films. In addition, the F4-TCNQ doping conductive PBTTT monolayer films displayed superior chemiresistive sensing toward ammonia. The proposed semiconducting and conducting conjugated polymer monolayer-based ideal platform can open new avenues for ultra-thin film organic electronics.

Easily Processable, Highly Transparent and Conducting Thiol-Functionalized Reduced Graphene Oxides Langmuir-Blodgett Films.

We report synthesis and fabrication of highly thionated reduced graphene oxide and its Langmuir-Blodgett (LB) film without an LB trough. As the synthesized product, mercapto reduced graphene oxide (mRGO) contains high thiol content estimated from XPS, corresponding to a surface coverage of 1.3 SH/nm2. The mRGO LB film shows two electronic transport properties, following Efros-Shklovskii variable-range hopping (VRH) and Mott VRH at low and high temperature, respectively. Optical and band gap of the LB film was estimated from Tauc plot and semi-logarithmic-scale plot of sheet resistance versus temperature to be 0.6 and 0.1 eV, respectively. Additionally, the sheet resistance of the mRGO LB film depends on the quantity of the thiol functional group with the same transmittance at 550 nm (500 kΩ for mRGO, 1.3 MΩ for tRGO with 92% transmittance).

Nonlinear electrical behaviors and conductivity mechanisms in Ca1‐xYbxCeNbWO8 ceramics

AbstractIn this study, we investigated the nonlinear electrical behaviors and conductivity mechanisms of Ca1‐xYbxCeNbWO8 ceramics, which are prepared by the solid‐state sintering method. CeO2 and CeNbO4 phases occur when the Yb3+ doping amount is greater than 0.1 in the CaCeNbWO8‐based ceramics. With the continuous incorporation of Yb3+, the grain size of the ceramics first decreases and then increases. The Ce3+ concentration in the ceramics decreases with increasing Yb3+ content. In the temperature range of 298.15 to 1073.15K, the relationship between ln ρ and 1000/T shows nonlinear electrical behaviors, which is attributed to the different conductivity mechanisms at high and low temperatures (ρ and T are resistivity and temperature, respectively). In the temperature range of 298.15 to 773.15K, the electrical conduction in Ca1‐xYbxCeNbWO8 ceramics follows the Efros‐Shklovskii variable‐range hopping (ES‐VRH) conduction mechanism, thermal activation conduction (x < 0.2), and two‐dimensional Mott VRH conduction mechanism (x = 0.2). Furthermore, the electrical conduction obeys the thermal activation conduction mechanism in the temperature range of 773.15 to 1073.15K. The activation energy for the electrical conduction is calculated based on the different hopping conduction mechanisms.

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.

Multiscale Charge Transport in van der Waals Thin Films: Reduced Graphene Oxide as a Case Study.

Large area van der Waals (vdW) thin films are assembled materials consisting of a network of randomly stacked nanosheets. The multiscale structure and the two-dimensional (2D) nature of the building block mean that interfaces naturally play a crucial role in the charge transport of such thin films. While single or few stacked nanosheets (i.e., vdW heterostructures) have been the subject of intensive works, little is known about how charges travel through multilayered, more disordered networks. Here, we report a comprehensive study of a prototypical system given by networks of randomly stacked reduced graphene oxide 2D nanosheets, whose chemical and geometrical properties can be controlled independently, permitting to explore percolated networks ranging from a single nanosheet to some billions with room-temperature resistivity spanning from 10-5 to 10-1 Ω·m. We systematically observe a clear transition between two different regimes at a critical temperature T*: Efros-Shklovskii variable-range hopping (ES-VRH) below T* and power law behavior above. First, we demonstrate that the two regimes are strongly correlated with each other, both depending on the charge localization length ξ, calculated by the ES-VRH model, which corresponds to the characteristic size of overlapping sp2 domains belonging to different nanosheets. Thus, we propose a microscopic model describing the charge transport as a geometrical phase transition, given by the metal-insulator transition associated with the percolation of quasi-one-dimensional nanofillers with length ξ, showing that the charge transport behavior of the networks is valid for all geometries and defects of the nanosheets, ultimately suggesting a generalized description on vdW and disordered thin films.

A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures

In this paper, we discuss low-temperature hopping-conductivity behavior in the insulating phase, in the absence of a magnetic field. We conduct a theoretical study of the crossover from hopping to activated transport in a GaAs two-dimensional hole system at low temperatures, finding that a crossover takes place from the Efros-Shklovskii variable-range hopping (VRH) regime to an activated regime in this system. This conductivity behavior in p-GaAs quantum wells is qualitatively consistent with the laws laid down in theories of localized electron interactions. Given sufficiently strong interactions, the holes in the localized states are able to hop collectively.

Deuteration Effects on the Transport Properties of (TMTTF)2X Salts

The electronic properties in the quasi-one-dimensional Fabre salts are strongly affected by electronic correlations along the molecular stacks, but also by the interactions with the anions located in a cage that is formed by the methyl end groups. We systematically compare the charge transport in deuterated and protonated (TMTTF)2X salts with the anions X = Br, PF6, SbF6, and ClO4, ranging from Mott and Efros–Shklovskii variable-range hopping to activated band transport with a temperature dependent energy gap. The strong dependence of charge localization and ordering on the anion size and deuteration confirms the subtle structural involvement of the anions in the charge transport along the TMTTF stack.