3D Variable Range Hopping Research Articles

Observation of Enhanced Long-Range Ferromagnetic Order in B-Site Ordered Double Perovskite Oxide Cd2CrSbO6.

A B-site ordered double perovskite oxide Cd2CrSbO6 was synthesized under high-pressure and high-temperature conditions. The compound crystallizes to a monoclinic structure with a space group of P21/n. The charge configuration is confirmed to be that of Cd2+/Cr3+/Sb5+. The magnetic Cr3+ ions form a tetrahedral structural frustrated lattice, while a long-range ferromagnetic phase transition is found to occur at TC = 16.5 K arising from the superexchange interaction via the Cr-O-Cd-O-Cr pathway. Electrical transport measurements indicate that Cd2CrSbO6 is an insulator that can be described by the Mott 3D variable range hopping mechanism. First-principles calculations reproduce well the ferromagnetic and insulating ground state of Cd2CrSbO6 with an energy band gap of 1.55 eV. The intrinsic ferromagnetic insulating nature qualifies Cd2CrSbO6 as a promising candidate for possible spintronics applications.

Charge Puddles Driven Complex Crossover of Magnetoresistance in Non-Topological Sulfur Doped Antimony Selenide Nanowires.

A race to achieve a crossover from positive to negative magnetoresistance is intense in the field of nanostructured materials to reduce the size of memory devices. Here, the unusual complex magnetoresistance in nonmagnetic sulfur-doped Sb2Se3nanowires is demonstrated. Intentionally, sulfur is doped in such a way to nearly achieve the charge neutrality point that is evident from switching of carrier type from p-type to n-type at 13 K as inferred from the low-temperature thermoelectric power measurements. A change from 3D variable range hopping (VRH) to power law transport with α = 0.18 in resistivity measurement signifies a Luttinger liquid transport with weak links through the nanowires. Interestingly, high magnetic field induced negative magnetoresistance (NMR) occurring in hole dominated temperature regimes can only be explained by invoking the concept of charge puddles. Spot energy dispersive spectroscopy (EDS), magnetic force microscopy (MFM) measurements, Tmottand Regel plot indicate an enhanced disorder in these sulfurized nanowires that are found to be the precursor for the formation of these charge puddles. Tunability of conducting states in these nanowires is investigated in the light of interplay of carrier type, magnetic field, temperature, and intricate intra-inter wire transport that makes this nanowires potential for large scale spintronic devices.

Resistive Avalanches in La1-xSrxCoO3-δ (x = 0, 0.3) Thin Films and Their Reversible Evolution by Tuning Lattice Oxygen Vacancies (δ).

Strong correlations are often manifested by exotic electronic phases and phase transitions. LaCoO3-δ (LCO) is a system that exhibits such strong electronic correlations with lattice-spin-charge-orbital degrees of freedom. Here, we show that mesoscopic oxygen-deficient LCO films show resistive avalanches of about 2 orders of magnitude due to the metal-insulator transition (MIT) of the film at about 372 K for the 25 W RF power-deposited LCO film on the Si/SiO2 substrate. In bulk, this transition is otherwise gradual and occurs over a very large temperature range. In thin films of LCO, the oxygen deficiency (0 < δ < 0.5) is more easily reversibly tuned, resulting in avalanches. The avalanches disappear after vacuum annealing, and the films behave like normal insulators (δ ∼0.5) with Co2+ in charge ordering alternatively with Co3+. This oxidation state change induces spin state crossovers that result in a spin blockade in the insulating phase, while the conductivity arises from hole hopping among the allowed cobalt Co4+ ion spin states at high temperature. The chemical pressure (strain) of 30% Sr2+ doping at the La3+ site results in reduction in the avalanche magnitude as well as their retention in subsequent heating cycles. The charge nonstoichiometry arising due to Sr2+ doping is found to contribute toward hole doping (i.e., Co3+ oxidation to Co4+) and thereby the retention of the hole percolation pathway. This is also manifested in energies of crossover from the 3D variable range hopping (VRH) type transport observed in the temperature range of 300-425 K, while small polaron hopping (SPH) is observed in the temperature range of 600-725 K for LCO. On the other hand, Sr-doped LCO does not show any crossover and only the VRH type of transport. The strain due to Sr2+ doping refrains the lattice from complete conversion of δ going to 0.5, retaining the avalanches.

Thermoelectric Properties of Cotton Fabrics Dip-Coated in Pyrolytically Stripped Pyrograf® III Carbon Nanofiber Based Aqueous Inks.

The transport properties of commercial carbon nanofibers (CNFs) produced by chemical vapor deposition (CVD) depend on the various conditions used during their growth and post-growth synthesis, which also affect their derivate CNF-based textile fabrics. Here, the production and thermoelectric (TE) properties of cotton woven fabrics (CWFs) functionalized with aqueous inks made from different amounts of pyrolytically stripped (PS) Pyrograf® III PR 25 PS XT CNFs via dip-coating method are presented. At 30 °C and depending on the CNF content used in the dispersions, the modified textiles show electrical conductivities (σ) varying between ~5 and 23 S m-1 with a constant negative Seebeck coefficient (S) of -1.1 μVK-1. Moreover, unlike the as-received CNFs, the functionalized textiles present an increase in their σ from 30 °C to 100 °C (dσ/dT > 0), explained by the 3D variable range hopping (VRH) model as the charge carriers going beyond an aleatory network of potential wells by thermally activated hopping. However, as it happens with the CNFs, the dip-coated textiles show an increment in their S with temperature (dS/dT > 0) successfully fitted with the model proposed for some doped multiwall carbon nanotube (MWCNT) mats. All these results are presented with the aim of discerning the authentic function of this type of pyrolytically stripped Pyrograf® III CNFs on the thermoelectric properties of their derived textiles.

Unveiling Charge-Transport Mechanisms in Electronic Devices Based on Defect-Engineered MoS2 Covalent Networks.

Device performance of solution-processed 2D semiconductors in printed electronics has been limited so far by structural defects and high interflake junction resistance. Covalently interconnected networks of transition metal dichalcogenides potentially represent an efficient strategy to overcome both limitations simultaneously. Yet, the charge-transport properties in such systems have not been systematically researched. Here, the charge-transport mechanisms of printed devices based on covalent MoS2 networks are unveiled via multiscale analysis, comparing the effects of aromatic versus aliphatic dithiolated linkers. Temperature-dependent electrical measurements reveal hopping as the dominant transport mechanism: aliphatic systems lead to 3D variable range hopping, unlike the nearest neighbor hopping observed for aromatic linkers. The novel analysis based on percolation theory attributes the superior performance of devices functionalized with π-conjugated molecules to the improved interflake electronic connectivity and formation of additional percolation paths, as further corroborated by density functional calculations. Valuable guidelines for harnessing the charge-transport properties in MoS2 devices based on covalent networks are provided.

3D Variable Range Hopping Electrical Conduction of a Carbon from Polyaniline Vapor

Carbon with a metallic reflection was prepared from polyaniline (PANI) vapor deposited on the inner quartz wall of a furnace. Electron probe microanalyzer analysis proved that the resultant contained carbon, oxygen, nitrogen, and sulfur atoms. A Dysonian line shape with paramagnetic properties was observed for the resulting carbon from PANI in the electron spin-resonance spectroscopy measurement. The resistance vs. temperature curve of the carbon indicated semiconductor-insulator properties in a low-temperature range. Electrical conduction in the carbon was carried out with 3D variable range hopping.

Thermoelectric Properties of N-Type Poly (Ether Ether Ketone)/Carbon Nanofiber Melt-Processed Composites.

The thermoelectric properties, at temperatures from 30 °C to 100 °C, of melt-processed poly(ether ether ketone) (PEEK) composites prepared with 10 wt.% of carbon nanofibers (CNFs) are discussed in this work. At 30 °C, the PEEK/CNF composites show an electrical conductivity (σ) of ~27 S m-1 and a Seebeck coefficient (S) of -3.4 μV K-1, which means that their majority charge carriers are electrons. The origin of this negative Seebeck is deduced because of the impurities present in the as-received CNFs, which may cause sharply varying and localized states at approximately 0.086 eV above the Fermi energy level (EF) of CNFs. Moreover, the lower S, in absolute value, found in PEEK/CNF composites, when compared with the S of as-received CNFs (-5.3 μV K-1), is attributed to a slight electron withdrawing from the external layers of CNFs by the PEEK matrix. At temperatures from 30 °C to 100 °C, the σ (T) of PEEK/CNF composites, in contrast to the σ (T) of as-received CNFs, shows a negative temperature effect, understood through the 3D variable-range hopping (VRH) model, as a thermally activated hopping mechanism across a random network of potential wells. Moreover, their nonlinear S (T) follows the same behavior reported before for polypropylene composites melt-processed with similar CNFs at the same interval of temperatures.

Study of the impact of interface traps associated with SiN X passivation on AlGaN/GaN MIS-HEMTs

In this work, we show that a bilayer SiN x passivation scheme which includes a high-temperature annealed SiN x as gate dielectric, significantly improves both ON and OFF state performance of AlGaN/GaN metal insulator semiconductor high electron mobility transistors (MISHEMTs). Surface and bulk leakage paths were determined from devices with different SiN x passivation schemes. Temperature-dependent mesa leakage studies showed that the surface conduction could be explained using a 2D variable range hopping mechanism; this is attributed to the mid-gap interface states at the GaN(cap)/SiN x interface generated due to the Ga–Ga metal like bonding states. It was found that the high temperature annealed SiN x gate dielectric exhibited the lowest interface state density and a two-step C–V indicative of a superior quality SiN x /GaN interface as confirmed from conductance and capacitance measurements. High-temperature annealing helps form Ga–N bonding states, thus reducing the shallow metal-like interface states. MISHEMT measurements showed a significant reduction in gate leakage and a four-orders of magnitude improvement in the ON/OFF ratio while increasing the saturation drain current (I DS) by a factor of 2. Besides, MISHEMTs with two-step SiN x passivation exhibited a relatively flat transconductance profile, indicating lower interface states density. The dynamic R on with gate and drain stressing measurements also showed about 3× improvements in devices with bilayer SiN x passivation.

Nonlinear Thermopower Behaviour of N-Type Carbon Nanofibres and Their Melt Mixed Polypropylene Composites.

The temperature dependent electrical conductivity σ (T) and thermopower (Seebeck coefficient) S (T) from 303.15 K (30 °C) to 373.15 K (100 °C) of an as-received commercial n-type vapour grown carbon nanofibre (CNF) powder and its melt-mixed polypropylene (PP) composite with 5 wt.% of CNFs have been analysed. At 30 °C, the σ and S of the CNF powder are ~136 S m−1 and −5.1 μV K−1, respectively, whereas its PP/CNF composite showed lower conductivities and less negative S-values of ~15 S m−1 and −3.4 μV K−1, respectively. The σ (T) of both samples presents a dσ/dT < 0 character described by the 3D variable range hopping (VRH) model. In contrast, their S (T) shows a dS/dT > 0 character, also observed in some doped multiwall carbon nanotube (MWCNT) mats with nonlinear thermopower behaviour, and explained here from the contribution of impurities in the CNF structure such as oxygen and sulphur, which cause sharply varying and localized states at approximately 0.09 eV above their Fermi energy level (EF).

Non-adiabatic small-polaron and 3D-Mott's variable range conductions above 100 K in Pb-substituted double-layered manganites LaSm0.4Ca1.6-xPbxMn2O7

In this study, the role of Pb substitution on the microstructural and magneto-transport properties of the double layered manganites LaSm0.4Ca1.6-xPbxMn2O7 (x = 0, 0.1 and 0.2), prepared by the solid-state reaction method, was investigated. On the samples, X-Ray Diffraction, Scanning Electron Microscopy and resistivity as a function of temperature measurements were performed. XRD measurements revealed that the samples crystallized in a tetragonal phase with an I4/mmm space group and that the lattice parameters increased with increasing Pb content. SEM measurements indicated the granular character and the average grain sizes ranged between 0.5 and 4 μm for all the samples. The temperature dependence of resistivity of all the samples shows insulating-like behavior for the studied range of temperature (T > 100 K). The maximum magnetoresistance (MR%) value was found to be 31.95% at 100 K for the sample with x = 0, while it was 11% and 8% for the samples with x = 0.1 and 0.2, respectively. The resistivity curves are found to be well described by the Adiabatic Small Polaron Model in the range and Mott's 3D Variable Range Hopping model in the range. The density of states near the Fermi level (DOS), mean hopping distance, and mean hopping energy values were computed in the range, and the role of Pb substitution on these parameters was discussed as well.

Tunable Low Crystallinity Carbon Nanotubes/Silicon Schottky Junction Arrays and Their Potential Application for Gas Sensing.

Highly ordered nanostructure arrays have attracted wide attention due to their wide range of applicability, particularly in fabricating devices containing scalable and controllable junctions. In this work, highly ordered carbon nanotube (CNT) arrays grown directly on Si substrates were fabricated, and their electronic transport properties as a function of wall thickness were explored. The CNTs were synthesized by chemical vapor deposition inside porous alumina membranes, previously fabricated on n-type Si substrates. The morphology of the CNTs, controlled by the synthesis parameters, was characterized by electron microscopies and Raman spectroscopy, revealing that CNTs exhibit low crystallinity (LC). A study of conductance as a function of temperature indicated that the dominant electric transport mechanism is the 3D variable range hopping. The electrical transport explored by I–V curves was approached by an equivalent circuit based on a Schottky diode and resistances related to the morphology of the nanotubes. These junction arrays can be applied in several fields, particularly in this work we explored their performance in gas sensing mode and found a fast and reliable resistive response at room temperature in devices containing LC-CNTs with wall thickness between 0.4 nm and 1.1 nm.

Magnetic and electrical properties by Ca2+ doping in SmCrO3 orthochromites

Spectroscopic (UV–vis and XPS) magnetic and electrical properties of the Ca2+ doped SmCrO3 system were phenomenologically investigated. The Cr3+, Cr5+, and Cr6+ species were identified by XPS spectroscopy in Sm1−xCaxCrO3 (0 ≤ x ≤ 0.20). Rietveld analyses of the X-ray diffraction data reveal a smooth decrease in the cel`l parameters assigned to the Cr6+ formation as a function of the Ca2+ content. Diffuse reflectance spectroscopy showed that the wider optical bandgap of the system corresponds to a charge transfer process, and it disappears for x ≥ 0.1, showing t2 g-eg electronic gaps. The electrical measurements were fitted in two temperature ranges; for low temperatures (85–150 K), a 3D variable-range hopping mechanism seems to prevail, while for the 150–300 K range, the electrical behavior is well represented by the small-polarons conduction mechanism. Magnetic properties of Sm1−xCaxCrO3 were highly sensitive to the Ca2+ content, and the TN values varied from 192 to 151 K for x = 0 and x = 0.20, respectively; TRS varied from 34 to 9 K for the same x values. Isothermal magnetization curves at 5 K suggest that, as a function of the Ca2+ content, the Γ4 ferromagnetic phase remains for x ≥ 0.04; while for x = 0 and x = 0.02, the Γ2 ferromagnetic phase is the only one observed.

Facile in-situ synthesis, microstructural, morphological and electrical transport properties of polypyrrole-cuprous iodide hybrid nanocomposites

In this study, polypyrrole cuprous iodide (PPy-CuI) hybrid nanocomposites were synthesized in an aqueous medium via an in-situ chemical oxidation route with ammonium persulphate as an oxidizing agent to report the microstructural, morphological, and electrical properties of as-synthesized specimens. By using an in-situ oxidative polymerization method, sonochemically synthesized γ-CuI nanocrystals were mixed with a PPy matrix in varying weight percentages (10–40 ​%). The purity, crystallinity and structure of hybrid nanocomposites were determined using X-ray diffractometry. The average crystallite size of hybrid nanocomposites was calculated using the Debye-Scherrer, Williamson-Hall and Size-Strain plot methods. All specimens' intrinsic strain was estimated using the Williamson-Hall plot and the Size-Strain plot methods. The field emission scanning microscopy revealed that the surface morphology changed from granular to overgrown clusters as the weight percent of CuI nanocrystals is increased from 10 to 40 ​% in PPy-CuI hybrid nanocomposites. The Fourier transform infrared spectroscopy indicates the formation of PPy and successful insertion of γ-CuI nanocrystals into the PPy matrix. The room temperature dc electrical conductivity is found to decrease from 6.3 ​× ​10−2 Scm−1 to 1.70 ​× ​10−3Scm−1as the wt% of γ-CuI nanocrystals increases from 10 to 40 ​% in hybrid nanocomposites. Furthermore, the increasing trend of dc conductivity with temperature is due to all samples' semiconducting nature. In the temperature range of 200–300 ​K, the measured experimental data followed the Arrhenius and Mott's 3d variable range hopping (VRH) model. The values of average activation energy, average hopping energy, density of states at Fermi level, average hopping distance and Mott's characteristic temperature of PPy-CuI (40 ​%) hybrid nanocomposites at 300 ​K were estimated to be ~60 ​meV, ~29 ​meV, 6.36 ​× ​1022 ​cm−3eV−1, 5.06 ​Å and 1901 K, respectively.

Investigation of temperature-dependent conduction mechanism in MnCo2O4/polypyrrole nanocomposites by three-dimensional variable range hopping (3D-VRH) and band-conduction model

Nanoparticles of manganese cobalt oxide (MnCo2O4) have been prepared with the hydrothermal method, while nanocomposites of MnCo2O4/polypyrrole (MCO/PPy) have been prepared by dispersing MCO nanoparticles in the PPy matrix by an in situ chemical polymerization method. MCO/PPy nanocomposites' structural characterizations were made by x-ray diffraction (XRD) and field-emission scanning electron microscope (FESEM). XRD and FESEM analyses give evidence that MCO nanoparticles are dispersed uniformly, and there is an effect on crystallinity and particle size. The observed shift in the stretching vibrations of Fourier transform infrared spectra for MCO/PPy nanocomposites confirms the interaction between MCO nanoparticles and PPy. Furthermore, the temperature-dependent (300–453 K) DC conductivity measurements of MCO/PPy nanocomposites depict the presence of different conduction mechanisms. The conductivity data are well fitted by the 3D variable range hopping (3D-VRH) model and the band conduction model at low and high temperatures. The characteristic temperature (T0) calculated from the 3D-VRH and the activation energy (Ea) calculated from the band conduction model support the observed highest conductivity for the 10 wt. % MCO/PPy nanocomposite.

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.

Comparison of temperature dependences of electrical conductivity of composite rGO-SWNT film with rGO and SWNT films

Temperature dependences of electrical conductivity of reduced graphene oxide composite with single-walled nanotubes (rGO-SWNTs) and rGO films has been studied in the temperature range of 25–290 K. Both films were obtained by vacuum filtration of aqueous suspensions. Temperature dependences of conductivity of films were found similar to the conductivity observed in disordered semiconducting systems. It was demonstrated that the behavior of the conductivity temperature dependence of pure rGO, SWNTs and composite film is different. The temperature dependences of the resistance R(T) of the films were analyzed within the framework of the variable range hopping (VRH) transport in which electron motion is due to the thermo-activated quantum tunneling between localized states. Two-dimensional Mott VRH (Mott 2D VRH) and Efros-Shklovskii VRH (ES VRH) models were applied for analysis. Mott 2D VRH was observed for rGO-SWNT film in the interval of 25–200 K. At higher temperatures R(T) of rGO-SWNT was fitted with Arrhenius-like equation describing electron activation from localized states to delocalized ones. R(T) of the rGO film followed the Mott 2D VRH model from 165 to 290 K, however, at lower temperatures ES VRH model was exploited. From approximation of R(T) by these models the parameters of the electron transport in rGO-SWNT and rGO films were estimated. It was suggested that nanotubes in rGO-SWNT composite serve as conductive bridges among rGO sheets enhancing the conductivity as compared to rGO. The conductivity of rGO also influences on the composite properties because 2D character of electron motion is kept in sharp contrast to SWNT film which demonstrated three-dimensional Mott VRH electron transport in the same temperature range.

Variable-range hopping conduction with positive and negative magnetoresistance transformation in reduced graphene oxide mesostructures

Graphene is a two-dimensional (2D) material with excellent physical properties, and its special charge transport characteristics promote extensive exploration based on graphene electronic devices. In order to determine the effect of the mesostructure on the electromagnetic transport properties of graphene, the temperature dependencies of the resistance and the magnetoresistance (MR) of reduced graphene oxide paper (rGOP) and reduced graphene oxide aerogel fiber (rGAF) were systematically measured. The conduction mechanism was systematically studied, and the graphene paper and aerogel fiber were in accordance with Mott’s 2D and 3D variable-range hopping (VRH) models, respectively. With the decrease of temperature, the transition from small-negative MR to large-positive MR was observed, the influences of wave function shrinkage and quantum interference effects on positive and negative MR were discussed in the framework of hopping conduction.

Weak antilocalization in Sb2Te3 nano-crystalline topological insulator

Microwave-assisted solvothermal route has been followed to synthesize Sb2Te3 nanomaterial. The morphology and topography of the material have been studied in FESEM and AFM measurements respectively. The optical band gap of the material is found to be ~ 0.25 eV as measured in IR spectroscopy. Temperature dependent resistivity of the nanostructure shows thermal activation behavior in the high temperature region as well as it follows 3D Variable Range Hopping mechanism in the moderate temperature region. Electron-electron interaction and quantum interference dominated upturn in the resistivity is observed at T < 24 K. Low field magnetoconductivity (MC) shows disorder induced weak localization (WL) which makes over to weak antilocalization (WAL) at T ≥ 4 K. MC after post annealing of the sample shows WAL behavior at T < 4 K also. Quantum correction to the low field magnetoconductivity of the material follows Hikami-Larkin-Nagaoka (HLN) equation. The obtained parameters of the HLN equation indicate that the system follows the 2D conduction mechanism and presence of a single conduction channel at low temperature. High field MR exhibits linear and positive magnetoresistance (LPMR) which suggests the survival of robust topological surface state conduction in the nanostructured bulk Sb2Te3 topological insulator.

Observation of Different Charge Transport Processes and Origin of Magnetism in rGO and rGO-ZnSe Composite

The effect of nanoparticle incorporation inside reduced graphene oxide (rGO) layers on the electrical transport properties has been investigated by temperature-dependent resistivity measurements on rGO and rGO-zinc selenide (rGO-ZnSe) thin films in a wide temperature range of 84–473 K. The fraction of ZnSe in rGO-ZnSe composite has been varied from 26 to 98%. Resistance curve derivative analysis reveals a conduction mechanism consistent with Mott two-dimensional (2D) variable range hopping (VRH) in rGO films, whereas different rGO-ZnSe samples exhibit three-dimensional (3D) VRH at lower temperatures (84–280 K). At higher temperatures (290–473 K), Arrhenius-like transport was observed for all of the samples. A model where ZnSe nanoparticles are incorporated inside wrinkled rGO layers to facilitate interlayer connections, thus 3D charge transport, has been proposed. Room-temperature carrier mobility values, calculated using trap-free space charge limited current conduction model in the dark, reach a maximum...

Transport properties of rocksalt-type cluster sulfides V4GeS8 and Mn substitution effect

We experimentally and theoretically investigated the electronic and thermoelectric properties of rocksalt-type cluster sulfides V4-xMnxGeS8 (x = 0, 0.02, 0.05). For a polycrystalline sample of V4GeS8, the lnρ-T−1 curve shows good linearity over 250 K. On the other hand, the lnρ-T−1/4 curve shows linearity at less than 250 K. This result indicates that the Arrhenius type is dominant over 250 K and the 3D variable range hopping is dominant in the low-temperature region. For the Mn substitution V4-xMnxGeS8 (x = 0.02, 0.05), the absolute value of ρ and S decreases with increasing x. This result indicates that the hole doping occurred by the substitution of V3+ to Mn2+. The calculated HOMO of V4GeS8 using density functional theory calculation shows that the V-3d orbital in the V4S4 cluster is dominant. This result indicates that the conduction holes pass through V4S4 to other V4S4.