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Graphene

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Full-Text Articles in Physics

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough May 2024

The Analysis Of Mechanical Exfoliation Of Graphene For Various Fabrication And Automation Techniques, Lance Yarbrough

Mechanical Engineering Undergraduate Honors Theses

Mechanical Exfoliation of Graphene is an often-overlooked portion of the fabrication of quantum devices, and to create more devices quickly, optimizing this process to generate better flakes is critical. In addition, it would be valuable to simulate test pulls quickly, to gain insight on flake quality of various materials and exfoliation conditions. Physical pulls of graphene at various temperatures, pull forces, and pull repetitions were analyzed and compared to the results of ANSYS simulations, solved for similar results. Using ANSYS’ ability to predict trends in exfoliations, flake thickness and coverage using stress and deflection analyses were investigated. Generally, both strongly …


Encapsulated 2d Materials And The Potential For 1d Electrical Contacts, Sarah Wittenburg May 2024

Encapsulated 2d Materials And The Potential For 1d Electrical Contacts, Sarah Wittenburg

Physics Undergraduate Honors Theses

The utilization of two-dimensional materials and heterostructures, particularly graphene and hexagonal boron nitride, have garnered significant attention in the realm of nanoelectronics due to their unique properties and versatile functionalities. This study focuses on the synthesis and fabrication processes of monolayer graphene encapsulated between layers of hBN, aiming to explore the potential of these heterostructures for various electronic applications. The encapsulation of graphene within hBN layers not only enhances device performance but also shields graphene from environmental contaminants, ensuring long-term stability. Experimental techniques, including mechanical exfoliation and stamp-assisted transfer, are employed to construct three-layer stacks comprising hBN-graphene-hBN. The fabrication process …


Synthesis, Characterization, And Simulation Of Two-Dimensional Materials, Lawrence Hudy Aug 2023

Synthesis, Characterization, And Simulation Of Two-Dimensional Materials, Lawrence Hudy

Theses and Dissertations

ABSTRACT

SYNTHESIS, CHARACTERIZATION, AND SIMULATION OF TWO-DIMENSIONAL MATERIALS

by

Lawrence Hudy

The University of Wisconsin-Milwaukee, 2023Under the Supervision of Professor Michael Weinert

This dissertation focuses on my journey through many aspects of surface science leading to the first principles investigation of transition metal dichalcogenides studying the impact of defects, twist, and decreasing interlayer separation to probe their effect on the electronic properties of these materials. My journey started out learning many aspects of material science such as methods for material synthesis and characterization but later ended on simulation of material properties using density functional theory. In the first experiments, we …


A Study Of Single Molecule Detection With Graphene Hall Bars, Kenneth Stephen Stephenson Apr 2023

A Study Of Single Molecule Detection With Graphene Hall Bars, Kenneth Stephen Stephenson

Theses and Dissertations

In 2007, detection of individual molecules with a solid-state gas sensor was reported for first time by Schedin et al. where they used micromechanically-cleaved graphene for their sensing material, which exhibits isotropic and homogeneous conduction [1]. However, despite the novelty and popularity of their work, it has never been repeated. Further, we found their associated calculations to be self-inconsistent by a factor of 103 . So, hoping to account for and resolve this discrepancy, we outline the plan we had to reproduce their experiment. We also justify any substantial modifications, particularly our choice to use epitaxial graphene instead. Then, we …


Low Energy Photon Detection, Tianyi Guo Jan 2023

Low Energy Photon Detection, Tianyi Guo

Graduate Thesis and Dissertation 2023-2024

Detecting long wave infrared (LWIR) light at room temperature has posed a persistent challenge due to the low energy of photons. The pursuit of an affordable, high-performance LWIR camera capable of room temperature detection has spanned several decades. In the realm of contemporary LWIR detectors, they can be broadly classified into two categories: cooled and uncooled detectors. Cooled detectors, such as MCT detectors, excel in terms of high detectivity and fast response times. However, their reliance on cryogenic cooling significantly escalates their cost and restricts their practical applications. In contrast, uncooled detectors, exemplified by microbolometers, are capable of functioning at …


Towards The Electronic Response Of Carbon-Based Van Der Waals Heterostructures In A Diamond Anvil Cell, George Thomas Foskaris Dec 2022

Towards The Electronic Response Of Carbon-Based Van Der Waals Heterostructures In A Diamond Anvil Cell, George Thomas Foskaris

UNLV Theses, Dissertations, Professional Papers, and Capstones

The nanoscale regime of materials has been at the forefront of research and interest in condensed matter physics for many years. In a merger of the fields of two-dimensional (2D) materials and high pressure physics, we present an investigation of the electronic response of carbon-based, van der Waals (vdW) heterostructures in a diamond anvil cell (DAC). Combining these fields presents us with the ability to study the characteristics of such systems both optically, and through electrical transport. Properties such as conductance, band structure, and layer number are considered. The samples in this study are assembled using exfoliation and stacking techniques …


Plasmon Damping Rates In Coulomb-Coupled 2d Layers In A Heterostructure, Dipendra Dahal, Godfrey Gumbs, Andrii Iurov, Chin-Sen Ting Nov 2022

Plasmon Damping Rates In Coulomb-Coupled 2d Layers In A Heterostructure, Dipendra Dahal, Godfrey Gumbs, Andrii Iurov, Chin-Sen Ting

Publications and Research

The Coulomb excitations of charge density oscillation are calculated for a double-layer heterostructure. Specifically, we consider two-dimensional (2D) layers of silicene and graphene on a substrate. From the obtained surface response function, we calculated the plasmon dispersion relations, which demonstrate how the Coulomb interaction renormalizes the plasmon frequencies. Most importantly, we have conducted a thorough investigation of how the decay rates of the plasmons in these heterostructures are affected by the Coulomb coupling between different types of two- dimensional materials whose separations could be varied. A novel effect of nullification of the silicene band gap is noticed when graphene is …


Custom Calibration And Correction Of Photoemission Electron Microscope Images Using Graphene, Henry Bell May 2022

Custom Calibration And Correction Of Photoemission Electron Microscope Images Using Graphene, Henry Bell

Macalester Journal of Physics and Astronomy

The Photoemission Electron Microscope (PEEM) is a full-field electron microscope that utilizes the photoelectric effect to image a surface. Due to a spatial resolution on the order of 10 nanometers and its ability to image both the morphology of a surface and its band structure, it is a useful tool for understanding the properties of materials for use in electronic devices. To correct for random sample misalignment and the experimental frame of reference in the spectroscopy mode of the PEEM, the 3D dataset must be rotated in both the momentum and energy coordinates which requires pixel calibration and energy alignment. …


Ab Initio Studies Of Structure And Properties Of Group-Iv Monochalcogenide Monolayers, Shiva Prasad Poudel May 2022

Ab Initio Studies Of Structure And Properties Of Group-Iv Monochalcogenide Monolayers, Shiva Prasad Poudel

Graduate Theses and Dissertations

The goal of this dissertation is to study the structure of ferroelectric group-IV monochalcogenide monolayers (MMLs) and their material properties. This work also established a new buckled honeycomb phase of these monolayers. Chapter 1 serves as an introduction where the motivation for these studies is established. In chapter 2, I used eight different exchange-correlation functionals (XC) to study the structure of these 2D ferroelectrics and found that their properties are independent of the choice of XC functionals. These findings reveal that the ground-state ferroelectric unit cell can be described by only five independent parameters, whereas their paraelectric (square or rectangular) …


Design, Fabrication, And Characterization Of An Array Of Graphene Based Variable Capacitors, Millicent Nkirote Gikunda May 2022

Design, Fabrication, And Characterization Of An Array Of Graphene Based Variable Capacitors, Millicent Nkirote Gikunda

Graduate Theses and Dissertations

Since it was first isolated and characterized in 2004, graphene has shown the potential for a technological revolution. This is due to its amazing physical properties such as high electrical conductivity, high thermal conductivity, and extreme flexibility. Freestanding graphene membranes naturally possesses an intrinsic rippled structure, and these ripples are in constant random motion even room temperatures. Occasionally, the ripples undergo spontaneous buckling (change of curvature from concave to convex and vice versa) and the potential energy associated with this is a double well potential. This movement of graphene is a potential source of vibrational energy.

In this dissertation, we …


Giant Acoustically-Induced Synthetic Hall Voltages In Graphene, Pai Zhao, Chithra H. Sharma, Renrong Liang, Christian Glasenapp, Lev Mourokh, Vadim M. Kovalev, Patrick Huber, Marta Prada, Lars Tiemann, Robert H. Blick Jan 2022

Giant Acoustically-Induced Synthetic Hall Voltages In Graphene, Pai Zhao, Chithra H. Sharma, Renrong Liang, Christian Glasenapp, Lev Mourokh, Vadim M. Kovalev, Patrick Huber, Marta Prada, Lars Tiemann, Robert H. Blick

Publications and Research

Any departure from graphene’s flatness leads to the emergence of artificial gauge fields that act on the motion of the Dirac fermions through an associated pseudomagnetic field. Here, we demonstrate the tunability of strong gauge fields in nonlocal experiments using a large planar graphene sheet that conforms to the deformation of a piezoelectric layer by a surface acoustic wave. The acoustic wave induces a longitudinal and a giant synthetic Hall voltage in the absence of external magnetic fields. The superposition of a synthetic Hall potential and a conventional Hall voltage can annihilate the sample’s transverse potential at large external magnetic …


Theoretical Investigation On Optical Properties Of 2d Materials And Mechanical Properties Of Polymer Composites At Molecular Level, Geeta Sachdeva Jan 2022

Theoretical Investigation On Optical Properties Of 2d Materials And Mechanical Properties Of Polymer Composites At Molecular Level, Geeta Sachdeva

Dissertations, Master's Theses and Master's Reports

The field of two-dimensional (2D) layered materials provides a new platform for studying diverse physical phenomena that are scientifically interesting and relevant for technological applications. Theoretical predictions from atomically resolved computational simulations of 2D materials play a pivotal role in designing and advancing these developments. The focus of this thesis is 2D materials especially graphene and BN studied using density functional theory (DFT) and molecular dynamics (MD) simulations. In the first half of the thesis, the electronic structure and optical properties are discussed for graphene, antimonene, and borophene. It is found that the absorbance in (atomically flat) multilayer antimonene (group …


Carbon And Other Low-Z Materials Under Extreme Conditions, Jonathan T. Willman Nov 2021

Carbon And Other Low-Z Materials Under Extreme Conditions, Jonathan T. Willman

USF Tampa Graduate Theses and Dissertations

This work is focused on understanding material's behavior and response to extreme conditions. Under extreme conditions, which is categorized as regions of high pressures and temperatures in (P-T) space, materials can undergo multiple types of phase transitions as well as exhibit substantial damage as well as other exotic behaviors. By studying matter at these extreme conditions, we can elucidate a broad range of fundamental physics including a material's energetic, mechanical, and electronic responses. This thesis describes work that makes contributions to the growing body of knowledge within these subsets of condensed matter physics. In the first thrust, crystal structure prediction …


Detecting Graphene Nanosheets On Leaves​ Of Ceratophyllum Demersum ​, Teresa A. Buragina Aug 2021

Detecting Graphene Nanosheets On Leaves​ Of Ceratophyllum Demersum ​, Teresa A. Buragina

Undergraduate Student Research Internships Conference

Since its discovery, applications of graphene, a material that is a single layer of carbon atoms, have been useful in many different fields. In this project, we aim to image graphene flakes, formed from graphene-RNA nanocomposites, on the surface of aquatic plant leaves. Graphene-RNA 6 solutions were vacuum filtrated onto leaves of Ceratophyllum Demersum, which were then imaged at different heights using confocal microscopy, producing 3D images of graphene flakes.


Computational Studies Of Carbon Nanocluster Solidification, Chathuri C. Silva Jul 2021

Computational Studies Of Carbon Nanocluster Solidification, Chathuri C. Silva

Dissertations

A subset of micron-size meteoritic carbon particles formed in red giant atmospheres show a core-rim structure, likely condensed from a vapor phase into super-cooled carbon droplets that nucleated graphene sheets (~40Å) on randomly oriented 5-atom loops during solidification, followed by coating with a graphite rim. Similar particles form during slow cooling of carbon vapor in the lab.

Here we investigate the nucleation and growth of carbon rings and graphene sheets using density functional theory (DFT). Our objectives: (1). explore different computational techniques in DFT-VASP for various carbon structures and compare the results with literature, (2). investigate the nucleation and growth …


Fundamental Aspects Of The Interaction Between Light And Nanostructures, Stephen Keith Sanders Jul 2021

Fundamental Aspects Of The Interaction Between Light And Nanostructures, Stephen Keith Sanders

Physics & Astronomy ETDs

Recent breakthroughs in nanophotonics have brought new opportunities to control and manipulate light at the nanoscale. The optical properties of metallic nanostructures have attracted particular interest because of their plasmon resonances, which couple strongly with visible light, and generate large near-field enhancements in their vicinity. In the first part of this thesis, we investigate the fundamental limits of the local density of photonic states near nanostructures by analyzing a sum rule relating its spectral integral to the field induced by a static dipole. Next, we analyze how the design of metallic nanoantennas can benefit from incorporating active materials that display …


Fabrication And Characterization Of Photodetector Devices Based On Nanostructured Materials: Graphene And Colloidal Nanocrystals, Wafaa Gebril Jul 2021

Fabrication And Characterization Of Photodetector Devices Based On Nanostructured Materials: Graphene And Colloidal Nanocrystals, Wafaa Gebril

Graduate Theses and Dissertations

Photodetectors are devices that capture light signals and convert them into electrical signals. High performance photodetectors are in demand in a variety of applications, such as optical communication, security, and environmental monitoring. Among many appealing nanomaterials for novel photodetection devices, graphene and semiconductor colloidal nanocrystals are promising candidates because of their desirable and unique properties compared to conventional materials.

Photodetector devices based on different types of nanostructured materials including graphene and colloidal nanocrystals were investigated. First, graphene layers were mechanically exfoliated and characterized for device fabrication. Self-powered few layers graphene phototransistors were studied. At zero drain voltage bias and room …


Two-Dimensional Bose–Hubbard Model For Helium On Graphene, Jiangyong Yu Jan 2021

Two-Dimensional Bose–Hubbard Model For Helium On Graphene, Jiangyong Yu

Graduate College Dissertations and Theses

An exciting development in the field of correlated systems is the possibilityof realizing two-dimensional (2D) phases of quantum matter. For a systems of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons (U ≈ ∞) and repulsive nearest-neighbor (V > 0) interactions. In this work, we focus on the calculations of single particle properties of the model such as the hopping parameter t. This is accomplished via Wannier Theory and Band structure calculations, which proves to be reliable …


Strongly Correlated Phases In Quantum Hall Systems, Amartya Saha Jan 2021

Strongly Correlated Phases In Quantum Hall Systems, Amartya Saha

Theses and Dissertations--Physics and Astronomy

Quantum Hall systems have a one-body energy spectrum consisting of dispersion-less Landau levels. Electron-electron interactions thus dominate in partially filled Landau levels, which exhibit a myriad of strongly correlated phases such as quantum hall ferromagnets and fractional quantum Hall phases. We study two examples of these phenomena.

In the first project, we explore the ground state of a system with an interface between two semi-infinite regions with fillings ν= 4 and ν= 3 respectively. The width of the interface can be controlled by varying the background potential, which provides an additional tuning parameter. For a certain range of …


Computational Studies Of Carbon Nanocluster Solidification, Chathuri Chandani Silva Jan 2021

Computational Studies Of Carbon Nanocluster Solidification, Chathuri Chandani Silva

Doctoral Dissertations

“A subset of micron-size meteoritic carbon particles formed in red giant atmospheres show a core-rim structure, likely condensed from a vapor phase into super-cooled carbon droplets that nucleated graphene sheets (~40Å) on randomly oriented 5-atom loops during solidification, followed by coating with a graphite rim. Similar particles form during slow cooling of carbon vapor in the lab.

Here we investigate the nucleation and growth of carbon rings and graphene sheets using density functional theory (DFT). Our objectives: (1). explore different computational techniques in DFT-VASP for various carbon structures and compare the results with literature, (2). investigate the nucleation and growth …


Experimental Investigations Of Contact Friction And Transport Properties Of Monolayer And Bilayer Graphene, Prakash Gajurel Jan 2021

Experimental Investigations Of Contact Friction And Transport Properties Of Monolayer And Bilayer Graphene, Prakash Gajurel

Graduate Theses, Dissertations, and Problem Reports

Results obtained from experimental investigations of contact friction in monolayer and bilayers graphene and the related effects on their transport properties are presented here along with their discussion and interpretation. For this purpose, chemical vapor deposited (CVD) graphene samples on SiO2/Si were prepared. The samples were characterized by atomic force microscopy (AFM), Raman and X-ray photoelectron spectroscopy (XPS). Summaries of the results are given below.

Defects-controlled friction in graphene is of technological importance but the underlying mechanism remains a subject of debate. The new results obtained from the analysis of lateral force microscopy images revealed that the contact …


Electronic Properties Of Flat And Curved Graphene Sheets, Deng Yanpei Jan 2021

Electronic Properties Of Flat And Curved Graphene Sheets, Deng Yanpei

Senior Projects Spring 2021

This paper explored the electronic properties of the graphene sheet and also developed basis for understanding the electronic properties of the curved graphene sheet. This paper began with setting up basic knowledge about solid-state physics including introducing band structure, band gap, crystal structure, and reviews for quantum mechanical operators. Then this paper described two potential models that are suitable for considering periodic potential: the weak potential and the tight-binding model. We discovered the tight-binding model is better for our graphene case and by applying this model we find the energies of the graphene sheet. Next, we constructed the 1D and …


Semi-Empirical Modeling Of Liquid Carbon's Containerless Solidification, Philip C. Chrostoski Jan 2021

Semi-Empirical Modeling Of Liquid Carbon's Containerless Solidification, Philip C. Chrostoski

Doctoral Dissertations

“Elemental carbon has important structural diversity, ranging from nanotubes through graphite to diamond. Previous studies of micron-size core/rim carbon spheres extracted from primitive meteorites suggest they formed around such stars via the solidification of condensed carbon-vapor droplets, followed by gas-to-solid carbon coating to form the graphite rims. Similar core/rim particles result from the slow cooling of carbon vapor in the lab. The long-range carbon bond-order potential was used to computationally study liquid-like carbon in (1.8 g/cm3) periodic boundary (tiled-cube supercell) and containerless (isolated cluster) settings. Relaxations via conjugate-gradient and simulated-annealing nucleation and growth simulations using molecular dynamics were …


Free Charge Carrier Properties In Two-Dimensional Materials And Monoclinic Oxides Studied By Optical Hall Effect, Sean Knight Aug 2020

Free Charge Carrier Properties In Two-Dimensional Materials And Monoclinic Oxides Studied By Optical Hall Effect, Sean Knight

Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research

In this dissertation, optical Hall effect (OHE) measurements are used to determine the free charge carrier properties of important two-dimensional materials and monoclinic oxides. Two-dimensional material systems have proven useful in high-frequency electronic devices due to their unique properties, such as high mobility, which arise from their two-dimensional nature. Monoclinic oxides exhibit many desirable characteristics, for example low-crystal symmetry which could lead to anisotropic carrier properties. Here, single-crystal monoclinic gallium oxide, an AlInN/GaN-based high-electron-mobility transistor (HEMT) structure, and epitaxial graphene are studied as examples. To characterize these material systems, the OHE measurement technique is employed. The OHE is a physical …


Synthesis Of Graphene By Liquid Precursors At Lower Temperatures, Clayton Hansen May 2020

Synthesis Of Graphene By Liquid Precursors At Lower Temperatures, Clayton Hansen

Physics Capstone Projects

Benzene, toluene, and xylene can be liquid precursors for graphene and carbon nanotube synthesis. However, the growth mechanisms can have greater variances for different carbon allotropes. In the case of graphene, Cu can be the catalyst for dehydrogenation and provides a weakly-coupled substrate for 2-dimensional graphene nucleation and growth. In the case of carbon nanotubes, Fe nanoparticles are essential to catalyze the C-C bonds breaking and dissolve carbon before the precipitation of a graphene cap over the catalyst particle where a tube forms. Controlling the precursor feed rate is crucial for a successful synthesis. In this research, we developed a …


Graphene In A Uniform Magnetic Field, Ankur Das Jan 2020

Graphene In A Uniform Magnetic Field, Ankur Das

Theses and Dissertations--Physics and Astronomy

We study monolayer graphene in a uniform magnetic field in the absence and presence of interactions. In the non-interacting limit, for p/q flux quanta per unit cell (p, q are coprime integer), the central two bands have 2q Dirac points in the Brillouin zone (BZ) in the nearest-neighbor model. These touchings and their locations are guaranteed by chiral symmetry and the lattice symmetries of the honeycomb structure. If we add a staggered potential and a next-nearest-neighbor hopping we find that their competition leads to a topological phase transition. We also study the stability of the Dirac touchings to one-body perturbations …


Synthesis Of Graphene Using Plasma Etching And Atmospheric Pressure Annealing: Process And Sensor Development, Andrew Robert Graves Jan 2020

Synthesis Of Graphene Using Plasma Etching And Atmospheric Pressure Annealing: Process And Sensor Development, Andrew Robert Graves

Graduate Theses, Dissertations, and Problem Reports

Having been theorized in 1947, it was not until 2004 that graphene was first isolated. In the years since its isolation, graphene has been the subject of intense, world-wide study due to its incredibly diverse array of useful properties. Even though many billions of dollars have been spent on its development, graphene has yet to break out of the laboratory and penetrate mainstream industrial applications markets. This is because graphene faces a ‘grand challenge.’ Simply put, there is currently no method of manufacturing high-quality graphene on the industrial scale. This grand challenge looms particularly large for electronic applications where the …


Investigating The Time Scales Of Electromechanical Motion In Graphene Drumheads Using Pump-Probe Spectroscopy With Stm, Alana P. Gudinas Jan 2020

Investigating The Time Scales Of Electromechanical Motion In Graphene Drumheads Using Pump-Probe Spectroscopy With Stm, Alana P. Gudinas

Honors Theses and Capstones

Scanning tunneling microscopy (STM) has transformed the field of condensed matter physics over the past few decades, allowing scientists to image materials at the atmomic scale, manipulate individual atoms, and probe electronic states on the surface of materials. In recent years, there have been numerous developments to introduce time-resolved measurements to STM in order to probe atomic-scale dynamic processes and combine spatial and temporal resolution. Advances like THz-STM setups achieve femtosecond resolution, but require complex external setups. All-electronic pump-probe spectroscopy for STM (directly analogous to optical pump-probe spectroscopy) has been pioneered by Loth et al., and newer applications (Natterer et …


Cyclotron Resonance In Graphene Heterostructurescyclotron Resonance In Graphene Heterostructures, Billy Jordan Russell Dec 2019

Cyclotron Resonance In Graphene Heterostructurescyclotron Resonance In Graphene Heterostructures, Billy Jordan Russell

Arts & Sciences Electronic Theses and Dissertations

We present observations of cyclotron resonance in graphene Van der Waals heterostructure devices. Such devices provide dramatic improvements in sample quality and allow for ad- vanced electronic control, opening windows on previously inaccessible physics. The design and construction of a dedicated system for the measurement of electronic transport and infrared magnetospectroscopy in microscopic samples of atomically thin materials at cryogenic temperatures is presented. In high-mobility encapsulated monolayer graphene, electron- electron interaction effects are unambiguously observed to impact the interband cyclotron resonance as the Landau level filling factor is varied in a quantizing magnetic field. Additionally, a splitting of transitions involving …


Gamma-Ray Radiation Effects In Graphene-Based Transistors With H-Bn Nanometer Film Substrates, E. J. Cazalas, Michael R. Hogsed, S. R. Vangala, Michael R. Snure, John W. Mcclory Nov 2019

Gamma-Ray Radiation Effects In Graphene-Based Transistors With H-Bn Nanometer Film Substrates, E. J. Cazalas, Michael R. Hogsed, S. R. Vangala, Michael R. Snure, John W. Mcclory

Faculty Publications

Radiation effects on graphene field effect transistors (GFETs) with hexagonal boron nitride (h-BN) thin film substrates are investigated using 60Co gamma-ray radiation. This study examines the radiation response using many samples with varying h-BN film thicknesses (1.6 and 20 nm thickness) and graphene channel lengths (5 and 10 μm). These samples were exposed to a total ionizing dose of approximately 1 Mrad(Si). I-V measurements were taken at fixed time intervals between irradiations and postirradiation. Dirac point voltage and current are extracted from the I-V measurements, as well as mobility, Dirac voltage hysteresis, and the total number of GFETs that remain …