Resistor Network Model Research Articles

Understanding disorder in monolayer graphene devices with gate-defined superlattices

Engineering superlattices (SLs)-which are spatially periodic potential landscapes for electrons-is an emerging approach for the realization of exotic properties, including superconductivity and correlated insulators, in two-dimensional materials. While moiré SL engineering has been a popular approach, nanopatterning is an attractive alternative offering control over the pattern and wavelength of the SL. However, the disorder arising in the system due to imperfect nanopatterning is seldom studied. Here, by creating a square lattice of nanoholes in the SiO2dielectric layer using nanolithography, we study the SL potential and the disorder formed in hBN-graphene-hBN heterostructures. Specifically, we observe that while electrical transport shows distinct SL satellite peaks, the disorder of the device is significantly higher than graphene devices without any SL. We use finite-element simulations combined with a resistor network model to calculate the effects of this disorder on the transport properties of graphene. We consider three types of disorder: nanohole size variations, adjacent nanohole mergers, and nanohole vacancies. Comparing our experimental results with the model, we find that the disorder primarily originates from nanohole size variations rather than nanohole mergers in square SLs. We further confirm the validity of our model by comparing the results with quantum transport simulations. Our findings highlight the applicability of our simple framework to predict and engineer disorder in patterned SLs, specifically correlating variations in the resultant SL patterns to the observed disorder. Our combined experimental and theoretical results could serve as a valuable guide for optimizing nanofabrication processes to engineer disorder in nanopatterned SLs.

Efficiency and controllability of stochastic boolean function generation by a random network of non-linear nanoparticle junctions

Amid efforts to address energy consumption in modern computing systems, one promising approach takes advantage of random networks of non-linear nanoscale junctions formed by nanoparticles as substrates for neuromorphic computing. These networks exhibit emergent complexity and collective behaviors akin to biological neural networks, characterized by self-organization, redundancy, and non-linearity. Based on this foundation, a generalization of n-inputs devices has been proposed, where the associated weights depend on all the input values. This model, called receptron, has demonstrated its capability to generate Boolean functions as output, representing a significant breakthrough in unconventional computing methods. In this work, we characterize and present two actual implementations of this paradigm. One approach leverages the nanoscale properties of cluster-assembled Au films, while the other utilizes the recently introduced Stochastic Resistor Network (SRN) model. We first provide a concise overview of the electrical properties of these systems, emphasizing the insights gained from the SRN regarding the physical processes within real nanostructured gold films at a coarse-grained scale. Furthermore, we present evidence indicating the minimum complexity level required by the SRN model to achieve a stochastic dynamics adequate to effectively model a novel component for logic systems. To support our argument that these systems are preferable to conventional random search algorithms, we discuss quantitative criteria based on Information-theoretic tools. This suggests a practical means to steer the stochastic dynamics of the system in a controlled way, thus focusing its random exploration where it is most useful.

Discrete element model for effective electrical conductivity of spark plasma sintered porous materials

AbstractThis paper aims to analyse electrical conduction in partially sintered porous materials using an original resistor network model within discrete element framework. The model is based on sintering geometry, where two particles are connected via neck. Particle-to-particle conductance depends on neck size in sintered materials. Therefore, accurate evaluation of neck size is essential to determine conductance. The neck size was determined using volume preservation criterion. Additionally, grain boundary correction factor was introduced to compensate for any non-physical overlaps between particles, particularly at higher densification. Furthermore, grain boundary resistance was added to account for the porosity within necks. For numerical analysis, the DEM sample was generated using real particle size distribution, ensuring a heterogeneous and realistic microstructure characterized by a maximum-to-minimum particle diameter ratio of 15. The DEM sample was subjected to hot press simulation to obtain geometries with different porosity levels. These representative geometries were used to simulate current flow and determine effective electrical conductivity as a function of porosity. The discrete element model (DEM) was validated using experimentally measured electrical conductivities of porous NiAl samples manufactured using spark plasma sintering (SPS). The numerical results were in close agreement with the experimental results, hence proving the accuracy of the model. The model can be used for microscopic analysis and can also be coupled with sintering models to evaluate effective properties during the sintering process.

Novel 3-D resistor network simulation method for mixed ionic and electronic conducting electrodes

In this study, we propose and analyze a new resistor network model designed for the analysis of electrodes with mixed conductivity in solid oxide fuel cells (SOFCs). Resistor networks simulation for electrodes with mixed ionic and electronic conductivity oxides (MIEC) is not typically used due to the presence of oxygen ions and electrons as charge carriers. To address this complexity within the model, two resistor networks are employed. These networks conduct the different electrical species, and are linked through a resistor representing the charge transfer (CT) process. In the case of mixed-conducting electrodes, this CT occurs at the surface exposed to the gas phase. The electrode simulated in this study is generated using the discrete element method of random sphere insertion, and subsequently voxelized to create the resistor network. This method considers the geometric and microstructural parameters of the electrode, such as porosity, particle size, and electrode thickness. Electrical parameters are incorporated into the network through the values of the various conductivities characterizing MIEC oxides and including CT interface conductivities. By integrating geometric, microstructural, and electrical parameters, the model accurately captures the behavior of the electrodes. The close agreement between simulation and experimental/theoretical results highlights the efficacy of the approach in elucidating the electrochemical processes occurring at the MIEC electrode.

Equivalent resistance of a periodic and asymmetric 2 × n resistor network

This article proposes a class of periodic and asymmetric 2 × n resistor network model, and adopts the RT-V theory to conduct in-depth research on this problem, achieving new theoretical breakthroughs. This study derived three original equivalent resistance formulae for this complex circuit network, and also discusses the analytical expressions for equivalent resistance in different special cases, verifying that the conclusions in special cases are completely consistent with the actual circuit or previous existing conclusions, indirectly verifying the correctness of the theoretical results obtained in this article. The resistor network model in this article has multifunctional characteristics, for example, when taking r1→∞, the model degenerates into a cobweb network model. The research methods and results of the article will provide a new theoretical basis for related scientific and engineering research.

Electrical characteristics of a fractional-order 3 × n Fan network

In this article a new achievement of fractional-order 3 × n Fan networks is presented. In the first step, the RT-I method is used to derive the general formulae of the equivalent impedance of fractional-order 3 × n Fan networks. In the second part, the effects of five system parameters (L, C, n, α and β) on amplitude-frequency and phase-frequency characteristics are analyzed. At the same time, the amplitude-frequency and phase-frequency characteristics of the fractional order 3 × n Fan network are revealed by Matlab drawing. This work has important theoretical and practical significance for resistor network models in the field of natural science and engineering technology.

Mechanics behaviors and electrical conductivity of beryllium bronze alloy entangled metallic wire material: Experimental study and theoretical modeling

In the present work, a novel entangled metallic wire material (EMWM) with good mechanical properties and electrical conductivity was developed by using beryllium bronze alloy wire as raw material. A series of thermal-mechanical-electrical coupling tests were carried out to investigate the mechanical properties (average stiffness, loss factor) and electrical conductivity of beryllium bronze alloy entangled metallic wire material (QBe2-EMWM) and austenitic stainless steel entangled metallic wire material (304-EMWM). The effect of the density and ambient temperature on mechanical performances and resistance properties of EMWM were analyzed in detail. It is found that the mechanical properties of QBe2-EMWM are similar to those of austenitic stainless steel entangled metallic wire material (304-EMWM). The electrical resistance of EMWM decreases with the increase of density. Moreover, the electrical resistance of QBe2-EMWM is significantly lower than 304-EMWM and is only 5 % of 304-EMWM. In the aspect of theoretical modeling, based on a cube unit-cell approach, a simplified electrical resistor network was derived from modeling low-frequency current flow through the EMWM. Considering the influence of ambient temperature, the simplified resistor network model was modified by referring to the temperature term of the Johnson-Cook model, and then the conductivity model considering temperature effect for EMWM was established. The accuracy of the theoretical electrical model of EMWM was verified by comparing the calculated results with the experimental data. The results show that the proposed model can adequately predict the electrical conductivity characteristics of EMWM under different temperatures.

Effect of the Interplay between Polymer-Filler and Filler-Filler Interactions on the Conductivity of a Filled Diblock Copolymer System.

We investigate the relative roles of the involved interactions and micro-phase morphology in the formation of the conductive filler network in an insulating diblock copolymer (DBC) system. By incorporating the filler immersion energy obtained by means of the phase-field model of the DBC into the Monte Carlo simulation of the filler system, we determined the equilibrium distribution of fillers in the DBC that assumes the lamellar or cylindrical (hexagonal) morphology. Furthermore, we used the resistor network model to calculate the conductivity of the simulated filler system. The obtained results essentially depend on the complicated interplay of the following three factors: (i) Geometry of the DBC micro-phase, in which fillers are preferentially localized; (ii) difference between the affinities of fillers for dissimilar copolymer blocks; (iii) interaction between fillers. The localization of fillers in the cylindrical DBC micro-phase has been found to most effectively promote the conductivity of the composite. The effect of the repulsive and attractive interactions between fillers on the conductivity of the filled DBC has been studied in detail. It is quantitatively demonstrated that this effect has different significance in the cases when the fillers are preferentially localized in the majority and minority micro-phases of the cylindrical DBC morphology.

Microstructural modeling on electrical conductivities of 3-D carbon/epoxy woven composites along different directions

Carbon fiber composites have widely been used in aircrafts and high speed vehicles. Electrical conductivity of the carbon fiber composites is critical to electrical safety for the aircrafts and vehicles under high voltage applications. Here we report microstructural modeling on electrical conductivities of three-dimensional (3-D) carbon/epoxy angle-interlock woven composites along on-axis and off-axis directions. A 3-D resistor network model and finite element analysis (FEA) model based on fabric microstructure have been developed to reveal the electric conductivities along different directions. We have found that the conductivity of the woven structure exhibits full anisotropy. The difference of electrical conductivity between in-plane and through-thickness direction decreased due to the existence of through-the-thickness carbon fibers. The electrical conductivity through-thickness direction increases with warp directional length. With increasing off-axis directional length, the conductivity perpendicular to the off-axis direction increases, while the conductivity parallel to the off-axis direction remains basically unchanged. Electric potential distribution and electrical current density are highly related with fabric structure and current directions. Owing to the dependence of mechanical properties are also related with fabric structure and directions, it is expected that both the electrical and mechanical properties of the 3-D woven carbon/epoxy composites could be optimized simultaneously from the composite microstructure designs.

The Effect of Interconnecting Ribbons in External Resistance of Crystalline Silicon Photovoltaic Modules

The interconnecting ribbons in commercial crystalline silicon (c-Si) photovoltaic (PV) modules significantly contribute to the external resistance of the modules. This external resistance plays a major role in resistive losses in the modules and thus measures should be taken in minimization of such resistances. A wider ribbon cause blockage for the incoming light in the solar cells. In addition, the selection of wrong ribbon configuration essentially leads to breakage in fingers which further enhances resistive losses in the modules. In this paper, an analytical approach using a resistive network model has been proposed which effectively describes the effect of ribbon dimension on the blockage area as well as external resistance of the modules. The model has been useful to understand the resistive effect in the PV modules in a quantitative manner. The results show that the number of busbars and the width of the busbars in a solar cell play a significant role in choosing the right ribbon configuration. The proposed approach is useful to understand the optimum ribbon configuration in newly manufactured c-Si PV modules.

Cooperation in bioluminescence: understanding the role of autoinducers by a stochastic random resistor model

Quorum sensing is a communication mechanism adopted by different bacterial strains for the regulation of gene transcription. It takes place through the exchange of molecules called autoinducers. Bioluminescence is an emergent threshold phenomenon shown by some bacteria strains. Its precise relationship to quorum sensing is a debated topic, particularly regarding the role of the different autoinducers used by bacteria. In this paper, assuming a direct relationship between bioluminescence and quorum sensing, we investigate the role of multiple autoinducers in the bioluminescence response of Vibrio harveyi, considered as a model bioluminescent strain, due to its quorum sensing circuitry involving an array of three different autoinducers. Experiments on mutants of this bacterium, obtained by suppression of one or more autoinducers, reveal their relative non-trivial relevance and cooperative interaction patterns. The proposed analysis is implemented on a regular lattice, whose nodes represent microbial entities equipped with charges, which represent the ability to up/down regulate the gene expression. Quorum sensing results from a Coulomb-type field, produced by the charges. In analogy with random resistor network models, the lattice is permeated by an effective current which accounts for the amount and distribution of the charges. We propose that the presence of different autoinducers correspond to a different up/down regulation of gene expression, i.e., to a different way to account for the charges. Then, by introducing a modulation of the charge dependence into the current flowing within the network, we show that it is able to describe the bioluminescence exhibited by V. harveyi mutants. Furthermore, modulation of the charge dependence allows the interactions between the different autoinducers to be taken into account, providing a prediction regarding the data obtainable under specific growth conditions.Graphical abstract

Exact novel formulas and fast algorithm of potential for a hammock resistor network

The establishment of a resistor network model has become a sharp edge to solve complex scientific problems. In this paper, we introduce Chebyshev polynomials to express the potential formula of the hammock resistor network and improve the general solution of the hammock resistor network. Moreover, through the change in different parameters, special potential formulas are proposed and displayed in 3D dynamic view. A fast algorithm of the calculating potential is given by using the matrix equation model, discrete cosine transform-II, and the fast matrix-vector multiplication. Finally, we show the advantages of our improved potential formula and fast algorithm by the calculation efficiency of the three methods. The modified potential formula and the presented fast algorithm provide a new tool for the field of science and engineering.

The Numerical and Experimental Investigation of Piezoresistive Performance of Carbon Nanotube/Carbon Black/Polyvinylidene Fluoride Composite.

The composites with multiple types of nano-carbon fillers have better electrical conductivity and piezoresistive properties as compared with composites with a single type of nano-carbon fillers. As previously reported, the nano-carbon fillers with various aspect ratios, such as carbon nanotube (CNT) and carbon black (CB), have synergistic enhanced effects on the piezoresistive performance of composite sensors. However, most of the works that have been reported are experimental investigations. The efficient and usable numerical simulation investigation needs to be further developed. In this study, based on an integrated 3D statistical resistor network model, a numerical simulation model was created to calculate the piezoresistive behavior of the CNT/CB/ Polyvinylidene Fluoride (PVDF) composite. This model also takes into account the tunneling effect between nearby nano-fillers. It is found from numerical simulation results that the piezoresistive sensitivity of composite simulation cells can be influenced by the fraction of CNT and CB. In the case that the CNT content is 0.073 wt.%, the best force-electrical piezoresistive sensitivity can be achieved when the CB loading is up to 0.2 wt.%. To verify the validity of the simulation model, the previous experimental investigation results are also compared. The experimental results confirm the validity of the model. The investigation is valuable and can be utilized to design a strain sensor for this nano-composite with increased sensitivity.

Percolation threshold and electrical conductivity of conductive polymer composites filled with curved fibers in two-dimensional space.

Quantifying the influence of fiber curvature on the percolation behavior of flexible conductive fiber and further on the electrical conductivity of conductive polymer composites (CPCs) is crucial for the design of CPCs. This study considers CPCs as a random packing of soft curved discorectangles (CDCRs) in a polymer matrix. The geometry of CDCR is developed, and an inter-CDCR contact detection algorithm is used to generate a random packing structure of CDCRs. The effects of aspect ratio α and bending central angles θ of CDCR on the percolation threshold ϕc of the overlapped CDCR system in a two-dimensional plane are then investigated using the finite-size scaling method. The result reveals that ϕc decreases monotonically as α grows and increases monotonically as θ rises. A shape-independent power law formula, denoted as ϕc = 2.2015 A-0.8172dex is developed to quantify the relationship between the Adex and ϕc. A comparison of our numerical simulations, published data, and predictions verifies the reliability and universality of the fitting model. Subsequently, a resistor network searching algorithm (RNSA) is proposed to construct the random resistor network model (RRNM). A power law model, denoted as is developed to evaluate the effects of the normalized reduced density (η - ηc)/ηc on the effective conductivity σeff of CPC. Comparing our predictions with data from the literature and our simulation verifies the reliability of our RNSA and the fitting model. This paper's methodology and findings may provide a theoretical hint for the CPC's design.

Contact optimisation strategy for wafer-scale field-effect transistors based on two-dimensional semiconductors

• Wafer-scale multilayered MoS2 films were fabricated by vacuum transferring technique. • A novel electrical contact architecture was proposed to improve the contact capability between 3D metal and 2D semiconductors. • A novel edge-treatment method for the MoS2 side was developed by employing a mature magnetron sputtering system. • Approximately 16 times lower contact resistivity (22.8 kΩ μm) and 3 times lower Schottky barrier height (34.6 meV) than that of the conventional top contacted devices were achieved. • Simplified resistor network model and energy-band diagrams were elaborately illustrated to discuss the mechanisms. Two-dimensional (2D) semiconductors can be utilized to continually miniaturize nanoscale electronic devices. However, achieving a practical solution for satisfying electrical contact with 2D semiconductors remains challenging. In this study, we developed a novel contact structure with transferred multilayer (t-ML) MoS 2 by integrating both edge and top contact. After in-situ plasma treatment for the edge of the MoS 2 channel and successive metal deposition, we achieved 16 times lower contact resistivity (22.8 kΩ µm) than that of the top contacted devices. The thickness-dependent electrical measurement indicates that edge contact is highly effective with thick MoS 2 due to the alleviated current-crowding effect resulting from the small contact area. The temperature-dependent transport measurement further confirms the effective minimization of the influence from the Schottky barrier and tunnelling barrier. Finally, the simplified resistor network model and energy-band diagram were proposed to understand the carrier transport mechanism. Our work provides a practical strategy for achieving excellent electrical contact between bulk metals and 2D semiconductors, paving the way for future large-scale 2D electronic devices.

Edge and Interface Resistances Create Distinct Trade-Offs When Optimizing the Microstructure of Printed van der Waals Thin-Film Transistors

Inks based on two-dimensional (2D) materials could be used to tune the properties of printed electronics while maintaining compatibility with scalable manufacturing processes. However, a very wide range of performances have been reported in printed thin-film transistors in which the 2D channel material exhibits considerable variation in microstructure. The lack of quantitative physics-based relationships between film microstructure and transistor performance limits the codesign of exfoliation, sorting, and printing processes to inefficient empirical approaches. To rationally guide the development of 2D inks and related processing, we report a gate-dependent resistor network model that establishes distinct microstructure-performance relationships created by near-edge and intersheet resistances in printed van der Waals thin-film transistors. The model is calibrated by analyzing electrical output characteristics of model transistors consisting of overlapping 2D nanosheets with varied thicknesses that are mechanically exfoliated and transferred. Kelvin probe force microscopy analysis on the model transistors leads to the discovery that the nanosheet edges, not the intersheet resistance, limit transport due to their impact on charge carrier depletion and scattering. Our model suggests that when transport in a 2D material network is limited by the near-edge resistance, the optimum nanosheet thickness is dictated by a trade-off between charged impurity screening and gate screening, and the film mobilities are more sensitive to variations in printed nanosheet density. Removal of edge states can enable the realization of higher mobilities with thinner nanosheets due to reduced junction resistances and reduced gate screening. Our analysis of the influence of nanosheet edges on the effective film mobility not only examines the prospects of extant exfoliation methods to achieve the optimum microstructure but also provides important perspectives on processes that are essential to maximizing printed film performance.

3D resistor-network modeling of infiltrated SOFC electrodes

For first time a 3D simulation for infiltrated electrodes taking into account the charge transfer resistance (CT) for computing the admittance is developed. By employing a three-dimensional voxelised resistor network, we study the electrode resistance as a function of electrode microstructure and material conductivities. The simulated electrodes consist of pores, metal and ion conductor material and were generated from a random sphere insertion model which emulates the experimental procedure of the infiltration process. To both evaluate and validate the proposed model, a comparison with numerical models and experimental results from the literature is used. More accurate results closely related to those observed experimentally and the use of the main characteristics of the infiltrated electrodes as input parameters are benefits of 3D modeling. The results show that the model for the admittance and TPBL curves have the same behavior as a function of the amount of infiltrated material. This similarity is fulfilled when the diffusion of gas in the pores of the electrode is not the limiting process for the calculation of the admittance, and when the percolation of the ionic and electronic conducting phases are considered in the calculation for TPBL.

Atomically Thin Synapse Networks on Van Der Waals Photo-Memtransistors.

A new type of atomically thin synaptic network on van der Waals (vdW) heterostructures is reported, where each ultrasmall cell (≈2nm thick) built with trilayer WS2 semiconductor acts as a gate-tunable photoactive synapse, i.e., a photo-memtransistor. A train of UV pulses onto the WS2 memristor generates dopants in atomic-level precision by direct light-lattice interactions, which, along with the gate tunability, leads to the accurate modulation of the channel conductance for potentiation and depression of the synaptic cells. Such synaptic dynamics can be explained by a parallel atomistic resistor network model. In addition, it is shown that such a device scheme can generally be realized in other 2D vdW semiconductors, such as MoS2 , MoSe2 , MoTe2 , and WSe2 . Demonstration of these atomically thin photo-memtransistor arrays, where the synaptic weights can be tuned for the atomistic defect density, provides implications for a new type of artificial neural networks for parallel matrix computations with an ultrahigh integration density.

Electrical characterization of the 2 × 6 × n cobweb cascaded resistor network model by the improved recursion-transform method

Since the cobweb model combines the properties of several network topologies, the cobweb resistor network based on the cobweb model has aroused the interest of scholars. However, owing to the complicated structure of the cobweb cascaded resistor network, it is very challenging to solve with conventional approaches. To address this issue, an improved recursion-transform approach was employed. The electrical characterization of the 2 × 6 × n cobweb cascade resistor network model was studied in this paper. Firstly, the equivalent circuit of the resistor network to be solved was found. Secondly, the recursive equation of the equivalent circuit was constructed. Then, the recursive equation was linearized. Finally, the equivalent resistance of the resistor network was obtained by solving the linear recursive equation. This approach significantly reduces the computation procedure because it adopts the scheme of simplifying the circuit first, then establishing the equation and solving it. The findings indicate that the equivalent resistances between the two nodes of this resistor network change with the change of the order n. When n tends to infinity, these equivalent resistances will have definite convergence values. The calculation results show that these equivalent resistances are already very close to their convergence values, respectively, when n takes 7 or 8.

A resistor network model for analysis of current and temperature distribution in carbon fibre reinforced polymers during induction heating

The interest in carbon fibre reinforced polymers (CFRP) is growing due to their high strength and stiffness compared to their weight, in industries such as automotive and aerospace. This creates a high demand for more effective production methods. Volumetric induction heating of the electrically conductive carbon fibres enable unmatched heat rates and can be used both during manufacturing and joining of parts, but also means technical challenges in terms of uniform temperature distribution. Understanding and prediction of the heating pattern is therefore an important step towards an industrial solution. This article presents a model for simulation of the current and temperature distribution in CFRP during induction heating in which the CFRP is modelled as a network of discrete resistors where the local currents are determined by Kirchhoff’s circuit laws and the temperature distribution is computed by the finite difference method. The model is a complement to traditional three-dimensional finite element simulations and allows for a better understanding of the current paths, and thereby the heating pattern, on a tow size level. Thermographic recordings during induction heating experiments validates the model.