Bandgap engineering in armchair graphene nanoribbon of zigzag-armchair-zigzag based Nano-FET: A DFT investigation

Journal Pre-proof Bandgap engineering in armchair graphene nanoribbon of zigzag-armchair-zigzag based Nano-FET: A DFT investigation Sukhbir Singh, Inderpreet Kaur PII:

S1386-9477(19)31442-0

DOI:

https://doi.org/10.1016/j.physe.2020.113960

Reference:

PHYSE 113960

To appear in:

Physica E: Low-dimensional Systems and Nanostructures

Received Date: 23 September 2019 Revised Date:

2 January 2020

Accepted Date: 9 January 2020

Please cite this article as: S. Singh, I. Kaur, Bandgap engineering in armchair graphene nanoribbon of zigzag-armchair-zigzag based Nano-FET: A DFT investigation, Physica E: Low-dimensional Systems and Nanostructures (2020), doi: https://doi.org/10.1016/j.physe.2020.113960. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

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Bandgap Engineering in Armchair Graphene Nanoribbon of ZigzagArmchair-Zigzag based Nano-FET: A DFT Investigation. Sukhbir Singhab, Inderpreet Kaura* a

Biomolecular Electronic and Nanotechnology Division (H-1), Council of Scientific and Industrial Research-Central Scientific Instruments Organisation, Sector-30C, Chandigarh - 160030, India.

b

Academy of Scientific and Innovative Research -Central Scientific Instruments Organisation, Sector30C, Chandigarh - 160030, India.

Abstract:

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Graphene nanoribbon (GNR) based nanotransistors (Nano-FET) are preferred part of concerns in present scenario in field of nanoelectronics devices. Various reports stated by theoretician has motivated experimentalist to design high performance GNR based NanoFET. A traditional approach of similar electrode and channel region material has been considered habitually in past. Here, in present work we report a unique approach for designing Nano-FET via considering zigzag-GNR and armchair-GNR as electrode and channel region respectively. The effect of defect in channel region i.e. stone wale (SW) and mono-vacancy (MV) has also been demonstrated and compared with its pristine form of Nano-FET. The electronic and quantum transport properties along with Nano-FET performance has be evaluated and analysed. Our findings shows that, MV based Nano-FET provides high transconductance and charge mobility in comparison to pristine and SW based Nano-FET. These outcomes will inspire experimentalist to design GNR based Nano-FET in proposed design and assists them in enhancing the performance.

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Keywords: Zigzag Graphene Nanoribbon, Armchair Graphene Nanoribbon, Graphene NanoFET, Monovacancy and Stone Wales Defect.

24

Introduction

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Graphene nanoribbon (GNR) a one dimension (1D) nanostrip is a potential candidate for designing nano field effect transistors (Nano-FET)[1][2][3][4][5]. These GNR are metallic and semiconducting in nature, depending upon its edge shaped structure named as zigzag graphene nanoribbon (ZGNR) and armchair graphene nanoribbon (AGNR)[6]. The electronic properties of graphene nanoribbons are tunable and depend upon its width N, whereas ’N’ is the number of carbon dimer (N) lines across the ribbon width[7]. As these electronic properties that can be tuned and facilitates in designing GNR based Nano-FET and can overcome the limitation of present Si-based technology[8][9]. Hence, an intense attempts has been made in past by theoretician and experimentalist to simulate and fabricate GNR based Nano-FET respectively. These efforts made in past has come-out with high performance GNR based Nano-FETs[10][11]. Using first-principle calculation, a two probe quantum transport method has been performed to analyse the GNR Nano-FET performance in comparison to single-walled carbon nanotubes that shows high Ion/Ioff ratios and transconductance of the order of 103-104 and 9.5 x 103 Sm-1 respectively[12]. In order to achieve negative differential resistance (NDR) in ZGNR-FET a DFT based simulation has 1

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been performed via boron, gallium and aluminium doping in electrode region along with nitrogen atom passivation[13]. A novel design of ZGNR-FET with top/back gate using external potential is analysed by iso-chemical potential scheme, that boost the current value by activating the device states[2]. The effect of defects on GNR properties has been reported that elaborates the digital and logic applications of its FET based performances[14]. A nitrogen atom passivated ZGNR based Nano-FET has been simulated in DFT framework and shows the NDR effect which can be controlled by gate voltage [15]. Using same template of N atom passivation the modulation in channel region has been proposed via crafting nanopore and determine the existence and enhancement in NDR effect by varying the nanopore size [16]. Further using Buttiker’s ac transport theory with non-equilibrium green’s function (NEGF), a dynamic conductance in L-shaped graphene nanosytems has also been explored which revels the significance of dynamic conductance in AGNR and ZGNR[17].

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These reported literature revels the perspective of GNR based Nano-FET. However, all these reported works assume identical type of GNR either ZGNR/AGNR for electrode and channel region that restricts its possibilities from experimental point of view. In addition to this, the experimentalist are unable to achieve high charge carrier mobility till date as claimed by theoreticians in past, for graphene-based Nano-FET due lattice mismatch between electrode and channel region fabricated of Au metal and graphene sheet respectively. Though, it is difficult for experimentalist team to design or fabricated Nano-FET of zero contact resistance between electrode and channel region by creating perfect lattice matching between atomic arrangement of electrode and channel region. This perplexing approach of theoreticians, makes many vital concepts unclear for real time designing of NanoFET.

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On the other hand as the modification in channel region is an ordinary practice to identify the variation in performance of Nano-FET. Hence the significance of vacancy defects plays a vital role from experimental point of view. In last few years these vacancy defects in GNR has been recognised while the synthesis of GNR and their effect on varying the electronic properties also been reported [18][19][20]. Numerous NanoFET has been explored in literature via considering the effects of defects that origin’s the variation in its performance [21][22]. A tight-binding approximation with NEGF has been used to explore the effect of stone-wales (SW) defect in mid channel region Nano-FET, that come out with 50% increase in Ion/Ioff ratio [23]. Similarly, a bilayer graphene Nano-FET has been evaluated in via real-space NEGF formalism under influence of mono-vacancy (MV) that results in higher Ion/Ioff ratio in comparison to its ideal states[24]. By using template, the electronic properties of GNR has been modified by divacancy defect results in the energy gains up to ≈7.7 eV [25]. Recently, the inverse stone thrower wales defect is also investigated in NEGF framework that evidences in favour of relatively better Ion/Ioff ratio upto 50 [26]. All these individual reports confirmations the connotation of defects in Nano-FETs designing and in its performance enhancement.

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Therefore, by keeping above discussion in mind and to provide better approach form fabrication viewpoint. It is essential to design electrode and channel region of metallic and 2

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semiconducting material of alike materials respectively. This methodology can overcome the restriction of lattice mismatch and can enhance the performance of Nano-FET. To fulfil such requirement, here we proposed a unique approach of ZGNR-AGNR-ZGNR based Nano-FET (Z-A-Z-FET) and calculated its various parameters and compared with experimental achievements. Further, the traditional defects that occur while synthesizing GNR i.e. stonewales (SW) and mono-vacancy (MV) has also been considered in channel region to evaluate its effects on the performance of Z-A-Z-FET.

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In present report, we have analysed the electronic, quantum transport properties and its FET characteristics using high dielectric constant (k=25) characteristics. The electronic properties i.e. geometrical structure, bandstructure and density of states (DOS) of (N=5 and 9) carbon dimer 5-ZGNR, 9-AGNR along with defected MV-AGNR and SW-AGNR are calculated. The quantum charge transport (I-V characteristics and transmission spectrum) is also analysed by simulating the device of Z-A-Z(MV), Z-A-Z(Pristine) and Z-A-Z(SW). Finally, the FET characteristics is also analysed of each device by considering the high dielectric constant (k=25) of hafnium dioxide and comparison of present work with experimental reported work has been tabulated.

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Computational Model

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The density functional theory (DFT) along with non-equilibrium green’s function (NEGF) based calculation has been performed in present work. The electronic properties of ZGNR, AGNR, MV-AGNR and SW-AGNR structures are studied using ATK–VNL. The DFT based calculations along with local density approximation (LDA) exchange-correlation interaction are preferred. Hydrogen atom passivated 5-ZGNR and 9-AGNR structures with 15 x 5 and 12 x 9 carbon atoms are studied respectively. The optimization of all structures is performed by considering Brillioun zone k-point sampling 1 x 1 x 100 for the calculations. The bandstructure has been calculated at Brillioun zone k-points i.e. Γ, Z, Γ for ZGNR; Z, Y, Γ, Z for AGNR; Γ, Z for SW-AGNR and Γ, Z for MV-AGNR. Double Zeta polarized basis set has been chosen for carbon and hydrogen atom. The cut off energy of 75 Hartree is set and periodic boundary conditions are selected, whereas each atom is relaxed at less than

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0.05eV/Å . The two probe method has been utilized to calculate quantum transport calculation via considering electrode region of ZGNR and channel region of AGNR.

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To measure the geometrical stability cohesive energies are calculated using the following formula:

3

114


 − ∑


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Where Ecoh is the cohesive energy of the system, Etot is the total energy of the system, n is the no. of atoms, E is the energy of an individual atom, x represents an individual atom and N is the total no. of atoms in the system. To calculate the current voltage (I-V) characteristics in the channel region, the Landauer Buttiker formula is used:


 =

(1)

3

 = 119 120 121 122

2   
,   
− μ  −  
− μ  !
 

(2)

Where fl (E - µl) and fr(E -µr) are the Fermi–Dirac distributions of electrons in the left and right electrodes, respectively. The energy region of the transmission spectra that contributes to the current is referred to as the bias window. The total transmission probability is 
,  =  " # $ " # %

123

(3)

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Where GR and GA are retarded and advanced Green’s function of the central region, respectively, and Gland Gr is the contact broadening functions associated with the left and right electrodes, respectively.

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I-V characteristics are evaluated from 0 to 2V and its Nano-FET analysis is performed by designing gate region with high dielectric constant (k=25) of hafnium dioxide (HfO2). The various parameters i.e. Ion/Ioff, transconcudances(gm) and electron-hole mobility(µ) has also been measured.

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Result and Discussion

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Geometrical Structure Analysis:

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The geometric structure of ZGNR, AGNR, MV-AGNR and SW-AGNR are optimized and stabilized to explore their electronic properties are shown in Figure.1. The C–C and C–H

Figure. 0: Optimized geometrical structure of (a) ZGNR pristine, (b) AGNR pristine, (c) SW defected AGNR and (d) MV defected AGNR.

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bond lengths in optimized geometries are found to be 1.42Å and 1.10Å respectively as shown in Figure. 1(a,b). The lattice constant in ZGNR and AGNR is 2.46Å and 2.88Å respectively, these values are in good accordance with experimental ones[27][28]. In case of AGNR and 4

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ZGNR the stabilized geometrical structure results in cohesive energy with -9.044eV and 9.3458eV respectively, which also resembles to the pervious literature[14]. Further to explore the effect of defect in the central region of AGNR, SW and MV are formed. In case of SWAGNR, the SW defect has been created by rotating two carbon atoms to 90° as shown in Figure. 1(c). The change in C-C bond length are observed to be 1.54Å, 1.42Å, 1.41Å and 1.25Å in two pentagons and two heptagons formed by the SW defect. The 2D structure of SW-AGNR remains preserved and stable that further results in cohesive energy -8.7227eV. Similarly, in case of MV-AGNR its 2D structure also remains preserved and stable that leads to cohesive energy -8.6462eV. The MV-AGNR is formed by creating C atom vacancy in AGNR structure and that results in variation of C-C bond length i.e, 1.40Å and 1.41Å as shown in Figure. 1(d). The geometrical stability analysis in terms of preservation of 2D lattice structure and cohesive energy calculations revels the mechanical stability of pristine ZGNR and AGNR along with defected SW-AGNR and MV-AGNR respectively.

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Electronic Properties Analysis:

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The electronic properties of each geometrically optimized GNR i.e., ZGNR, AGNR, MVAGNR and SW-AGNR are calculated via considering band structures and DOS analysis

Figure. 2: Band structure and density of states (a, b) ZGNR pristine, (c, d) AGNR pristine, (e, f) SW defected AGNR, and (g, h) MV defected AGNR.

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investigation as shown in Figure. 2. Firstly, ZGNR and AGNR shows semi-metallic and semiconducting nature respectively, in its band structure plot as shown in Figure. 2(a,c), which resembles with reported literature[14][6]. The ZGNR results in bandgap of 0eV whereas AGNR shows 0.70eV bandgap at the Fermi level (Ef). The DOS of ZGNR and AGNR is also evaluated as shown in Figure. 2(b,d). In ZGNR the DOS peaks are observed in 5

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conduction band (CB) to be at 11.20eV-1 at energy value 0.34eV, in valance band (VB) to be at 11.20eV-1 at energy value -0.22eV and at Fermi level (Ef) to be 11.35eV-1 at energy value 0.0eV. The DOS peak at Ef verifies the metallic nature of ZGNR as energy bands of CB and VB overlaps at wave vector ‘Z’ as shown in Figure. 2(a). Further the energy gap (Eg) is observed in CB and VB, of 1.2eV and 1.0eV respectively of DOS as shown in Figure. 2(b)(blue line). This due to quantum confinement effect in one dimensional geometrical structure of ZGNR that give rise to negligible availability of DOS in correspondence band structure w.r.t. energy value. On the other hand in case of AGNR the DOS peaks are observed in CB to be 5.61eV-1 and 16.94eV-1 at energy 0.34eV and 1.29eV, besides in VB to be at 5.61eV-1 and 5.55eV-1 at energy value -0.34eV and -1.07eV respectively. The absence of DOS peak at Ef revels the existences of bandgap and verifies its semiconducting nature. In addition to it, the Eg in DOS shows resembles to its band structure in correspondences to available energy states w.r.t energy value and gives rise to various Eg between DOS peaks i.e., 0.5eV, 0.5eV and 0.3eV at CB, Ef and VB respectively as shown in Figure 2(d)(blue colour). Similarly, SW-AGNR and MV-AGNR band structure are also analysed as shown in Figure. 2(e, g). These defects i.e., SW and MV give rise to flat bands near Ef in band structure of AGNR and results in various energy gaps (Eg). The Eg observed in SWAGNR are 1eV and 0.52eV, whereas in MV-ZGNR shows more no. of Eg 0.91eV in CB, 0.80eV in VB and 0.1eV at Ef as shown in Figure. 2(e,g). In SW-AGNR these Eg further modifies the DOS in CB at 5.96eV-1, 5.96eV-1 and 5.58eV-1 at energy value 1.20eV, 1.03eV and 1.50eV beside in VB the DOS peaks are observed at 5.63eV-1, 5.69eV-1 and 5.58eV-1 at energy value -0.47eV, -0.69eV and -0.94eV as shown in Figure. 2(f). On the contrary to pristine GNR as discussed earlier, the SW-AGNR shows alteration in its DOS. The presence of Stone Wales defects causes stress and increase in the bond length of C-C bond as shown in Figure 1(c). This origins the existences of Eg in CB and near Ef at 0.25eV and 0.75eV respectively as shown in Figure 2(f)(blue colur), due to presences of flat band raised in band structure as shown in Figure 2(e). The occurrences flat-band in band structure confirms the existences SW in AGNR that resembles the reported literature and results in individual DOS peak at 0.5eV in CB [29]. On the other hand, in MV-AGNR the DOS peaks are observed at CB is 11.20eV-1 at energy value 0.99eV, beside at VB is 10.28eV-1 at -0.82eV along with at Ef is 12.71eV-1 as shown in Figure. 2(h). As monovacancy (MV) in AGNR arises due to missing of a single C atom. This generates various flat-bands in CB, VB and Ef and give rise to Eg i.e., 0.91eV, 0.80eV and 0.1eV respectively, Further in correspondence to these Eg of band structure correspondingly the DOS also shows Eg in CB and VB i.e., 0.60eV and 0.35eV respectively as shown in Figure 2(h)(blue line). As the concentration or availability of flat-band near the Ef is maximum hence this provides enlargement and enhancement in DOS peak at Ef with value of 12.71 eV-1 as shown in Figure 2(h). Finally, it has been observed that SW and MV defects tunes the electronic properties of AGNR in terms of Eg in band structure along with DOS that varies the position and enhancement in DOS peak values also.

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Quantum Transport properties:

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The quantum transport properties of optimized structure are analysed by creating their device as shown in Figure. 3. As ZGNR and AGNR shows semi-metallic nature and semiconducting nature respectively, the device is formed by considering ZGNR as an electrode region for source and drain formation, whereas channel region consists of AGNR as shown in Figure. 3(a). Further to detect the effect of defect, the channel region with MV-AGNR and

Figure. 3: Device configuration of Z-A-Z with (a) MV defect (b) SW defect and (c) pristine.

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SW-AGNR are also designed as shown in Figure. 3(b, c). The current voltage (I-V) characteristics and its analyses with the provision of transmission spectrum of each devices is shown in Figure. 4. Z-A-Z(Pristine) and Z-A-Z(SW) shows diode like I-V characteristics with threshold voltage (VTh) of 0.65V(red colour) and 1.00V(blue colour) respectively, whereas Z-A-Z(MV) shows NDR behaviour with IP and IV such as 1.86µA and 0.89µA along with PVR = 2.08 as shown

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Figure. 1: (a) I-V characteristics of Z-A-Z(MV), Z-A-Z(Pristine) and Z-A-Z(SW), and transmission spectrum of device (b) Z-A-Z(Pristine), (c) Z-A-Z(SW) and (d) Z-A-Z(MV).

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in Figure. 4(a)(green colour line). The maximum current value is achieved in Z-A-Z(Pristine) with 30.46µA followed by Z-A-Z(SW) with 22.7µA and Z-A-Z(MV) with 8.19µA. The indepth behaviour of I-V characteristics can be understood by analysing the transmission spectrum of each device as shown in Figure. 4(b,c and d). Firstly, in case of Z-A-Z(Pristine) the transmission spectrum is shown in Figure. 4(b), reveals that T(E)= 0.606 at applied voltage 0V at Ef. Now as applied voltage is increased upto 1V, the energy window opens with EL and ER and allows charge to flow by resulting T(E) values in terms of 0.094sq unit area under curve. Finally, at applied voltage 2V the T(E) value in terms of area under curve is 0.8017sq unit/eV which is very high value as compared to T(E) at 1V. This abrupt rise in value of T(E) result in rise of current value at 2V with VTh 0.65V. By using similar template, the I-V characteristics of Z-A-Z(SW) can also be explained in terms of T(E) by calculating its area under curve w.r.t EL and ER as shown in Figure. 4(c). At applied 0V the T(E) is 0.196, also at 1V the T(E) is 0.021 sq unit and at 2V the calculated T(E) is 0.595 sq unit. This clearly shows that value of T(E) in Z-A-Z(SW) is low in comparison to Z-A-Z(Pristine) and hence result in lower value of current. Similarly, the NDR behaviour of Z-A-Z(MV) is also explained as shown in Figure. 4(d). At 0V and 1V the T(E) is observed to be 0.361sq unit and 0.042sq unit respectively, which is higher than Z-A-Z(SW) and lower than Z-A-Z(Pristine). This results in higher value of current of Z-A-Z(MV) in comparison to Z-A-Z(SW) and lower 8

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than Z-A-Z(Pristine) upto 1V. Further at 1.5V the T(E) is 0.032sq unit which is low value in comparison to T(E) at 1V which is 0.042sq unit, hence this results in fall of current value and provide NDR region with PVR=2.08. Now at 2V the T(E) value is observed to be 0.105sq unit which results in hike of current value. In comparison to Z-A-Z(Pristine) and Z-AZ(SW), the NDR behaviour is solitary observed in Z-A-Z(MV) due to the availability of DOS peak raised at Ef in correspondence to existences of flat-band in band structure. Further at higher energy value the occurrences of Eg in DOS or band structure results in fall of current value that origins the NDR effect. In the end, as the T(E) at 2V is also less than Z-A-Z(SW) and Z-A-Z(Pristine) hence least maximum current (Imax) value is observed in Z-A-Z(MV).

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GNR based Nano-FET Analysis:

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To analyse and examine the performance of AGNR based FET from device point of view. We optimized the geometrical structure of Z-A-Z(Pristine), Z-A-Z(MV) and Z-A-Z(SW) based FET as shown in Figure. 5(a). The structure is formed by using the high dielectric constant (k=25) material, hafnium oxide (HfO2). The applied voltage from source to drain is 2V with gate voltage (Vg) varying from -1.0V to +1.0V as shown in Figure. 5(b). The

Figure. 2: (a) Optimized geometrical structure of GNR based Nano-FET, and (b) comparison of transverse characteristics of Z-A-Z(MV), Z-A-Z(Pristine) and Z-A-Z(SW).

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dimensions of dielectric material and

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metallic region that we preferred are (32.09×3.07×20.92)Å and (32.09×0.5×20.92)Å respectively, and its geometrical structure is optimized and stabilized by keeping ambient room temperature with similar configuration of electrodes (source and drain) and channel region as used in quantum transport calculation. It has been observed that each AGNR based FET shows ambipolar nature with a dirac point at Vg=0.0V and the transverse characteristics is also analysed of each AGNR based FET by calculating its Id vs Vg characteristics as shown in Figure. 5(b).

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Now starting with Z-A-Z(MV) based FET, the transconductance(gm) is calculated as 8.00µS and 4.30µS, with Ion/off ratio 0.25 and 0.47 in hole and electron conduction region respectively. Similarly, in case of Z-A-Z(Pristine) based FET the gm is calculated as 4.40µS 9

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and 4.64µS, with Ion/off ratio 0.40 and 0.34 in hole and electron conduction region respectively. By using same template, in case of Z-A-Z(SW) based FET the gm is observed as 1.12µS and 1.30µS, with Ion/off ratio 0.47 and 0.47 in hole and electron conduction region respectively. The performance of each Nano-FET exhibiting ambipolar nature can be easily examined on the basis of metal-semiconductor tunnelling junction band-bending model[12]. The Ioff state is located for each Nano-FET on Ef at Vg=0.0V representing dirac cone, that simulate the least Ioff current in Z-A-Z(MV)(black colour) followed by Z-A-Z(Pristine)(red colour) and Z-A-Z(SW)(blue colour) as shown in Figure .5(b). This is due to the reason that structural defects in channel region of graphene Nano-FET i.e., MV-AGNR and SW-AGNR causes charge scattering which is absences in the case of pristine one. However, MV-AGNR causes higher charge scattering in comparison to SW since the vacancy defect causes more perturbation in comparison to dislocation type of defect which is the case of SW. These perturbation in structure of AGNR modulates the DOS and is responsible for low Ioff state. On the other hand the effect of these defects on the Ion current state is negligible due to the reason, that it independent of low applied voltage and typically depends upon higher value of energy states which relatively similar in case of each type AGNR channel region. Furthermore the comparison between each AGNR based FET is also analysed by in terms of hole and electron conduction region as shown in table 1. Mobility (µ) Nano-FET Hole Conduction Region (cm2V-1s-1)

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Electron Conduction Region (cm2V-1s-1)

Z-A-Z(MV) 4.7x106 cm2V-1s-1 Z-A-Z(Pristine) 2.6x106 cm2V-1s-1 Z-A-Z(SW) 6.6x105 cm2V-1s-1 Table 0: Comparison of charge mobility, peak electron conduction region.

Hole peak current density (103A/m2)

2.5x106 cm2V-1s-1 2.7x106 cm2V-1s-1 7.6x105 cm2V-1s-1 current density of each

Electron peak current density (A/m2)

17.06x103 0.34x103 3 23.5x10 23.5x103 3 8.87x10 8.7x103 AGNR based FET in hole and

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It has been clearly observed that high charge carries mobility is obtained in Z-A-Z(MV) followed by Z-A-Z(Pristine) and Z-A-Z(SW) respectively. On the other hand high peak current density is observed in the Z-A-Z(Pristine) followed by Z-A-Z(MV) and Z-A-Z(SW) in case of hole peck current density, whereas in case of electron peak current density the again Z-A-Z(Pristine) dominates followed by Z-A-Z(SW) and Z-A-Z(MV) respectively. Hence, this leads to the variation in Nano-FET performance and afford the capability to architect the desired outcomes of graphene based Nano-FET.

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Eventually, to analyse the performance of our simulated Nano-FET with previously reported graphene based Nano-FET in literature, we tabulated our results as shown in table 2 in terms of achieving higher charge mobilities [µ= L x gm/W x Cgs x Vds; L and W is length and width, gm is transconductance, Cgs is gate source capacitance and Vds is drain source voltage] while utilising similar formulation approach. Sr. No

Approach Utilized

Charge Mobility(cm2V-1s-1) Electron Hole

Reference

10

1. 2. 3. 4.

5.

6.

Lithographic technique GFET, Ion-Gel Gate Dielectric Polymer Doping in Graphene Spray of Liquid-Metal Electrode in Graphene FET Organic Gated Dielectrics for Graphene FET as a Sensor Our Work

120 91± 50

60 203 ± 57

[30] [31]

2087

3105

[32]

663.5

689.9

[33]

154.6

154

[34]

2.7x106

2.6x106

Our Results

291

Table:2 Comparison of our results with reported literature in terms of achieving high charge mobilities.

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Our results shows the almost three times higher enhancement in charge mobilities in comparison to other approaches made in literature. This is due to the reason of lattice mismatch generated between electrodes of Ti/Au and channel of graphene sheet that assist in increment of contact resistances [30][31][32][33][34]. However in our approach the electrode and channel region are of alike material that aids the charge transfer and reduces contact resistance and provides high charge transfer characteristics with high charge mobility.

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Conclusion:

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In conclusion, we report that a superior model for simulating GNR based Nano-FET, in which ZGNR and AGNR has been utilized in electrode and channel region respectively. The geometrical structure, electronic properties and quantum transport properties of pristine and defected GNR has been calculated. These results confirms the metallic and semiconducting nature of pristine ZGNR and AGNR. Further, the electronic property of AGNR has been tuned by creating SW and MV defect on its surface. Finally, the GNR based Nano-FET has been simulated via considering high dielectric constant (k=24) HfO2 in gate region and its transverse characteristics has been analysed. Our results shows that Z-A-Z(MV) provides high transconductance and charge carrier mobility in comparison to Z-A-Z(Pristine) Z-AZ(SW). Our findings has great application in terms of building and fabricating GNR based Nano-FET from experimental point of view to achieve high speed nanodevices.

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Acknowledgement: The authors are thankful to University Grant commission-Rajiv Gandhi National Fellowship for SC (UGC-RGNF) for financial support and Central Scientific Instruments Organisation (CSIR-CSIO) for computational facilities. Furthermore, authors are also thankful to Indian Institute of Information Technology & Management (IIITM), Gwalior for sharing computational services. Finally, we are thankful to our labmates i.e., Dr. Parveen Kumar, Ms. Vipasha Shrama, Mr. Ravi Mehla and Mrs Vandana Gupta for their valuable support.

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References:

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[1]

J. Guo, Modeling of graphene nanoribbon devices, Nanoscale. 4 (2012) 5538–5548. doi:10.1039/C2NR31437A. 11

321 322 323

[2]

J. Yun, G. Lee, K.S. Kim, Electron Transport in Graphene Nanoribbon Field-Effect Transistor under Bias and Gate Voltages: Isochemical Potential Approach, J. Phys. Chem. Lett. 7 (2016) 2478–2482. doi:10.1021/acs.jpclett.6b00996.

324 325 326 327 328 329

[3]

J.P. Llinas, A. Fairbrother, G. Borin Barin, W. Shi, K. Lee, S. Wu, B. Yong Choi, R. Braganza, J. Lear, N. Kau, W. Choi, C. Chen, Z. Pedramrazi, T. Dumslaff, A. Narita, X. Feng, K. Müllen, F. Fischer, A. Zettl, P. Ruffieux, E. Yablonovitch, M. Crommie, R. Fasel, J. Bokor, Short-channel field-effect transistors with 9-atom and 13-atom wide graphene nanoribbons, Nat. Commun. 8 (2017) 8–13. doi:10.1038/s41467-017-00734x.

330 331 332

[4]

J.M. Marmolejo-Tejada, J. Velasco-Medina, Review on graphene nanoribbon devices for logic applications, Microelectronics J. 48 (2016) 18–38. doi:10.1016/j.mejo.2015.11.006.

333 334

[5]

F. Schwierz, J. Pezoldt, R. Granzner, Two-dimensional materials and their prospects in transistor electronics, Nanoscale. 7 (2015) 8261–8283. doi:10.1039/C5NR01052G.

335 336 337

[6]

G.P. Tang, J.C. Zhou, Z.H. Zhang, X.Q. Deng, Z.Q. Fan, Altering regularities of electronic transport properties in twisted graphene nanoribbons, Appl. Phys. Lett. 101 (2012) 10–15. doi:10.1063/1.4733618.

338 339

[7]

S. Dutta, S.K. Pati, Novel properties of graphene nanoribbons: A review, J. Mater. Chem. 20 (2010) 8207–8223. doi:10.1039/c0jm00261e.

340 341

[8]

M. Chhowalla, D. Jena, H. Zhang, Two-dimensional semiconductors for transistors, Nat. Rev. Mater. 1 (2016) 1–15. doi:10.1038/natrevmats.2016.52.

342 343

[9]

F. Schwierz, Graphene transistors, Nat. Nanotechnol. 5 doi:10.1038/nnano.2010.89.

344 345 346 347

[10] J.G. Son, M. Son, K.J. Moon, B.H. Lee, J.M. Myoung, M.S. Strano, M.H. Ham, C.A. Ross, Sub-10 nm graphene nanoribbon array field-effect transistors fabricated by block copolymer lithography, Adv. Mater. 25 (2013) 4723–4728. doi:10.1002/adma.201300813.

348 349 350

[11] D.M. Sun, C. Liu, W.C. Ren, H.M. Cheng, A review of carbon nanotube- and graphene-based flexible thin-film transistors, Small. 9 (2013) 1188–1205. doi:10.1002/smll.201203154.

351 352 353 354

[12] Q. Yan, B. Huang, J. Yu, F. Zheng, J. Zang, J. Wu, Nanoribbon Transistors and Effect of Edge Doping Intrinsic Current − Voltage Characteristics of Graphene Nanoribbon Transistors and Effect of Edge Doping, Nano Lett. 7 (2007) 1469–1473. doi:10.1021/nl070133j.

355 356 357

[13] S.K. Gupta, G.N. Jaiswal, Study of Nitrogen terminated doped zigzag GNR FET exhibiting negative differential resistance, Superlattices Microstruct. 86 (2015) 355– 362. doi:10.1016/j.spmi.2015.07.069.

358 359 360 361

[14] S. Singh, A.D. Sarkar, I. Kaur, A comparative and a systematic study on the effects of B, N doping and C-atom vacancies on the band gap in narrow zig-zag graphene nanoribbons via quantum transport calculations, Mater. Res. Bull. 87 (2017). doi:10.1016/j.materresbull.2016.11.038.

(2010) 487–496.

12

362 363 364 365

[15] A. Kumar, V. Kumar, S. Agarwal, A. Basak, N. Jain, A. Bulusu, S.K. Manhas, Nitrogen-Terminated Semiconducting Zigzag GNR FET With Negative Differential Resistance, IEEE Trans. Nanotechnol. 13 (2014) 16–22. doi:10.1109/TNANO.2013.2279035.

366 367

[16] W. Qiu, P.D. Nguyen, E. Skafidas, Graphene nanopores as negative differential resistance devices, J. Appl. Phys. 117 (2015) 54306. doi:10.1063/1.4907265.

368 369

[17] E.-J. Ye, Y. Nie, H. Shi, C. Zhang, X. Zhao, Dynamic conductance in L-shaped graphene nanosystems, J. Appl. Phys. 117 (2015) 14303. doi:10.1063/1.4905225.

370 371 372

[18] J. Haskins, A. Kınacı, C. Sevik, H. Sevinçli, G. Cuniberti, T. Çağın, Control of thermal and electronic transport in defect-engineered graphene nanoribbons, ACS Nano. 5 (2011) 3779–3787.

373 374

[19] G. Yang, L. Li, W.B. Lee, M.C. Ng, Structure of graphene and its disorders: a review, Sci. Technol. Adv. Mater. 19 (2018) 613–648.

375 376 377

[20] L. Vicarelli, S.J. Heerema, C. Dekker, H.W. Zandbergen, Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices, ACS Nano. 9 (2015) 3428–3435.

378 379 380

[21] A. Nazari, R. Faez, H. Shamloo, Improving ION/IOFF and sub-threshold swing in graphene nanoribbon field-effect transistors using single vacancy defects, Superlattices Microstruct. 86 (2015) 483–492.

381 382 383

[22] A. Nazari, R. Faez, H. Shamloo, Modeling comparison of graphene nanoribbon field effect transistors with single vacancy defect, Superlattices Microstruct. 97 (2016) 28– 45.

384 385

[23] H. Shamloo, A. Nazari, R. Faez, A. Shahhoseini, Local impact of Stone–Wales defect on a single layer GNRFET, Phys. Lett. A. (2019) 126170.

386 387 388

[24] H. Shamloo, R. Faez, A. Nazari, Performance comparison of ideal and defected bilayer graphene nanoribbon FETs, Superlattices Microstruct. 111 (2017) 262–272. doi:https://doi.org/10.1016/j.spmi.2017.06.039.

389 390

[25] Z. Sahan, S. Berber, Divacancy in graphene nano-ribbons, Phys. E Low-Dimensional Syst. Nanostructures. 106 (2019) 239–249.

391 392 393

[26] M.B. Nasrollahnejad, P. Keshavarzi, Inverse Stone Throwers Wales defect and enhancing ION/IOFF ratio and subthreshold swing of GNR transistors, Eur. Phys. J. Appl. Phys. 86 (2019) 20202.

394 395 396

[27] D. Bhatnagar, S. Singh, S. Yadav, A. Kumar, I. Kaur, Experimental and theoretical investigation of relative optical band gaps in graphene generations, Mater. Res. Express. 4 (2017). doi:10.1088/2053-1591/4/1/015101.

397 398 399

[28] A. Akbari-Sharbaf, S. Ezugwu, M.S. Ahmed, M.G. Cottam, G. Fanchini, Doping graphene thin films with metallic nanoparticles: Experiment and theory, Carbon N. Y. (2015). doi:10.1016/j.carbon.2015.08.021.

400 401

[29] F. OuYang, B. Huang, Z. Li, J. Xiao, H. Wang, H. Xu, Chemical Functionalization of Graphene Nanoribbons by Carboxyl Groups on Stone-Wales Defects, J. Phys. Chem. 13

402

C. 112 (2008) 12003–12007. doi:10.1021/jp710547x.

403 404 405 406

[30] J.G. Son, M. Son, K.-J. Moon, B.H. Lee, J.-M. Myoung, M.S. Strano, M.-H. Ham, C.A. Ross, Sub-10 nm Graphene Nanoribbon Array Field-Effect Transistors Fabricated by Block Copolymer Lithography, Adv. Mater. 25 (2013) 4723–4728. doi:10.1002/adma.201300813.

407 408 409

[31] B.J. Kim, H. Jang, S.-K. Lee, B.H. Hong, J.-H. Ahn, J.H. Cho, High-Performance Flexible Graphene Field Effect Transistors with Ion Gel Gate Dielectrics, Nano Lett. 10 (2010) 3464–3466. doi:10.1021/nl101559n.

410 411 412

[32] J.M. Yun, S. Park, Y.H. Hwang, E.-S. Lee, U. Maiti, H. Moon, B.-H. Kim, B.-S. Bae, Y.-H. Kim, S.O. Kim, Complementary p- and n-Type Polymer Doping for Ambient Stable Graphene Inverter, ACS Nano. 8 (2014) 650–656. doi:10.1021/nn4053099.

413 414 415

[33] J.L. Melcher, K.S. Elassy, R.C. Ordonez, C. Hayashi, A.T. Ohta, D. Garmire, Spray-on liquid-metal electrodes for graphene field-effect transistors, Micromachines. 10 (2019) 54.

416 417 418

[34] K. Kam, B. Tengan, C. Hayashi, R. Ordonez, D. Garmire, Polar organic gate dielectrics for graphene field-effect transistor-based sensor technology, Sensors. 18 (2018) 2774.

419 420

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Highlights:1. A density functional theory and non-equilibrium greens function calculations has been considered for geometrical, electronic and transport properties analysis of armchair and zigzag graphene nanoribbion. 2. The electronic properties armchair graphene nanoribbion has been modulated via emphasizing it with surface defects i.e., stone wales and mono-vacancy defects. 3. The quantum transport analysis are performed by focusing I-V characteristics along with transmission spectrum and their in-depth analysis is performed on the basis of DOS contributing at low applied voltages. 4. Finally, the Nano-FET has been designed via considering ZGNR and AGNR as an electrode and channel region respectively, that outcomes with high charge mobility. 5. Our findings have great application in the field of designing Nano-FET.

The contribution made by authors are follows

Sukhbir Singh: Conceptualization, Methodology, Result Analysis and Investigation, Writing- Original draft preparation. Inderpreet Kaur: Supervision, Visualization, Software, Validation, WritingReviewing and Editing

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

We the authors of present research work declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper