Sarcoidosis is a chameleon disease of unknown etiology, characterized by the growth of non-necrotizing and non-caseating granulomas and manifesting with clinical pictures that vary on the basis of the organs that are mainly affected. Lungs and intrathoracic lymph nodes are the sites that are most often involved, but virtually no organ is spared from this disease. Histopathology is distinctive but not pathognomonic, since the findings can be found also in other granulomatous disorders. The knowledge of these findings is important because it could be helpful to differentiate sarcoidosis from the other granulomatous-related diseases. This review aims at illustrating the main clinical and histopathological findings that could help clinicians in their routine clinical practice.  Sarcoidosis has a heterogeneous presentation, since it can involve every organ and tissue, though lungs and intrathoracic lymph nodes are the sites that are most commonly involved. Clinical onset can be asymptomatic or manifest with acute, subacute or chronic form .Recent data about epidemiology show that Sweden is the country at the highest incidence and prevalence , while it is rarely found in countries such as Japan and South Korea   The worsSome forms, such as Lofgren syndrome, a clinical picture characterized by hilar lymph nodes enlargement, erythema nodosum, symmetrical arthritis of the ankles and often anterior uveitis, are specific and virtually diagnostic of an acute form of sarcoidosis . HeerforSubacute onset of sarcoidosis is characterized instead by vanished and non-specific signs and symptoms such as fever, asthenia, weight loss and peripheral lymphadenopathies for less than two years. Here differential diagnosis is impossible on the basis of the clinical picture only .Almost two-thirds of patients with sarcoidosis have an acute course of disease and may undergo spontaneous resolution , while 1The traditional diagnostic criteria for sarcoidosis have been based on the triad of suggestive clinical picture, non-necrotizing granulomas found at biopsy samples and exclusion of other causes of granulomatous tissue . AlthougIn sarcoidosis lungs are affected in 90% of cases, and involvement of mediastinal (hilar) lymph nodes is almost always present . RespiraSarcoid granulomas are most frequently located along the perilymphatic regions and along the bronchoscular branches . The airEven the pleura, especially the visceral side, can be involved in sarcoidosis by manifesting in most cases with pleural effusion (exudate) and more rarely with pleural masses .In advanced stages, fibrotic and cystic changes can involve the lungs extensively and these alterations can translate into a restrictive ventilatory deficiency at spirometry .Distortion and compression of vessels due to fibrotic changes and sarcoid granulomas can be associated with pulmonary hypertension . AspergiUveitis is the most common clinical presentation and can be anterior or posterior, its clinical detection is important to avoid permanent damage to sight .Anterior uveitis is an inflammation process of the portion that goes from the iris to the ciliary body and clinically manifests with a red, painful eye and photophobia. with a slit lamp examination it is possible to detect keratin precipitates floating in the anterior chamber of the eye .Posterior uveitis is less common and can manifest with decreased vision due to the presence of papilledema and vitreous hemorrhages. The nodules of the choroid give a characteristic appearance called wax drops .Sarcoid conjunctivitis is characterized by the presence of small yellowish and translucent nodules on the conjunctiva, particularly affecting the lower fornix. Sarcoid conjunctivitis occurs only in 5% of affected patients .A particular ophthalmological clinical picture that can accompany sarcoidosis is that of Fuchs’ heterochromic uveitis (FHU); it is a particular form of chronic uveitis, characterized by the development of numerous iris nodules which, subsequently, are accompanied by keratin precipitates and peripheral retinal periplebitis .Lacrimal gland involvement manifests with keratoconjunctivitis sicca, causing itching and burning in the eye with the sensation of a foreign body and swelling of the gland itself .Skin manifestations affect 25% of patients with sarcoidosis, and the two most well-known presentations are represented by erythema nodosum and lupus pernio ,31. ErytLupus pernio is instead characterized by a rash consisting of bluish-red or purplish lumps that are located on the nose, cheeks, ears, and fingers. Lupus pernio is often associated with severe lung involvement and indicates a poor prognosis .Lupus pernio is characterized by granulomatous vasculitis at the histological examination; it manifests as an organized infiltrate of histiocytes and, above all, of lymphocytes in the reticular dermis, in the perivascular site, with compression of the vascular structures and development of confluent ischemic areas .Other chronic skin lesions consist of plaques or nodules located mainly in the trunk and limbs. Furthermore, the development of granulomas on old scars is not uncommon .Cardiac sarcoidosis is clinically evident in 2–10% of patients with sarcoidosis, though occult involvement is more frequent as demonstrated by autopsy studies .Although clinically silent, cardiosarcoidosis represents a major cause of death with a mortality rate that can be greater than 85% in autopsy studies. The symptoms and signs of cardiac sarcoidosis depend on the location and extent of the granulomatous inflammation that can affect the myocardium, endocardium, pericardium, and the valvular apparatus .The most frequent manifestations are conduction anomalies including complete atrioventricular block and tachyarrhythmias including ventricular arrhythmias (ventricular or non-sustained tachycardia and ventricular extrasystoles), triggered by anomalous activity of the myocardium or reentry arrhythmias. Other arrhythmias have also been reported such as ectopic atrial activity, paroxysmal atrial tachycardia, atrial flutter and atrial fibrillation . Heart fThe differential diagnosis of sarcoid cardiopathy should always be considered in young or adult persons with cardiac symptoms and those having a diagnosis of sarcoidosis and clinical picture characterized by arrhythmias, conduction abnormalities or heart failure .The hepatic involvement in sarcoidosis, more frequent in the African American male population, is most often asymptomatic and can manifest only with hepatomegaly and, in 10% of cases, with an increase of transaminases and alkaline phosphatase .Less frequently, hepatic damage from sarcoidosis can evolve toward clear nodules or overt cirrhosis, liver dysfunction and portal hypertension with varices, hepato-pulmonary syndrome and refractory hypoxemia (1% of cases) ,42.Hepatic sarcoidosis is characterized histologically by the presence of numerous scattered non-necrotizing granulomas, located more often in the portal spaces. The microscopic structure of the granuloma is the same as that observed in the other organs .Spleen involvement in sarcoidosis usually manifests with asymptomatic splenomegaly, while platelet sequestration and thrombocytopenia are less frequently observed. Splenomegaly is rarely so important to lead to splenectomy .Sometimes splenic nodules can be observed at imaging such as ultrasound, and appear as hypoechoic and vascular rounded lesions, that can be misdiagnosed with those observed in malignant processes such as lymphomas . In suchAt histological examination, the sarcoid granulomas are small greyish or yellowish-white lesions macroscopically, usually sized less than 1 mm in diameter and similar to miliary tubercles, though unlike miliary tubercles they are more accentuated and have defined margins.Neurosarcoidosis can affect both the central and the peripheral nervous system . The most frequent localizations are leptomeninges, with symptoms similar to other forms of meningitis such as fever, headache and neck rigidity . CSF anaMacroscopically, nodular lesions have raised appearance, gray-yellowish color and hard consistency, and are sized a few millimeters in diameter. The brain involvement is instead characterized by lesions of various sizes that are located at the periventricular white matter, appearing very similar to the lesions observed in multiple sclerosis. Symptoms depend on the location of these lesions. Brain granulomas are usually larger than those that occur in meningeal granulomatosis; their solid nature and grayish-white appearance often make the differential diagnosis difficult with respect to neoplastic brain lesions, especially gliomas .Other common sites involved in neurosarcoidosis are the cranial nerves, especially the seventh, this can clinically manifest with Bell’s palsy , while the involvement of the optic nerve is associated with visual impairment .Less frequently, the peripheral nervous system may be affected due to both the isolated infiltration of the nerves from epithelioid cells and the development of well-structured granulomatous lesions. Both small and large nerve fibers can be affected causing mononeuropathies, polyradiculopathies and distal and symmetrical polyneuropathies .The infiltration of the pituitary region by sarcoid granulomas can be associated with diabetes insipidus, amenorrhea and galactorrhea .Bone involvement is reported with a frequency between 1% and 13%, but these percentages are likely to be an underestimation because this localization is usually asymptomatic .Bone lesions mainly affect the phalanges of the hands and feet and the metacarpal and metatarsal bones . The typThe lesions usually involve the cancellous bone tissue and spare the periosteum; in rare cases there is an extension of the process with the involvement of the adjacent joint structures. These lesions are a consequence of the osteodestructive and lytic action of the sarcoid process, rather than a result of bone resorption. Joint involvement manifests with swelling and arthralgia. Overt arthritides are rare and mainly affect large joints, usually ankles in the Lofgren’s syndrome . ArthritBone marrow infiltration from sarcoid granulomas has been exceptionally reported in the literature (incidence of 0.3–2% at biopsy), and can be suggested by variable cytopenia at laboratory exams . More frRenal involvement in sarcoidosis can manifest with kidney stones and nephrocalcinosis due to increased calcium reabsorption, hypercalciuria and altered calcium metabolism related to the increased production of 1-alpha-hydroxylase by activated macrophages present in granulomas, which causes an increased synthesis of Vitamin D .Renal sarcoid granulomas can be found in both cortical and medullary compartments. Sarcoid nodules can sometimes reach a diameter of 1 cm, thus becoming difficult to differentiate from neoplastic lesions .The histological sites of renal sarcoidosis should be differentiated into interstitial and glomerular. Granulomatous interstitial nephropathy affects approximately 20% of patients with sarcoidosis and represents the most typical histopathological finding of nephrosarcoidosis. Acute and clinically overt renal failure that leads to hemodialysis is uncommon and derives most frequently from an acute granulomatous tubulointerstitial nephritis . GlomeruA correct diagnosis of sarcoidosis is suggested by clinical and radiological context, but it is usually reached by showing the presence of noncaseating granulomas at biopsy. These granulomas affect several organs, such as the lungs, skin, spleen, lymph nodes, eye, bone tissue, salivary and lacrimal glands, striated muscles, CNS, endocrine glands and liver, and a correct site of biopsy should be chosen on the basis of the best accessible site and at the lowest risk of complications .Granulomatous inflammation is a well-defined chronic inflammatory process, in which the activated macrophage is the predominant cell and has the appearance of epithelial cells, taking for this reason the name of “epithelioid cell”. Granuloma is a circumscribed and well-organized area of granulomatous inflammation, formed by epithelioid cells, lymphocytes, leukocytes and, sometimes, plasma cells. Epithelioid cells can at times merge to create giant cells, which are sometimes located in the periphery, sometimes in the center of the granuloma. Giant cells can reach a diameter of about 50 microns and are composed of abundant cytoplasm containing over 20 small nuclei that are peripherally localized (Langherans-type giant cells) or dispersed in the cytoplasm (foreign body-like giant cells) .Lymphocytes appear more numerous in stages and surround clusters of epitheliod cells. In the initial stages, CD4+ T helper cells are found, and facilitate the formation and maintenance of the granulomatous lesion through the release of specific cytokines .Subsequently, the number of T helper lymphocytes of the granuloma reduce, favoring an increase of T CD8+; the increase of cytotoxic lymphocytes is associated with a tendency to the resolution of the granulomatous lesion  66]..66].The number of plasma cells is usually very low; their presence indicates an increase of local humoral immunity .The natural tendency of the sarcoid granulomatous lesion is towards healing; most inflammatory cells tend to disappear. In other cases, the granuloma evolves towards the development of typical rings of collagen fibers at the periphery of the lesion (ring fibrosis), which are then replaced by a hyaline and dense scar ,68.Scar tissue, the result of the previous granuloma, can sometimes persist over time; the tendency to persistent fibrosis is more typical of some organs such as the skin and lungs. Fibrosis can sometimes accompany the deposit of substances such as oxalate or calcium carbonate .A central area of fibrinoid necrosis can be present in 6–35% of cases, this area of necrosis is distinguishable from caseous necrosis due to the persistence of an intact reticular pattern . The preSome inclusion bodies can be found inside granulomas and can lead to a suspicion of sarcoidosis, though they are not pathognomonic of it. These bodies are the Schaumann  bodies, laminated and birefringent concretions consisting of calcium and proteins usually in the cytoplasm of giant cells , asteroiIn addition to the classic non-necrotizing form, sarcoidosis can give other histopathological types, called necrotizing sarcoid granulomatosis and nodular sarcoidosis.Necrotizing sarcoid granulomatosis (NSG) is a rare and controversial histopathological picture, it is still debated whether to consider it a form of sarcoidosis or a distinct pathological entity . It mainThe granulomatous lesions can sometimes involve the lymphatic tracts or be associated with an interalveolar granulomatous component. A characteristic of necrotizing sarcoid granulomatosis is the presence of extensive areas of necrosis and vasculitis, mainly involving the muscular arteries and pulmonary veins, characterized by the presence of necrotizing giant cell granulomas or by the infiltration of lymphocytes and macrophages in the vessel wall  74]..74].Such necrotic areas can give diagnostic issues with those found in granulomas associated with infectious agents, especially mycobacteria .Nodular sarcoidosis is instead a histological variant characterized by the presence of non-necrotizing granulomas confluent in large masses, often accompanied by extensive fibrosis of the contiguous tissues. The prevalence of this histological variant of benign lymphogranulomatosis ranges from 2% to 4% of patients with sarcoidosis. Nodular sarcoidosis usually affects the lung parenchyma, and nodular lesions with a diameter of 1–5 cm are described, rarely they can reach a size of 7 cm. Nodular sarcoidosis can sometimes manifest as a solitary, ‘tumor-like’ mass. This variant of sarcoidosis is usually accompanied by hilar lymphadenopathy and affects young patients, aged between 20 and 40 years .Although sarcoid granuloma is distinctive, it is not pathognomonic of sarcoidosis being common also in other non-necrotizing granulomatous disorders . Some diHP is a chronic granulomatous pulmonary disease triggered by the inhalation of organic substances that act as antigens such as bacteria, fungi, drugs or animal-derived proteins. The characteristic features are the presence of non-caseous epithelioid granulomas smaller than those of sarcoidosis at biopsy. Unlike sarcoidosis, the hilar lymph nodes are not affected, and granulomas are mainly located in the peribronchiolar region. The alveolar septa present infiltrates consisting of macrophages, lymphocytes and plasma cells. There is bronchiolar obstruction correlated to the ulceration of the surface coating. Foamy macrophages are present in the alveolar lumen and, in some cases, Schaumann bodies are present in the giant cells of the granuloma. The bronchoalveolar lavage can give some diagnostic clues because CD8+ suppressor lymphocytes are predominant in hypersensitivity pneumonitis .The granulomatous reaction to Beryllium is caused by the activation of CD4+ lymphocytes that recognize Beryllium and produce IL-2 and IFN gamma, activating the multinucleated phagocytes and starting the formation of granulomas in the interstitium and in the pulmonary lymph nodes. The granuloma in berylliosis is indistinguishable from those found in sarcoidosis, the main structure is always a non-caseous granuloma consisting of epithelioid and Langherans cells with areas of hyalinosis and bodies including asteroids. A history of beryllium exposition or the demonstration of the presence of beryllium in biological fluids or tissues are diagnostics of berylliosis .GPA is a systemic disease characterized by necrotizing granulomatous lesions affecting both the upper and lower airways. Unlike sarcoidosis, GPA has no distinct granulomas, multinucleated giant cells are present in low quantity and the area of necrosis has irregular contours similar to a geographical map, with a large amount of cellular debris and it is surrounded by histiocytes. Other typical features are the presence of a necrotizing vasculitis with fibrinoid necrosis of the media of the affected vessels and that granulomas, unlike other granulomatous diseases, do not affect the lymph nodes .Various fungal infections such as Aspergillosis, Coccidioidomycosis, Blastomycosis, Histoplasmosis can produce granulomatous reactions in the lungs that enter into differential diagnosis with sarcoidosis. Unlike sarcoidosis, the granulomas of these fungal infections most often present suppurative necrosis .Occasionally, Histoplasma may not be visible in granulomas through the usual hematoxylin-eosin staining, unlike other fungal infections, and often it is necessary to use the Silver methenamine, Giemsa or periodic acid-Schiff (PAS) staining .The histopathological features of M. tuberculosis, both in the miliary and in the isolated nodular form, often pose significant issues in the differential diagnosis of sarcoidosis. The histological differentiation between sarcoid granuloma and tuberculoma is based on the characteristics of the tuberculous granuloma . In its In a large case series, a Ziehl–Neelsen stain demonstrated the presence of acid-fast organisms in approximately 77% of solitary necrotizing granulomas, but showed a low accuracy to identify the presence of these organisms in non-necrotizing or hyalinized granulomas. In these cases, sarcoid granulomas can be differentiated with difficulty .The history of potential exposure to bacilli, diagnostic imaging showing suggestive patterns of tuberculosis and also the gene amplification tests can orient toward the correct diagnosis. The Xpert MTB/RIF assay is a novel semi-automatic DNA amplification assay that can simultaneously identify M. tuberculosis and rifampicin resistance .Other forms of non-tuberculous mycobacterial infection can produce granulomas, especially in the lung or skin, similar to those of sarcoidosis. Mycobacteria mainly involving the lungs are M. avium, M. complex and M. Kansasii. Traditionally it was thought that NTM infection of the lungs was associated with immunodeficiency or pre-existing lung disease. However, it is now recognized that NTM infection of the lungs also occurs in immunocompetent and healthy patients .In immunocompromised patients, NTM infection is characterized by ill-defined granulomas consisting of foamy macrophages containing mycobacteria . In immuHistologically, foreign body granulomas typically consist of multinucleated giant cells and macrophages. These giant cells are typically of the “foreign body type” and have nuclei scattered irregularly throughout the cytoplasm .In many cases the foreign body can be recognized within these granulomas . These gSeveral drugs have been associated with the onset of granulomatous inflammation that is histologically indistinguishable from the reaction observed in patients with sarcoidosis. Interferons, tumor necrosis factor-α, the combination of antiretroviral therapies, monoclonal antibodies, immune checkpoint inhibitors and other immunosuppressive agents are just a few drugs which can be the cause of granulomatous formation, effect of a drug-induced alteration of the immune response ,91. AlthIn most of the cases, the diagnosis of sarcoidosis is achieved by obtaining a sample biopsy of the affected tissue and by recognizing the presence of the characteristic non-caveating and non-necrotizing granulomas. However, histopathology is not always pathognomonic since these findings can be found also in other granulomatous disorders. A thorough assessment of the case, by considering all the aspects of the disease including clinical, radiological and histopathological findings, is mandatory to achieve a correct diagnosis, and to differentiate sarcoidosis from the other granulomatous-related diseases.


The large bandgap energy of SiC allows the sensor to operate in the visible and near-infrared wavelength ranges, which effectively reduces the light absorption in water to improve the sensitivity. The sensor was characterized by comparing the shift of the resonance wavelength peak with change of the refractive index (RI), which mimics the change of analyte concentration in the sensing medium. The study showed that in the RI range of 1.33~1.36, the sensitivity was improved when the graphene layers were increased. With 10 graphene layers, a sensitivity of 2810 nm/RIU (refractive index unit) was achieved, corresponding to a 39.1% improvement in sensitivity compared to the Au/SiC sensor without graphene. These results demonstrate that the graphene/Au/SiC waveguide SPR sensor has a promising use in portable biosensors for chemical and biological sensing applications, such as detection of water contaminations (RI = 1.33~1.34), hepatitis B virus (HBV), and glucose (RI = 1.34~1.35), and plasma and white blood cells (RI = 1.35~1.36) for human health and disease diagnosis.A new waveguide-based surface plasmon resonance (SPR) sensor was proposed and investigated by numerical simulation. The sensor consists of a graphene cover layer, a gold (Au) thin film, and a silicon carbide (SiC) waveguide layer on a silicon dioxide/silicon (SiO Surface plasmons resonance (SPR)-based chemical and biosensors have been widely used for the detection of a variety of chemicals and biomolecules ,2,3,4,5.In conventional SPR sensors, a thin metal film is inserted between the light-guiding layer and sensing medium, with the excited surface plasmon wave propagating along the metal and sensing medium interface. Different metal films such as gold (Au), silver (Ag), and aluminum (Al) have been discussed in the literature ,14,15. A2/Si substrate, Au can be deposited via evaporation or sputtering with precisely controlled thickness. For graphene, CVD process has been explored extensively to synthesize uniform graphene monolayer and multilayer [In this paper, we proposed and numerically simulated a new waveguide-based SPR sensor with a wide bandgap semiconductor silicon carbide (SiC) as the waveguide layer, a Au thin film, and a graphene cover layer as BRE. Due to the wide bandgap energy (2.2 eV of 3C-SiC polytype), the SiC waveguide layer enables the sensor to operate in the visible wavelength range, which avoids the absorption of large amounts of water in the near-infrared range when sensing in a water-based sensing medium ,19,20. Tltilayer , which c2 layer (RI = 1.45) was inserted between a Si (RI = 3.5) substrate and SiC waveguide layer for optical isolation since the RI of SiC (RI = 2.62) is smaller than Si. The permittivity of Au can be found in [2 isolation layer was selected to be 3 μm thick, which is sufficient to prevent optical field leakage onto the Si substrate. Thicknesses of the SiC waveguide layer was kept at 100 nm based on our previous study [The cross-sectional schematic of the graphene/Au/SiC waveguide SPR sensor is shown in found in . The SiOus study , which sus study  so the ti is the imaginary unit and λ0 is the vacuum wavelength. In [A, can be expressed as [P0 and aP are the light intensities without and with energy absorption in the sensing medium, respectively; f is the confinement factor, which is defined as the ratio of the optical power confined in the sensing medium over the total optical power; α is the absorption coefficient; l is the waveguide length; and c is the analyte concentration. The change in c leads to the change in RI. The sensitivity, S, is proportional to the ratio of the change in absorbance, A, over the concentration change in the sensing medium:The optical properties of a monolayer graphene can be found in , which pngth. In , the optessed as ,29:(2)A=S, is improved by adding graphene layers, as shown in Equation (4):k is the enhancement of adsorption efficiency and k > 1.It is clear in Equation (3) that for a given waveguide length, a higher confinement factor value results in an improved sensitivity of the waveguide sensor. In addition, with the graphene layer serving as BRE, the adsorption efficiency is enhanced. This can be defined as the percentage of analyte being effectively adsorbed into the sensor surface, which leads to the change of RI. Therefore, the overall sensitivity, k and α are generally obtained by experimental measurement. In this study, we applied an effective index method (EIM) [f. The results were compared with the Au/SiC waveguide SPR sensor without a graphene layer. In the model, a 3-μm thick perfectly matched layer (PML) surrounding the sensor structure was used as the outer boundary condition to truncate the computation region. At the boundary of each layer, the tangential components of the electric and magnetic fields were defined as the continuous inner boundary condition. Since SPP can only be excited by transverse magnetic (TM) polarized light, and the fundamental TM mode (TM0) in the waveguide has the lowest loss, the TM0 mode was investigated.Note that in Equation (4), the values of od (EIM) ,31 using0 mode as a function of Au film thickness at its resonance wavelength  in a sensing medium where RI = 1.344. Ten graphene layers were applied to the Au film. The confinement factor increases as the Au film becomes thicker. Considering that thicker Au would lead to higher optical loss, the 50 nm thickness was selected in this sensitivity study of the graphene/Au/SiC waveguide SPR sensor. This thickness allowed for strong coupling between the waveguide and SP modes.The typical resonance wavelength shift for different numbers of graphene layers in a RI = 1.344 sensing medium is shown in Modification of the SPP field also improves sensitivity. The sensitivities in the three RI ranges  are summarized in α, and the enhanced adsorption efficiency, k, are dependent on analyte materials; therefore, the sensitivity of the waveguide SPR sensor would vary when probing different analytes. Moreover, more sensitivity improvement can be expected since k is always greater than one when adding more graphene layers. However, further coverage of additional graphene layers may not effectively further the transfer of the electrons from the Au film to the graphene. As a result, the resonance peak shift would reach its maximum and no more peak shift could be obtained. On the other hand, the broadened peak linewidth with increased graphene layers also needs to be considered, and the optimal number of graphene layers for maximal sensitivity requires future study.It is worth noting that according to Equation (4), both the absorption coefficient, In this work, we proposed and investigated a new graphene/Au/SiC waveguide SPR sensor. The confinement factors of the sensors with 0 to 10 graphene layers were studied by an effective index method, and the sensitivity was studied by a spectral interrogation method by comparing the shift in the resonance wavelength peak. The sensor operates in the visible light range with the wide bandgap SiC as the waveguide layer. When combined with the advantages of good control of light path, easy measurement of input and output light intensity, and high degree of on-chip integration, this sensor is highly desirable for the next generation of PICs. This study shows that when the number of graphene layers is increased, sensitivity increases, and up to 2810 nm/RIU can be achieved in the RI range of 1.33~1.36. The results demonstrate that a graphene/Au/SiC waveguide SPR sensor is promising for important chemical and biological sensing applications.


A tunable κ is found with the variation of the interlayer coupling strength χ. The interlayer thermal resistance R across graphene/2D-SiC interface reaches 2.71 –7R. This work unveils the mechanism of heat transfer and interface thermal conductance engineering across the graphene/2D-SiC vdW heterostructure.Graphene based two-dimensional (2D) van der Waals (vdW) materials have attracted enormous attention because of their extraordinary physical properties. In this study, we explore the temperature and interlayer coupling induced thermal transport across the graphene/2D-SiC vdW interface using non-equilibrium molecular dynamics and transient pump probe methods. We find that the in-plane thermal conductivity  The effectiveness of heat energy dissipation is firmly based on phonon transportation ability because phonons are the key thermal energy carriers in semiconducting and insulating materials5. Overpopulated phonons can be caused by the high electrical flow of current, which in effect dramatically enhances electron–phonon scattering as well as phonon–phonon scattering. These processes play into the joule heating effects of regional heat localization and develops local thermal hot spots7. Failure to effectively dissipate such a robust amount of generated heat will result in reduced performance, types of defects, and even material disruption. For effective development and design of nano-electronic and optoelectronic devices, it is therefore very important to know the device heat transport characteristics. Of late, two-dimensional (2D) materials have acquired enormous interest with regard to solving the problem of heat-energy dissipation and providing an efficient approach to handle the thermal transport phenomenon in nanoscale devices17. 2D materials offer appealing electronic, mechanical, and phononic properties, which are highly demanded for nano-electronics, optoelectronics, and phononic devices23.The performance of nano-electronics, optoelectronics, and phononic devices relies strongly on the efficiencies of heat energy dissipation33. In this regard, numerous vdWHs have been proposed using graphene and related 2D materials with superior electronic properties, exceptional thermal characteristics, unique mechanical properties as well as other physical properties. In particular, the graphene/2D-SiC vdWH has recently been explored with exotic thermal behavior and unique electronic properties being reported28. In our earlier study, we also reported that graphene/2D-SiC2 shows exceptional thermal transport across the interface to mitigate the heat dissipation problem in next generation nanoelectronic devices. However, thermal transport at the nanoscale shows diverse temperature dependent behaviors36. At high temperatures, the thermal twitching characteristics increase considerably and therefore phonon anharmonicity increases significantly, leading to a decrease in thermal conductivity κ. Usually, the κ obeys the 1/T rule in single atomic crystals such as graphene, phosphorene, and stanene at high temperatures39. However, some binary atomic structures exhibit a peculiar, slowly diminishing characteristic of κ with increasing temperature owing to the overwhelming impact of high-frequency optical phonons36. It is thus crucial to know what types of temperature dependent behavior could be found from this promising graphene/2D-SiC vdWH. In addition, the compact structure of thermal interface materials in vdWHs may change the contact pressure variations, which can significantly hinder the thermal transport performance43. Along with the temperature effects, a detailed insight into contact pressure effects is also required to efficiently lower the thermal resistance across graphene/2D-SiC interface.On the other hand, advanced structures of 2D materials where two or more atomic sheets are held together by a van der Waals forces, and thus form hybrid structures known as van der Waals heterostructures (vdWHs), can retain their all stacked monolayer propertiesHere, we explore the temperature and interface contact pressure effects on thermal transport across the graphene/2D-SiC interface employing reverse non-equilibrium molecular dynamics (RNEMD) simulations and the transient pump–probe (TPP) method. The thermal resistance across the graphene/2D-SiC interface and in-plane thermal conductivity have been evaluated by varying the temperature from 100 to 700 K and the coupling strength from 0.1 to 25. When estimating thermal conductivity at lower temperatures, classical MD simulations neglect quantum effects. The thermal transport at the interface incorporating the quantum correction effect is also investigated. Furthermore, the key mechanisms of heat transfer in the in-plane and out-of-plane directions of the heterobilayer are explored estimating various phonon modes.rc, and χ, and it may be changed to control the interface strength. The parameters 44.The interlayer coupling x, y, z) to eradicate the edge effect. A 10 nm thick vacuum distance in the z-direction was also used to remove atomic contact with the system image. The dimension of the structure considered here was 100 × 10.8 45. Optimized Tersoff potentials formulated by Lindsay et al.46 and Erhart et al.47 were employed to explain C–C and Si–C interactions in the graphene and SiC layers, respectively. These potentials were previously utilized to accurately measure the thermal transport behavior of graphene and 2D-SiC.The graphene/2D-SiC heterostructure was built using a supercell consisting of a lateral periodicity of 2 × 2 for graphene and 3 × 3 for 2D-SiC, respectively. To maintain commensurability, the graphene/2D-SiC lattice parameter was set to 48 were carried out in two phases: the relaxation of the system and the thermal foisting steps. The structure was first brought to an equilibrated position at the desired temperature during the relaxation process. After minimizing the energy with the Conjugated Gradient Algorithm, an isothermal-isobaric (NPT) ensemble simulation was performed for 105 time steps to tune the system to the desired pressure and temperature, where each time step ∆t was 0.5 fs. The velocity-verlet integration method was employed to reach the required temperature. The initial temperature was then raised to the target temperature using 50 ps of microcanonical (NVE) ensemble simulation with a time step of 10 ps. As the temperature was shifted to a new value, the temperature and pressure of the system were further stabilized by applying an additional NPT ensemble simulation for 100 ps. The structure was then further subjected to an additional NVE ensemble simulation for 400 ps to check whether the system was relaxed or not and to stabilize the conserved energy. If the temperature of the system does not change with time, indicating that the system is equilibrated at that particular temperature. The quantitative atomic velocity distribution in the system was further estimated and compared to the Maxwell–Boltzmann predictions to confirm that the structure becomes stable. If the structure becomes stable, the velocities of the atoms in the heterostructure follow the Maxwell–Boltzmann distribution as follows:ν, m represent the probability, velocity, Boltzmann constant, and mass of the atom. We also monitor the process temperature over time to ensure that the temperature stays stable. After the system has been relaxed, the NEMD simulation was done to determine the in-plane thermal conductivity of the graphene/2D-SiC vdWH using Fourier's law as follows:x-direction heat flux. A hot and cold chunk with a width of 20 Å was introduced in the system positioning at L/4 and 3L/4 locations, respectively, where L represents the length. The heat flux passing through the system can be computed as Δε is the energy difference of the thermostat at every M (heat exchange frequency) time steps, and A = wh, is the cross-sectional area. The value of M was set to 1000 (500 fs)34. t denotes the time step of the MD simulations. Following the imposition of heat energy, the time-averaged temperature distribution was calculated to perform NVE ensemble simulation for an additional To quantify the in-plane thermal transport, the RNEMD simulationsR. We employed TPP to probe the R at the heterobilayer interface49. The schematic of the TPP technique is portrayed in Fig. 43. The system was relaxed at a specific temperature to calculate the R across the graphene/2D-SiC interface using the same steps as the κ measurement portion. Following the system's relaxation, the graphene layer was subjected to a 50 fs ultrafast heat pulse. As a result, the graphene layer's temperature rises, while the 2D-SiC layer's temperature stays unchanged. Once the heat impulse is withdrawn, the graphene temperature will gradually drop, while the temperature of the SiC sheet would gradually rise. The temperature evolution of graphene (TG) and 2D-SiC (T2D-SiC) was tracked throughout the entire thermal equilibrium procedure. At each step, the total energy of graphene (Et) was also collected in order to calculate the R according to2AR is the graphene/2D-SiC contact area. To reduce data noise, the data points acquired at each time step were averaged after every 100 time steps.Finally, the thermal transport across interface was investigated by calculating the interfacial thermal resistance T + ∆T and T-∆T are used to control the temperature of the hot and cold chunks, respectively, where ∆T is around 50 K. A rapid temperature fall can be seen near the heating and cooling areas. Similar results have been obtained in NEMD simulations for a variety of systems34. There are rapid energy transfers between potential and kinetic energies near the hot and cold points. ∇T is calculated from the average temperature of the regions indicated by the black brackets as displayed in Fig. T’s are calculated to be 0.336, 0.426, and 0.378 K/nm, respectively.Observing the time dependent system temperature and the atomic velocities, the stability of the developed vdWHs was confirmed at steady-state conditions. As revealed in Fig. κ, a widely varying temperature, ranging from100 K to 700 K and χ = 1, is considered. Figure κ for the vdWH as well as the 2D sheet of graphene and SiC. The in-plane thermal transport behavior of vdWHs is largely affected by the system thickness. Although, the height of a 2D system is normally taken as the thickness of that specific monolayer51, the total thickness of a vdWH system should be estimated carefully since there is an interlayer gap between the two materials. During the investigation, the overall thickness of the vdWH was measured as the summation of two distinct material thicknesses. The thicknesses of 2D-SiC and graphene were assumed to be d2D-SiC = 3.5 Å, and dG = 3.35 Å52. Hence, the total thickness of the graphene/2D-SiC vdWHs was 6.85 Å. Nonetheless, Wu et al.53 proposed that the sheet thickness of different 2D configurations does not change with alteration of the material. They discovered that the thickness of the graphene (3.35 Å) could be applied for computing thermal conductivity in all types of 2D structures. Consequently, both dG and d2D-SiC are considered to be 3.35 Å. In this perspective, the total thickness of the vdWH is 6.7 Å. We counted both of these thicknesses in our study, which we designated as vdW thickness (6.85 Å) and unified thickness (6.7 Å).To investigate the temperature effect on κ is almost the same for both thicknesses. With increasing temperature, a monotonic decreasing trend of κ is observed for both vdWH and individual layer of graphene and 2D-SiC, as anticipated for phonon mediated heat conduction in nanomaterials. The maximum value of κ reaches to 586.47 W/mK at 100 K for the graphene/2D-SiC vdWH, and reduces to 346.81 W/mK at 700 K. The maximum drop of κ for graphene/2D-SiC vdWH, and individual sheet of graphene and 2D-SiC are found as 41.0%, 43.3%, and 39.8%, respectively. Several forgoing studies on 2D materials based vdWH also yielded similar results55. Ahammed et al.5 revealed that as the temperature rises from 100 to 700 K, the κ of stanene/2D-SiC heterostructure reduces from ~ 70 W/mK to ~ 24.81 W/mK. With increasing temperature from 100 to 600 K, the κ declines from ~ 365 W/mK to 150 W/mK for the stanene/Graphene heterostructure41,  ~ 1964.71 W/mK to ~ 438.19 W/mK for the graphene/43, and ~ 9 W/mK to ~ 2 W/mK for the stanene/silicene hetero-bilayer56, which all are in well agreed with our findings. Moreover, similar outcomes were also reported for heterostructures based on MoS2 and MoSe258.It is obvious from Fig. κ of heterobilayer is based on the Fourier law, we observe that the κ digresses from the standard 1/T law at high temperatures. As interatomic force fields have a crucial effect on κ, we calculate the temperature dependent κ behavior for two different potentials. As demonstrated in Fig. κ differs slightly from the standard 1/T law for both types of potentials. The amount of divergence from the Fourier law was also calculated, yielding κ at high temperatures has also been observed in Si/Ge superlattice59, stanene/2D-SiC5 vdWH, single layer 2D-SiC sheet34 and monolayer GaN35. As mentioned in Ref.60, the enhanced phonon–phonon Umklapp scattering causes this 1/Tα trend. Moreover, Qin et al.35 demonstrated that the contribution of high-frequency phonons may increase with increasing temperature, leading to this slow rate reduction behavior.Though the estimation of 6. We calculated the VACF according toith particle velocities of element α (C or Si) at time 0and t, respectively. The PDOS was determined from the VACF according to following formula:F(ω) stands for the phonon spectrum at the vibrational frequency of ω.To understand this unusual behavior, the temperature dependent phonon spectrum was calculated. The phonon density of states (PDOS) was measured by means of Fourier transform of velocity auto-correlation function (VACF)κ with temperature. Moreover, a redshift is perceived from the fourth peak (29-31THz) and fifth peak (46-48THz) of the PDOS curve. This redshift indicates that the phonon energy decreases at increasing temperatures, which might cause the reduction in κ for graphene/2D-SiC vdWH. In 2D atomic crystals, low-frequency acoustic phonons play a substantial role in the transmission of heat energy. However, at high temperatures, the contribution of low-frequency acoustic phonons are reduced5. High-frequency optical phonons predominate at elevated temperatures, resulting in a generation of Umklapp phonon scattering35. Generally, the Umklapp phonon scattering enhances as the temperature of a crystal increases. This leads to the shortening of the mean free path (MFP) of phonons, resulting in a limited phonon heat conduction43.Figure κ, we calculated the temperature dependent phonon-dispersion relation, as depicted in Fig. 61 As shown in Fig. κ. We also estimated the percentage contribution of each phonon mode with increasing temperature, as shown in Fig. κ. There could be other reasons for this minor deviation, because such a slight deviation is fairly common in defective structures (here heterostructure), as described in Refs63.To further explain the temperature effects on κ estimated from the MD simulation up to this point is not fully accurate. Ultimately, to study low-temperature κ, quantum corrections are required. Using the PDOS of the graphene/2D-SiC heterobilayer, we first calculated the normal mode-specific heat. At constant volume, the specific heat (34F(ω) signifies the phonon spectrum, u = κ can be estimated according to κ-lowering effect. As a result, beyond the Debye limit, the quantum corrected results show a declining trend in thermal conductivity. Furthermore, when compared to the At low temperatures, atomic vibrations remain in a resting place, also known as a frozen state, and remain in that state until the surrounding temperature is raised to a proper level. The sufficient temperature level is known as the Debye temperature level, and the κ considering the linear region of the temperature profile as described in most previous NEMD simulations, a recent study64 demonstrated that the nonlinear portion should also not be ignored when calculating thermal transport of finite system. Here, we also calculated the κ by considering the average temperature of the thermostats to incorporate the nonlinear region of the temperature profile. The calculated temperature dependent κ while considering the average temperature of heat source and sinks is depicted in Fig. κ reaches to 523.93 W/mK, 885.43 W/mK, and 178.65 W/mK at 100 K for the graphene/2D-SiC vdWH, graphene, and 2D-SiC, respectively, and reduces to 259.10 W/mK, 421.10 W/mK, and 77.10 W/mK at 700 K. It is apparent that at all temperatures, the κ is slightly smaller than the estimated κ using only the linear portion, which is in line with the demonstration in Ref64. This result also implies that the temperature drop close to the thermostat is physical in finite system, as stated in Refs66.Although we calculated the 67. The interlayer coupling has long been known to have a substantial impact on the thermal transport characteristics. The LJ coupling strength χ was used to study the interfacial contact pressure dependent κ for graphene/2D-SiC vdWH. A wide variety of χ values ranging from 0.1 to 25 were chosen to determine the coupling strength dependence of κ. First, the stability of the structures was checked for these diverse values of χ and then the κ dependence of χ was calculated. Figure κ of graphene/2D-SiC decreases monotonically from 468.62 to 207.09 W/mK. The κ, for the independent layer of graphene, drops dramatically from 842.88 to 357.23 W/mK, while the κ for 2D-SiC drops steadily from 158.32 to 71.82 W/mK. The flexural mode phonons of 2D-SiC constrain the flexural mode phonons of graphene, resulting in a reduction in the κ of the graphene/2D-SiC vdWH when compared to the independent layer of graphene or 2D-SiC sheet. With increasing χ, restrictions between the flexural mode phonons of the two layers increases as the interaction of the graphene layer and 2D-SiC layer is enhanced67. Accordingly, the κ of graphene, 2D-SiC, as well as of the graphene/2D-SiC vdWH decreases as the restriction is increased.Improving thermal transport is crucial for novel materials to be used in nanodevices. Various approaches, such as modulating the interface interaction or varying the rotational angle of substrate, have recently been discovered to improve the thermal transport behaviors of vdWHsκ, we calculated the phonon overlapping factor (S) of graphene/2D-SiC heterobilayer, which demonstrates the capacity of thermal energy exchanging between graphene and 2D-SiC phonon. The following equation is used to compute the overlapping factor S:S shows a decreasing trend ranging from ~ 0.026 to ~ 0.020 with the increase of χ from 0.1 to 25, as depicted in Fig. 69. Due to the increase of phonon scattering between two layers with increasing χ, the capacity of exchange thermal energy reduces. It can also be observed that the PDOS of graphene is slightly flattened with increasing χ. Such flattening can broaden some phonon modes, potentially reducing phonon lifetime and MFP70. Eventually, this may reduce the overall thermal conductivity of the heterobilayer.Moreover, to have a better understanding of the χ dependence of R at χ = 1 is depicted in Fig. R reaches to a maximum value ~ 3.559 57.This is because high-frequency phonons may disintegrate into multiple low-frequency phonons at high temperatures, causing the enhancement of inelastic scattering probability. Low-frequency phonons have a better chance of being transmitted through the interface than high-frequency phonons. As a result, phonon transmission coefficients at the interface are enhanced, and R is decreased. Anharmonicity within the materials is discovered to have an essential role in heat transportation at interface by enhancing energy transmission between distinct phonon modes. Wu et al.71 explored the influence of anharmonicity in heat transfer across an interface composed of monatomic and diatomic lattices. At higher temperatures, increased anharmonic scattering results in more effective energy redeployment to low-frequency phonons, which can more efficiently transmit heat across the interface, resulting in a reduced R. To further explain the temperature effects on R, we calculated the temperature dependent out-of-plane phonon-dispersion and phonon-group velocities. As depicted in Fig. R. The estimated group velocity for ZA mode phonon as shown in Fig. R as temperature rises.Although 2D materials have superior in-plane heat transport behavior, out-of-plane heat transport is often the barrier for thermal energy exchange due to the poor vdW interaction at the interface. The ability to control the heat flow has led to possible fascinating applications, which strongly depends on the better understanding of the thermal conduction mechanism at the interface. The temperature dependence of R on the graphene/2D-SiC vdWH. Figure R at 300 K. The computed R drops monotonically when χ varies from 0.1 to 25. Usually, boosting the χ increases the interaction at the interface, which enhances the coupling of phonons between SiC and graphene layers and unswervingly raises transmission of phonon probability across the contact. Moreover, atoms in one surface might be scattered more strongly by the other layer’s atoms with increasing χ, leading to the increasing of interface scattering. The capability of energy interchange between in-plane and out-of-plane phonons is manifested by calculating the overlap in the PDOS as shown in Fig. S for graphene, 2D-SiC, and the graphene/2D-SiC vdWH is 0.022, 0.026, and 0.023, respectively, and increases to 0.026, 0.034, and 0.028 when χ = 25. It indicates that the interfacial thermal transfer capacity grows when the coupling of in-plane and out-of-plane phonons improves. Because of the scattering of high frequency phonons, the S of graphene has a slight improvement. The R of the system decreases as a result of the improved coupling strength. Therefore, we conclude that interlayer coupling strength may efficiently tune the thermal resistance across the graphene/2D-SiC vdW interface.Next, we study the χ dependence of κ was found to be considerably reduced by system temperature, with maximum reductions of43.3%, 39.8%, and 41.0% for graphene, 2D-SiC, and the bilayer, respectively. Different from the typical 1/T law, an abnormal κ for the graphene/2D-SiC bilayer was observed at high temperatures. A coupling strength dependent tunable κ was observed for this heterostructure, which is advantageous for nanodevice production since thermal performance may be adjusted by contact pressure. The calculated R was also found to decrease monotonically with increase of the temperature and coupling strength. The heat conduction mechanism across the heterostructure interface was demonstrated using phonon calculations. The cross-plane phonon interaction between the graphene and 2D-SiC layers is revealed to be the primary thermal channel for interfacial heat conduction. The Umklapp scattering converts the high-frequency phonons into more low-frequency phonons, which can subsequently be linked with the phonons in other layer and contributing to interface thermal transport and lowering R. Moreover, enhanced phonon coupling with increasing χ facilitates the heat transfer from graphene to SiC and thus bring about the decrease in R. This study reveals the mechanism of heat dissipation and interfacial engineering for thermal conductance manipulation in the graphene/2D-SiC vdW heterostructure.In conclusion, we used NEMD and TPP simulations to systematically investigate temperature and contact pressure induced thermal transport across graphene/2D-SiC vdWH. The computed in-plane Supplementary Information.


Milián-Sánchez et al.; Scientific Reports 10.1038/s41598-020-64497-0 (2020).3 observed fluctuations in radioactive decay rate measurement series, and after excluding environmental influences (measured indoors) as root causes, they looked for possible correlations with astrophysical variables. They reported positive or negative correlations with geomagnetic activity (GMA) and cosmic-ray activity (CRA). This assertion is at variance with the most accurate measurements of radioactivity, which support the validity of the exponential-decay law14. If a causal relationship between ‘space weather’ and radioactive decay rates were true, it would invalidate the notion of invariable decay constants and have unforeseeable practical and theoretical implications.In recent work, Milián-Sánchez et al.226Ra source with a Geiger–Müller counter3 is shown together with measured ambient humidity data in a weather station in the Valencia region15. There appears to be a positive correlation between the humidity and the observed decay rates. This is even more striking when applying a toy physical model in which the humidity data are accumulated as moisture in the set-up16, shown as a line overlaid on the decay rates in Fig. In spite of the authors’ efforts to investigate possible influences of environmental parameters—such as ambient temperature, pressure and humidity—on the detectors’ stability, it turns out that the influence of ambient humidity on the instrumentation has been underestimated. In Fig. The moisture accumulation model was devised in a simple manner: The relative air humidity data series, No hard claims are made about the physical rigour of this toy model, but it allows to smooth out the humidity data in time (by accumulation), to adjust the baseline  with the humidity model (Figure The moisture model has also been applied to the other decay rate measurements, the background measurements, as well as the additional tests performed on the capacitance of the detector cable and a reference capacitancel Figure . It seem3 may be regarded as exploratory research, and the sought-after correlation with space weather as highly speculative. With the discovery of hitherto unnoticed correlations with terrestrial weather conditions, the hypothesised causal correlation between space weather and radioactive decay turns out to be unsubstantiated by evidence and remains unlikely to be true.In conclusion, the work in Refs.


We believe the scheme may pave the way for graphene-based optical active devices.Graphene-based optical modulators have been widely investigated due to the high mobility and tunable permittivity of graphene. However, achieving a high modulation depth with a low insertion loss is challenging owing to low graphene-light interaction. To date, only waveguide-type modulators have been extensively studied to improve light-graphene interaction, and few free-space type modulators have been demonstrated in the optical communication wavelength range. In this study, we propose two graphene-based optical free-space type modulators in a simple silicon photonic crystal structure that supports bound states in the continuum. The designed modulator with an ultra-high quality factor from the bound states in the continuum achieves a high modulation depth (MD = 0.9972) and low insertion loss (IL = 0.0034) with a small Fermi level change at the optical communication wavelength. In addition, the proposed modulators support outstanding modulation performance in the normal chemical vapor deposition (CVD) graphene (mobility = 0.5 m Numerous graphene-based optical devices have been studied for many years; these include photo detectors7, optical absorbers11, and nonlinear devices15. In particular, graphene-based optical modulators, one of the key components of photonics systems, have been extensively investigated. The outstanding carrier mobility and gate-tunable carrier concentration of graphene enable it to be used as an active medium in optical modulators; the carrier concentrations of graphene can be tuned by applying different gate-voltage (Fermi level variation), which enables gate-tunable absorption of graphene16.Graphene, where a single layer of atoms is arranged in a two-dimensional honeycomb lattice, has gained considerable attentions owing to its various exceptional properties, such as its high thermal conductivity, ultra-high saturable absorption, and wide optical bandwidth17, graphene metamaterials21, graphene antennas22. In contrast, graphene loss is largely determined by the interband transition in the optical communication wavelength region, which is nearly independent of the Fermi level of graphene. Therefore, waveguide-type modulators have been extensively studied to improve light-graphene interaction in this wavelength range. A graphene-coated Si waveguide-type optical modulator operating in the optical communication wavelength was the first to be experimentally demonstrated23. This device had a small device area (~ 25 μm2) with a high modulation depth (MD = 0.1 dB/μm), compared to conventional Si-based optical modulators. Subsequently, double graphene layer-coated waveguide-type optical modulators25, suspended graphene modulators26, and hybrid graphene modulators27 have been demonstrated with improved the modulator performance. However, waveguide-type modulators have a limited range of applications because they exhibit a trade-off between modulation depth and insertion loss (IL). In particular, they are not suitable for free-space applications that require a low insertion loss. Lee et al. proposed a free-space graphene modulator composed of a quarter-wavelength-thick insulator layer and a metal reflector to increase graphene absorption by placing the graphene layer where the amplitude of the electric field was maximized28. However, this modulator showed a very low modulation depth of 4% owing to the low absorption of graphene .To date, many waveguide and free-space optical modulators using graphene loss variation have been proposed over a wide wavelength range. Optical transitions, including interband and intraband transitions, are the main processes that determine the loss of graphene. In the terahertz and mid-infrared wavelength regions, where intraband transition is dominant, absorption in graphene is largely tuned by adjusting the drive voltage. Therefore, many highly efficient graphene-based optical modulators have been demonstrated in these wavelength regions, such as optical modulators using metal reflectors30. These devices achieved a high modulation depth with an extremely enhanced electric field in the graphene layer. However, the epsilon-near-zero effect in graphene is highly debated and has not been experimentally demonstrated. Another approach to increase light-graphene interaction is to place a graphene layer near high Q-factor resonators, such as photonic crystal resonators31 and whispering gallery modes33. However, these resonators show relatively low Q values (Q = 103 ~ 104), which is not enough to achieve highly efficient modulators; Scattering loss by imperfect fabrication and graphene loss deteriorate the Q value.To increase absorption in graphene, optical modulators using the epsilon-near-zero effect have been introduced40. In addition, high Q (> 105) is maintained in the symmetry broken structures due to imperfect fabrication: tiled, imperfectly etched, or bent structure34. In the proposed scheme, the high Q transmission resonance from the BIC facilitates a sharp transmission variation from the tuning of the Fermi level of graphene, which enables the proposed modulators to simultaneously achieve a very high modulation depth and low insertion loss. We also investigate the effect of graphene mobility on modulation efficiency. The proposed modulators maintain high performance if the graphene mobility is higher than μ = 0.5 m2/Vs, and this value can be obtained from normal graphene.In this study, we propose two graphene-based optical modulators using bound states in the continuum (BICs) in a simple one-dimensional photonic crystal structure. Theoretically, BICs support infinite Q resonance as a result of destructive interference between radiative waves, and they can be easily obtained from photonic crystal structuresp is the period, f is the fill factor, h is the height of Si, and θ is the incident angle. The refractive indices of Si, ion gel, and SiO2 are 3.45, 1.45 and 1.45, respectively. The permittivity of graphene is calculated from the Kubo formula41, and the height of the graphene layer is assumed to be 0.34 nm. Ion gel is used for the electrical doping of graphene in the ISLG modulator structure. Note that there are many kinds of ion-gel materials. The refractive index of most of the ion gels is in the range of 1.4 ~ 1.45, and IL-P14 and IL-AP3 have the refractive index of 1.4544. In recent years, ion-gel materials have been actively utilized as an efficient gating medium. They have great advantages such as transparent, good mechanical flexibility, thermal stability, easy fabrication, and compatibility with various substrates. The electric double layer with extremely high capacitance at the graphene-ion gel interface enables the chemical potential (Fermi level) of graphene to be adjusted with a low electric gate voltage47. In the DLG structure, graphene doping is implemented by applying a gate voltage between two graphene layers.Figure p = 870 nm, h = 150 nm, and f = 0.3. The parameters were selected to induce the BIC phenomenon near the operating wavelength. The BIC phenomenon is observed near λ = 1.54 μm and θ = 12°, and the reflection peak (transmission dip) disappears in this region due to the infinite Q because of BIC.First, we designed a photonic crystal structure to induce a BIC phenomenon. Figure μ = 1 m2/Vs. In this case, the BIC disappears owing to the graphene loss; Q is inversely proportional to the loss, and the loss of graphene breaks the infinite Q condition of the BIC. However, an ultra-high Q is maintained because the loss of doped graphene is insignificant, which facilitates the design of high-performance modulators. Figure F = 0.4 eV to 0.7 eV at the incident angle of θ = 11.937°. By choosing the incident angle slightly apart from the BIC, the transmission resonance with ultra-high Q at the operating wavelength can be achieved. The other parameters are assumed to be the same as in the previous calculations. As increase in the Fermi level leads to a decrease in the graphene loss, the Q of the transmission dip increases with an increase in the Fermi level. The Q of the resonance for EF = 0.7 eV is Q ~ 2 × 105, and it can be simply increased by adjusting the incident angle. In addition, it has been shown that increasing the Fermi level of graphene leads to a transmission dip blue shift because the permittivity of graphene decreases as the Fermi level increases. Generally, graphene doping (Fermi level variation) has little effect on tuning the resonant wavelength in resonators because the variation of the graphene permittivity does not significantly change the effective index of the structure due to the very thin graphene. However, in this ultra-high Q resonance system, a small resonant wavelength tuning results in a very high transmission variation. The transmission variation for the Fermi level variation at λ = 1.55013 μm is shown in Fig. F = 0.615 (off-state) and EF = 0.672 eV (on-state), respectively. Therefore, a very high modulation efficiency was achieved: MD = 0.9972 and IL = 0.0034, where the modulation depth was obtained as MD = (Ton-Toff)/Ton, and insertion loss, which is ratio of the transmitted power for on-state and input power, was calculated as IL = 1 − Ton.We investigated the variation in the transmission spectra for Fermi level variation in the proposed ISLG structure. The mobility of graphene is assumed to be μ = 0.1 m2/Vs to μ = 10 m2/Vs for EF = 0.6 eV. Because the mobility is inversely proportional to the loss, a higher Q is observed for a higher graphene mobility. However, the high Q is maintained even though the mobility is μ = 0.1 m2/Vs, and the transmission spectra for μ > 0.5 m2/Vs are almost the same. Therefore, a high modulation efficiency can be sustained for μ > 0.5 m2/Vs. Note that the real part of graphene permittivity is almost constant for the mobility variation. Therefore, the resonant wavelength hardly shifts for the mobility variation. In addition, as the mobility increases, the imaginary part of the graphene permittivity sharply decreases in the range of μ = 0 ~ 0.5 m2/Vs. Therefore, the transmission spectra largely change when the mobility is varied from μ = 0.1 to 0.5 m2/Vs. It should be noted that a mobility of μ = 0.5 m2/Vs can be obtained from the chemical vapor deposition (CVD) method that is considered the most promising method for producing graphene49.Figure μ = 1 m2/Vs. The Q of the resonance is slightly reduced compared to that of ISLG owing to the multiplied graphene loss. However, this modulator also supports a very high Q transmission. The transmission variation for the Fermi level at an operating wavelength of λ = 1.55028 μm is illustrated in Fig. Although the ion gel-based modulator shows outstanding modulation performance, the low stability and slow modulation speed of the ion gel are obstacles to realizing high-speed optical modulators. To solve these problems, we designed an optical modulator composed of two graphene layers Fig. b. By app5, and this value is about ten times higher than previous reported graphene-based resonators. In addition, the Q can increase easily by tuning the incident angle. The proposed modulators could simultaneously support a high modulation depth and low insertion loss: MDISLG = 0.9972, ILISLG = 0.0034, MDISLG = 0.9889, and ILISLG = 0.011. The effect of graphene mobility on the performance of the modulators was also investigated. Although low graphene mobility (μ = 0.1 m2/Vs) deteriorated the efficiency of the modulator, an outstanding efficiency could be maintained for standard quality graphene (μ > 0.5 m2/Vs). These promising features are likely to generate new avenues for graphene-based optical devices for free-space applications.In this study, we proposed two graphene-based free-space high-performance optical modulators with a simple photonic crystal structure. The very high Q transmission resonance from BIC facilitated a remarkable transmission change with a small variation in the Fermi level. The Q of the proposed structure is approximate ~ 2 × 106 m/s. The reflection spectrum of the photonic crystal structure without graphene as a function of the incident angle was calculated using rigorous coupled-wave analysis (RCWA), and the transmission spectra of the modulators were calculated using the COMSOL Multiphysics software. Periodic boundary condition was used for the calculations, and a sufficiently small mesh size was used for accurate calculations.The permittivity of graphene was calculated using the Kubo formula, assuming a graphene thickness of 0.34 nm and Fermi velocity of 10


D-VGS is explored, which indicates that the threshold voltage is increased by diameter and number of twists in this type of transistor.The outstanding properties of graphene-based components, such as twisted graphene, motivates nanoelectronic researchers to focus on their applications in device technology. Twisted graphene as a new class of graphene structures is investigated in the platform of transistor application in this research study. Therefore, its geometry effect on Schottky transistor operation is analyzed and the relationship between the diameter of twist and number of twists are explored. A metal–semiconductor–metal twisted graphene-based junction as a Schottky transistor is considered. By employing the dispersion relation and quantum tunneling the variation of transistor performance under channel length, the diameter of twisted graphene, and the number of twists deviation are studied. The results show that twisted graphene with a smaller diameter affects the efficiency of twisted graphene-based Schottky transistors. Additionally, as another main characteristic, the I The n and m are important coefficients in the chiral vector.In the last decade, most efforts of nanotechnology researchers have been devoted to the study and characterization of electronic properties of graphene ,4,5,6,7.n, 0). Based on this theory, ,  and  are metallic, since (n − 1) is a multiple of three, and hence ,  and  are semiconducting. These different features of twisted graphene lead to great attention from researchers.In the zigzag edge, the pairs are converted to  and chiral (C) vectors as shown in T and C vectors are defined as:a1 and a2 are the basic vectors:To investigate the electronic properties of twisted graphene, the dispersion relation based on the geometrical effect of twisted graphene should be studied. The graphene sheet has two perpendicular vectors called translation L=|T→Z is the diameter of the twist and S is the number of twists in twisted graphene. Hence, for any zigzag vector C , we have:On the other hand, for the length of twist graphene, we have:S, the diameter of twist can be obtained as:Consequently, using various values of Z is proportional to:In the other words, it means that Now, the electronic properties of graphene twist are surveyed. Using the Taylor expansion series, the E-K relation of graphene band structure can be given by :(11)E=3tEc is assumed as [Using some simplification, we have:sumed as :(13)Ec=0Consequently, the amount of K1 to K2 should be calculated. K1 is the wave vector in the metallic region, K2 is the wave vector in the semiconducting region and L′ is the length of the barrier. The transmission probability (T (E)) is given by [Based on our proposed structure in given by :(15)T(E)By replacement of wave vectors in each region, we have: V to the gate of Schottky transistor, the quantum current density (J) can be calculated as in [The geometry effect in (16) can also be seen. Now, by applying a voltage ed as in ,28:(17)JConsequently, by knowing that the current density definition in 1-D materials, Equation (17) is converted to:I-V characteristic relation is obtained by (20):The applied voltage is given by:DSI-V at diverse values of GSV. It can be seen that the drain current rises substantially as the gate-source voltage is increased from 0.5 to 1 v which means that the gate-source voltage controls the current in the channel region (DI).In this part, the performance of twisted graphene-based Schottky transistor is studied and results, based on the analytical method using MATLAB software, are also discussed. L′ = 15 nm, it can be said that the electrons move easier than other values of L′ and the tunneling effect not occurred in this case. In the other words, the electron passes through the barrier (moving directly), because the energy of the electron is more than the barrier  leads to the decrease in drain current that is controlled by the gate-source voltage. In the other words, small diameters of twisted graphene led to the transportation of electrons in one dimension, hence, the drain current increases [Fλ) represents that the wavefunctions of carriers that completely fill the diameter of the nanostructure. In the one-dimensional structure that the diameter is smaller than the Fλ, the electrons in the 1D channel cannot screen the Coulomb potential from the gate and consequently, high current flows and great channel length modulation can be attained [Although the ncreases . In factattained .S is more, the amount of stress-strain of material is higher, and consequently, it leads to some defects in the structure. Defects caused the C-C bonds to break and new barriers to be generated. This phenomenon causes the perturbation of the drain current.Also, the stress-strain of the twisted structure plays an important role in the variation of different properties ,33. HereZ  are not generated on graphene structure, the Z will not vary. In the other words, Z is a function of S ((S) = Zf). Additionally, in the saturation region, that gradient of D-VDSI characteristic is zero, we have:Hence, the drain current decreases. In comparison with D-VGSI characteristic for our proposed model can be written as:Therefore, the D-VGSI characteristic for the diverse value of S. To investigate the Z effect on D-VGSI characteristic, S = 10.Based on this exceptional equation, the threshold voltage of our transistor can be achieved. Z) has an inverse relation on the threshold voltage of the transistor.TV), as shown in To compare L). As indicated in Finally, a comparative study of our modeled transistor and typical I-V characteristic of other transistors is depicted in T) and chiral (C) vectors are explored and the relationship between diameter and number of twists for all zigzag vectors are calculated, considering the dispersion relation and tunneling effect the wave vector changes from K1 to K2 . By applying a voltage to the proposed structure, the I-V characteristics are studied. It is concluded that increasing the gate-source voltage leads to an increment in drain current. On the other hand, a reduction in diameter and number of twists can increase the drain current. The effect of twisted graphene geometry on the threshold voltage of Schottky transistor indicates that the great number of twists and small values of diameters leads to a low threshold voltage of the transistor. So, it is concluded that in order to promote the performance of twisted graphene-based Schottky transistor, twisted graphene with a small diameter and more number of twists is appropriate. Additionally, the temperature effect on transistor performance is explored, and observations show that temperature increases lead to an increment in the drain current. Finally, the proposed transistor is compared with similar research which represents the superiority of twisted graphene-based Schottky transistor over the graphene nanoscrolls-based Schottky transistor. Altogether, twisted graphene is a desirable nominee for transistor devices in integrated circuits as high-speed switching applications.Twisted graphene with a novel structure is a promising material for nanoelectronic applications due to its remarkable electrical properties. In the presented work, a twisted graphene-based Schottky transistor is analytically modeled. The proposed structure with zigzag twisted graphene as metallic and semiconducting properties depends on its chirality numbers, which are assumed to be  and , respectively. The geometry of twisted graphene by translation (


Dermal cells containing TDP-43 were fibroblasts as identified by co-labeling against vimentin. ROC analyses  showed that detection of 24.1% cells with cytoplasmic TDP-43 positivity in the dermis had 85% sensitivity and 80% specificity for detecting ALS. We have identified significantly increased TDP-43 levels in epidermis and in the cytoplasm of dermal cells of ALS patients. Our findings provide support for the use of TDP-43 in skin biopsies as a potential biomarker.Diagnosis of ALS is based on clinical symptoms when motoneuron degeneration is significant. Therefore, new approaches for early diagnosis are needed. We aimed to assess if alterations in appearance and cellular localization of cutaneous TDP-43 may represent a biomarker for ALS. Skin biopsies from 64 subjects were analyzed: 44 ALS patients, 10 healthy controls (HC) and 10 neurological controls (NC) (Parkinson’s disease and multiple sclerosis). TDP-43 immunoreactivity in epidermis and dermis was analyzed, as well as the percentage of cells with TDP-43 cytoplasmic localization. We detected a higher amount of TDP-43 in epidermis ( Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disorder affecting motor neurons from cortex, brainstem, and spinal cord. While most are sporadic cases, 10–15% are familial forms . StudiesForty-four subjects with definite ALS and 10 healthy controls (HC) were prospectively recruited by the ALS units from Hospital del Mar and Hospital de Bellvitge, Barcelona. A third group of 10 neurological controls (NC) were also selected. ALS patients fulfilled the diagnostic criteria   and wereThree-millimeter skin punch biopsies were obtained from the distal leg after local anesthesia with mepivacaine. Skin biopsies were fixed in paraformaldehyde solution at 4% and maintained at 4 °C in PB (phosphate buffer) with sucrose. Then, biopsies were cut by cryotome into 60 µm thick sections collecting the slices in PBS.p-TDP-43, finding no labeling in one of them [For immunofluorescence, sections were blocked with endogenous Biotin-Blocking Kit (Invitrogen), TBS-Triton 0.3% and normal donkey serum 10%, and subsequently incubated overnight at 4 °C with anti-TDP-43 antibody , anti-vimentin  and rabbit anti-protein gene product 9.5  as primary antibodies. After washes, sections were incubated overnight at 4 °C with horse anti-rabbit biotinylated antibody , conjugated streptavidin Alexa Fluor 488  or streptavidin Alexa Fluor 594  and donkey anti-rabbit cyanine 3  as secondary antibodies. Slices were then transferred to gelatinized slides and mounted in Fluoromount G . To assess antibody specificity, control samples were processed in parallel as described before but without primary antibodies. DAPI staining was used to ensure correct recognition of tissue structures. The anti-TDP43 antibody used in this study recognizes the C terminal cleavage product (20–30 KDa) and the native and phosphorylated forms of TDP-43. Antibodies against the non-phosphorylated form have been widely used to determine the TDP-43 translocation to the cytoplasm without the risk of missing different post-translational modifications and non-phosphorylated cytosolic distribution of TDP-43 ,25. In t of them  and labe of them . The res of them ,19,20,21Immunolabeled sections were first viewed under an Olympus BX-51 microscope equipped for epifluorescence using appropriate filters. Areas of interest were analyzed with a scanning confocal microscope .2 each) of each case, using ImageJ software . The mean of the two measures of the percentage of area with TDP-43 labeling was calculated after defining the threshold background correction. Epidermal TDP-43 amount was measured in microphotographs taken from two representative areas of epidermis (101.61 × 101.61 µm2 each) of papillary and reticular dermis were taken and analyzed. The representative areas were selected in a systematic way, avoiding areas of the section that might have artefacts and then selecting 2 evenly separated fields  at low magnification, and then viewing them under higher magnification for capture and analysis. The levels of cytoplasmic TDP-43 were quantified as (1) percentage of cytoplasmic TDP-43 immunoreactivity and (2) percentage of cells with positive TDP-43 into the cytoplasm in each defined area. For calculating the percentage of cytoplasmic TDP43 immunoreactivity, first, a threshold was defined for background correction, then the percentage of pixels in the area above threshold of TDP-43 labeling was measured using ImageJ software. Additionally, the mean percentage of cells with TDP-43 positivity within their cytoplasm was calculated in the analyzed confocal images, relative to the total number of vimentin positive cells (fibroblasts) in these areas. Results are expressed as the mean of the two measures per subject and layer.The two layers of the dermis (papillary and reticular dermis) were evaluated separately. This distinction was made given that papillary and reticular cells have different patterns of protein synthesis and expression ,28. DiffTo study the possible colocalization of TDP-43 in the cutaneous innervation, we performed immunohistochemical co-labeling for PGP9.5 and TDP-43. Confocal images were taken with a confocal microscope for counting intraepidermal nerve fibers (IENF) and for TDP-43 colocalization assessment. IENF were measured in a subset of ALS and HC subjects. Individual fibers were counted as they pass through the basement membrane, whereas branching occurring within the epidermis did not increase the number of the IENFs counted. IENF density was expressed as the number of fibers per 1 mm length of the epidermis. Average density of IENFs in two images per sample was then derived. p < 0.05. Pearson’s correlation coefficient was used to assess possible linear association between two continuous quantitative variables. In order to obtain an estimate of sensitivity and specificity of TDP-43 quantification regarding ALS diagnosis, ROC curves and area under the curve (AUC) were calculated and optimal cut-off values were selected using Youden’s index. Data are expressed as mean ± SEM. Means were compared by ANOVA, applying Tukey’s post hoc test when necessary . The level of significance was set at To determine cytoplasmic TDP-43 accumulation, a signature of ALS pathology, skin biopsies, were labeled with polyclonal antibody against TDP-43. The results of TDP-43 immunoreactivity levels and proportion of cells with cytoplasmic TDP-43 positivity in epidermis, papillary and reticular dermis are summarized in p < 0.001) in the ALS group (12.9 ± 1.0%) compared to HC (7.2 ± 1.0%) and NC (4.4 ± 1.2%)  .Cytoplasmic TDP-43 was detected in dermal cells of ALS patients and controls. However, a higher number of positive cells for cytosolic labeling of TDP-43 was found in ALS patients than in healthy and NC. Those dermal cells were identified as fibroblasts as they were positively marked with vimentin . Unlike p < 0.001; CI 95% 0.800–0.935) were calculated for TDP-43-positive dermal cells, including measures from superficial/deep dermis, and cut-off values were selected according to optimal Youden’s index. Detection of 24.14% of cells with cytoplasmic TDP-43 positivity in the dermis had 85.2% sensitivity and 80.0% specificity, with a positive predictive value of 90.4% and a negative predictive value of 71.1%  and cut-off values of 0.26%, with 88.6% sensitivity, 82.5% specificity, 91.8% positive predictive value and 76.7% negative predictive value for detecting ALS. We performed an ROC analysis based on the percentage of TDP-43 cytoplasmic-positive cells of the overall dermis as well as on the percentage of immunoreactivity to achieve a theoretical cut-off point as a proof of concept of its value as a marker of the disease. ROC curves and AUC  in epidermis and papillary dermis according to gender and site of onset in ALS patients. Only in the reticular dermis we found a significant lower TDP-43 immunoreactivity in bulbar onset patients, but no differences were found considering the percentage of cells with cytoplasmic TDP-43 localization. No significant correlations were found between TDP-43 expression measurements and age of onset of the disease, time from symptoms onset to biopsy and ALSFRS-R slope .p = 0.831), superficial dermis  and deep dermis  between the initial biopsy and 12 months later. The increase in levels of TDP-43 in the dermis at the second biopsy did not achieve statistical significance due to the low number of samples analyzed. However, the percentage of cells with cytoplasmic TDP-43 translocation in the dermis increased in the second biopsy, with differences being significant for the papillary dermis , but not for the reticular dermis .A small subset of ALS patients  underwent a second skin biopsy 12 months later. There were no significant differences in levels of TDP-43 immunoreactivity in epidermis  compared with HC (12.75 ± 2.20) and NC (10.89 ± 1.77). However, no colocalization of TDP-43 was found in PGP9.5-labeled fibers in ALS patients, HC or NC  , even wiTDP-43 accumulation is not homogenous throughout the motor nervous system of ALS patients . Full-leWe did not find a correlation between TDP-43 deposition and clinical data. There are only few previous reports about clinical correlation, and only disease duration was analyzed with contradictory results. In the subgroup of patients with a second biopsy 12 months later, there was a high variability of TDP-43 immunoreactivity between the first and second biopsies. Although changes were not significant, a higher number of dermal cells with cytoplasmic TDP-43 deposition were detected in the superficial dermis. However, the conclusions from this subgroup should be taken with caution due to the small number of patients, and the limited time interval between biopsies in a fast-progression disease such as ALS.Albeit having some distinctive histopathological features, ALS lacks an accessible biomarker. Diagnosis is based on clinical criteria and supported by neurophysiological studies ,38,39. ATDP-43 cytoplasmic localization is present in epidermal keratinocytes and in dermal fibroblasts of ALS and HC, but quantitative analyses show significantly larger amounts in ALS patients. Quantitative values of dermal cells with TDP-43 appear to offer a sensitive and minimally invasive biomarker. Further experiments are needed to specifically explore the levels of post-translational modifications of TDP-43 in these samples, such as phosphorylation, ubiquitylation and truncated forms. Although the number of skin samples from ALS patients represents the larger series reported to date, a higher amount is needed to achieve practical cut-off values of TDP-43 deposition for diagnostic purposes. Nevertheless, even considering the limitations, this work represents the proof of concept of cutaneous TDP-43 as a potential biomarker for ALS.


The identification of atomic vacancy defects in graphene is an important and challenging issue, which involves inhomogeneous spatial randomness and requires high experimental conditions. In this paper, the fingerprints of resonant frequency for atomic vacancy defect identification are provided, based on the database of massive samples. Every possible atomic vacancy defect in the graphene lattice is considered and computed by the finite element model in sequence. Based on the sample database, the histograms of resonant frequency are provided to compare the probability density distributions and interval ranges. Furthermore, the implicit relationship between the locations of the atomic vacancy defects and the resonant frequencies of graphene is established. The fingerprint patterns are depicted by mapping the locations of atomic vacancy defects to the resonant frequency magnitudes. The geometrical characteristics of computed fingerprints are discussed to explore the feasibility of atomic vacancy defects identification. The work in this paper provides meaningful supplementary information for non-destructive defect detection and identification in nanomaterials. Defects are recognized as the unpredictable and stochastic existence in the lattice of graphene, which seriously compromises the expected performances and properties ,2. HowevAt present, it is hard to precisely identify the atomic vacancy defects in graphene by the available experimental instruments. Even atomic force microscopes provide satisfactory three-dimensional imaging of defects in local spaces, but the detection of specific locations on the global scale has low efficiency. On the other hand, scanning tunnelling microscopes and transmission electron microscopes are more competitive in the global feature observation, but the resolution for local defects needs improvement. Moreover, defects are unsteady local structure and easily affected by the disturbances of light, heat, or electromagnetic waves , which lIn order to develop efficient methods for defects identification in graphene, many analytical and numerical approaches are attempted, such as molecular dynamics (MD) simulation , densityThe fingerprints of graphene are imaged by vibrational sum-frequency spectroscopy and Raman spectroscopy, etc. For example, vibrational fingerprints of residual polymer on transferred CVD graphene are provided by the use of vibrational sum-frequency spectroscopy . The RamIn this study, the fingerprints of resonant frequency for atomic vacancy defect identification in graphene are depicted, based on finite element computation. The geometrical configuration of graphene lattice and the atomic vacancy defects are introduced in 3, respectively, according to the reported literature , [D], and For free vibration, the stiffness and mass matrix in the element domain are written as follows:In addition, the Block Lanczos extraction method is used in this work for its efficiency in large symmetric eigenvalue problems . As the The geometrical configuration of graphene lattice and the corresponding geometrical and material parameters are defined as above, while the resonant frequencies and deformations under different vibration modes are computed based on the finite element method. The first four order resonant frequencies of the pristine graphene without vacancy defects are 1.7282, 3.2925, 3.7442, and 5.189 THz, respectively, which reaches good agreement with the reported literature ,31.By the sequential introduction of atomic vacancy defects in the pristine perfect graphene, the relative deviations between the resonant frequencies of pristine graphene and that of vacancy-defected graphene exist. In order to analyze the impacts of atomic vacancy defects in the resonant frequencies, the numbers of vacancy-defected atoms are recorded as the input information, while the corresponding resonant frequencies of graphene are used as the output data. The flowchart of the fingerprint compiler for the relationship between the location of atomic vacancy defects and the resonant frequencies of graphene are presented in Step 1: Define the initial configuration of the pristine graphene and settle the related material and geometrical parameters, which include Young’s modulus, Poisson’s ratio, mass density, cross-section diameter, and length of carbon covalent bonds, etc.Step 2: Compute the resonant frequencies of pristine graphene by the finite element method, and also verify the finite element model for the pristine graphene.Step 3: Number the carbon atoms in the graphene lattice and mark the location of carbon atoms with the corresponding numbers.Step 4: Propagate the atomic vacancy defects in graphene lattice and perform finite element method for modal analysis.Step 5: Record the location information of atomic vacancy defects and output the resonant frequencies for different resonant vibration modes, creating the database based on the huge sample space.Step 6: Perform the atomic vacancy defect propagation and modal analysis procedure until the circles reach 4212 times. In other words, the loop recycles until all the possible situations of atomic vacancy defects are sampled and simulated.Step 7: Picture the fingerprints of resonant frequencies according to the location distribution of atomic vacancy defects in graphene, so that the relationship between the locations of vacancy defects and resonant frequencies are visibly imaged.In order to make the structure of the fingerprint compiler program more readable, the main framework is categorized into three components marked with different colors. The green box presents the finite element model creation procedures for pristine graphene and model verification. The violet box shows the program and recycling execution of atomic vacancy propagation. In contrast, the pink box demonstrates the last component of the fingerprint compiler, in which the database of locations of the atomic vacancy defects is mapped to the magnitudes of the resonant frequency. Then, the patterns of resonant frequency fingerprints reflect the location of atomic vacancy defects.Different from the stochastic sampling process of atomic vacancy defects propagation, all the possible locations of the atomic vacancy defects in graphene are considered and sequentially simulated. In order to analyze the impacts of atomic vacancy defects and the statistic characteristics of resonant frequencies, the probability density distributions of resonant frequencies are computed and presented, as shown in From The relationship between the locations of the defects and the corresponding resonant frequencies can be visualized by fingerprint patterns. In order to figure out the fingerprint patterns, the parallel data of the location of the atomic vacancy defects and the corresponding resonant frequencies of graphene are recorded and paired. The fingerprints of resonant frequencies for atomic vacancy defects in graphene are presented in In the fingerprint patterns, all the first ten resonant vibration modes present geometrical symmetry. Even the values of resonant frequencies have the inhomogeneous and unsymmetrical probability density distribution, as shown in Furthermore, the contour patterns of fingerprints vary from each other for the first ten resonant vibration modes. The variances in the fingerprints are useful information for defect location identification. However, the symmetry in the patterns may bring ambiguity in the identification process since the vacancy defects located in the symmetric positions present approximated resonant frequencies. In order to predict the unknown locations of the vacancy defects by fingerprints, the symmetrical features in the patterns of fingerprints are an important issue. However, since the patterns of different fingerprints do not have the same shape and distribution, the fingerprint overlay approaches are the available methods to predict the unknown location. Therefore, the difficulties in the atomic vacancy defect identification, caused by the geometrical periodicity and symmetry of the honeycomb lattice, are foreseen, and it is necessary to discuss the identification feasibility based on the resonant frequency fingerprints.−4, 10−5, 10−6, and 10−7 Thz. At the first identification level, when the relative errors are smaller than 10−4 Thz, the corresponding atoms are supposed to be indistinguishable. The improvement of identification level is directly related to the distinguishable relative errors.In order to discuss the feasibility of atomic vacancy identification by the fingerprints of resonant frequency, the numbers of atoms that have the approximated resonant frequencies are counted in the honeycomb lattice. In addition, relative errors are introduced to measure the identification level. Four different identification levels are settled as 10−4 Thz. The number distributions of indistinguishable atoms present different patterns for different resonant vibration modes. According to the color bars in In −6 Thz in With the more advanced identification level, the distinguishable relative error is settled as 10Furthermore, the number distributions of indistinguishable atoms with different identification limitations are recorded, as shown in In this paper, the fingerprints of resonant frequencies for atomic vacancy defect identification in graphene are provided, based on finite element computation. The atomic vacancy defects are sequentially introduced and propagated in the graphene honeycomb lattice. The geometrical characteristics of the fingerprint contours and interference distribution are analyzed and discussed. In this work, the following points can be concluded.The impacts of atomic vacancy defects on resonant frequencies are not completely homogeneous nor symmetric.The fingerprint patterns produced by mapping the resonant frequencies of graphene with the locations of atomic vacancy defects present the geometrical symmetry of the periodic honeycomb lattice.The fingerprints of resonant frequencies contain fundamental information of geometrical characteristics of the honeycomb lattice of graphene.The improvement of the distinguishable level is an efficient method for atomic vacancy identification.The discrepancies in the fingerprints of resonant frequencies for different resonant vibration modes have the potential of overlay feasibility.The work in this paper provides an important reference for the identification of non-destructive atomic vacancy in graphene.