Nano Electronics: A New Era of Devices

Solid State Phenomena Vol. 222 (2015) pp 99-116 © (2015) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/SSP.222.99

Nano Electronics: A New Era of Devices Inderpreet Kaura, Shriniwas Yadavb , Sukhbir Singhc , Vanish Kumard, Shweta Arorae, Deepika Bhatnagarf Biomolecular Electronics and Nanotechnology Division (BEND), Central Scientific Instruments Organization (CSIR-CSIO), Sector-30C, Chandigarh, 160030, India. a [email protected] (corresponding author), [email protected] , c [email protected], [email protected] , [email protected], f [email protected], Key words: Nanoelectronics, Molecular electronics, Nanogap fabrication, Graphene, CNTs, Band gap, HOMO-LUMO, CNT-FET

Abstract: The technical and economic growth of the twentieth century was marked by evolution of electronic devices and gadgets. The day-to-day lifestyle has been significantly affected by the advancement in communication systems, information systems and consumer electronics. The lifeline of progress has been the invention of the transistor and its dynamic up-gradation. Discovery of fabricating Integrated Circuits (IC’s) revolutionized the concept of electronic circuits. With advent of time the size of components decreased, which led to increase in component density. This trend of decreasing device size and denser integrated circuits is being limited by the current lithography techniques. Non-uniformity of doping, quantum mechanical tunneling of electrons from source to drain and leakage of electrons through gate oxide limit scaling down of devices. Heat dissipation and capacitive coupling between circuit components becomes significant with decreasing size of the components. Along with the intrinsic technical limitations, downscaling of devices to nanometer sizes leads to a change in the physical mechanisms controlling the charge propagation. To deal with this constraint, the search is on to look around for alternative materials for electronic device application and new methods for electronic device fabrication. Such material is comprised of organic molecules, proteins, carbon materials, DNA and the list is endless which can be grown in the laboratory. Many molecules show interesting electronic properties, which make them probable candidates for electronic device applications. The challenge is to interpret their electronic properties at nanoscale so as to exploit them for use in new generation electronic devices. Need to trim downsize and have a higher component density have ushered us into an era of nanoelectronics. Contents of Paper 1. Introduction 2. Molecular Electronics 2.1. Potential Organic Molecules That Mimic the Traditional Semiconductor Electronic Components 2.1.1. Molecular Wires 2.1.2. Molecular Resistor 2.1.3. Molecular Diodes 2.2. Reason for Molecules as Electronic Components 2.3. Recognizing the Components of the Molecules in the Circuit 3. Metal –Molecule-Metal Junctions 3.1. Methods for Fabricating Nanogap Electrodes 3.1.1. Mechanical Controllable Break Junctions (MCB) 3.1.2. Angle Shadow Evaporation And Shadow Masking 3.1.3. Scanning Probe Lithography (SPL) 3.1.4. Electron Beam Lithography All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 115.248.234.162-05/11/14,07:03:32)

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3.1.5. Electromigration 3.2. Nano Architectures and Arrays 4. Carbon Electronics 4.1. Carbon Nanotubes based Electronics 4.1.1. Carbon Nanotube based FET 4.2. Graphene based Electronics 4.2.1. Band gap Modulation and Graphene devices 5. Theoretical point of view and quantum phenomena 5.1. A Fundamental Approach to Electron Transport 5.1.1. The Electron Transfer theory 5.1.2. Landauer Formula and Electron Transport through Molecular Junction 5.2. The Relationship between Electron Transfer Rates and Molecular Conduction 5.3. A Frontier Molecular Orbital Approach to Electron Transport 5.3.1. Forward-bias condition 5.3.2. Reverse-bias condition 6. Conclusions References 1. Introduction The invention of the transistor in 1947 is one of the most important inventions of the 20th century. Since its inception, we have witnessed dramatic advances in electronics that have found uses in computing, communications, automation and other applications that affect just about every aspect of our lives. To a large extent these advances have been the result of the continuous miniaturization or ‘scaling’ of electronic devices, particularly of silicon-based transistors, that has led to denser, faster and more power-efficient circuitry. Unfortunately, the scaling down must eventually end. Increasing power, capital costs, and ultimately theoretical size limitations, are poised to halt the process of continually shrinking the transistor. The realization of the approaching limits has inspired a worldwide effort to develop alternative device technologies. Some approaches involve moving away from traditional electron transport-based electronics: for example, the development of spinbased devices. Another approach, maintains the operating principles of the currently used devices primarily that of the field effect transistor, but replaces a key component of the device, the conducting channel, with alternate material which have superior electrical properties. Taking into consideration the second approach, inexpensive, functional and atomically precise molecules could be the basis of future electronic devices, but integrating them into circuits will require the development of new ways to control the interface between molecules and electrodes. Molecular-electronics show promise as a technology to continue the miniaturization of ICs. However, whether molecular-electronics will be a replacement for conventional ICs, or as a complimentary technology, is yet to be determined. What has already been shown is that components such as wires and molecular switches can be fabricated and integrated into architectures. It is also known that these devices will be prone to defects, fluctuations and that fault tolerance schemes will be an integral part of any architecture. The greatest progress has been made in the research of the components that may make up nanoelectronics. Researchers have been able to fabricate molecules that have two states, such that the molecules can be switched “on” and “off”. Some of these molecules have shown the functionality of diodes or variable resistors. Scientists have also been able to fabricate silicon nanowires and carbon nanomaterials such as one-dimensional (1D) carbon nanotubes (CNT) or twodimensional (2D) graphene layers. Both of these technologies can be used as wires or devices, and in some cases both. Nanoimprint lithography, probably the most promising wire fabrication technique, has been used to produce working memories on the nanometer scale. While all of these

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devices have been demonstrated, more lot of research is required to reliably produce such analogues. 2. Molecular Electronics The field of molecular electronics has been around for more than 40 years, but only recently has some fundamental problems been overcome. It is now time for researchers to move beyond simple descriptions of charge transport and explore the numerous intrinsic features of molecules. Fundamentals of electronics say that all the electronic operations take place through the transport of the electron in the circuit. Robert Mulliken and Albert Szent-Gyorgi in 1940 [1] advanced the theory of molecular conduction and did an interesting study of charge transfer in "donor-acceptor" systems. Bringing out correlation in such donor-acceptor systems where the charge transfer can be achieved easily suggested these systems would be suitable for the molecular electronic devices [2]. In the early 1970s, a visionary concept of exploiting the intrinsic functionality of molecules for electronics was sketched out by Arieh Aviram and Mark Ratner [3]. In their pioneering theoretical work, Aviram and Ratner suggested that a single molecule (Fig. 1) could function as a rectifier. The molecule would mimic a semiconductor-like band structure by taking advantage of electron-rich and electron-poor moieties to achieve one-way conduction through differently aligned molecular orbitals with respect to the Fermi energy of the electrodes [2, 3]. With this excellent article by Aviram-Ratner the era of molecular electronics was established.

Fig. 1: Proposed molecular rectifier by Aviram and Ratner [3]. 2.1. Potential Organic Molecules that Mimic the Traditional Semiconductor Electronic Components: Traditional electronics has many components like conductor (wires), resistor (insulating connection), diode (rectifier), transistor (triode), logic circuits, etc. [4]. Among all these, the most fundamental components are wire, resistor and rectifier, which are discussed below. Transistor is also having equal importance in the field of electronics, but it can be easily fabricated from the diode by utilizing a suitable doping of a gate electrode. 2.1.1. Molecular Wires: Electronic wires are the components through which electric current can pass from one end to the other end freely. Organic molecules, which can mimic the wire function, are the π-type systems as shown in fig. 2.

Fig. 2: Potential organic molecular wires. In these molecules, the process of electron transfer takes place through the backbone of fully delocalized π-bridges, and consequently energetically closely spaced frontier molecular orbitals

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(reduced HOMO-LUMO gap or in short, HLG) are the conduction channels. Due to very small HLG, the process is thermodynamically favorable and ultimately gives rise to efficient wire function. 2.1.2. Molecular Resistor: Organic molecules to achieve resistor type of behavior are as shown below in Fig. 3.

Fig. 3: Potential organic molecular resistors. In these types of molecules, the presence of the saturated –CH2 - units creates nodes in their electron densities above the atomic nuclei. For this reason and also due to large HLG, they cannot transport electrical current. This enables aliphatic molecules or groups to act like resistors. 2.1.3. Molecular Diodes: Starting from the AR rectifier [3] to till date, the common construction principle of organic molecular rectifier adopted is as shown in Fig. 4. A comparison of the AR rectifier (Fig.1) with that of the semiconductor diode will give a clear idea about the rectification ability of general organic molecular rectifiers.

Fig. 4: Potential organic molecular rectifiers. A structural correlation of the AR rectifier to a normal silicon junction diode shows that, acceptor part of the molecule can be mimicked with p-type semiconductor, donor part can be mimicked with n-type semiconductor and σ-bond can mimic the pn-junction barrier. With these favorable structural features of an organic molecule, it can be expected to result in similar characteristics like that of a semiconductor rectifier. 2.2. Reason for Molecules as Electronic Components: The distinguished points, which can be put in favor of molecules as electronic components are: (1) Molecules are of very small size. A molecule is around few thousand times smaller in size than that of the presently used semiconductor transistor. (2) In semiconductor devices, due to the band structure, electron can stay at any level of the band, which can probably interfere with other devices. In the molecule, the energy levels are quantized and discrete and hence the interference can be nullified. (3) Due to delocalizable π-systems present in the molecule, the electron transport will be thermodynamically more favorable compared to the semiconductor systems. (4) Due to the flexible nature of the molecule (especially in π-systems due to cis- & transisomerism) switching function (on and off control) can be easily achieved by the simple alternation of the two conformations. (5) Due to exact chemical equivalence of the molecules, it can be fabricated in a defect free fashion. (6) Another important property of organic molecules is its self-assembling nature, which will be helpful in manufacturing large arrays of identical devices. 2.3. Recognizing the Components of the Molecules in the Circuit: There are some fundamental questions which can arise in one’s mind that how molecules can be interleaved in an electronic circuit. The various widely used methods (for inserting a molecule in an electronic

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circuit) include scanning tunneling microscopy (STM), conducting atomic force microscopy (AFM), break junctions, fixed-gap nanojunctions, nanopores, mercury drop contacts and crosswire assemblies. All the methods discussed above have their advantages, but the major difficulty in all this is counting the number of contacts molecules and the characterization of their bonding patterns. “Tour-de-force assembly mechanism” for interleaving a molecule into circuit is one such outstanding method [4, 5]. For a better understanding of the circuital operation of the inserted molecule into the nano-junction, a schematic diagram is shown in Fig. 5.

Fig. 5: Schematic representation of the circuital operation of an organic (a) Molecular wire, and (b) Molecular rectifier. Though the actual measurement process is not so simple, the above circuit diagram presents the essential components and the background operation principles of the molecular wire or rectifier in a simpler way. The diagram shows that, besides the external power supply and the output measurement components, there are three most important components, which are essential in the device fabrication as described below: The Molecule: Here the molecule is either the wire or the rectifier. In both the cases, the molecule is needed to be both ends selected in order to make contact with the electrodes. Gold contacts: There are two gold contacts; left contact is named as Cathode and right contact as Anode. These create the connection between the molecule and the external power supply.

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Alligator Clip: The two thiol groups present in the molecules are known as alligator clips and the name comes as it clips the molecule to the two electrode contacts. It serves the channel between the electrodes and the molecule. In a simplified way, the operation can be explained as the alligator clips present in the molecule, hook up the molecule to the two metal nano-electrodes and these two electrodes are connected to the external circuit. Once a bias voltage is applied in the external circuit, one electron from the left (by convention) electrode will be loaded to the molecule through the metal-molecule junction and travels through the molecule to escape to the right electrode through the right hand side metalelectrode junction. During this process of the electron transport, a current will be realized in the outer circuit. 3.

Metal –Molecule-Metal Junctions

The ultimate aim of molecular scale electronics or single molecule electronics is to use the individual molecule or atom as a functional component. The struggle to control the position and distance of smaller and smaller numbers of atoms in the active regions of devices can be made using top-down methods. However, already in the earliest experiments, the vision of molecular electronics encountered tremendous difficulties. First, and in contrast to silicon where research was facilitated by the availability of large crystals, the size of an individual molecule cannot be easily scaled up, which means that atomic-sized electrodes are needed to contact an individual molecule. By pulling and then breaking ductile metal wires, suitable electrodes can be fabricated, and over the past 15 years a variety of innovative approaches have been developed to experimentally conduct charge-transport studies at the few molecular levels. Second, when the number of active molecules in the junction was reduced down to a single molecule, the variability of the ‘devices’ increased because the molecular junction became sensitive to every microscopic detail of its atomistic configuration [6]. Until now, only a few experiments have gained control over the crucial atoms in the junction, but such atomic control is essential for the development of molecular electronic applications. This can be achieved by miniaturizing electrical circuits and connections for device functioning. Several approaches have been used to provide electrical connections to molecules and cluster of molecules. Nanogap electrodes are a pair of electrodes separated by a nanometer gap to form metalmolecule-metal junctions for practical device fabrication. 3.1. Methods for fabricating nanogap Electrodes: Precise control of spacing makes it more difficult and challenging because it goes beyond the capability of micro-fabrication techniques like photolithography. In the last few years, several effective and creative methods for nanogap electrode fabrication have been reported, including mechanically controllable break junctions, angle shadow evaporation and shadow masking [5], scanning probe lithography [7], electron beam lithography [8], and electro-migration [9]. 3.1.1. Mechanical controllable break junctions (MCB): A mechanical controllable break (MCB) junction was first introduced by Moreland and his co-workers from the US National Bureau of Standards to form an electron tunneling junction [10]. This technique was then adopted by various researchers to create nanogap junctions with several nanometer separations. In this method a notched metallic wire is glued over an elastic substrate, which works as the bending beam. The substrate is bent by pushing its center with a driving rod to fracture the notched wire, after which an adjustable tunneling gap can be established. The breaking process is mostly conducted under low temperature and high vacuum conditions to avoid contamination. Although the MCB junction method was useful for fundamental investigation, it was not facile to fabricate highly integrated molecular devices and also difficult to controllably fabricate relatively large gaps.

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3.1.2. Angle shadow evaporation and shadow masking: The angle shadow evaporation method was established by Dolan in 1977 [11, 12]. This technique was then accepted and refined for the fabrication of nanogap electrodes. Shadow evaporation is often combined with optical and electronbeam lithography to define metal leads [13]. The gap size can be adjusted by changing stepwise the tilt angle until a desired space is obtained. Some researchers have also utilized physical shadowing of nanoscale objects like carbon nanotubes for creation of nanogap electrodes. Sun et al. [14] achieved 3 nm gap electrodes and applied them to the electrical study of nanocrystals successfully. 3.1.3. Scanning probe lithography (SPL): This method is also known as dip pen nanolithography used in nanofabrication developed by Zhang et al. [16] in Northwestern University. In this technique an atomic force microscope tip is used to pattern directly on a range of substances with a variety of inks. There are two basic types of SPL. One is a destructive method that physically, chemically, or electronically deforms the substrate’s surface to make up the pattern [7]. The other is a constructive way in which the patterning is done by directly transferring chemical species to the surface [16]. The main limitation of this technique was the damage of the probe and unsatisfactory material removal due to a sharp tip. 3.1.4. Electron beam lithography: Electron beam lithography (EBL) is quite efficient and controllable technique for nanoscale fabrication. In this technique a highly energized and focused electron beam is used to create nanopatterns over resist coated substrate. EBL is generally used to firstly realize nanogap electrodes with space at 10–20 nm [13], and then other techniques, such as electro deposition, shadow mask evaporation, are implemented to further narrow the gap width to a 1-5nm scale. The major drawback of this method involves back scattering of highly energetic electrons, which affects the feature size. 3.1.5. Electromigration: Electromigration is a thermally assisted process where nanogap is created by high current density to create nanogap in thin metal substrates by joule heating. However, excessive heating should be avoided because it would cause undesired melting of the metal. More recently, it has been well utilized to fabricate nanogap electrodes for nanodevices. Recently, researchers have also performed electromigration in carbon nanotubes and graphene for nanogap electrode fabrication [17, 18]. Compared with thin metal wires (20 nm) that could only be prepared by electron-beam lithography, carbon nanotubes possess high conductivity, more favorable configurations, and better contacts to organic molecules by C-C bonding; thus they are considered good substitutes for metal wires to fabricate nanogap electrodes. 3.2. Nano Architectures and Arrays: One of the big questions for the future nano-electronics is whether nano-scale devices can be reliably assembled into architectures. Some small-scale successes have been achieved, but to get the benefit of nano-electronics the enormous integration levels may be desired. The most promising architectures to date are array based. This is because arrays have a regular structure which is easier to build with self-assembly. Arrays also make good use of the available devices (nanowires, carbon nanotubes, and molecular electronics), and they are easy to configure in the presence of defects. There are other more random architectures that would require even less stringent fabrication techniques, but there is some doubt about how they will scale to larger systems. Overall, it is difficult to evaluate architectures as the underlying components are not fully understood nor developed yet. One thing that seems clear is that nano-electronics will, at least for the first few generations, need the support of conventional lithography based electronics for things such as I/O, fault tolerance, and even simple signal restoration. Fault tolerance is another big problem for nano-electronics. It seems evident that the manufacturing techniques may never be able to produce defect free chips, so fault tolerance will be key to the success of nano-electronics. For manufacturing defects, detecting and configuring around the defects is the most economical technique, since nano-electonics will be configurable devices. The

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hard problems are detecting the defects among 1012 devices in an economical manner, and how to best manage the large defect map. It also appears that transient faults will be a problem with nanoelectronics due to their small size and low current levels. To handle transient faults, a hardware redundancy method such as multiplexing or NMR will have to be used to dynamically detect and repair faults. Unfortunately, these methods would require too much redundancy to handle the number of manufacturing defects expected [6]. 4.

Carbon Electronics

Apart from organic molecules, there are so many potential molecules available which can be explored for molecular electronics, e.g. Biomolecules: DNA, Proteins, and Carbon materials: Carbon nanotubes, Graphene, etc. Since biomolecules are highly unpredictable in the environmental conditions hence DNA and protein’s electron transport is necessary to understand life processes but are not sufficient for nanoelectronics. Rather, carbon materials having intriguing electrical properties can be a very good future option for nanoelectronics. 4.1. Carbon Nanotubes based Electronics: Carbon Nanotubes (CNTs) are allotropes of carbon with cylindrical shapes and very high length to diameter ratio of the order of 1,32,000,000:1 [19]. CNTs are of hollow structure formed by rolling, one atom thick sheet of sp2 hybridized carbon atoms named as graphene. CNTs are characterized as single wall CNTs (SWCNTs) and multiwall CNTs (MWCNTs). Electronic properties of CNTs depend upon its chiral angle (angle along which graphene sheet is rolled) and radius of nanotube.

(a) (b) Fig. 6: (a) The (n, m) nanotube naming scheme can be thought of as a vector (Ch) in an infinite graphene sheet that describes how to "roll up" the graphene sheet to make the nanotube. T denotes the tube axis, and a1 and a2 are the unit vectors of graphene in real space, and (b) Different types of CNTs. The structure of a SWNT can be conceptualized by wrapping planar sheet of graphene into a seamless cylinder as shown in fig. 6. The way, the graphene sheet is wrapped is represented by a pair of indices (n, m). The integers, n and m, denote the number of unit vectors along two directions in the honeycomb crystal lattice of graphene. If m = 0, the nanotubes are called zigzag nanotubes, and if n = m, the nanotubes are called armchair nanotubes. Otherwise, they are called chiral nanotubes. Diameter of ideal CNT can be calculated from its unit vector (n, m) as follows: D (in pm) = 78.3(n2+m2+nm)0.5 All MWCNTs are of metallic in nature but nature of SWCNTs varies with chiral vectors n and m. SWCNTs are very important type of CNTs, because their properties vary significantly with chiral vectors. The band gap of SWCNTs can vary from 0 to 2eV, thus electrical properties can be metallic as well as semiconducting. A major problem in synthesis of SWCNTs is the lack of

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synthetic methods that yield exclusively semiconducting nanotubes, which has stimulated numerous attempts to either separate semiconducting tubes from the as-prepared material or to selectively eliminate the metallic tubes [20]. The separation approach has mainly depended on non-covalent chemical functionalization by various types of polymers capable of selectively wrapping semiconducting SWCNTs, most conspicuously polyfluorenes [21]. Another method based upon the selective binding of semiconducting tubes by the terminal amino groups of the silane layer on the silica has been explored for self-sorting of SWCNTs by spin-coating nanotubes from solution onto appropriately surface-functionalized Si/SiO2 substrates [22, 23]. Some other efficient chemical methods including effect of dizonium salt and plasma ion etching to eliminate metallic nanotubes are also used [24]. 4.1.1. Carbon Nanotube based Field Effect Transistor: Carbon Nanotube based Field Effect Transistor (FET) (Fig. 7) functions as Schottky barrier transistor rather than conventional bulk transistors. In the conventional transistors the gate bias not only affects the carrier density through conducting channel but also the transmission through junctions [25]. Hence, both junction potential as well as carrier potential was affected by gate potential. That is why, to minimize Schottky barrier for one type of charge carrier, proper contact metal choice is needed. It was first demonstrated for palladium contacts enabling nearly barrier-free access to the valence band of semiconducting tubes [26]. Schottky barrier potential can be reduced by selectively doping contacts of carbon nanotubes which has been realized on the basis of complex charge transfer between CNTs and adsorbed molecules. In order to optimize the gate switching, the capacitive coupling of the gate electrode has to be enhanced. In the ideal case, the classical electrostatic capacitance Cg would become larger than the quantum capacitance Cq of the tube (Cq= 10-16 F/µm), and therefore, dominates the switching action [27, 28].

Fig. 7: CNT-FET having patterned drain and source contacts of Au/Ti over CNT. A promising approach takes advantage of the excellent insulating capability of high-quality organic self-assembled monolayers in combination with a thin, oxygen-plasma-grown oxide layer for strong gate coupling to CNTs. It has been reported that SWCNT-FET using SiO2 with silane, showed excellent operating voltage of 1V and sub-threshold swing of 60mV per decade (A decade corresponds to a 10 times increase of the drain current Id) [29]. Significant progress has also been achieved in the development of FETs incorporating highly ordered SWCNT arrays produced via oriented CVD growth on quartz substrates. Remarkably, even without enrichment of

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semiconducting tubes, the transistors display excellent performance, as reflected in sub-threshold swings as low as 140mV per decade, mobility of up to 80cm2/Vsec., and operation voltages below 5 V. A key factor to achieve this has been to reduce the probability of metallic pathways through use of sufficiently narrow network stripes. The major disadvantage of CNTs, however, is their random distribution, which clearly hampers their utilization as a replacement for silicon as a substrate. This leaves two options for carbonelectronics: either self-organization methods for CNTs or carbon “substrates”, thin layers with similar properties to CNTs. High on the list is graphene, planar sheets of honeycomb carbon rings just one atom thick. This nanomaterial supports a range of properties including ultra-strength, transparency (because of its thinness) and blisteringly fast electron conductivity—that make it promising for flexible displays and super speedy electronics. 4.2. Graphene Based Electronics: The impressive physical properties of graphene like unique optical transparency, superior mechanical strength, and excellent charge carrier mobility make it a suitable candidate for device applications which include electronics, optoelectronics, photonics, and spintronics. The most significant electrical property of graphene is due to the presence of massless, chiral, Dirac fermions which manifest as high carrier mobility of the order of 10,000 cm2/Vs in experimental measurement [30] and a theoretically 27,000 cm2/Vs [31]. Therefore it should enable transistors of very high frequency. Isolated only four years ago, graphene already appears in prototype transistors, memories and other devices. Graphene is an extremely promising material in the field of electronics. It comes majorly in two variants: Zigzag and Arm chair, depending on the edge pattern as visible in fig. 8. However, when using it as a material for transistor channel without any further improvement, the insufficient on/off ratio has been pointed out due to inadequate band gap. Nevertheless, many potential solutions to band gap formation have been proposed, such as application of the vertical electric field, forming graphene in a ribbon structure or modulating band gap with chemical functional groups.

Fig. 8: (a) Graphene sheet with both the zigzag (red) and the arm chair (green) directions, (b) AGNRs, and (c) ZGNR [32].

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4.2.1. Band gap Modulation and Graphene Devices: Many theoretical and experimental approaches have been demonstrated to tailor the graphene electronic structure for opening up energy band gap (Eg). The main methods include quantum confinement of charge carriers from 2D graphene to 1D graphene nanoribbons (GNR), pi-pi stacking on graphene, chemical doping, and application of strain. Electronic properties of GNR vary with the edge pattern as well as the width of the sheet. Edge pattern can be armchair [AGNR] and zigzag graphene nanoribbon [ZGNR] {Fig. 8(b) and (c)}. Zigzag GNRs possess metallic characteristics and is independent of width, while there is a lot of scope of band gap modulation in AGNRs. These fall into three families, depending on their width. With N being number of carbon dimer lines across the ribbon width, these families are N=3p-1, 3p, and 3p+1, where “p” is a positive integer. When N=3p and 3p+1, AGNRs have semiconductor-like behaviors, while N=3p-1, AGNRs and ZGNRs are quasi-metallic (narrow gap semiconductor). It was demonstrated that chemical functionalization of semiconducting GNRs with Stone-Wales (SW) defects by carboxyl (COOH) groups forms a stable structure. Theoretically it has been demonstrated that when the geometrical structure changes, electronic properties of the GNR changes significantly. It is further reported that electrical conductivity of the system considerably enhanced with the increase of the axial concentration of Stone-Wales Defects Carboxyl Pairs (SWDCPs), the system transforms from semiconducting behavior to p-type metallic behavior [33]. The simulation work based on DFT, the chemistry of imperfect graphene with a broad class of defects such as Stone-Wales (SW) defects [33], bi-vacancies, nitrogen substitution impurities, and edges has been reported [34]. Study have also proved an effect of finite width, chemical surface bonding such as hydrogenation, chlorination, bromination, halogenation, amidation and many surface attachment of aromatic molecules using pi-pi stacking on the electronic properties of the graphene. The electronic transport properties of zigzag graphene nanoribbons (ZGNRs) are also reported with two kinds of triangular defects. Abnormal behavior has been reported, if the orientation of the triangle is changed to rightward, the current is depressed much and shows negative differential resistance behavior [35]. Their findings indicate that defect designs can be an efficient way to tune the electronic transport of GNR nanodevices. No of reports are there showing that electronic transport properties are sensitive to twisting deformations for semiconductor-type AGNRs, but are robust against twisting deformations for quasi-metallic AGNRs and ZGNRs. The electronic conduction becomes weaker gradually for moderate-gap semiconductor-type AGNRs, but gets stronger for wide-gap semiconductor-type AGNRs when the twisted angle increases to 120o. While for quasi-metallic AGNRs and ZGNRs, the electronic conduction is strong and obeys Ohm’s law of resistance strictly [34]. Experimentally, STM measurements are done on GNRs to study the edge states and observe localized near defects [36]. The tight binding calculation based on the atomic arrangements observed by STM reproduces the observed spatial distributions of the local density of states. The symmetry of ZGNRs plays an important role in electron transport behavior. Asymmetric ZGNR displays monotonic transport behavior. However, in symmetric ZGNRs systems, negative differential resistance (NDR) has been reported in papers [37]. More recently, more instances of NDR were observed or predicted in molecular devices of GNR. Since edges and defects are playing major role in defining the characteristic behavior of GNR, hence, these can be exploited for using them in futuristic nanolelectronic devices. Some systematic ab initio investigations of the possibility to create a band gap in a few-layer graphene (FLG) via a perpendicular electric field are provided by K. Tang et al. [38]. Arbitrarily stacked FLG remain semi-metallic, but rhombohedral stacked FLG demonstrates a variable band

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gap. The maximum band gap in ABC stacked FLG decreases with increasing layer number and can be fitted by the relationship ∆ max= 1/ (2.378 + 0.521N + 0.03 5 N2) eV [38]. Further, the first-principle calculations explore a band-gap opening of 300 meV for graphene under 1% uniaxial tensile mechanical strain. The strained graphene provides an alternative way to experimentally tune the band gap of graphene, which would be more efficient and more controllable than other methods that are used to open the band gap in graphene. The results suggest that the flexible substrate is ready for such a strain process, and Raman spectroscopy can be used as an ultrasensitive method to determine the strain [39]. Hence to open the energy band gap in graphene is to work with graphene nanoribbons. Therefore, to modulate its band gap according to device application one can functionalize and apply external electric field on graphene surface to tune the behavior of charge carriers. Recently, it has been reported that graphene based transistors were fabricated. Electrical transport experiments showed that, unlike single-walled carbon nanotubes, unzipped CNTs forming GNR, all of the sub 10nm were semiconductors and afforded graphene field effect transistors with on-off ratios of about 107 at room temperature [40]. Many efforts have been made to increase the performance of GFET by doping with other elements such as boron and nitrogen for synthesizing ptype and n-type graphene. Till now, a few doping methods have been exploited, including substitutional doping, electrostatic doping by external field, and charge transfer doping. Whereas, these approaches reveal intrinsic drawbacks, such as undesired defect formation, complex processing steps, and subtle sensitivity to environment. To increase electron transport properties, the thiol and thiolate groups are used at the edges of graphene to form bond with drain source electrode. This side substitution enhances the performance of FET according to their electron withdrawing ability [41]. 5. Theoretical point of view and Quantum Phenomena 5.1. A Fundamental Approach to Electron Transport: To understand the molecular conduction we need to understand the electron transfer (ET) in a donor–acceptor system, Landauer formula and electron transport through molecular junction, the relationship between electron transfer rates and molecular conduction and a frontier molecular orbital approach to electron transport. 5.1.1. The Electron Transfer theory: The electron transfer (ET) in a donor–acceptor system, where the charge transfer is from the donor to acceptor can be represented as a non-adiabatic ET rate (KD→A) equation as is shown in equation 1, as follows: KD→A = (2π/ћ) V2Φ

(1)

Where V is the effective electronic coupling and Φ is the thermally averaged nuclear vibrational Franck-Condon factor. Also the constant ћ is equal to h/2π, where h is the Planck’s constant. The concept of this ET process is based on the Born-Oppenheimer separability of electronic & nuclear motion and works in the domain where the initial electronic state of the system represented by a one electron wave function of the donor (D) transforms in a diabatic way, to the final state represented by the one electron wave function of the acceptor (A). 5.1.2. Landauer Formula and Electron Transport through Molecular Junction: As discussed earlier, in a molecular junction, the two major parts are the electrodes (metals) and the molecule. In an applied bias voltage, when an electron is transformed from one electrode (say left electrode) to the other electrode (say right), the resultant process creates conductance through the molecule.

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Under the condition of a thermal equilibrium existing at the metal junction, the Landauer formula for the coherent conductance through the junction can be represented by Eq. 2.

(2) Here g is the conductance, Φ is the applied voltage, T is the transmission through the molecular junction, f is the Fermi levels of the metal electrodes and E is the energy variable between the two levels. Using the above equation, the current through a molecular junction can be derived by considering the product of population term and a scattering probability. 5.2. The Relationship between Electron Transfer Rates and Molecular Conduction: Eq. 2 has the same role like that of Eq. 1 as described earlier. In other words, both the processes are based on the tunneling of electron. The equivalent facet of the process taking place in both the phenomena can be described as conductance in the former and rate constant in the latter, and also the transport process in the former is taking place in an electronic bath whereas in the latter it is in vibronic bath. Comparing the electron transport process through a molecular junction with that of the Fig. 5, it can be matched up the discrete levels for the molecule with that of the two adiabatic surfaces, i.e., the two surfaces (D and A in Fig. 5) can be more or less compared with that of the HOMO and LUMO of the molecule, respectively, and the ∆E can be equated with HOMO-LUMO GAP (HLG). Hence, electron transport to occur through the molecule, the primary need is that the Fermi energy of the electrode (Ef) must lie within the HLG. With a proper applied bias voltage through the junction, the two Fermi levels (of the left and right electrode) differ by =φe, i.e., the voltage times electronic charge. Once one of the Fermi levels overcomes the molecular energy level, the resonant electron transfer occurs, and as a result of this, the conductance can be realized through the molecule. When the molecule is placed between the metallic contacts, e.g. gold, without applying the bias voltage and the contacts are coupled (Chemisorbed or adsorbed) to the base, the electrons flow in and out of the device bringing them all in equilibrium with a common electrochemical potential µ. In this equilibrium state the average number of electrons in any energy level is typically not an integer, but is given by the Fermi function: f0 (E- µ) = {1+exp [(E- µ)/KBT]}-1

(3)

The electrochemical potential for the Gold contact is 5.5eV. Energy levels far below the µ are always filled so that f0 =1, while energy levels far above µ are always empty with f0 =0. Energy levels within a few KBT of µ are occasionally full and occasionally empty so that the average no. of electrons lies between 0 and 1: 0 < f0