Low-frequency 1/f noise in graphene devices.

Low-frequency noise with a spectral density that depends inversely on frequency has been observed in a wide variety of systems including current fluctuations in resistors, intensity fluctuations in music and signals in human cognition. In electronics, the phenomenon, which is known as 1/f noise, flicker noise or excess noise, hampers the operation of numerous devices and circuits, and can be a significant impediment to the development of practical applications from new materials. Graphene offers unique opportunities for studying 1/f noise because of its two-dimensional structure and widely tunable two-dimensional carrier concentration. The creation of practical graphene-based devices will also depend on our ability to understand and control the low-frequency noise in this material system. Here, the characteristic features of 1/f noise in graphene and few-layer graphene are reviewed, and the implications of such noise for the development of graphene-based electronics including high-frequency devices and sensors are examined.

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title: 1/f noise in human cognition.
abstract: When a person attempts to produce from memory a given spatial or temporal interval, there is inevitably some error associated with the estimate. The time course of this error was measured in a series of experiments where subjects repeatedly attempted to replicate given target intervals. Sequences of the errors in both spatial and temporal replications were found to fluctuate as 1/f noises. 1/f noise is encountered in a wide variety of physical systems and is theorized to be a characteristic signature of complexity.

title: The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer
abstract: A new type of electrometer is described that uses a single-electron transistor (SET) and that allows large operating speeds and extremely high charge sensitivity. The SET readout was accomplished by measuring the damping of a 1.7-gigahertz resonant circuit in which the device is embedded, and in some ways is the electrostatic "dual" of the well-known radio-frequency superconducting quantum interference device. The device is more than two orders of magnitude faster than previous single-electron devices, with a constant gain from dc to greater than 100 megahertz. For a still-unoptimized device, a charge sensitivity of 1.2 x 10(-5) e/hertz was obtained at a frequency of 1.1 megahertz, which is about an order of magnitude better than a typical, 1/f-noise-limited SET, and corresponds to an energy sensitivity (in joules per hertz) of about 41 Planck's over 2pi.

title: Low flicker-noise GaN/AlGaN heterostructure field-effect transistors for microwave communications
abstract: We report a detailed investigation of flicker noise in novel GaN/AlGaN heterostructure field-effect transistors (GaN HFET). Low values of 1/f noise found in these devices (i.e., the Hooge parameter is on the order of 10/sup -1/) open up the possibility for applications in communication systems. We have examined the scaling of the noise spectral density with the device dimensions in order to optimize their performance. It was also found that the slope /spl gamma/ of the 1/f/sup /spl gamma// noise density spectrum is in the 1.0-1.3 range for all devices and decreases with the decreasing (i.e., more negative) gate bias. The results are important for low-noise electronic technologies requiring a low phase-noise level.

title: The rise of graphene.
abstract: Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

title: Detection of individual gas molecules adsorbed on graphene.
abstract: The ultimate aim of any detection method is to achieve such a level of sensitivity that individual quanta of a measured entity can be resolved. In the case of chemical sensors, the quantum is one atom or molecule. Such resolution has so far been beyond the reach of any detection technique, including solid-state gas sensors hailed for their exceptional sensitivity. The fundamental reason limiting the resolution of such sensors is fluctuations due to thermal motion of charges and defects, which lead to intrinsic noise exceeding the sought-after signal from individual molecules, usually by many orders of magnitude. Here, we show that micrometre-size sensors made from graphene are capable of detecting individual events when a gas molecule attaches to or detaches from graphene's surface. The adsorbed molecules change the local carrier concentration in graphene one by one electron, which leads to step-like changes in resistance. The achieved sensitivity is due to the fact that graphene is an exceptionally low-noise material electronically, which makes it a promising candidate not only for chemical detectors but also for other applications where local probes sensitive to external charge, magnetic field or mechanical strain are required.

title: Graphene transistors.
abstract: Graphene has changed from being the exclusive domain of condensed-matter physicists to being explored by those in the electron-device community. In particular, graphene-based transistors have developed rapidly and are now considered an option for post-silicon electronics. However, many details about the potential performance of graphene transistors in real applications remain unclear. Here I review the properties of graphene that are relevant to electron devices, discuss the trade-offs among these properties and examine their effects on the performance of graphene transistors in both logic and radiofrequency applications. I conclude that the excellent mobility of graphene may not, as is often assumed, be its most compelling feature from a device perspective. Rather, it may be the possibility of making devices with channels that are extremely thin that will allow graphene field-effect transistors to be scaled to shorter channel lengths and higher speeds without encountering the adverse short-channel effects that restrict the performance of existing devices. Outstanding challenges for graphene transistors include opening a sizeable and well-defined bandgap in graphene, making large-area graphene transistors that operate in the current-saturation regime and fabricating graphene nanoribbons with well-defined widths and clean edges.

title: Channel length scaling in graphene field-effect transistors studied with pulsed current-voltage measurements.
abstract: We investigate current saturation at short channel lengths in graphene field-effect transistors (GFETs). Saturation is necessary to achieve low-output conductance required for device power gain. Dual-channel pulsed current-voltage measurements are performed to eliminate the significant effects of trapped charge in the gate dielectric, a problem common to all oxide-based dielectric films on graphene. With pulsed measurements, graphene transistors with channel lengths as small as 130 nm achieve output conductance as low as 0.3 mS/μm in saturation. The transconductance of the devices is independent of channel length, consistent with a velocity saturation model of high-field transport. Saturation velocities have a density dependence consistent with diffusive transport limited by optical phonon emission.

title: Graphene Ambipolar Multiplier Phase Detector
abstract: We report the experimental demonstration of a multiplier phase detector implemented with a single top-gated graphene transistor. Ambipolar current conduction in graphene transistors enables simplification of the design of the multiplier phase detector and reduces its complexity in comparison to phase detectors based on conventional unipolar transistors. Fabrication of top-gated graphene transistors is essential to achieve the higher gain necessary to demonstrate phase detection. We report a phase detector gain of -7 mV/rad in this letter. An analysis of key technological parameters of the graphene transistor, including series resistance, top-gate insulator thickness, and output resistance, indicates that the phase detector gain can be improved by as much as two orders of magnitude.

title: Shot noise in graphene.
abstract: We report measurements of current noise in single-layer and multilayer graphene devices. In four single-layer devices, including a p-n junction, the Fano factor remains constant to within +/-10% upon varying carrier type and density, and averages between 0.35 and 0.38. The Fano factor in a multilayer device is found to decrease from a maximal value of 0.33 at the charge-neutrality point to 0.25 at high carrier density. These results are compared to theories for shot noise in ballistic and disordered graphene.

title: Shot noise measurements in graphene
abstract: We have investigated shot noise at microwave frequencies in wide-aspect-ratio graphene sheets in the temperature range of 4.2–30 K. We find that for our short ( L 300 nm ) graphene samples with width over length ratio W / L > 3 , the Fano factor F reaches a maximum F ∼ 1 / 3 at the Dirac point and that it decreases substantially with increasing charge density. Our results agree with the theoretical prediction that electrical transport at the Dirac point is governed by evanescent electronic states.

title: Shot noise suppression and hopping conduction in graphene nanoribbons
abstract: We have investigated shot noise and conduction of graphene field-effect nanoribbon devices at low temperature. By analyzing the exponential I-V characteristics of our devices in the transport gap region, we found out that transport follows variable range hopping laws at intermediate bias voltages 1< Vbias <12 mV. In parallel, we observe a strong shot noise suppression leading to very low Fano factors. The strong suppression of shot noise is consistent with inelastic hopping, in crossover from one- to two-dimensional regime, indicating that the localization length lloc

title: Shot noise in graphene with long-range Coulomb interaction and local Fermi distribution
abstract: We calculate the shot noise power in ballistic graphene using the kinetic equation approach based on the Keldysh technique. We find that the local energy distribution function obeys Poisson's equation, indicating a mapping into a diffusive metal system. We derive the conductance and noise including the long range Coulomb interaction to first order. We find that the shot noise increases due to interaction, leading to a frequency dependence. Furthermore, we find that the Fano factor at degeneracy is 1/3, the same as without the Coulomb interaction.

title: Electrical Noise and Transport Properties of Graphene
abstract: We present a study of the noise properties of single-layer exfoliated graphene as a function of gate bias. A tunnel/trap model is presented based on the interaction of graphene electrons with the underlying substrate. The model incorporates trap position, energy, and barrier height for tunneling into a given trap—along with the band-structure of the graphene—and is in good accord with the general characteristics of the data.

title: Disorder-Induced Low-Frequency Noise in Small Systems: Point and Tunnel Contacts in the Normal and Superconducting State
abstract: A theory of disorder-induced low-frequency noise produced by soft atomic potentials in normal conductors and superconductors is developed. Our theoretical predictions are in reasonable agreement with experimental data by Buhrman and co-workers.

title: On the Hooge relation in semiconductors and metals
abstract: The expressions describing the low frequency noise caused by defects in semiconductors and metals have been obtained in the framework of a general unified approach for both fluctuations in the number of carriers and their mobility. When fluctuations in the number of carriers are responsible for noise, the spectral noise density is inversely proportional to the carrier concentration squared and to the volume of the sample. The spectral density of the noise caused by mobility fluctuations is inversely proportional to the sample volume, and does not depend either on carrier concentration or on the total number of carriers. In the case when both mechanisms contribute to noise and they are correlated, the dependence of the noise on the number of carriers depends on the relative contribution of these two noise mechanisms. The expressions obtained can be associated with corresponding cases of the 1/f noise. The physical basis and limitations of the Hooge formula are discussed.

title: Noise in Receiving Systems
abstract: A systematic and unified treatment of thermal noise from an engineering viewpoint. This reference presents the methods used for characterizing and measuring thermal noise in RF communication systems and components. Defines power gain and its applicability to noise problems, shows how to calculate the final signal-to-noise ratio in RF systems using the known gains and noise temperatures of individual system building blocks, and discusses the dependence of dynamic range on the noise factor and noise temperature of a given transducer.

title: Materials and transducers toward selective wireless gas sensing.
abstract: Wireless sensors are devices in which sensing electronic transducers are spatially and galvanically separated from their associated readout/display components. The main benefits of wireless sensors, as compared to traditional tethered sensors, include the non-obtrusive nature of their installations, higher nodal densities, and lower installation costs without the need for extensive wiring.1–3 These attractive features of wireless sensors facilitate their development toward measurements of a wide range of physical, chemical, and biological parameters of interest. Examples of available wireless sensors include devices for sensing of pH, pressure, and temperature in medical, pharmaceutical, animal health, livestock condition, automotive, and other applications.4–7 
 
Some implementations of wireless gas sensors can be already found in monitoring of analyte gases (e.g. carbon dioxide, water vapor, oxygen, combustibles) in relatively interference-free industrial and indoor environments.8,9 However, unobtrusive wireless gas sensors are urgently needed for many more diverse applications ranging from wearable sensors at the workplace, urban environment, and battlefield, to monitoring of containers with toxic industrial chemicals while in transit, to medical monitoring of hospitalized and in-house patients, to detection of food freshness in individual packages, and to distributed networked sensors over large areas (also known as wireless sensor networks, WSNs). Unfortunately, in these and numerous other practical applications, the available wireless gas sensors fall short of meeting emerging measurement needs in complex environments. In particular, existing wireless gas sensors cannot perform highly selective gas detection in the presence of high levels of interferences and cannot quantitate several components in gas mixtures. 
 
1.1. Diversity Of Monitoring Needs Of Volatiles 
The monitoring of numerous gases of environmental, industrial, and homeland security concern is needed over the broad range of their regulated exposure concentrations.  1 illustrates the relationships between several regulated exposure levels spanning several orders of magnitude of gas concentrations. Typical examples of concentrations of regulated exposure are presented in Table 110–14 for three groups of toxic volatiles such as volatile organic compounds (VOCs), toxic industrial chemicals (TICs), and chemical warfare agents (CWAs). These examples demonstrate the need for gas sensing capabilities with broad measurement dynamic ranges to cover 2 – 4 orders of magnitude in gas concentrations. 
 
 
 
Figure 1 
 
Examples of regulated vapor-exposure limits established by different organizations: 
 
GPL: General Population Limit, established by USACHPPM – U.S. Army Center for Health Promotion and Preventative Medicine; 
 
 
PEL: Permissible Exposure Limit, established 
 
 
... 
 
 
 
 
 
Table 1 
 
Examples of regulated concentration levels (in ppm by volume) from three representative classes of toxic gases: VOCs, TICs, and CWAs.10–14 
 
 
 
Additional needs for detection of volatiles originate from medical diagnostics, food safety, process monitoring, and other areas.15–17 In those applications, the types and levels of detected volatiles can provide the needed information for further control actions.

title: Strong suppression of electrical noise in bilayer graphene nanodevices.
abstract: Low-frequency 1/f noise is ubiquitous and dominates the signal-to-noise performance in nanodevices. Here we investigate the noise characteristics of single-layer and bilayer graphene nanodevices and uncover an unexpected 1/f noise behavior for bilayer devices. Graphene is a single layer of graphite, where carbon atoms form a two-dimensional (2D) honeycomb lattice. Despite the similar composition, bilayer graphene (two graphene monolayers stacked in the natural graphite order) is a distinct 2D system with a different band structure and electrical properties. 1,2In graphene monolayers, the 1/f noise is found to follow Hooge's empirical relation with a noise parameter comparable to that of bulk semiconductors. However, this 1/f noise is strongly suppressed in bilayer graphene devices and exhibits an unusual dependence on the carrier density, different from most other materials. The unexpected noise behavior in graphene bilayers is associated with its unique band structure that varies with the charge distribution among the two layers, resulting in an effective screening of potential fluctuations due to external impurity charges. The findings here point to exciting opportunities for graphene bilayers in low-noise applications.

title: Graphene nano-ribbon electronics
abstract: We have fabricated graphene nano-ribbon field-effect transistor devices and investigated their electrical properties as a function of ribbon width. Our experiments show that the resistivity of a ribbon increases as its width decreases, indicating the impact of edge states. Analysis of temperature-dependent measurements suggests a finite quantum confinement gap opening in narrow ribbons. The electrical current noise of the graphene ribbon devices at low frequency is found to be dominated by the 1/f noise.

title: Flicker Noise in Bilayer Graphene Transistors
abstract: We present results of the experimental investigation of the low-frequency noise in bilayer graphene transistors. The back-gated devices were fabricated using the electron beam lithography and evaporation. The charge neutrality point for the transistors was around +10 V. The noise spectra at frequencies f > 10-100 Hz were of the 1/f type with the spectral density on the order of S1 ~ 10-23-10-22 A2/Hz at the frequency of 1 kHz. The deviation from the 1/f spectrum at f < 10-100 Hz suggests that the noise is of the carrier-number fluctuation origin due to the carrier trapping by defects. The Hooge parameter was determined to be as low as ~ 10-4. The gate dependence of the normalized noise spectral density indicates that it is dominated by the contributions from the ungated parts of the device and can be reduced even further. The obtained results are important for graphene electronic and sensor applications.

title: Resistance noise in electrically biased bilayer graphene.
abstract: We demonstrate that the low-frequency resistance fluctuations, or noise, in bilayer graphene are strongly connected to its band structure and display a minimum when the gap between the conduction and valence band is zero. Using double-gated bilayer graphene devices we have tuned the zero gap and charge neutrality points independently, which offers a versatile mechanism to investigate the low-energy band structure, charge localization, and screening properties of bilayer graphene.

title: Ultralow noise field-effect transistor from multilayer graphene
abstract: We present low-frequency electrical resistance fluctuations, or noise, in graphene-based field-effect devices with varying number of layers. In single-layer devices, the noise magnitude decreases with increasing carrier density, which behaved oppositely in the devices with two or larger number of layers accompanied by a suppression in noise magnitude by more than two orders in the latter case. This behavior can be explained from the influence of external electric field on graphene band structure, and provides a simple transport-based route to isolate single-layer graphene devices from those with multiple layers.

title: Low-frequency noise and hysteresis in graphene field-effect transistors on oxide S.A.
abstract: The authors report measurements of low-frequency noise and hysteresis in graphene monolayer and bilayer field-effect transistors (FETs) fabricated on 90 and 290 nm oxidised silicon substrates. The authors observe hysteresis induced by stressing the oxide up to fields of 2 MV/cm and have characterised the hysteresis against stress time and sample temperature. Low-frequency current noise with a 1/
 f
 2
 spectral density arises from the drift of neutrality point voltage, and subsequent drift of graphene FET channel current. A simple model of charge trapping at the graphene-oxide interface and thermally activated ion motion accounts for the temperature dependence of the observed hysteresis.

title: Suspended graphene sensors with improved signal and reduced noise.
abstract: We report enhanced performance of suspended graphene field effect transistors (Gra-FETs) as sensors in aqueous solutions. Etching of the silicon oxide (SiO(2)) substrate underneath graphene was carried out in situ during electrical measurements of devices, which enabled systematic comparison of transport properties for same devices before and after suspension. Significantly, the transconductance of Gra-FETs in the linear operating modes increases 1.5 and 2 times when the power of low-frequency noise concomitantly decreases 12 and 6 times for hole and electron carriers, respectively, after suspension of graphene in solution from the SiO(2) substrate. Suspended graphene devices were further demonstrated as direct and real-time pH sensors, and complementary pH sensing with the same nanodevice working as either a p-type or n-type transistor was experimentally realized by offsetting the electrolyte gate potential in solution. Our results highlight the importance to quantify fundamental parameters that define resolution of graphene-based bioelectronics and demonstrate that suspended nanodevices represent attractive platforms for chemical and biological sensors.

title: Charge noise in graphene transistors.
abstract: We report an experimental study of 1/f noise in liquid-gated graphene transistors. We show that the gate dependence of the noise is well described by a charge-noise model, whereas Hooge's empirical relation fails to describe the data. At low carrier density, the noise can be attributed to fluctuating charges in close proximity to the graphene, while at high carrier density it is consistent with noise due to scattering in the channel. The charge noise power scales inversely with the device area, and bilayer devices exhibit lower noise than single-layer devices. In air, the observed noise is also consistent with the charge-noise model.

title: Observation of the memory steps in graphene at elevated temperatures
abstract: We found that the current-voltage characteristics of graphene transistors exhibit an intriguing feature—an abrupt change in the current near zero gate bias at temperatures above 500 K. The strength of this effect, which we refer to as the memory step by analogy with the memory dips—known phenomenon in electron glasses, depends on the rate of the gate voltage sweep. The slower the sweep, the more pronounced is the step in the current. Despite differences in examined graphene transistors, the memory step always appears at Vg≈0 V. The observed memory steps are likely related to the slow relaxation processes in graphene. This new phenomenon in graphene can be used for applications in sensors and switches.

title: Mobility-dependent low-frequency noise in graphene field-effect transistors.
abstract: We have investigated the low-frequency 1/f noise of both suspended and on-substrate graphene field-effect transistors and its dependence on gate voltage, in the temperature range between 300 and 30 K. We have found that the noise amplitude away from the Dirac point can be described by a generalized Hooge's relation in which the Hooge parameter α(H) is not constant but decreases monotonically with the device's mobility, with a universal dependence that is sample and temperature independent. The value of α(H) is also affected by the dynamics of disorder, which is not reflected in the DC transport characteristics and varies with sample and temperature. We attribute the diverse behavior of gate voltage dependence of the noise amplitude to the relative contributions from various scattering mechanisms, and to potential fluctuations near the Dirac point caused by charge carrier inhomogeneity. The higher carrier mobility of suspended graphene devices accounts for values of 1/f noise significantly lower than those observed in on-substrate graphene devices and most traditional electronic materials.

title: Correlation of low frequency noise characteristics with the interfacial charge exchange reaction at graphene devices
abstract: Graphene based low noise amplifier has been studied actively because the noise characteristics of graphene devices are known to be superior to those of silicon devices. However, 1/f noise characteristics of graphene grown by chemical vapor deposition (CVD) may increase by an order of magnitude when measured before the charge exchange reaction at the interface of the graphene and substrate is saturated. Based on the close correlation between the level of low frequency noise signal and fast charge exchange reaction (in milliseconds), the conductivity fluctuation of graphene caused by the interfacial charge exchange reaction may be the source of the increased low frequency noise. This result suggests that the current assessment of noise characteristics is too optimistic for graphene and that the defect density of CVD graphene needs to be further reduced to minimize the charge exchange reaction.

title: Reduced graphene oxide molecular sensors.
abstract: We demonstrate reduced graphene oxide as the active material for high-performance molecular sensors. Sensors are fabricated from exfoliated graphene oxide platelets that are deposited to form an ultrathin continuous network. These graphene oxide networks are tunably reduced toward graphene by varying the exposure time to a hydrazine hydrate vapor. The conductance change of the networks upon exposure to trace levels of vapor is measured as a function of the chemical reduction. The level of reduction affects both the sensitivity and the level of 1/ f noise. The sensors are capable of detecting 10 s exposures to simulants of the three main classes of chemical-warfare agents and an explosive at parts-per-billion concentrations.

title: Microscopic mechanism of 1/f noise in graphene: role of energy band dispersion.
abstract: A distinctive feature of single-layer graphene is the linearly dispersive energy bands, which in the case of multilayer graphene become parabolic. A simple electrical transport-based probe to differentiate between these two band structures will be immensely valuable, particularly when quantum Hall measurements are difficult, such as in chemically synthesized graphene nanoribbons. Here we show that the flicker noise, or the 1/f noise, in electrical resistance is a sensitive and robust probe to the band structure of graphene. At low temperatures, the dependence of noise magnitude on the carrier density was found to be opposite for the linear and parabolic bands. We explain our data with a comprehensive theoretical model that clarifies several puzzling issues concerning the microscopic origin of flicker noise in graphene field-effect transistors (GraFET).

title: Low frequency noise in degenerate semiconductors
abstract: We present a model of low frequency noise for degenerate semiconductors. The model links the 1/f noise to tail states near the band edges with a capture cross section that is strongly energy dependent. It predicts that the low frequency noise is not very sensitive to a particular shape of the density of the tail states and that, in degenerate semiconductors, the level of noise should decrease with an increase in the degree of degeneracy. The model also explains the dependence of the noise level on the band-to-band illumination, in qualitative agreement with experimental data.

title: Low-frequency noise in graphene field-effect transistors
abstract: The low frequency noise has been studied in mechanically exfoliated single- and bilayer graphene deposited on Si/SiO2 substrates. Measurements were performed in 2- and 4-probe configuration schemes. The analysis of the gate voltage dependences of noise showed that noise in graphene transistors does not comply with the McWhorter model. Aging of graphene transistors due to exposure to ambient resulted in increased noise attributed to the decreasing mobility of graphene and increasing contact resistance. The model linking noise in graphene to the mobility fluctuations is discussed.

title: 1/ƒ noise is no surface effect
abstract: Noise is inversely proportional to the total number of mobile charge carriers in homogeneous samples. This excludes surface effects as the main source of 1/ƒ noise.

title: 1/f noise
abstract: A survey is given of the recent literature on 1/ f noise. Proposals for mathematical models, for empirical relations and for physical models are discussed. The present situation is evaluated and some unsolved problems are indicated.

title: Origin of 1/f noise in graphene multilayers: Surface vs. volume
abstract: Low-frequency noise with the spectral density S(f)∼1/fγ (f is the frequency and γ ≈ 1) is a ubiquitous phenomenon, which hampers operation of many devices and circuits. A long-standing question of particular importance for electronics is whether 1/f noise is generated on the surface of electrical conductors or inside their volumes. Using high-quality graphene multilayers, we were able to directly address this fundamental problem of the noise origin. Unlike the thickness of metal or semiconductor films, the thickness of graphene multilayers can be continuously and uniformly varied all the way down to a single atomic layer of graphene—the actual surface. We found that 1/f noise becomes dominated by the volume noise when the thickness exceeds ∼7 atomic layers (∼2.5 nm). The 1/f noise is the surface phenomenon below this thickness. The obtained results are important for continuous downscaling of conventional electronics and for the proposed graphene applications in sensors and communications.

title: LOW-FREQUENCY ELECTRONIC NOISE IN GRAPHENE TRANSISTORS: COMPARISON WITH CARBON NANOTUBES
abstract: We report results of the experimental investigation of the low-frequency noise in graphene transistors. The graphene devices were measured in three-terminal configuration. The measurements revealed low flicker noise levels with the normalized noise spectral density close to 1/f (f is the frequency) and the Hooge parameter αH ~10-3. Both top-gate and back-gate devices were studied. The analysis of the noise spectral-density dependence on the gate biases helped us to elucidate the noise sources in these devices. We compared the noise performance of graphene devices with that of carbon nanotube devices. It was determined that graphene devices works better than carbon nanotube devices in terms of the low-frequency noise. The obtained results are important for graphene electronic, communication and sensor applications.

title: Graphene thickness-graded transistors with reduced electronic noise
abstract: The authors demonstrate graphene thickness-graded transistors with high electron mobility and low 1/f noise (f is a frequency). The device channel is implemented with few-layer graphene with the thickness varied from a single layer in the middle to few-layers at the source and drain contacts. It was found that such devices have electron mobility comparable to the reference single-layer graphene devices while producing lower noise levels. The metal doping of graphene and difference in the electron density of states between the single-layer and few-layer graphene cause the observed noise reduction. The results shed light on the noise origin in graphene.

title: Contact and edge effects in graphene devices.
abstract: Electrical transport studies on graphene have been focused mainly on the linear dispersion region around the Fermi level and, in particular, on the effects associated with the quasiparticles in graphene behaving as relativistic particles known as Dirac fermions. However, some theoretical work has suggested that several features of electron transport in graphene are better described by conventional semiconductor physics. Here we use scanning photocurrent microscopy to explore the impact of electrical contacts and sheet edges on charge transport through graphene devices. The photocurrent distribution reveals the presence of potential steps that act as transport barriers at the metal contacts. Modulations in the electrical potential within the graphene sheets are also observed. Moreover, we find that the transition from the p- to n-type regime induced by electrostatic gating does not occur homogeneously within the sheets. Instead, at low carrier densities we observe the formation of p-type conducting edges surrounding a central n-type channel.

title: Reduction of 1/f noise in graphene after electron-beam irradiation
abstract: We investigated experimentally the effect of the electron-beam irradiation on the level of the low-frequency 1/f noise in graphene devices. It was found that 1/f noise in graphene reduces with increasing concentration of defects induced by irradiation. The increased amount of structural disorder in graphene under irradiation was verified with micro-Raman spectroscopy. The bombardment of graphene devices with 20-keV electrons reduced the noise spectral density, SI/I2 (I is the source-drain current) by an order-of magnitude at the radiation dose of 104 μC/cm2. We analyzed the observed noise reduction in the limiting cases of the mobility and carrier number fluctuation mechanisms. The obtained results are important for the proposed graphene applications in analog, mixed-signal, and radio-frequency systems, integrated circuits and sensors.

title: Enhanced conductance fluctuation by quantum confinement effect in graphene nanoribbons.
abstract: Conductance fluctuation is usually unavoidable in graphene nanoribbons (GNR) due to the presence of disorder along its edges. By measuring the low-frequency noise in GNR devices, we find that the conductance fluctuation is strongly correlated with the density-of-states of GNR. In single-layer GNR, the gate-dependence of noise shows peaks whose positions quantitatively match the subband positions in the band structures of GNR. This correlation provides a robust mechanism to electrically probe the band structure of GNR, especially when the subband structures are smeared out in conductance measurement.

title: Low-noise submicron channel graphene nanoribbons
abstract: We present a graphene nanoribbon fabrication method based on a nanowire mask. Using a four-probe setup, single-layer nanoribbon (SLR) and bilayer nanoribbon (BLR) show low-frequency noise levels lower than (comparable to) the SLRs (BLRs) achieved by hydrogen-silsesquioxane based methods. Submicron channel SLR and BLR both show conductance quantization at 77 K, which suggests that quasi-one-dimensional quantum transport can be achieved. The conductance plateaus in BLR are less pronounced than those in SLR.

title: Low-frequency noise due to site energy fluctuations in hopping conductivity
abstract: The noise in hopping conductivity arising due to hopping sites energy fluctuations (as suggested by Shlimak et al., Solid State Commun., 93 , 829, 1995) is considered. The fluctuations are related to changes of local potentials resulting due to hops within some pairs of sites not incorporated into the percolation cluster; such pairs can be identified as “electronic two-level systems” or “fluctuators”. A dependence of the noise on both fluctuators statistics and percolation cluster morphology is analyzed. An analog of Hooge relation for the mechanism discussed is derived. For the case of nearest neighbor hopping an independence of relative noise power from temperature is predicted in agreement with recent experimental results by Shlimak et al.

title: Variability Effects in Graphene: Challenges and Opportunities for Device Engineering and Applications
abstract: Variability effects in graphene can result from the surrounding environment and the graphene material itself, which form a critical issue in examining the feasibility of graphene devices for large-scale production. From the reliability and yield perspective, these variabilities cause fluctuations in the device performance, which should be minimized via device engineering. From the metrology perspective, however, the variability effects can function as novel probing mechanisms, in which the “signal fluctuations” can be useful for potential sensing applications. This paper presents an overview of the variability effects in graphene, with emphasis on their challenges and opportunities for device engineering and applications. The discussion can extend to other thin-film, nanowire, and nanotube devices with similar variability issues, forming general interest in evaluating the promise of emerging technologies.

title: Selective gas sensing with a single pristine graphene transistor.
abstract: We show that vapors of different chemicals produce distinguishably different effects on the low-frequency noise spectra of graphene. It was found in a systematic study that some gases change the electrical resistance of graphene devices without changing their low-frequency noise spectra while other gases modify the noise spectra by inducing Lorentzian components with distinctive features. The characteristic frequency f(c) of the Lorentzian noise bulges in graphene devices is different for different chemicals and varies from f(c) = 10-20 Hz to f(c) = 1300-1600 Hz for tetrahydrofuran and chloroform vapors, respectively. The obtained results indicate that the low-frequency noise in combination with other sensing parameters can allow one to achieve the selective gas sensing with a single pristine graphene transistor. Our method of gas sensing with graphene does not require graphene surface functionalization or fabrication of an array of the devices with each tuned to a certain chemical.