Memristive Behavior Research Articles

Memristive behavior of ferrocene-functionalized polymer for artificial nociceptor application

Organic memristors have attracted widespread attention as highly promising candidates for implementing neuromorphic systems and wearable electronic devices. The donor–acceptor (D-A) polymers P1 and P2 are designed and successfully synthesized where the only disparity between the two polymers is the inclusion of a ferrocene (Fc) pendant group. The as-fabricated memristors Ag/P1/ITO and Ag/P2/ITO exhibit volatile threshold switching (TS) behavior, which is dominated by pseudo-bridging conductive filaments (CFs) depending on the diffusion dynamics of the Ag active metal species in the active layer. The more stable TS behavior of the P1-based memristor under a positive voltage sweep is attributed to the Fc units, which can reduce the random growth of CFs to some extent. The volatile ternary switching behavior in the negative working window can be attributed to the synergistic effect of Ag CFs and bilayer ICT process originated from two acceptor units of DPP2T and azobenzene groups. Moreover, the characteristics related to the application of the P1-based memristor on artificial nociceptors are demonstrated, including threshold, relaxation, no adaptation, and sensitization. This work demonstrated that leveraging the effect of constructing bilayer ICT mechanism represents an efficient strategy for building up multi-level memristors capable of versatile applications.

A reconfigurable memristor diode based on a CuInP2S6/graphene lateral heterojunction.

The conventional reconfiguration of transistors requires an additional independent terminal for controllable gate input, which complicates the device structure and makes circuit integration difficult. In this work, we propose a reconfigurable diode based on a 2D layered copper indium thiophosphate (CIPS) and graphene (Gr) van der Waals lateral heterojunction, exhibiting distinctively bias-dependent reconfiguration. The reconfiguration characteristics include reversible memristive behaviors with a current on/off ratio of about 103 and switchable rectifying polarity with a rectifying ratio of up to 3 × 103. This reconfigurable mechanism arises from the lateral bias-induced migration of Cu+ ions, effectively modulating the barrier height at the CIPS and Gr interface. This work provides a simplified reconfigurable solution for electrostatically modulated circuits.

Ferroelectric Domain Wall Warp Memristor.

Domain walls are quasi-one-dimensional topological defects in ferroic materials, which can harbor emergent functionalities. In the case of ferroelectric domain wall (FEDW) devices, an exciting frontier has emerged: memristor-based information storage and processing approaches. Memristor solid-state FEDW devices presented thus far, however predominantly utilize a complex network of domain walls to achieve the desired regulation of density and charge state. Here, using epitaxial bismuth ferrite thin films as a prototype ferroelectric and advanced scanning probe microscopy and stroboscopic methods, we demonstrate controlled single-wall memristive behavior through deterministic electric field-driven conformal changes. Our design exploits memristive functionality through surface pinning of topological domain walls. That is, although the FEDW is constricted by the surface, it is free to twist in the thickness direction. The resulting vertical variation of FEDW morphology creates a complex interplay between surface-induced pinning and field-induced wall bending. This gives rise to metastable electronic transitions, and hence memristive attributes. Moreover, being a single FEDW memristor, once injected there is no need for repeated injection or erasure. Microscopic insight into device operation from phase field modeling indicates controllable warping of the wall, causing memristive conductivity changes. Our results reaffirm the promise of FEDWS for brain-inspired neuromorphic and in-memory computing applications based on integrated ferroelectric devices.

Exploring the Conductive Dynamics of Sb2(S,Se)3-Based Memristors for Non-Volatile Memory and Neuromorphic Applications.

Advancing the development of novel materials or architectures for random access memories, coupled with an in-depth understanding of their intrinsic conduction mechanisms, holds the potential to transcend the conventional von Neumann bottleneck. In this work, a novel memristor based on the Sb2(S,Se)3 material with an alloy of S and Se was fabricated. A systematic investigation of the correlation between the Se/(S + Se) ratio and memristive performance revealed that Ag/Sb2(S,Se)3/FTO memristive behavior is uniquely associated with the formation and disruption of anion vacancies and silver filaments. The resultant Ag/Sb2(S,Se)3/FTO memristor devices demonstrated good resistive switching, with durability surpassing 3 × 104 cycles, showcasing multilevel conductivity states. Furthermore, these devices successfully emulated the synaptic functionality. This research has established the foundation for the intrinsic conduction mechanisms of antimony chalcogenide memristor artificial synapses.

Resistive switching behavior of quasi-2D CsPbBr3 memristors: Impact of ambient atmosphere on logic storage and computing integration with anti-crosstalk and reconfiguration features

Passive units integrating storage and computing with anti-crosstalk and multi-logic reconstruction are crucial for high computing power and high-density non-volatile storage. In this study, we report an anti-crosstalk and reconfigurable logic memory based on a single passive quasi-two-dimensional (2D) CsPbBr3 device. The effect of the ambient atmosphere (air and N2 environments) on the resistive behavior of the memristors is explored. In air, these devices exhibit negative differential resistance (NDR) effects and antipolar resistive switching behavior, while in N2, they display irreversible switching from low-resistance state to high-resistance state. Various active electrodes (Ag, Cu, Au, and C) were employed to investigate this phenomenon. It is proposed that in air, O ions interact with surface defects under high alternating voltage, retaining a significant quantity of Br− ions within the quasi-2D CsPbBr3, resulting in capacitive-like behavior. Conversely, in N2, surface defects capture Br− ions, leading to the absence of a hysteresis loop in the I-V characteristic. Under N2 operation, write-once-read-many (WORM) capability is achieved. Surprisingly, operating under air enables integrated non-volatile storage and computing, facilitating 12 reconfigurable logic operations in a passive 1R structure and suppressing sneak current in crosstalk setups. This study emphasizes the pivotal role of air in the resistive switching mechanism and provides novel insights for developing next-generation memories tailored for high-density integrated circuits and storage-computing integration.

Angstrom Scale Ionic Memristors' Engineering with van der Waals Materials: A Route to Highly Tunable Memory States.

Memristors that mimic brain functions are crucial for energy-efficient neuromorphic devices. Ion channels that emulate biological synapses are still in the early stages of development, especially the tunability of memory states. Here, we demonstrate that cations such as K+, Na+, Ca2+, and Al3+ intercalated in the interlayer spaces of vermiculite result in highly confined channels of size 3-5 Å. They host exotic memristor properties through ion exchange dynamics, even at high salt concentrations of 1 M. The bipolar memristor characteristics observed are tunable with frequency, geometric asymmetry, ion concentration, and intercalants. Notably, we observe polarization-flipping memristor behavior in two cases: one with Al3+ ions and another with devices having a geometric asymmetry ratio greater than 15. This inversion is attributed to the overscreening of counterions due to their accumulation at the channel entrance. Our results suggest that ion exchange dynamics, ion-ion interactions, and ion accumulation/depletion mechanisms, particularly with multivalent ions, can be harnessed to develop advanced memristor devices.

Bending effect on synaptic behavior of MoS2-based flexible memristors under low temperatures

Bending effect on synaptic behavior of MoS2-based flexible memristors under low temperatures

Memristor & its application in biological field

Abstract Demand for highly integrated, low-power nonvolatile memories to get beyond the drawbacks of traditional memory systems has led to, Memristive/resistive switching devices which are excellent choices for non-volatile memory technology. Memristor is the 4th fundamental unit proposed by Professor Chua to give a relation between charge and magnetic flux. If a memristor’s constitutive relation is a straight line with a slope of M that passes through the origin in the ɸ –q plane, it is considered linear. The memristor’s physical realizations and potential uses remain a fascinating area for investigation.Semiconductor nanoparticles specially ZnO, ZnS QD exhibit Memristive characteristics. Employing this Memristive behaviour of biofunctionalized nanoscale particles and “voltage gap” as a novel sensing metric, several investigators attempted to assess the precise amount of microbiological contamination. Here in this work, Memristive property of some semiconductor nanoparticles like ZnO, ZnS as well as metal nanoparticle like PbS, Ag particles are studied and tried to focus on application of Memristive devices in near future in biological fields. The switching properties of bio-voltage memristors can now be used to achieve bio-voltage matching.

Observation of memristive behavior in PDMS-glass nanofluidic chip

Observation of memristive behavior in PDMS-glass nanofluidic chip

Memristor-like Electrical Resistivity Behavior of SiO2 Nanofilms and Their Applicability in Wireless Internet of Things Communications

Memristors, capable of altering their resistance based on past voltage inputs, have emerged as promising components for various applications, including resistive memory, neuromorphic devices, and chaotic circuits. Over the years, a variety of nanomaterials and nanodevices, such as nanocrystal arrays [1], metal-doped dielectrics [2,3], and ferroelectric switching devices [4], have been reported to exhibit memristive properties. In this study, we demonstrated memristor-like behavior in metal-contacted SiO2 nanofilms. Unlike conventional methods used for inducing memristive behavior in oxide films, such as adjusting the density distribution of mobile ions or creating/disrupting conductive filaments within the oxide, we leveraged the unique electrical conductivity of the nanofilms to achieve memristor-like current–voltage (I–V) characteristics. This conductivity likely results from the many-body effects arising from the electron-electron and/or electron-hole interactions between metals and SiO2 nanofilms [5]. A notable deviation from conventional memristors was observed when the resistance shifted from low to high resistance states as the voltage returned to 0 V. Despite this behavior, the SiO2 nanofilms exhibited a pinched hysteresis loop in their I–V characteristics, and were thus suitable for application in chaotic circuits. The use of SiO2 nanofilms offers advantages such as facile integration into Si microfabrication processes and realization of memristor-like properties through the intrinsic characteristics of SiO2, eliminating the need for precise doping processes.Herein, we investigated the alternating current characteristics of SiO2 nanofilms in contact with Au films and Ag-pastes. The SiO2 nanofilms were thermally grown on low-resistance Si substrates, followed by the deposition of metal electrodes. The deposited metals served not only as electrodes for injecting carriers into the nanofilms but also as inducers of many-body effects. SiO2 nanofilms with thicknesses of ~1 nm, which facilitated easy carrier tunneling, exhibited resistance-specific behaviors in their I–V characteristics. Conversely, films with thicknesses exceeding 50 nm, which prevented carrier injection into SiO2, showed capacitance-specific properties. Memristor-like behavior was achieved by adjusting the SiO2 film thicknesses to their intermediate values. For example, a 9-nm-thick SiO2 nanofilm demonstrated a resistance change from over 1 kΩ·cm during voltage increase to below 10 Ω·cm during voltage decrease. This phenomenon is attributed to the SiO2 nanofilms acting as wide-bandgap semiconductors upon metal contact, as well as in the presence of Schottky barriers and/or Fowler–Nordheim tunneling at the metal/SiO2 interfaces. Based on our experimental results, we propose utilization of SiO2 nanofilms in chaotic circuits for secure internet of things (IoT) device communication. Simulations were conducted using LTspice and MATLAB Simulink to encrypt digital signals by modulating chaotic voltage oscillation rates with the digital signals. The modulated voltage wave patterns were transmitted with white noise added to mimic real-world scenarios. At the receiving end, decryption was achieved using a similar SiO2 nanofilm-integrated chaotic circuit, representing a form of hardware based symmetric key encryption. Simulations showed that the image data encryption/decryption performance degraded only slightly with increasing noise levels, even at signal-to-noise ratios of approximately 10 dB. Thus, the proposed device exhibits secure communication capabilities comparable to those of conventional memristor–incorporated circuits [6].

Piezoresistive, Piezocapacitive and Memcapacitive Silk Fibroin-Based Cement Mortars.

Water-stable proteins may offer a new field of applications in smart materials for buildings and infrastructures where hydraulic reactions are involved. In this study, cement mortars modified through water-soluble silk fibroin (SF) are proposed. Water-soluble SF obtained by redissolving SF films in phosphate buffer solution (PBS) showed the formation of a gel with the β sheet features of silk II. Electrical measurements of SF indicate that calcium ions are primarily involved in the conductivity mechanism. By exploiting the water solubility properties of silk II and Ca2+ ion transport phenomena as well as their trapping effect on water molecules, SF provides piezoresistive and piezocapacitive properties to cement mortars, thus enabling self-sensing of mechanical strain, which is quite attractive in structural health monitoring applications. The SF/cement-based composite introduces a capacitive gauge factor which surpasses the traditional resistive gauge factor reported in the literature by threefold. Cyclic voltammetry measurements demonstrated that the SF/cement mortars possessed memcapacitive behavior for positive potentials near +5 V, which was attributed to an interfacial charge build-up modulated by the SF concentration and the working electrode. Electrical square-biphasic excitation combined with cyclic compressive loads revealed memristive behavior during the unloading stages. These findings, along with the availability and sustainability of SF, pave the way for the design of novel multifunctional materials, particularly for applications in masonry and concrete structures.

ZnO-Based Memristive Device for Temperature Sensing: Design, Modeling, and Performance Evaluation

This paper presents the design and modeling of a highly sensitive ZnO-based memristive temperature sensor, underpinned by the fundamental physics of memristive behavior. Utilizing a multi-physics simulation tool, the proposed model accurately maps temperature variation contours within the ZnO pyroelectric material, paving the way for its application in temperature sensing. An in-depth exploration of the sensor's electrical properties under varying temperature conditions reveals exceptional sensitivity (8.9 µV/K) and showcases the inherent non-volatile memory switching behavior of the memristor, making it ideally suited for dynamic applications. Moreover, this sensor operates inherently bias-free, functioning as a self-powered solution for emerging fields like the Internet of Things.

Bioactive Ion-Confined Ultracapacitive Memristors with Neuromorphic Functions.

The field of bioinspired iontronics, bridging electronic devices and ionic systems, has multiple biological applications. Carbon-based ultracapacitive devices hold promise for controlling bioactive ions via electric double layers due to their high-surface-area and biocompatible porous carbon electrodes. However, the interplay between complex bioactive ions and porous carbons remains unclear due to the variety of structures of bioactive ions present in biological systems. Herein, we investigate the adsorption behavior of a series of bioactive ammonium-based cations with varying alkyl chain lengths in nanoporous carbons. We find that strong physisorption results from the synergistic hydrophobic interaction and electrostatic attraction between porous carbons (with a negative zeta potential) and bioactive cations. Bioactive cations with varying alkyl chain lengths can be irreversibly physically adsorbed and confined within nanoporous carbons resulting in anion enrichment and depletion during electric polarization. This situation, in turn, results in a characteristic memristive behavior in all-carbon capacitive ionic memristor devices. Our findings highlight the relationship between the resistance state of the memristor and ion adsorption mechanisms in all-carbon capacitive devices, which hold potential for future transmitter delivery, biointerfacing, and neuromorphic devices.

Elucidation of Switching Mechanisms in Memristive Junctions Integrating a Iron(II)‐Ter Pyridine Diazoted Complex

AbstractAn original way of elaborating vertical metal/molecules/metal memristive junctions through diazonium electrografting of the organic layer and inkjet‐printed top electrodes is reported here. The molecule of interest is a FeII coordination complex with ter‐pyridine ligands, having a diazonium anchoring group. The resulting junction exhibits a memristive behavior characterized by a high ON/OFF ratio and plasticity property. Through the application of advanced techniques such as UV–vis and Raman time‐resolved spectroelectrochemistry, the study demonstrates the significant role of switchable azo bonds derived from diazo electrografting in memristive behavior.

Bioactive Ion‐Confined Ultracapacitive Memristors with Neuromorphic Functions

AbstractThe field of bioinspired iontronics, bridging electronic devices and ionic systems, has multiple biological applications. Carbon‐based ultracapacitive devices hold promise for controlling bioactive ions via electric double layers due to their high‐surface‐area and biocompatible porous carbon electrodes. However, the interplay between complex bioactive ions and porous carbons remains unclear due to the variety of structures of bioactive ions present in biological systems. Herein, we investigate the adsorption behavior of a series of bioactive ammonium‐based cations with varying alkyl chain lengths in nanoporous carbons. We find that strong physisorption results from the synergistic hydrophobic interaction and electrostatic attraction between porous carbons (with a negative zeta potential) and bioactive cations. Bioactive cations with varying alkyl chain lengths can be irreversibly physically adsorbed and confined within nanoporous carbons resulting in anion enrichment and depletion during electric polarization. This situation, in turn, results in a characteristic memristive behavior in all‐carbon capacitive ionic memristor devices. Our findings highlight the relationship between the resistance state of the memristor and ion adsorption mechanisms in all‐carbon capacitive devices, which hold potential for future transmitter delivery, biointerfacing, and neuromorphic devices.

Mimicking somatic behavior of neurons using the integrate and fire model of 2D SnS memristive switching characteristics

This Letter presents the fabrication and characterization of a 2D SnS memristor, proposing its integrate and fire (I&F) model as a potential hardware implementation of neuronal somatic behavior. The memristor comprises a thin layer of tin (II) sulfide (SnS) sandwiched between copper (Cu) electrodes on a silicon (Si) substrate. This structure exhibits an impressive Roff:Ron ratio of 103 at a read voltage Vrd of 0.25 V with exceptionally low switching Vsw and set Vset voltages of 0.3 and 0.35 V, respectively, with ∼3 order variation between the maximum Rmax and Rmin resistances offered during single voltage sweep cycle. We have explained the memristive behavior using the dual ionic conduction mechanism in the SnS active layer. We extracted the real-time band diagram of SnS using ultraviolet photoelectron spectroscopy, explaining the low Vsw observed. We propose that the emulation of the I&F artificial neuron model exhibited by the fabricated device could serve as a promising application in the field of artificial neuron spiking.

Photodual-Responsive Anthracene-Based 2D Covalent Organic Framework for Optoelectronic Synaptic Devices.

To facilitate the development of efficient neuromorphic perception and computation, it is crucial to explore optoelectronic synaptic devices that integrate perceptual and computational capabilities. Various materials such as oxide semiconductors, conjugated organic polymers, transition metal sulfides, perovskite materials, and metal nanoparticles, along with their composites, are utilized in constructing these devices. However, optoelectronic synaptic devices based on 2D covalent organic frameworks (COFs) is rarely reported. In this study, an anthracene-based 2D COF (COF-DaTp) film is prepared using a room-temperature interface-confined strategy and utilized it as the active layer in an optoelectronic synaptic device with an Al/COF-DaTp/ITO configuration. The device demonstrated dual optoelectronic modulation, exhibiting significant optoelectronic resistive switching in response to light pulses, achieving 32 photoconductive states. Moreover, it exhibited history-dependent memristive behavior in voltage scans and electrical pulses, with a comparable diversity of 32 conductive states. The photodual-responsive properties of the COF-DaTp-based synaptic device enable it to simultaneously perform optical sensing and basic image denoising and recognition tasks, significantly enhancing recognition accuracy and reducing the number of training epochs compared to datasets without noise mitigation. This work opens the door for the application of 2D COF-based optoelectronic synaptic devices in visual computational processing.

Synthesis and Anisotropic Memristive Behavior of Borophene Nanosheets

AbstractNeuromorphic computing, marked by its parallel computational abilities and low power usage, has become pivotal in advancing artificial intelligence. However, the advancement of neuromorphic computing has faced significant obstacles due to the performance limitations of traditional memory devices struggling with high power consumption and limited reliability. Two‐dimensional (2D) materials have been extensively investigated as high‐performance memristive materials, but they are often restricted by fixed memristive properties, which complicate circuit design and limit flexibility. Here, we report that multilayer borophene nanosheets represent a breakthrough material, displaying anisotropic variable memristive properties. The nanosheets, comprising semiconductor α’‐4H‐borophene sheets and metal β12‐borophene sheets, have been synthesized on aluminum foil surface through chemical vapor deposition method. The multilayer borophene nanosheets exhibit volatile memory behavior in the vertical direction and non‐volatile memory behavior in the planar direction. This innovative class of 2D nanosheets not only overcomes the limitations of conventional memory devices but also expands the potential applications of borophene‐based memories in information storage and in‐memory computing.

Synthesis and Anisotropic Memristive Behavior of Borophene Nanosheets.

Neuromorphic computing, marked by its parallel computational abilities and low power usage, has become pivotal in advancing artificial intelligence. However, the advancement of neuromorphic computing has faced significant obstacles due to the performance limitations of traditional memory devices struggling with high power consumption and limited reliability. Two-dimensional (2D) materials have been extensively investigated as high-performance memristive materials, but they are often restricted by fixed memristive properties, which complicate circuit design and limit flexibility. Here, we report that multilayer borophene nanosheets represent a breakthrough material, displaying anisotropic variable memristive properties. The nanosheets, comprising semiconductor α'-4H-borophene sheets and metal β12-borophene sheets, have been synthesized on aluminum foil surface through chemical vapor deposition method. The multilayer borophene nanosheets exhibit volatile memory behavior in the vertical direction and non-volatile memory behavior in the planar direction. This innovative class of 2D nanosheets not only overcomes the limitations of conventional memory devices but also expands the potential applications of borophene-based memories in information storage and in-memory computing.

Assessment of functional performance in self-rectifying passive crossbar arrays utilizing sneak path current

Self-rectifying memristive devices have emerged as promising contenders for low-power in-memory computing, presenting numerous advantages. However, characterizing the functional behavior of passive crossbar arrays incorporating these devices remains challenging due to sophisticated parasitic currents stemming from rich memristive dynamic behavior. Conventional methods using read margin assessments to evaluate functional behavior in passive crossbars are hindered by the voltage divider effect from the pull-up resistor. In this study, we propose a novel performance metric, Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta$$\\end{document}SC, harnessing sneak path currents to assess functional behavior. Through the application of a pair of negative rectification factors, RFn,L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {RF}_\ ext {n, L}$$\\end{document} and RFn,H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {RF}_\ ext {n, H}$$\\end{document}, we comprehensively delineate dynamic rectification behavior in both positive and negative bias regimes, as well as in low-resistance state and high-resistance state, deviating from conventional metrics such as on/off ratios, nonlinearity, and rectifying factors. Notably, Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta$$\\end{document}SC provides a quantitative evaluation of the interaction between sneak path currents and read margin, demonstrating its efficacy and addressing a pivotal research gap in the field. For instance, employing self-rectifying BiFeO3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} memristive cells featuring RFn,L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {RF}_\ ext {n, L}$$\\end{document} = 1.22E3 and RFn,H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {RF}_\ ext {n, H}$$\\end{document} = 9.27, we showcase the successful functional performance of a passive crossbar array, achieving Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta$$\\end{document}SC < 2.19E−2, while ensuring a read margin > 0.