Finite Element Modelling of Bandgap Engineered Graphene FET with the Application in Sensing Methanethiol Biomarker

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Article Finite Element Modelling of Bandgap Engineered Graphene FET with the Application in Sensing Methanethiol Biomarker

Paramjot Singh , Parsoua Abedini Sohi and Mojtaba Kahrizi *

Department of Electrical and Computer Engineering, Concordia University, Montreal, QC H3G1M8, Canada; [email protected] (P.S.); [email protected] (P.A.S.) * Correspondence: [email protected]; Tel.: +1-51-48-482-424 (ext. 3089)

Abstract: In this work, we have designed and simulated a graphene ﬁeld effect transistor (GFET) with the purpose of developing a sensitive biosensor for methanethiol, a biomarker for bacterial infections. The surface of a graphene layer is functionalized by manipulation of its surface structure and is used as the channel of the GFET. Two methods, doping the crystal structure of graphene and decorating the surface by transition metals (TMs), are utilized to change the electrical properties of the graphene layers to make them suitable as a channel of the GFET. The techniques also change the surface chemistry of the graphene, enhancing its adsorption characteristics and making binding between graphene and biomarker possible. All the physical parameters are calculated for various variants of graphene in the absence and presence of the biomarker using counterpoise energy-corrected density functional theory (DFT). The device was modelled using COMSOL Multiphysics. Our studies show that the sensitivity of the device is affected by structural parameters of the device, the electrical properties of the graphene, and with adsorption of the biomarker. It was found that the devices made of graphene layers decorated with TM show higher sensitivities toward detecting the biomarker compared with those made by doped graphene layers.

Keywords: GFET; methanethiol biosensor; COMSOL modelling; bandgap engineering; DFT; functionalized graphene Citation: Singh, P.; Abedini Sohi, P.; Kahrizi, M. Finite Element Modelling of Bandgap Engineered Graphene FET with the Application in Sensing Methanethiol Biomarker. Sensors 2021, 1. Introduction 21, 580. https://doi.org/10.3390/ Yielding monolayer of honeycomb networked carbon (C) atoms from the graphite s21020580 leads to one of the most promising materials for photonics and electronics research and industry [1,2]. sp2 hybridised carbon in this 2D material, called graphene, reveals remark- Received: 19 December 2020 able electronic and mechanical properties such as very large mobility of charge carriers Accepted: 12 January 2021 and high electric and thermal conductivities [1,2]. Graphene is a zero-bandgap material Published: 15 January 2021 considered to be a semimetal [3] a the property that conceals its functionalities and limits its applications especially for semiconductor technology [4–6]. To overcome this limitation, Publisher’s Note: MDPI stays neu- this hexagonally structured material is transformed into a semiconductor through various tral with regard to jurisdictional clai- band gap engineering methods including creating edge and quantum confinement effects ms in published maps and institutio- by fabrication of one-dimensional graphene nanoribbons [7–11], passivation with foreign nal affiliations. molecules [12,13], as an outcome of straintronics [14,15], and doping with impurities [16,17] and by applying electric field perpendicular to the graphene surface [18,19]. Using the above techniques, not only do we induce a gap in the band structure of the graphene, but we Copyright: © 2021 by the authors. Li- are able to tune the gap. Graphene has potential for many applications, such as graphene censee MDPI, Basel, Switzerland. field effect transistor (GFET) [20–24], photonic devices such as photodetectors [25–30], This article is an open access article phototransistors [31–33], and mode-locked lasers [34]. distributed under the terms and con- Moreover, due to the high surface-to-volume ratio and the possibility of generat- ditions of the Creative Commons At- ing high adsorption site density [35], graphene is extensively used in sensor technology. tribution (CC BY) license (https:// Schedin et. al. [36] developed the first graphene-based gas sensor. The sensor works based creativecommons.org/licenses/by/ on the change in the hall resistance of the graphene layer as the local carrier concentration 4.0/).

Sensors 2021, 21, 580. https://doi.org/10.3390/s21020580 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 580 2 of 16

varies due to the adsorption of NO2 molecules on the surface. Thereafter, researchers work extensively on graphene and its derivatives for sensory activities based on piezoelectric effects [37–40], opticalUSV effects Symbol [41 Macro(s)–43], surface phenomenon [44–46], and others. TheDescription con- temporary graphene sensor technology is mostly based on a GFET [20,23,47]. GFETs are reported for sensing0241 severalɁ chemical/biomolecules\textglotstopvari such as OH ions [48], monosodiumLATIN CAPITAL LETTER GLOTTAL STOP 0242 ɂ \textglotstopvarii LATIN SMALL LETTER GLOTTAL STOP L-glutamate [49], Escherichia coli (E. coli)[50], ethanol [51], glucose [52], hydrogen gas [53], 0243 Ƀ \textbarcapitalb LATIN CAPITAL LETTER B WITH STROKE exosomes [54], and nitrogen-based gases [55]. 0244 Ʉ \textbarcapitalu LATIN CAPITAL LETTER U BAR In this report, we model, design, and analyse GFET biosensors. For this, graphene is 0245 Ʌ \textturnedcapitalv LATIN CAPITAL LETTER TURNED V transmuted into semiconducting material using two methods. The ﬁrst approach is doping 0246 Ɇ \textstrokecapitale LATIN CAPITAL LETTER E WITH STROKE graphene with impurities such as boron (B), aluminium (Al), and gallium (Ga) as n-type and 0247 ɇ \textstrokee LATIN SMALL LETTER E WITH STROKE nitrogen (N) phosphorous (P) and arsenic (As) as p-type dopants. Decorating the graphene 0248 Ɉ \textbarcapitalj LATIN CAPITAL LETTER J WITH STROKE surface with a transition0249 metalɉ (TM)\textbarj such as palladium (Pd) is the second techniqueLATIN SMALL that LETTER J WITH STROKE

we use to manipulate024A the bandɊ gap\texthtcapitalq structure of the graphene. Using these techniquesLATIN CAPITAL not LETTER SMALL Q WITH HOOK TAIL only allows for transferring024B ɋ of the\texthtq semimetal graphene to a semiconducting materialLATIN SMALL but LETTER Q WITH HOOK TAIL

also gives the capability024C toɌ generate\textbarcapitalr and control the concentration of adsorption sitesLATIN on CAPITAL the LETTER R WITH STROKE surface of graphene024D layersɍ to attach\textbarr the biomolecules under investigation. The preparedLATIN SMALL LETTER R WITH STROKE graphene layers are024E then usedɎ to\textbarcapitaly design GFET-based biosensors to detect biomarkersLATIN CAPITALsuch LETTER Y WITH STROKE as methanethiol.024F ɏ \textbary LATIN SMALL LETTER Y WITH STROKE Methanethiol0250 is volatileɐ organo-sulphur\textturna material that is considered as a biomarkerLATIN SMALL LETTER TURNED A for the diseases caused0251 byɑ microorganisms\textscripta like Helicobacter pylori bacteria (H. pyloriLATIN)[ SMALL56], LETTER ALPHA Porphyromonas gingivalis0252 (ɒP. Gingivalis\textturnscripta) phylum Bacteroidetes [57,58]. To the bestLATIN of SMALL our LETTER TURNED ALPHA knowledge, this0253 is the firstɓ time\m{b} that a graphene-based electronic device is usedLATIN to SMALL de- LETTER B WITH HOOK \m{b} tect methanethiol. \texthtb Density functional theory (DFT)\textbhook accompanied by drift-diffusion formalism is used to calculate the physical0254 propertiesɔ \m{o} of the semiconducting graphene such as bandLATIN struc- SMALL LETTER OPEN O ture, mobility, and effective density\textopeno of states. Adsorption energy is also calculated to \textoopen analyse the surface phenomena on all variants of graphene with or without adsorption of 0255 ɕ \textctc LATIN SMALL LETTER C WITH CURL methanethiol. The calculated parameters are used to design and simulate the GFET devices 0256 ɖ \M{d} LATIN SMALL LETTER D WITH TAIL using COMSOL Multiphysics. The\textrtaild dependencies of I-V curves on the electronic properties of the graphene layer as well as the\textdtail geometrical parameters of the device are considered to evaluate the device’s0257 sensingɗ performance.\m{d} LATIN SMALL LETTER D WITH HOOK \texthtd \textdhook 2. Device Structure 0258 ɘ \textreve LATIN SMALL LETTER REVERSED E The semiconductor0259 moduleə \schwa of COMSOL Multiphysics was used to design andLATIN simu- SMALL LETTER SCHWA late a GFET biosensor. The geometrical\textschwa configuration of the proposed device is illustrated in Figure1. The device025A comprisesɚ \m{\schwa} a one-atom-thick graphene monolayer laying on aLATIN silicon- SMALL LETTER SCHWA WITH HOOK \texthookabove{\schwa} oxide/silicon (SiO2/Si) substrate.\textrhookschwa The SiO2 is an insulating layer, serving as a dielectric with a dielectric constant025B (ɛr) of 3.99.\m{e} For the sake of calculations, the boundary conditionsLATIN SMALL LETTER OPEN E at all terminals are considered ohmic.\textepsilon I-V measurements were used to determine the per- \texteopen formance and characteristics of the\textniepsilon device. These measurements were subjected to varying the dimensions of025C the grapheneɜ channel\textrevepsilon and its surface chemistry (functionalization),LATIN SMALL the LETTER REVERSED OPEN E thickness of the dielectric025D ɝ layer, and\texthookabove{\textrevepsilon} the doping concentration of the Si substrate. LATIN SMALL LETTER REVERSED OPEN E WITH HOOK The graphene layer serves\textrhookrevepsilon as a channel in the above structure and must be in the semiconducting state.025E As itɞ was a\textcloserevepsilon semimetal material in nature, we needed to manipulateLATIN SMALL LETTER CLOSED REVERSED OPEN E its band structure025F to transferɟ it to\B{j} a semiconductor. Among several methods toLATIN induce SMALL LETTER DOTLESS J WITH STROKE \textbardotlessj bandgap in the graphene band structure,\textObardotlessj we used the following two methods. In the first method,0260 theɠ graphene\texthookabove{g} was doped with both donors and acceptors,LATIN making SMALL LETTER G WITH HOOK it compensated. Here, although graphene\texthtg is doped with impurities, the material remains intrinsic since the0261 concentrationɡ \textscriptg of the introduced n-type and p-type dopantsLATIN will SMALL be LETTER SCRIPT G the same. 0262 ɢ \textscg LATIN LETTER SMALL CAPITAL G 0263 ɣ \m{g} LATIN SMALL LETTER GAMMA \textbabygamma \textgammalatinsmall \textipagamma 0264 ɤ \textramshorns LATIN SMALL LETTER RAMS HORN

0265 ɥ \textturnh LATIN SMALL LETTER TURNED H

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FigureFigure 1. 1. The proposed graphene graphene field ﬁeld effect effect transistor transistor (GFET) (GFET) model. model. The The back-gate back-gate structure structure en- enablesables binding binding of of the the biomarker biomarker to to the the channel channel surface. surface.

MostIn the common first method, dopants the usedgraphene in graphene was doped are elementswith both from donors group and III acceptors, for acceptors mak- anding fromit compensated. group V for Here, donors although (as carbon graphene is in group is doped IV). In with this impurities, work, the semiconducting the material re- propertiesmains intrinsic of graphene since the are concentration studied for B-N, of th Al-P,e introduced and Ga-As n-type doping. and p-type dopants will be theIn same. the second method, the bandgap opening for graphene arises by adsorption of TMs toMost the graphenecommon dopants surface. Theused adsorption in graphene happens are elements without from introducing group III crystal for acceptors defects inand graphene from group lattice. V for Among donors TMs,(as carbon we used is in group Pd due IV). to In its this high work, stability the semiconducting and catalytic activitiesproperties [59 of– 64graphene]. The electrical are studied properties for B-N, ofAl-P, the and functionalized Ga-As doping. graphene layer in the absence and presence of the biomarker are crucial parameters to determine the overall In the second method, the bandgap opening for graphene arises by adsorption of sensing performance of the device. These parameters are evaluated precisely by atomistic TMs to the graphene surface. The adsorption happens without introducing crystal de- analytical studies through DFT implemented in Quantum ATK (QATK) software. fects in graphene lattice. Among TMs, we used Pd due to its high stability and catalytic 3.activities Results and[59–64]. Discussion The electrical properties of the functionalized graphene layer in the 3.1.absence Atomistic and Modellingpresence viaof the Quantum biomarker ATK are crucial parameters to determine the overall sensing performance of the device. These parameters are evaluated precisely by atomistic 3.1.1. Band Gap Engineering of Graphene analytical studies through DFT implemented in Quantum ATK (QATK) software. Compensated Doping Method 3. ResultsFigure 2anda illustrates Discussion the atomic structure of Al-P doped graphene lattice. Optimization is performed to achieve the lowest energy structure and therefore the most stable atomic 3.1. Atomistic Modelling via Quantum ATK conformation. The zoomed-in areas in the figure present the calculated Al—C, P—C and C—C3.1.1. bondBand lengthsGap Engineering of a ground-state of Graphene optimal structure. CompensatedIn the proposed Doping structure, Method the P atom with one extra electron than C atom acts as an 2 n-typeFigure impurity 2a illustrates by incorporating the atomic one structure electron perof Al-P nm dopedinto the graphene graphene lattice. lattice, Optimiza- whereas thetion Al is atom performed is one electronto achieve deficient the lowest and actsenergy as a structure p-type impurity and therefore by incorporating the most stable one 2 holeatomic per conformation. nm to the lattice The structure. zoomed-in areas in the figure present the calculated Al—C, P—CAfter and geometryC—C bond optimization, lengths of a ground-state it was found optimal that co-doping structure. of graphene with Al-P atomsIn did the not proposed destroy structure, the Clar’s the structure P atom but with slightly one extra deformed electron it, asthan shown C atom in Figure acts as2a. an Figure2b illustrates the doped graphene structure with semi-infinite extension in [100] and n-type impurity by incorporating one electron per nm2 into the graphene lattice, whereas [010] directions considered for energy-band structure calculations. the Al atom is one electron deficient and acts as a p-type impurity by incorporating one hole per nm2 to the lattice structure.

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FigureFigure 2. Ground-state 2. Ground-state optimal optimal structure structure of Al-P of Al-P doped doped graphene; graphene; (a) (optimizeda) optimized bond bond lengths lengths of Al—C, of Al—C, P—C, P—C, and and C—C; C—C; (b)( bextended) extended structure structure of ofco-doped co-doped graphene graphene considered considered for for the the en energyergy band band structure structure calculations. calculations.

AfterThe geometry same analyses optimization, were also it performedwas found forthat B-N co-doping and Ga-As of graphene dopants. Eachwith dopantAl-P atomsatom did was not linked destroy with the three Clar’s C structure atoms and but forms slightly different deformed bond it, lengths. as shown The in bond Figure lengths 2a. Figurealong 2b with illustrates the induced the doped bandgap graphene are summarized structure with in Tablesemi-infinite1. All the extension DFT calculations in [100] andwere [010] performed directions onconsidered the same for concentration energy-band of structure dopants calculations. of one donor–acceptor pair per 2 nmThe. It same was foundanalyses that were the Ga-Asalso performed pair has inducedfor B-N and maximum Ga-As bandgapdopants. asEach compared dopant to atomother was dopants. linked with three C atoms and forms different bond lengths. The bond lengths along with the induced bandgap are summarized in Table 1. All the DFT calculations wereTable performed 1. Induced on bandgap the same and C—dopantconcentration bond of length dopants in different of one doped donor–acceptor graphene. pair per 2 nm . It was found that the Ga-As pair hasB-N induced Doped maximumAl-P bandgap Doped as Ga-Ascompared Doped to Material other dopants. Graphene Graphene Graphene Bandgap (eV) 0.24 0.24 0.55 Table 1. Induced bandgap and C—dopant bond length in different doped graphene. Acceptor 1.47 1.62 1.71 Bond length 1 (Å) DonorB-N Doped 1.4 Al-P Doped 1.7 Ga-As Doped 1.7 Material Acceptor 1.47 1.65 1.72 Bond length 2 (Å) Graphene Graphene Graphene Donor 1.41 1.72 1.72 Bandgap (eV) 0.24 0.24 0.55 Acceptor 1.48 1.65 1.72 Bond length 3 (Å) Acceptor 1.47 1.62 1.71 Bond length 1 (Å) Donor 1.41 1.72 1.72 Donor 1.4 1.7 1.7 Acceptor 1.47 1.65 1.72 Bond length 2 (Å) Transition Metal DecorationDonor 1.41 1.72 1.72 TMs have highAcceptor adsorption capabilities1.48 compared 1.65 to other elements 1.72 [65 ]. In this Bond length 3 (Å) method, a Pd hetero atomDonor was used to functionalize1.41 graphene1.72 surface [66– 1.7272]. The most stable position of a Pd atom on graphene is a bridge position (the position between Transitiontwo consecutive Metal Decoration atoms attached through a bond), as shown in Figure3a [ 73]. Mulliken populationTMs have analysis high adsorption shows that capabilities bond formation compared between to other C and elements Pd atom [65]. occurs In duethis to method,interaction a Pd betweenhetero atom pz orbital was used of C to atom functi (whichonalize is perpendiculargraphene surface to the [66–72]. plane The of C most atoms) stableand position d orbital of of a PdPd valenceatom on band. graphene After is optimization, a bridge position bond (the length position between between the Pd two and C is 5.44 Å, as depicted in Figure3a. The extended surface of Pd decorated graphene is consecutive atoms attached through a bond), as shown in Figure 3a [73]. Mulliken pop- shown in Figure3b with one Pd atom per nm 2. In semiconductor industries, an appropriate ulation analysis shows that bond formation between C and Pd atom occurs due to inter- concentration of the dopant is usually considered to eliminate the effects of dopant–dopant action between pz orbital of C atom (which is perpendicular to the plane of C atoms) and interaction. In this work, we considered the 1 Pd atom per/ 1 nm2, by which there will be d orbital of Pd valence band. After optimization, bond length between the Pd and C is the least interaction between Pd atoms. 5.44 Å, as depicted in Figure 3a. The extended surface of Pd decorated graphene is shown in Figure 3b with one Pd atom per nm2. In semiconductor industries, an appropriate

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concentration of the dopant is usually considered to eliminate the effects of dopant– Sensors 2021, 21, 580 dopantconcentration interaction. of Inthe this dopant work, is we usually considered cons ideredthe 1 Pd to atom eliminate per/ 1 thnme 2effects, by which of dopant– there5 of 16 2 willdopant be the interaction. least interaction In this between work, we Pd considered atoms. the 1 Pd atom per/ 1 nm , by which there will be the least interaction between Pd atoms.

Figure 3. (a) The Pd-decorated graphene structure with C—Pd bond length; (b) extended surface of Pd decorated gra- pheneFigureFigure considered 3.3.( a()a) The The for Pd-decorated Pd-decorated the energy grapheneband graphene structure structure structure calculations. with with C—Pd C—Pd bond bond length; length; (b) extended(b) extended surface surface of Pd of decorated Pd decorated graphene graphene considered for the energy band structure calculations. considered for the energy band structure calculations. 3.1.2. Interaction with Methanethiol Biomarker 3.1.2.3.1.2. InteractionInteraction withwith MethanethiolMethanethiol BiomarkerBiomarker Characteristics of the interactions between the methanethiol, (CH3SH), and gra- Characteristics of the interactions between the methanethiol, (CH3SH), and graphene Characteristicsis determined by of thetheir interactions binding energy between (EAD the) [74]. methanethiol, Figure 4a,b (CH present3SH), the and most graphene sta- bleisphene position determined is determined of methanethiol by their by binding their on thebinding energy surfac energye (E ofAD Al-P)[ (E74 ADco-doped].) [74]. Figure Figure and4a,b Pd-decorated 4a,b present present the mostthe graphene, most stable sta- respectively,positionble position of in methanethiol of terms methanethiol of high on adsorption on the the surface surfac energy. ofe of Al-P Al-P co-doped co-doped and and Pd-decorated Pd-decorated graphene,graphene, respectively,respectively, in in terms terms of of high high adsorption adsorption energy. energy.

(a) (a)

(b) (b) Figure 4. Optimized structuresFigure of graphene-biomolecule 4. Optimized structures complex of graphene-biomolecule show (a) physiosorbed complex methanethiol show (a) physiosorbed biomolecule methanethiol on Figure 4. Optimized structures of graphene-biomolecule complex show (a) physiosorbed methanethiol biomolecule on Al-P-doped graphene lattice andbiomolecule (b) chemisorbed on Al-P-doped methanethiol graphene biomolecul lattice ande on (b Pd-decorated) chemisorbed graphene methanethiol lattice. biomolecule on Pd- Al-P-doped graphene lattice and (b) chemisorbed methanethiol biomolecule on Pd-decorated graphene lattice. decorated graphene lattice.

Compensated doped graphene shows a powerful association with the methanethiol through interaction between sulphur (S) and Al atoms. As illustrated in the Figure4a, the Sensors 2021, 21, 580 6 of 16

Al atom relocates itself by rising towards the methanethiol molecule, causing curvature in the structure. However, there is no chemical bond formed between the biomarker and Al-P co-doped graphene, and adsorption of biomarker by the graphene is due to physisorption phenomena. Even though P atoms do not show strong enticement towards the biomarker, it plays a crucial role in opening the bandgap of the graphene. A single impurity atom, like Al or P, opens the Dirac point, but the material remains metallic in nature as some valence bands overlap with Fermi level. Contrary to what was observed for the case of compensated graphene, Figure4b illustrates that a bond formation occurs between the methanethiol molecule and Pd-decorated graphene. The involvement of an S atom in bond formation with Pd conﬁrms the occurrence of chemisorption, representing stronger binding between the guest–host complex. Table2 summarizes the calculated adsorption energies in proposed complexes. The values are counterpoise-corrected interaction energies (EAD+CP), which correct the errors arising due to overlapping of basis orbitals of the two interacting atoms [74].

Table 2. The total energies, adsorption energies between biomarker and graphene.

Material EAD+CP (eV) Methanethiol adsorbed Pd decorated graphene −1.22 Methanethiol adsorbed B-N doped graphene −0.01 Methanethiol adsorbed Al-P doped graphene −0.90 Methanethiol adsorbed Ga-As doped graphene −0.02

The negative values of the EAD+CP in Table2 indicates the favourable host–guest molecules adsorption. Furthermore, larger negative EAD+CP corresponds to more efﬁcient adsorption and consequently higher sensing functionalities toward methanethiol. There- fore, the comparison between the values shows that the graphenes doped with B-N and Ga-As do not have efﬁcient adsorption energy towards the indicated biomarker. As a result, for further analyses, we only considered Al-P-doped graphene and Pd-decorated graphene with adsorption energies of −0.90 eV and −1.22 eV, respectively.

Electrical Properties of Al-P Doped Graphene before and after Interactions with Methanethiol Figure5 illustrates the calculated band structure of Al-P-doped graphene before and after methanethiol adsorption. As is seen, methanethiol adsorption increases the bandgap Sensors 2021, 21, x FOR PEER REVIEW 7 of 17 of the graphene from 0.24 eV to 0.45 eV. However, the intrinsic behaviour of material remains the same after adsorption.

Figure 5. Band structure of Al-P-doped graphene and methanethiol adsorbed Al-P-doped graphene. Figure 5. Band structure of Al-P-doped graphene and methanethiol adsorbed Al-P-doped graphene.

Table 3. Physical parameters of different variants of graphene before and after methanethiol adsorption calculated by DFT analysis.

Methanethiol Ad- Methanethiol Ad- Al-P Doped Gra- Pd Decorated sorbed Al-P Doped sorbed Pd Decorated phene Graphene Graphene Graphene

E (eV) 0.24 0.45 0.018 0.026 E E 0.12 0.23 0.011 0.019 (eV) E E (eV) 0.12 0.23 0.007 0.007 E (eV) 5.32 4.99 4.97 4.88 Nature Semiconductor Semiconductor Semiconductor Semiconductor mle) 0.048 0.160 0.003 0.004 me mt1e) 0.099 1.909 0.007 0.010 me ) 0.092 0.174 0.005 0.008 ) 0.052 0.164 0.003 0.004 ) 0.108 2.287 0.007 0.010 ) 0.098 0.176 0.005 0.008 0.120 0.596 0.00748 0.011 0.130 0.641 0.00748 0.011 −3 18 19 16 16 N(cm ) 1.04 × 10 1.15 × 10 1.61 × 10 2.88 × 10 −3 18 19 16 16 N(cm ) 1.17 × 10 1.28 × 10 1.61 × 10 2.88 × 10 Φ(eV) 4.200 4.500 4.010 4.700 χ (eV) 4.080 4.270 4.003 4.693 2 5 4 4 5 μ (cm /Vs) 1.25 × 10 1.79 × 10 9.58 × 10 1.28 × 10 2 5 4 4 5 μ(cm /Vs) 2.29 × 10 4.00 × 10 3.5 × 10 1.90 × 10

Boltzmann Transport Equation (BTE) with relaxation time approximation (RTA) is used to calculate mobility (μ) in graphene structures. μ is directly proportional to the relaxation time of carrier (Ԏ) [78]. Acoustic phonon scatterings have a major contribution to the value of Ԏ at room temperature. In graphene, there are three acoustic phonon modes: longitudinal acoustic (LA), transverse acoustic (TA), and out-of-plane acoustic (ZA) modes [79]. These modes affect the electron–phonon coupling matrix, which is used to calculate Ԏ. As is tabulated in Table 3, our calculations show that carriers mobilities are

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The effective density of states (Nc or Nv) represents the sum of quantum states disseminated on the entire band in the form of two Dirac delta function deﬁned at the edge dos dos dos dos of the band [75]. Nc (Nv) is a function of the carrier mass (me or mh )[76]. me (mh ) is the longitudinal (transverse) effective mass and depends on the valley degeneracy of the energy bands [77]. In all cases, valley degeneracy is constant, which means only the values of longitudinal and transverse effective masses affect the Nc and Nv. The longitudinal and transverse effective mass of electron decrease as conduction band minima (CBM) and valence band maxima (VBM) converge towards the Fermi level, and they become massless at the Dirac point, which is the same as those of intrinsic graphene. After the adsorption of the biomarker, the bandgap increases, and consequently effective masses increase; as a result, Nc and Nv increase as tabulated in Table3. The work function ( Φ) expresses the total amount of energy required to knock out one electron from Fermi level toFigure vacuum 5. levelBand [structure75] and it of is Al-P-doped inversely proportional graphene and to methanethiol Fermi energy adsorbed (Ef). Since Al-P-doped adsorption gra- ofphene. methanethiol decreases Ef, it leads to increment in the work function of methanethiol adsorbed complexes. As is summarized in Table3, Al-P-doped graphene has a work functionTable 3. of Physical 4.2 eV, parameters which increases of differ toent 4.5 variants eV once of thegraphene biomarker before is and adsorbed. after methanethiol adsorption calculated by DFT analysis. Table 3. Physical parameters of different variants of graphene before and after methanethiol adsorp- Methanethiol Ad- Methanethiol Ad- Al-P Doped Gra- Pd Decorated tion calculated by DFT analysis. sorbed Al-P Doped sorbed Pd Decorated phene Graphene Graphene Graphene Methanethiol Methanethiol E (eV) Al-P0.24 Doped Adsorbed0.45 Al-P Pd0.018 Decorated Adsorbed 0.026 Pd E E Graphene0.12 0.23Doped Graphene0.011 Decorated 0.019 (eV) Graphene Graphene E E (eV) 0.12 0.23 0.007 0.007 Eg (eV) 0.24 0.45 0.018 0.026 E (eV) 5.32 4.99 4.97 4.88 EVBM − EF (eV) 0.12 0.23 0.011 0.019 Nature Semiconductor Semiconductor Semiconductor Semiconductor ECBM − EF (eV) 0.12 0.23 0.007 0.007 mle) E (eV) 0.048 5.32 0.160 4.99 0.003 4.97 4.880.004 F me Naturemt1e) Semiconductor Semiconductor Semiconductor Semiconductor m 0.099 1.909 0.007 0.010 ml(ee) 0.048 0.160 0.003 0.004 me) m ( ) t1 e 0.092 0.174 0.005 0.008 m 0.099 1.909 0.007 0.010 me) t2(e) 0.0520.092 0.164 0.174 0.003 0.005 0.008 0.004 me ml(h)) 0.1080.052 2.287 0.164 0.007 0.003 0.004 0.010 me mt1(h) ) 0.108 2.287 0.007 0.010 me 0.098 0.176 0.005 0.008 mt1(h) 0.098 0.176 0.005 0.008 me mdos 0.120 0.596 0.00748 0.011 e 0.120 0.596 0.00748 0.011 me dos mh 0.130 0.641 0.00748 0.011 0.130 0.641 0.00748 0.011 me −−33 18 18 19 19 1616 1616 NNc(cm(cm )) 1.04 1.04 × ×1010 1.151.15 × ×1010 1.611.61 ×× 1010 2.88 2.88× × 1010 −−33 18 18 19 19 1616 1616 NNv(cm(cm )) 1.17 1.17 × ×1010 1.281.28 × ×1010 1.611.61 ×× 1010 2.88 2.88× × 1010 Φ(eV) 4.200 4.200 4.500 4.500 4.010 4.010 4.700 4.700 χ (eV) 4.080 4.080 4.270 4.270 4.003 4.003 4.693 4.693 µ 2 × 5 × 4 × 4 × 5 μe (cm(cm2/Vs)/Vs) 1.25 1.25 × 10510 1.791.79 × 10104 9.589.58 × 10104 1.28 1.28 × 10105 2 5 4 4 5 µh(cm 2/Vs) 2.29 × 510 4.00 × 104 3.5 × 104 1.90 × 10 5 μ(cm /Vs) 2.29 × 10 4.00 × 10 3.5 × 10 1.90 × 10

BoltzmannBoltzmann Transport Transport Equation Equation (BTE) (BTE) with with relaxation relaxation time time approximation approximation (RTA) (RTA) is is usedused to to calculate calculate mobility mobility ( µ(μ)) in in graphene graphene structures.structures. μµ isis directly directly proportional proportional to to the the re- relaxationlaxation time of carrier (Ԏ)[) [78].78]. Acoustic Acoustic phonon phonon scattering scatteringss have have a a major major contribution contribution to tothe the value value of of Ԏ atat room room temperature. temperature. In graphene, In graphene, there there are three are three acoustic acoustic phonon phonon modes: modes:longitudinal longitudinal acoustic acoustic (LA), (LA), transverse transverse acou acousticstic (TA), (TA), and and out-of-plane acousticacoustic (ZA) (ZA) modesmodes [79 [79].]. These These modes modes affect affect the the electron–phonon electron–phonon coupling coupling matrix, matrix, which which is is used used to to calculatecalculate .Ԏ As. As is is tabulated tabulated in in Table Table3, our3, our calculations calculations show show that that carriers carriers mobilities mobilities are are decreased when methanethiol is adsorbed in Al-P-doped graphene, which afﬁrms that the velocity of the electrons and holes are also decreased. The structural distortion in Al-P graphene during the biomarker adsorption is the major cause of reduction of mobility. Sensors 2021, 21, x FOR PEER REVIEW 8 of 17

decreased when methanethiol is adsorbed in Al-P-doped graphene, which affirms that

Sensors 2021, 21, 580 the velocity of the electrons and holes are also decreased. The structural distortion in 8Al-P of 16 graphene during the biomarker adsorption is the major cause of reduction of mobility.

Electrical Properties of Pd-Decorated Graphene before and after Interactions with Me- thanethiolElectrical Properties of Pd-Decorated Graphene before and after Interactions with Methanethiol The Pd decorated graphene shows n-type behaviour with a bandgap of 0.018 eV. As is illustratedThe Pd in decorated Figure 6, graphenethe adsorption shows of n-type the biomarker behaviour increases with a the bandgap bandgap of 0.018 to 0.026 eV. eV. As is illustrated in Figure6, the adsorption of the biomarker increases the bandgap to 0.026 eV.

Figure 6. Band structure of Pd-decorated graphene and methanethiol adsorbed Pd-decorated graphene. Figure 6. Band structure of Pd-decorated graphene and methanethiol adsorbed Pd-decorated graphene.Our calculations show that the longitudinal and transverse effective mass of carriers increases as the methanethiol molecule is adsorbed on the graphene. Consequently, Nc and Our calculations show that the longitudinal and transverse effective mass of carriers Nv also increase with adsorption. Biomarker adsorption also reduces the EF of the system increases as the methanethiol molecule is adsorbed on the graphene. Consequently, Nc as presented in Table3. Due to the inverse relationship of E F with Φ, Φ of Pd-decorated andgraphene Nv also changes increase from with 4.01 adsorption. to 4.77 eV Biomarker after adsorption. adsorption also reduces the EF of the systemStructural as presented distortion in Table increases 3. Du thee phononto the inverse scattering relationship in the lattice, of E whichF with adverselyΦ, Φ of Pd-decoratedaffects the mobility graphene of thechanges material. from Decoration4.01 to 4.77 eV of Pdafter atom adsorption. on the graphene decreases the mobilityStructural to distortion 105 as it increases creates distortion the phonon in lattice.scattering Pd in atom the lattice, acts as which a linking adversely agent affectsbetween the graphene mobility andof the analyte material. and Decoration impedes graphene of Pd atom distortion. on the Therefore,graphene decreases adsorption the of 5 mobilitymethanethiol to 10 increases as it creates mobility distortion as summarized in lattice. Pd in Tableatom3 acts. as a linking agent between graphene and analyte and impedes graphene distortion. Therefore, adsorption of me- thanethiol3.2. Device increases Characterization mobility via as COMSOL summarized in Table 3. COMSOL Multiphysics is used to investigate the DC characteristics of the proposed 3.2.GFET Device devices. Characterization The software via efﬁcientlyCOMSOL allows assigning physical properties of materials to modelCOMSOL the device. Multiphysics The investigated is used to investigat semiconductinge the DC properties characteristics of the of functionalized the proposed GFETgraphene devices. in the The presence software and efficiently absence allows of the biomarkerassigning physical (as summarized properties in of Table materials3) are toapplied model in the the device. material The properties investigated section semicond requireducting by the properties model. of the functionalized grapheneThe Al-Pin the doped presence GFET and (AlP-GFET) absence of and the Pd biomarker decorated (as GFET summarized (Pd-GFET) in performances Table 3) are appliedare characterized in the material by considering properties thesection effect required of geometrical by the model. and physical parameters of the devices.The Al-P doped GFET (AlP-GFET) and Pd decorated GFET (Pd-GFET) perfor- mancesThe are impact characterized of device by parameters considering variation the effect on the of sensitivitygeometrical of and the sensorphysical is discussedparame- tersin the of the following devices. sections. The impact of device parameters variation on the sensitivity of the sensor is dis- cussed3.2.1. DC in the Characteristics following sections. of Device A GFET is a three-electrode device, composed of a graphene channel between two electrodes and a gate contact to modulate the electronic response of the channel. In this section, the electrical characteristics of the AlP-GFET and Pd-GFET devices in the absence of biomarkers are evaluated. For these analyses, the channel length (L, the source-drain spacing) and channel width (W) of the device are considered 2 µm and 1 µm, respectively. A p-type Si with the doping concentration of 1018 cm−3 is used as the substrate. While

the source is grounded, the drain current (Id) is measured by sweeping the gate voltage (Vg) from 0 to 2 V at a drain voltage (Vd) of 10 mV. I-V characteristics of the devices are Sensors 2021, 21, x FOR PEER REVIEW 9 of 17

3.2.1. DC Characteristics of Device A GFET is a three-electrode device, composed of a graphene channel between two electrodes and a gate contact to modulate the electronic response of the channel. In this section, the electrical characteristics of the AlP-GFET and Pd-GFET devices in the absence of biomarkers are evaluated. For these analyses, the channel length (L, the source-drain Sensors 2021, 21, 580 spacing) and channel width (W) of the device are considered 2 μm and 1 μm, respec-9 of 16 tively. A p-type Si with the doping concentration of 1018 cm−3 is used as the substrate. While the source is grounded, the drain current (Id) is measured by sweeping the gate voltage (Vg) from 0 to 2 V at a drain voltage (Vd) of 10 mV. I-V characteristics of the de- vicesshown are in shown Figure 7ina Figure (AlP-GFET) 7a (AlP-GFET) and Figure and7b (Pd-GFET).Figure 7b (Pd-GFET). Two distinct Two regions distinct appear regions in appearthe graphs: in the negative graphs: differentialnegative differential resistance re (NDR)sistance and (NDR) the positive and the differential positive differential resistance resistance(PDR). A minimum(PDR). A minimum happens as happens these two as regionsthese two meet, regions which meet, is known which as is the known Dirac as point the at gate voltage, V (neutral voltage). According to the graphs, the V of 0.93 V and 1.09 V Dirac point at gaten voltage, Vn (neutral voltage). According to the graphs,n the Vn of 0.93 V andwere 1.09 observed V were for observed AlP-GFET for andAlP-GFET Pd-GFET, and respectively. Pd-GFET, respectively.

FigureFigure 7. 7. I–VI-V characteristics show two distinct regions and the particular VVn forfor ( (a)) AlP-GFET, AlP-GFET, (b) Pd-GFET.

ThisThis peculiar behaviourbehaviour ofof the the I-V I-V characteristics characteristics of of the the device device is dueis due to the to ambipolarthe ambi- polartransport transport nature nature of graphene, of graphene, which which implies implies the coupled the coupled motion motion of holes of holes and electrons.and electrons.Therefore, Therefore, the charge the charge carrier carrier concentration concentration along thealong graphene the graphene channel channel gives more gives insight more insightinto the into Id-V theg curve Id-Vg discussedcurve discussed in Figure in 7Figure. 7. TheThe densitydensity ofof the the carriers carriers for for AlP-GFET AlP-GFET and and Pd-GFET Pd-GFET devices devices versus versus the gate the voltage gate voltageare shown are inshown Figure in8 Figurea,b, respectively. 8a and 8b, Theresp ﬁgureectively. shows The figure that the shows holes that are the majorityholes are carrier when the value of V is below the value of V of the device. At V , the concentration the majority carrier when theg value of Vg is below then value of Vn of then device. At Vn, the Sensors 2021, 21, x FOR PEER REVIEWof both carriers is equal, and as V increases beyond V , a channel inversion is observed10 of 17 concentration of both carriers is equal,g and as Vg increasesn beyond Vn, a channel inversion isand observed the electrons and the will electrons dominate will the do carrierminate concentrations. the carrier concentrations. The conductance of the channel is determined by the abundance of charge carriers, which is influenced by the applied gate voltage. The conductance, in return, determines the Id. Therefore, in Figure 7, the negative slope of Id in the NDR region corresponds to the decreasing. The trend of carrier hole concentration and the positive slope of Id in the PDR region correspond to the increasing trend of the carrier electron concentration.

Figure 8. CarrierCarrier concentration concentration in in the the graphene graphene channel channel versus versus VgV forg for (a) (AlP-GFET,a) AlP-GFET, (b) (Pd-GFET.b) Pd-GFET. This This confirms conﬁrms the theoc- currence of inversion of the device channel at Vn. occurrence of inversion of the device channel at Vn.

FigureThe conductance 9a illustrates of thethe channelId-Vg curve is determined of AlP-GFET by theat different abundance drain of charge voltages. carriers, It is observedwhich is inﬂuencedthat with an by theincrement applied of gate the voltage. drain voltage, The conductance, the I-V curve in return, shifts determinestoward the higher current values. The Vn of 0.93 V remains nearly constant for all Vd values. Id-Vg characteristics of Pd-GFET shown in Figure 9b follow the same trend as discussed for AlP-GFET. For this device, Vn is at the voltage of 1.09 V, which is higher than what is observed for AlP-GFET. Moreover, the lower current intensity of Pd-GFET is due to the lower carrier mobilities in this device compared to AlP-GFET, as summarized in Table 3.

Figure 9. I–V characteristics as a function of applied Vd for (a) Al-P doped GFET (b), Pd-decorated GFET. According to the graphs, Vn of the devices remains constant as Vd varies.

To give a more authenticated perception to the device study, Id-Vg curves were calculated at Vd of 10 mV for the devices with different channel dimensions (W × L). Figure 10a presents the obtained results for the AlP-GFET devices, and Figure 10b presents those for Pd-GFET devices. As the results show, the value of Vn for both devices remains constant and is independent of the device geometry. This is one of the positive characteristics of the device that shows the sensing properties of the device will not be affected by the structural device dimensions. However, the device Id is a function of channel length and width, ∝ .The effect of the channel dimension on the device Id follows the following equation [80].

Sensors 2021, 21, x FOR PEER REVIEW 10 of 17

Sensors 2021, 21, 580 10 of 16

the Id. Therefore, in Figure7, the negative slope of I d in the NDR region corresponds to the decreasing. Figure 8. Carrier concentration in the graphene channel versus Vg for (a) AlP-GFET, (b) Pd-GFET. This confirms the oc- The trend of carrier hole concentration and the positive slope of I in the PDR region currence of inversion of the device channel at Vn. d correspond to the increasing trend of the carrier electron concentration.

FigureFigure9 9aa illustrates illustrates the the I Idd-V-Vgg curve ofof AlP-GFETAlP-GFET atat differentdifferent draindrain voltages.voltages. ItIt isis observedobserved that withwith anan incrementincrement ofof thethe draindrain voltage,voltage, thethe I-VI-V curvecurve shiftsshifts towardtoward thethe higher current values. The V of 0.93 V remains nearly constant for all V values. I -V higher current values. The Vnn of 0.93 V remains nearly constant for all Vd d values. dId-Vgg characteristicscharacteristics of Pd-GFETPd-GFET shown in FigureFigure9 9bb followfollow thethe same same trend trend as as discussed discussed for for AlP-GFET. For this device, V is at the voltage of 1.09 V, which is higher than what is AlP-GFET. For this device, Vnn is at the voltage of 1.09 V, which is higher than what is observedobserved for AlP-GFET. Moreover,Moreover, thethe lowerlower currentcurrent intensityintensity ofof Pd-GFETPd-GFET isis duedue toto thethe lowerlower carriercarrier mobilitiesmobilities inin thisthis devicedevice comparedcompared toto AlP-GFET,AlP-GFET, as as summarized summarized in in Table Table3 .3.

Figure 9. I–V characteristics as a function of applied Vd for (a) Al-P doped GFET (b), Pd-decorated GFET. According to Figure 9. I-V characteristics as a function of applied Vd for (a) Al-P doped GFET (b), Pd-decorated GFET. According to the the graphs, Vn of the devices remains constant as Vd varies. graphs, Vn of the devices remains constant as Vd varies.

To give a more authenticated perception to the device study, Id-Vg curves were cal- To give a more authenticated perception to the device study, Id-Vg curves were culated at Vd of 10 mV for the devices with different channel dimensions (W × L). Figure calculated at Vd of 10 mV for the devices with different channel dimensions (W × L). Figure 1010aa presentspresents thethe obtainedobtained resultsresults forfor thethe AlP-GFETAlP-GFET devices,devices, andand FigureFigure 1010bb presentspresents thosethose forfor Pd-GFETPd-GFET devices. devices. As As the the results results show, show, the the value value of Vofn forVn for both both devices devices remains remains constant con- andstant is and independent is independent of the of device the device geometry. geometry. This This is one is one of the of the positive positive characteristics characteristics of theof the device device that that shows shows the the sensing sensing properties properties of of the the device device will will not not bebe affectedaffected byby thethe structuralstructural devicedevice dimensions.dimensions. However,However, thethe devicedevice IIdd isis aa functionfunction ofof channelchannel lengthlength andand W width,width, I ∝∝ . .TheThe effecteffect ofof thethe channelchannel dimension dimension on on the the device device I Idfollows follows thethe followingfollowing d L d equationequation [[80].80]. W Z Vd µp+µn Id = (qµpp + qµnn + q npud) (1) L Vs 2

where the parameters W and L are width and length of the channel, respectively; µn and µp are electron and hole mobility, respectively; and σ = qµnn + qµpp is the conductivity µp+µn of the channel. The term, q 2 npud denotes that the residual charge occurs due to the spatial homogeneity. Sensors 2021, 21, x FOR PEER REVIEW 11 of 17

V W d μp+μn Sensors 2021, 21, x FOR PEER REVIEW I = (qμ p+ qμ n+q n ) 11 of (1)17 d L p n 2 pud Vs where the parameters W and L are width and length of the channel, respectively; μ and μ are electron and hole mobility, respectively; and σ qμ nqμ p is the con- Vd μ +μ W p n ductivity of the channel. TheI = term, q(qμ p+n qμ denotesn+q thatn the) residual charge occurs(1) d p n pud L V 2 due to the spatial homogeneity. s where the parameters W and L are width and length of the channel, respectively; μand μ are electron and hole mobility, respectively; and σ qμnqμp is the con- Sensors 2021, 21, 580 11 of 16 ductivity of the channel. The term, q n denotes that the residual charge occurs due to the spatial homogeneity.

Figure 10. I–V characteristics as a function of channel dimension (W × L), for (a) AlP-GFET (b) Pd-GFET. The Id of the devices with equal ratios are overlapped.

We also investigated the characteristics of the device with respect to electrical FigureFigure 10.10. I-VI–V characteristicscharacteristicsproperties asas aa functionfunction of the ofof channel channelsilicon dimensionsubstratedimension (Wfor(W × both× L), forvariants ((aa)) AlP-GFETAlP-GFET of the device. ((bb)) Pd-GFET.Pd-GFET. The results TheThe IId ofofshow thethe that d devices with equal W ratiosthey are overlapped. have a significant effect on the value of Vn as we change the doping type and its devices with equal ratios are overlapped. L concentration of the substrate. The I-V characteristics in Figure 11a (AlP-GFET) and Fig- ure 11bWe (Pd-GFET) alsoalso investigated investigated illustrate the the characteristicsthat characteristics as the conc ofentration theof devicethe ofdevice withdopants respectwith increases, respect to electrical tothe electrical position proper- tiespropertiesof V ofn moves the siliconof toward the substratesilicon higher substrate for voltages both for variants for both p-type ofva theriants substrates, device. of the The device.while results it The moves show results thattoward show they lower have that atheyvoltages signiﬁcant have for a effectthesignificant n-type on the substrate effect value on of case.Vthen as value we change of Vn theas we doping change type the and doping its concentration type and its of theconcentration substrate.Figure 12a Theof showsthe I-V substrate. characteristics the measured The I-V in FigurecharacteristicsId-Vg for 11 athe (AlP-GFET) AlP-GFET in Figure and 11adevice, Figure (AlP-GFET) and 11b Figure (Pd-GFET) and Fig-12b illustrateureshows 11b it (Pd-GFET) for that the as Pd-GFET the illustrate concentration device that for as of twothe dopants concdifferentration increases,ent oxide of thethicknesses, dopants position increases, of200 V nnmmoves andthe position400 toward nm. higherofAccording Vn moves voltages to toward the for graphs, p-type higher substrates,the voltages variation for while ofp-type itth movese oxidesubstrates, toward layer whilethickness lower it voltages moves does fortowardnot theaffect n-type lower the substratevoltagessensing properties for case. the n-type of the substrate devices case.as the value of Vn remains the same for both cases. Figure 12a shows the measured Id-Vg for the AlP-GFET device, and Figure 12b shows it for the Pd-GFET device for two different oxide thicknesses, 200 nm and 400 nm. According to the graphs, the variation of the oxide layer thickness does not affect the sensing properties of the devices as the value of Vn remains the same for both cases.

Figure 11. I–VI-V characteristicscharacteristics asas aa functionfunction ofof dopingdoping typetype andand concentrationconcentration forfor ((aa)) AlP-GFET,AlP-GFET, ((bb)) Pd-Pd- GFET.GFET.

Figure 12a shows the measured Id-Vg for the AlP-GFET device, and Figure 12b shows it for the Pd-GFET device for two different oxide thicknesses, 200 nm and 400 nm. According Figure 11. I–V characteristicsto the graphs, as a function the variation of doping of type the oxide and concentration layer thickness for does(a) AlP-GFET, not affect (b the) Pd- sensing GFET. properties of the devices as the value of Vn remains the same for both cases.

3.2.2. Detection of Methanethiol Biomarker

To check the sensitivity of the device against biomarkers, the device DC characteristics are typically evaluated in the presence of a biomarker and compared with a reference test in the absence of biomarkers. Sensors 2021, 21, x FOR PEER REVIEW 12 of 17

Sensors 2021, 21, 580 12 of 16 Sensors 2021, 21, x FOR PEER REVIEW 12 of 17

Figure 12. I–V characteristics as a function of dielectric layer thickness (a) AlP-GFET (b) Pd-GFET.

3.2.2. Detection of Methanethiol Biomarker To check the sensitivity of the device against biomarkers, the device DC characteristics are typically evaluated in the presence of a biomarker and compared with a reference FigureFigure 12.12.I-V I–V characteristics characteristics as as a a function function of of dielectric dielectric layer layer thickness thickness ( a()a) AlP-GFET AlP-GFET ( b(b)) Pd-GFET. Pd-GFET. test in the absence of biomarkers. 2 3.2.2.ForFor Detection this this study, study, of Methanethiol a a device device with with Biomarker channel channel dimensions dimensions of of 1 ×1 ×2 2µ mμm2 (W (W× ×L) L)and and a a p-type p-type substrate with doping concentration 101818 cm−-33 is considered. Vg is swept from 0 to 2 V, substrateTo check with the doping sensitivity concentration of the device 10 cm againstis considered.biomarkers, Vtheg is device swept DC from characteris- 0 to 2 V, while a constant Vd of 10 mV is applied on the drain. One biomolecule per nm2 was2 con- whiletics are a typically constant evaluated Vd of 10 mV in the is appliedpresence on of thea biomarker drain. One and biomolecule compared with per a nm referencewas sidered for the adsorption concentration of the biomarker on the graphene layer. consideredtest in the absence for the adsorption of biomarkers. concentration of the biomarker on the graphene layer. Figure 13a illustrates the Id-Vg characteristics of the AlP-GFET device, and Figure FigureFor this 13 study,a illustrates a device the Iwithd-Vg channelcharacteristics dimensions of the of AlP-GFET 1 × 2 μm device,2 (W × L) and and Figure a p-type 13b illustrates13b illustrates it for it the for Pd-GFET the Pd-GFET device, device, in the18 in presence th-3e presence of the of methanethiol the methanethiol as compared as compared to a substrate with doping concentration 10 cm is considered. Vg is swept from 0 to 2 V, referenceto a reference test in test absence in absence of the of biomarker. the biomarker. while a constant Vd of 10 mV is applied on the drain. One biomolecule per nm2 was considered for the adsorption concentration of the biomarker on the graphene layer. Figure 13a illustrates the Id-Vg characteristics of the AlP-GFET device, and Figure 13b illustrates it for the Pd-GFET device, in the presence of the methanethiol as compared to a reference test in absence of the biomarker.

FigureFigure 13.13.I-V I–V characteristics characteristics before before and and after after adsorption adsorption of of methanethiol methanethiol for for ( a()a) AlP-GFET, AlP-GFET, (b ()b Pd-GFET.) Pd-GFET.

Id-Vg curves obtained for AlP-GFET show a clear shift in Vn from 0.93 V to 0.63 V after Id-Vg curves obtained for AlP-GFET show a clear shift in Vn from 0.93 V to 0.63 V the adsorption of methanethiol by the channel surface, while for the Pd-GFET, it changed after the adsorption of methanethiol by the channel surface, while for the Pd-GFET, it from 1.09 V to 0.42 V. The shift in Vn is attributed to the change of µ, bandgap, Nc or Nv, changed from 1.09 V to 0.42 V. The shift in Vn is attributed to the change of μ, bandgap, Nc Figure 13. I–V characteristicsand Φ of before the functionalized and after adsorption graphene of methanethiol once it is exposedfor (a) AlP-GFET, to themethanethiol (b) Pd-GFET. molecule. or Nv, and Φ of the functionalized graphene once it is exposed to the methanethiol mol- As summarized in Table3, these physical quantities show variation after adsorption of ecule. As summarized in Table 3, these physical quantities show variation after adsorp- methanethiol,Id-Vg curves which obtained affects for the AlP-GFET Vn value. show The observeda clear shift shift in inVn V fromn for the0.93 Pd-GFET V to 0.63is V tion of methanethiol, which affects the Vn value. The observed shift in Vn for the Pd-GFET largerafter the than adsorption that of the of AlP-GFET, methanethiol which by afﬁrms the channel the higher surface, sensitivity while tofor the the biomarker Pd-GFET, for it thischanged device. from 1.09 V to 0.42 V. The shift in Vn is attributed to the change of μ, bandgap, Nc or NItv, and is observed Φ of the thatfunctionalized the overall graphene current intensity once it is for exposed AlP-GFET to the decreases methanethiol after mol- the adsorptionecule. As summarized of the biomarker. in Table However, 3, these for physical the case quantities of Pd-GFET, show the intensityvariation of after the currentadsorp-

slightlytion of methanethiol, increases after which biomarker affects adsorption. the Vn value. This The behaviour observed of shift the devicein Vn for corresponds the Pd-GFET to

Sensors 2021, 21, 580 13 of 16

the effect of adsorption on the carrier mobility of the graphene channel (as summarized in Table3). The increase in mobility of the carriers will be correlated with an increase in I d of the device and vice versa. Based on the results discussed in Section 3.2.1, the Vn of the device is only a function of semiconductive properties of the graphene channel and varies by functionalization of the graphene and its interaction with the molecules. The geometry of the device and the biasing parameters does not alter the V , and therefore the sensitivity of the sensors n ∼ ∆Vn towards exposure to methanethiol could be simply deﬁned as S = Vn . The calculated sensitivity of the AlP-GFET towards methanethiol when the Vn changes from 0.93 V to 0.63 V is 32.25%; similarly, Vn in the Pd-GFET changes from 1.09 V to 0.42 V, which shows 60.55% sensitivity towards this biomarker. There are other reports in the literature regarding applying methanethiol as a biomarker to develop biosensors [81–83]. Compared to those, the present work proposes a design to develop a device with higher sensitivity and simpler structure.

4. Conclusions In this work, we demonstrated the possibility of using a GFET biosensor for the detection of methanethiol biomarker, which is used to identify diseases caused by microorganisms such as Helicobacter pylori bacteria (H. pylori) and Porphyromonas gingivalis (P. Gingivalis) phylum Bacteroidetes. Surface chemistry of the graphene layers is manipulated using two methods: (a) doping the graphene crystals and (b) decorating the surface of the graphene with TMs before using it as the channel of the GFET. The device was designed and characterized using COMSOL Multiphysics. The NDR characteristic of the graphene, which is due to its ambipolar behaviour, was observed using three-terminal measurements. The deep that appeared in the I-V characteristics of the device is used to study the sensitivity of the sensors. The results show that the device characteristic is only sensitive to the doping level of the silicon substrate; otherwise, it is independent of other physical parameters of the device. However, our investigations show that electrical properties of the functionalized graphene layers particularly in the absence and presence of the biomarkers are largely affected the characteristics of the sensor. The device is more sensitive to the adsorbed biomarker in the case of Pd-GFET compared to the devices developed using Al-P doping.

Author Contributions: Conceptualization, P.S., P.A.S. and M.K.; methodology, P.A.S.; software, P.S.; validation, P.S., P.A.S. and M.K.; formal analysis, P.S., P.A.S. and M.K.; investigation, P.S.; resources, M.K.; data curation, P.A.S. and M.K.; writing—original draft preparation, P.S.; writing—review and editing, P.A.S. and M.K.; visualization, P.S.; supervision, M.K.; project administration, P.A.S. and M.K.; funding acquisition, M.K. All authors have read and agreed to the published version of the manuscript. Funding: This work was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Gina Cody School of Engineering and Computer Science at Concordia University. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Schwierz, F. Graphene transistors. Nat. Nanotechnol. 2010, 5, 487–496. [CrossRef][PubMed] 2. Grigorenko, A.N.; Polini, M.; Novoselov, K.S. Graphene plasmonics. Nat. Photonics 2012, 6, 749–758. [CrossRef] 3. Gui, G.; Li, J.; Zhong, J. Band structure engineering of graphene by strain: First-principles calculations. Phys. Rev. B Condens. Matter Mater. Phys. 2008, 78, 1–6. [CrossRef] Sensors 2021, 21, 580 14 of 16

4. Barone, V.; Hod, O.; Scuseria, G.E. Electronic Structure and Stability of Semiconducting Graphene Nanoribbons. Nano Lett. 2006, 6, 2748–2754. [CrossRef][PubMed] 5. Lu, G.; Yu, K.; Wen, Z.; Chen, J. Semiconducting graphene: Converting graphene from semimetal to semiconductor. Nanoscale 2013, 5, 1353. [CrossRef] 6. Prestigiacomo, J.C.; Nath, A.; Osofsky, M.S.; Hernández, S.C.; Wheeler, V.D.; Walton, S.G.; Gaskill, D.K. Determining the nature of the gap in semiconducting graphene. Sci. Rep. 2017, 7, 1–5. [CrossRef] 7. Fang, T.; Konar, A.; Xing, H.; Jena, D. Mobility in semiconducting graphene nanoribbons: Phonon, impurity, and edge roughness scattering. Phys. Rev. B Condens. Matter Mater. Phys. 2008, 78, 1–8. [CrossRef] 8. Wang, Z.F.; Jin, S.; Liu, F. Spatially separated spin carriers in spin-semiconducting graphene nanoribbons. Phys. Rev. Lett. 2013, 111, 1–5. [CrossRef] 9. Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 2008, 319, 1229–1232. [CrossRef] 10. Jacobberger, R.M.; Arnold, M.S. High-Performance Charge Transport in Semiconducting Armchair Graphene Nanoribbons Grown Directly on Germanium. ACS Nano 2017, 11, 8924–8929. [CrossRef] 11. Cai, J.; Ruffieux, P.; Jaafar, R.; Bieri, M.; Braun, T.; Blankenburg, S.; Muoth, M.; Seitsonen, A.P.; Saleh, M.; Feng, X.; et al. Atomically precise bottom-up fabrication of graphene nanoribbons. Nature 2010, 466, 470–473. [CrossRef][PubMed] 12. Singh, S.; Kaur, I. Bandgap engineering in armchair graphene nanoribbon of zigzag-armchair-zigzag based Nano-FET: A DFT investigation. Phys. E Low-Dimens. Syst. Nanostruct. 2020, 118, 113960. [CrossRef] 13. AlZahrani, A.Z.; Srivastava, G.P. Structural and electronic properties of H-passivated graphene. Appl. Surf. Sci. 2010, 256, 5783–5788. [CrossRef] 14. Verberck, B.; Partoens, B.; Peeters, F.M.; Trauzettel, B. Strain-induced band gaps in bilayer graphene. Phys. Rev. B Condens. Matter Mater. Phys. 2012, 85, 1–10. [CrossRef] 15. Sahalianov, I.Y.; Radchenko, T.M.; Tatarenko, V.A.; Cuniberti, G.; Prylutskyy, Y.I. Straintronics in graphene: Extra large electronic band gap induced by tensile and shear strains. J. Appl. Phys. 2019, 126.[CrossRef] 16. Huang, B. Electronic properties of boron and nitrogen doped graphene nanoribbons and its application for graphene electronics. Phys. Lett. Sect. A Gen. At. Solid State Phys. 2011, 375, 845–848. [CrossRef] 17. Nath, P.; Sanyal, D.; Jana, D. Semi-metallic to semiconducting transition in graphene nanosheet with site specific co-doping of boron and nitrogen. Phys. E Low-Dimens. Syst. Nanostruct. 2014, 56, 64–68. [CrossRef] 18. Avetisyan, A.A.; Partoens, B.; Peeters, F.M. Electric field tuning of the band gap in graphene multilayers. Phys. Rev. B Condens. Matter Mater. Phys. 2009, 79, 1–7. [CrossRef] 19. Sławińska,J.; Zasada, I.; Klusek, Z. Energy gap tuning in graphene on hexagonal boron nitride bilayer system. Phys. Rev. B Condens. Matter Mater. Phys. 2010, 81, 1–9. [CrossRef] 20. Kanai, Y.; Ohmuro-Matsuyama, Y.; Tanioku, M.; Ushiba, S.; Ono, T.; Inoue, K.; Kitaguchi, T.; Kimura, M.; Ueda, H.; Matsumoto, K. Graphene Field Effect Transistor-Based Immunosensor for Ultrasensitive Noncompetitive Detection of Small Antigens. ACS Sens. 2020, 5, 24–28. [CrossRef] 21. Salehi-Khojin, A.; Estrada, D.; Lin, K.Y.; Bae, M.-H.; Xiong, F.; Pop, E.; Masel, R.I. Graphene Sensors: Polycrystalline Graphene Ribbons as Chemiresistors. Adv. Mater. 2012, 24, 52. [CrossRef] 22. Soltani, A.; Kuschewski, F.; Bonmann, M.; Generalov, A.; Vorobiev, A.; Ludwig, F.; Wiecha, M.M.; Cibiraitˇ e,˙ D.; Walla, F.; Winnerl, S.; et al. Direct nanoscopic observation of plasma waves in the channel of a graphene field-effect transistor. Light Sci. Appl. 2020, 9.[CrossRef][PubMed] 23. Salehirozveh, M.; Dehghani, P.; Zimmermann, M.; Roy, V.A.L.; Heidari, H. Graphene Field Effect Transistor Biosensors based on Aptamer for Amyloid-β Detection. IEEE Sens. J. 2020, 20, 12488–12494. [CrossRef] 24. Fakih, I.; Durnan, O.; Mahvash, F.; Napal, I.; Centeno, A.; Zurutuza, A.; Yargeau, V.; Szkopek, T. Selective ion sensing with high resolution large area graphene field effect transistor arrays. Nat. Commun. 2020, 11, 1–12. [CrossRef] 25. De Nicola, F.; Puthiya Purayil, N.S.; Miseikis,ˆ V.; Spirito, D.; Tomadin, A.; Coletti, C.; Polini, M.; Krahne, R.; Pellegrini, V. Graphene Plasmonic Fractal Metamaterials for Broadband Photodetectors. Sci. Rep. 2020, 10, 1–10. [CrossRef] 26. Xia, F.; Mueller, T.; Lin, Y.M.; Valdes-Garcia, A.; Avouris, P. Ultrafast graphene photodetector. Nat. Nanotechnol. 2009, 4, 839–843. [CrossRef] 27. Guo, J.; Li, J.; Liu, C.; Yin, Y.; Wang, W.; Ni, Z.; Fu, Z.; Yu, H.; Xu, Y.; Shi, Y.; et al. High-performance silicon−graphene hybrid plasmonic waveguide photodetectors beyond 1.55 µm. Light Sci. Appl. 2020, 9.[CrossRef] 28. Mišeikis, V.; Marconi, S.; Giambra, M.A.; Montanaro, A.; Martini, L.; Fabbri, F.; Pezzini, S.; Piccinini, G.; Forti, S.; Terrés, B.; et al. Ultrafast, Zero-Bias, Graphene Photodetectors with Polymeric Gate Dielectric on Passive Photonic Waveguides. ACS Nano 2020, 14, 11190–11204. [CrossRef] 29. Zhuo, L.; Fan, P.; Zhang, S.; Liu, X.; Guo, X.; Zhang, Y.; Zhan, Y.; Li, D.; Che, Z.; Zhu, W.; et al. A broadband all-fiber integrated graphene photodetector with CNT-enhanced responsivity. Nanoscale 2020, 12, 14188–14193. [CrossRef] 30. Gosciniak, J.; Rasras, M.; Khurgin, J.B. Ultrafast Plasmonic Graphene Photodetector Based on the Channel Photothermoelectric Effect. ACS Photonics 2020, 7, 488–498. [CrossRef] 31. Konstantatos, G.; Badioli, M.; Gaudreau, L.; Osmond, J.; Bernechea, M.; De Arquer, F.P.G.; Gatti, F.; Koppens, F.H.L. Hybrid graphenegquantumˆ dot phototransistors with ultrahigh gain. Nat. Nanotechnol. 2012, 7, 363–368. [CrossRef][PubMed] Sensors 2021, 21, 580 15 of 16

32. Pan, R.; Han, J.; Zhang, X.; Han, Q.; Zhou, H.; Liu, X.; Gou, J.; Jiang, Y.; Wang, J. Excellent performance in vertical graphene-C60- graphene heterojunction phototransistors with a tunable bi-directionality. Carbon N. Y. 2020, 162, 375–381. [CrossRef] 33. Han, J.; He, M.; Yang, M.; Han, Q.; Wang, F.; Zhong, F.; Xu, M.; Li, Q.; Zhu, H.; Shan, C.; et al. Light-modulated vertical heterojunction phototransistors with distinct logical photocurrents. Light Sci. Appl. 2020, 9.[CrossRef][PubMed] 34. Sun, Z.; Hasan, T.; Torrisi, F.; Popa, D.; Privitera, G.; Wang, F.; Bonaccorso, F.; Basko, D.M.; Ferrari, A.C. Graphene mode-locked ultrafast laser. ACS Nano 2010, 4, 803–810. [CrossRef] 35. Green, N.S.; Norton, M.L. Interactions of DNA with graphene and sensing applications of graphene field-effect transistor devices: A review. Anal. Chim. Acta 2015, 853, 127–142. [CrossRef] 36. Schedin, F.; Geim, A.K.; Morozov, S.V.; Hill, E.W.; Blake, P.; Katsnelson, M.I.; Novoselov, K.S. Detection of individual gas molecules adsorbed on graphene. Nat. Mater. 2007, 6, 652–655. [CrossRef] 37. Panth, M.; Cook, B.; Zhang, Y.; Ewing, D.; Tramble, A.; Wilson, A.; Wu, J. High-Performance Strain Sensors Based on Vertically Aligned Piezoelectric Zinc Oxide Nanowire Array/Graphene Nanohybrids. ACS Appl. Nano Mater. 2020, 3, 6711–6718. [CrossRef] 38. Chen, Z.; Wang, Z.; Li, X.; Lin, Y.; Luo, N.; Long, M.; Zhao, N.; Xu, J. Bin Flexible Piezoelectric-Induced Pressure Sensors for Static Measurements Based on Nanowires/Graphene Heterostructures. ACS Nano 2017, 11, 4507–4513. [CrossRef] 39. Lian, Y.; He, F.; Wang, H.; Tong, F. A new aptamer/graphene interdigitated gold electrode piezoelectric sensor for rapid and specific detection of Staphylococcus aureus. Biosens. Bioelectron. 2015, 65, 314–319. [CrossRef] 40. Zhu, S.E.; Krishna Ghatkesar, M.; Zhang, C.; Janssen, G.C.A.M. Graphene based piezoresistive pressure sensor. Appl. Phys. Lett. 2013, 102, 111–114. [CrossRef] 41. Xing, F.; Liu, Z.B.; Deng, Z.C.; Kong, X.T.; Yan, X.Q.; Chen, X.D.; Ye, Q.; Zhang, C.P.; Chen, Y.S.; Tian, J.G. Sensitive real-time monitoring of refractive indexes using a novel graphene-based optical sensor. Sci. Rep. 2012, 2, 1–7. [CrossRef][PubMed] 42. Deng, X.; Tang, H.; Jiang, J. Recent progress in graphene-material-based optical sensors. Anal. Bioanal. Chem. 2014, 406, 6903–6916. [CrossRef][PubMed] 43. Xing, F.; Meng, G.X.; Zhang, Q.; Pan, L.T.; Wang, P.; Liu, Z.B.; Jiang, W.S.; Chen, Y.; Tian, J.G. Ultrasensitive flow sensing of a single cell using graphene-based optical sensors. Nano Lett. 2014, 14, 3563–3569. [CrossRef][PubMed] 44. Liang, X.Y.; Ding, N.; Ng, S.P.; Wu, C.M.L. Adsorption of gas molecules on Ga-doped graphene and effect of applied electric field: A DFT study. Appl. Surf. Sci. 2017, 411, 11–17. [CrossRef] 45. Mehdi Pour, M.; Lashkov, A.; Radocea, A.; Liu, X.; Sun, T.; Lipatov, A.; Korlacki, R.A.; Shekhirev, M.; Aluru, N.R.; Lyding, J.W.; et al. Laterally extended atomically precise graphene nanoribbons with improved electrical conductivity for efficient gas sensing. Nat. Commun. 2017, 8, 1–9. [CrossRef] 46. Yang, S.; Lei, G.; Xu, H.; Xu, B.; Li, H.; Lan, Z.; Wang, Z.; Gu, H. A DFT study of CO adsorption on the pristine, defective, In-doped and Sb-doped graphene and the effect of applied electric field. Appl. Surf. Sci. 2019, 480, 205–211. [CrossRef] 47. He, Q.; Wu, S.; Yin, Z.; Zhang, H. Graphene-based electronic sensors. Chem. Sci. 2012, 3, 1764–1772. [CrossRef] 48. Wang, Z.; Yi, K.; Lin, Q.; Yang, L.; Chen, X.; Chen, H.; Liu, Y.; Wei, D. Free radical sensors based on inner-cutting graphene field-effect transistors. Nat. Commun. 2019, 10.[CrossRef] 49. Ahn, S.R.; An, J.H.; Jang, I.H.; Na, W.; Yang, H.; Cho, K.H.; Lee, S.H.; Song, H.S.; Jang, J.; Park, T.H. High-performance bioelectronic tongue using ligand binding domain T1R1 VFT for umami taste detection. Biosens. Bioelectron. 2018, 117, 628–636. [CrossRef] 50. Thakur, B.; Zhou, G.; Chang, J.; Pu, H.; Jin, B.; Sui, X.; Yuan, X.; Yang, C.H.; Magruder, M.; Chen, J. Rapid detection of single E. coli bacteria using a graphene-based field-effect transistor device. Biosens. Bioelectron. 2018, 110, 16–22. [CrossRef] 51. Chen, B.; Liu, H.; Li, X.; Lu, C.; Ding, Y.; Lu, B. Fabrication of a graphene field effect transistor array on microchannels for ethanol sensing. Appl. Surf. Sci. 2012, 258, 1971–1975. [CrossRef] 52. Kwak, Y.H.; Choi, D.S.; Kim, Y.N.; Kim, H.; Yoon, D.H.; Ahn, S.S.; Yang, J.W.; Yang, W.S.; Seo, S. Flexible glucose sensor using CVD-grown graphene-based field effect transistor. Biosens. Bioelectron. 2012, 37, 82–87. [CrossRef] 53. Zhang, Z.; Zou, X.; Xu, L.; Liao, L.; Liu, W.; Ho, J.; Xiao, X.; Jiang, C.; Li, J. Hydrogen gas sensor based on metal oxide nanoparticles decorated graphene transistor. Nanoscale 2015, 7, 10078–10084. [CrossRef][PubMed] 54. Kwong Hong Tsang, D.; Lieberthal, T.J.; Watts, C.; Dunlop, I.E.; Ramadan, S.; del Rio Hernandez, A.E.; Klein, N. Chemically Functionalised Graphene FET Biosensor for the Label-free Sensing of Exosomes. Sci. Rep. 2019, 9, 2–11. [CrossRef] 55. Kim, C.-H.; Yoo, S.-W.; Nam, D.-W.; Seo, S.; Lee, J.-H. Effect of Temperature and Humidity on NO2 and NH3 Gas Sensitivity of Bottom-Gate Graphene FETs Prepared by ICP-CVD. IEEE Electron Device Lett. 2012, 33, 1084–1086. [CrossRef] 56. Kai Zhang, L.Z. Volatile Organic Compounds as Novel Markers for the Detection of Bacterial Infections. Clin. Microbiol. Open Access 2014, 3.[CrossRef] 57. Elmassry, M.M.; Piechulla, B. Volatilomes of Bacterial Infections in Humans. Front. Neurosci. 2020, 14, 1–11. [CrossRef][PubMed] 58. Roslund, K.; Lehto, M.; Pussinen, P.; Groop, P.-H.; Halonen, L.; Metsälä, M. On-line profiling of volatile compounds produced in vitro by pathogenic oral bacteria. J. Breath Res. 2019, 14, 016010. [CrossRef] 59. Kim, J.H.; Mirzaei, A.; Kim, H.W.; Kim, S.S. Improving the hydrogen sensing properties of SnO2 nanowire-based conductometric sensors by Pd-decoration. Sens. Actuators B Chem. 2019, 285, 358–367. [CrossRef] 60. Sharma, A.; Arya, S. Economical and Efficient Electrochemical Sensing of Folic Acid using a Platinum Electrode Modified with Hydrothermally Synthesized Pd and Ag Co-Doped SnO2 Nanoparticles. J. Electrochem. Soc. 2019, 166, B1107–B1115. [CrossRef] Sensors 2021, 21, 580 16 of 16

61. Zhang, D.; Li, Q.; Li, P.; Pang, M.; Luo, Y. Fabrication of Pd-Decorated MoSe2 nanoflowers and density functional theory simulation toward ammonia sensing. IEEE Electron. Device Lett. 2019, 40, 616–619. [CrossRef] 62. Liu, B.; Xu, Y.; Li, K.; Wang, H.; Gao, L.; Luo, Y.; Duan, G. Pd-Catalyzed Reaction-Producing Intermediate S on a Pd/In2O3 Surface: A Key to Achieve the Enhanced CS2 -Sensing Performances. ACS Appl. Mater. Interfaces 2019, 11, 16838–16846. [CrossRef] [PubMed] 63. Zhang, Y.H.; Li, Y.L.; Gong, F.L.; Xie, K.F.; Zhang, H.L.; Fang, S.M. Double-platelet Pd@ZnO microcrystals for NO2 chemical sensors: Their facile synthesis and DFT investigation. Phys. Chem. Chem. Phys. 2019, 21, 22039–22047. [CrossRef][PubMed] 64. Zhang, Y.H.; Wang, C.N.; Gong, F.L.; Wang, P.; Guharoy, U.; Yang, C.; Zhang, H.L.; Fang, S.M.; Liu, J. Ultrathin agaric-like ZnO with Pd dopant for aniline sensor and DFT investigation. J. Hazard. Mater. 2020, 388, 122069. [CrossRef][PubMed] 65. Montemore, M.M.; Medlin, J.W. A unified picture of adsorption on transition metals through different atoms. J. Am. Chem. Soc. 2014, 136, 9272–9275. [CrossRef][PubMed] 66. Khodadadi, Z. Evaluation of H2S sensing characteristics of metals–doped graphene and metals-decorated graphene: Insights from DFT study. Phys. E Low-Dimens. Syst. Nanostruct. 2018, 99, 261–268. [CrossRef] 67. Bo, Z.; Guo, X.; Wei, X.; Yang, H.; Yan, J.; Cen, K. Density functional theory calculations of NO2 and H2S adsorption on the group 10 transition metal (Ni, Pd and Pt) decorated graphene. Phys. E Low-Dimens. Syst. Nanostruct. 2019, 109, 156–163. [CrossRef] 68. Wong, J.; Yadav, S.; Tam, J.; Veer Singh, C. A van der Waals density functional theory comparison of metal decorated graphene systems for hydrogen adsorption. J. Appl. Phys. 2014, 115.[CrossRef] 69. Zhang, X.; Yu, L.; Wu, X.; Hu, W. Experimental Sensing and Density Functional Theory Study of H2S and SOF2 Adsorption on Au-Modified Graphene. Adv. Sci. 2015, 2, 1–10. [CrossRef] 70. Poh, H.L.; Šimek, P.; Sofer, Z.; Pumera, M. Halogenation of graphene with chlorine, bromine, or iodine by exfoliation in a halogen atmosphere. Chem. A Eur. J. 2013, 19, 2655–2662. [CrossRef] 71. Huang, C.; Li, C.; Shi, G. Graphene based catalysts. Energy Environ. Sci. 2012, 5, 8848–8868. [CrossRef] 72. Cheng, S.H.; Zou, K.; Okino, F.; Gutierrez, H.R.; Gupta, A.; Shen, N.; Eklund, P.C.; Sofo, J.O.; Zhu, J. Reversible fluorination of graphene: Evidence of a two-dimensional wide bandgap semiconductor. Phys. Rev. B Condens. Matter Mater. Phys. 2010, 81, 1–5. [CrossRef] 73. López-Corral, I.; Germán, E.; Juan, A.; Volpe, M.A.; Brizuela, G.P. DFT Study of Hydrogen Adsorption on Palladium Decorated Graphene. J. Phys. Chem. C 2011, 115, 4315–4323. [CrossRef] 74. Walia, G.K.; Randhawa, D.K.K. Adsorption and dissociation of sulfur-based toxic gas molecules on silicene nanoribbons: A quest for high-performance gas sensors and catalysts. J. Mol. Model. 2018, 24.[CrossRef][PubMed] 75. Valizadeh, P. Electronic Materials and Charge Transport. In Field Effect Transistors, A Comprehensive Overview; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2016; pp. 1–118. 76. Patterson, J.D.; Bailey, B.C. Semiconductors. In Solid State Physics; Springer: Berlin, Germany, 2018; pp. 293–351. 77. Green, M.A. Intrinsic concentration, effective densities of states, and effective mass in silicon. J. Appl. Phys. 1990, 67, 2944–2954. [CrossRef] 78. Gunst, T.; Markussen, T.; Stokbro, K.; Brandbyge, M. First-principles method for electron-phonon coupling and electron mobility: Applications to two-dimensional materials. Phys. Rev. B 2016, 93, 035414. [CrossRef] 79. Kaasbjerg, K.; Thygesen, K.S.; Jacobsen, K.W. Unraveling the acoustic electron-phonon interaction in graphene. Phys. Rev. B Condens. Matter Mater. Phys. 2012, 85, 165440. [CrossRef] 80. Haddad, P.A.; Flandre, D.; Raskin, J.P. Intrinsic rectification in common-gated graphene field-effect transistors. Nano Energy 2018, 43, 37–46. [CrossRef] 81. Hulko, M.; Hospach, I.; Krasteva, N.; Nelles, G. Cytochrome C biosensor-A model for gas sensing. Sensors 2011, 11, 5968–5980. [CrossRef] 82. Kubo, I.; Karube, I.; Takeuchi, B.; Furusawa, M.; Arikawa, Y.; Kanagawa, T. A biosensor based on Thiobacillus thioparus for measuring thiosulfate and methanethiol. Can. J. Microbiol. 1995, 41, 366–371. [CrossRef] 83. Hidalgo, F.; Rubio-Ponce, A.; Noguez, C. Tuning Adsorption of Methylamine and Methanethiol on Twisted-Bilayer Graphene. J. Phys. Chem. C 2019, 123, 15273–15283. [CrossRef]