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- Copyright
- Copyright © 2020 The Author(s). Published by IOP Publishing Ltd
- eISSN
- 2053-1583
- DOI
- 10.1088/2053-1583/abc187
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Abstract
JNE Two-dimensional(2D)materialsholdgreatpromiseforfuturenanoelectronicsasconventional semiconductortechnologiesfaceseriouslimitationsinperformanceandpowerdissipationfor 10.1088/1741-2552/ab57c0 futuretechnologynodes.Theatomicthinnessof2Dmaterialsenableshighlyscaledfield-effect transistors(FETs)withreducedshort-channeleffectswhilemaintaininghighcarriermobility, essentialforhigh-performance,low-voltagedeviceoperations.Therichnessoftheirelectronic bandstructureopensupthepossibilityofusingthesematerialsinnovelelectronicand optoelectronicdevices.Theseapplicationsarestronglydependentontheelectricalpropertiesof2D materials-basedFETs.Thus,accuratecharacterizationofimportantpropertiessuchas conductivity,carrierdensity,mobility,contactresistance,interfacetrapdensity,etcisvitalfor progressinthefield.However,electricalcharacterizationmethodsfor2Ddevices,particularly FET-relatedmeasurementtechniques,mustberevisitedsinceconventionalcharacterization methodsforbulksemiconductormaterialsoftenfailinthelimitofultrathin2Dmaterials.Inthis paper,wereviewthecommonelectricalcharacterizationtechniquesfor2DFETsandtherelated issuesarisingfromadaptingthetechniquesforuseon2Dmaterials. 1.Introduction inspired experimental research in the fields of con- densedmatterphysics,semiconductornanoelectron- Two-dimensional (2D) van der Waals materials or ics,photonics,andenergystorage[6–8]. layered materials are characterized by materials with Inadditiontographene,other2Dmaterialshave an anisotropic electronic and chemical structure of beeninvestigatedwithgreatintensityforfutureelec- strong covalent bonds along the in-plane direction tronic and optoelectronic applications [9–14], as and weak van der Waals bonds along the out-of- these materials offer a range of bandgaps with high plane direction. Among such materials, graphene carrier mobility and efficient electrostatic control. has been studied most extensively, due to its high These properties, combined with mechanical flex- mobility, widely tunable carrier concentration, and ibility [15–18] and tunability of electronic prop- the occurrence of phenomena such as the quantum erties, make 2D materials especially promising as Hall effect in atomically thin samples prepared by a a channel material in high-performance 2D field- simple Scotch tape exfoliation method [1–3]. Sub- effect transistors (FETs), which could be oper- sequently, the development of large-scale chem- ated in emerging future mobile and IoT environ- ical vapor deposition (CVD) graphene synthesis ment [19–23]. In light of this, accurate character- has enabled the fabrication of wafer-scale electronic ization of 2D FETs and extraction of important 31 and photonic devices [4, 5]. Meanwhile, theoret- deviceparameters,suchasresistivity,carrierdensity, ical studies on carrier transport in graphene have mobility, contact resistance, charge trap densities, January ©© 22020 020 I The OPP Author(s). ublishingL Published td by IOP Publishing Ltd 2020 2DMater.8(2021)012002 SBMittaetal dielectric permittivity, and anisotropy in carrier 2.2Ddevices transport, are essential to explore 2D materials and 2.1.2DFETs to correlate them with the performance of 2D FETs The basic structure of a FET comprises of a metal- [24–27]. licgate,asemiconductorchannelbetweenthesource A mainstay of 2D materials-based semicon- and drain electrodes, and an insulating gate oxide ductor device research focuses on developing FETs (the barrier between the channel and gate). The cur- with high ON/OFF ratios, high conductivity, high rent flow in the semiconductor channel (drain cur- carrier mobility, and low power consumption rent, I ) is established by the source–drain voltage [24,25,28–30]. It is critically important to under- (V ) and is modulated by the applied gate voltage DS stand the electrical properties of such devices, since (V ) by changing the conductivity of the channel GS the use of conventional electrical characterization region. Figure2(a) shows schematic and circuit dia- methodscanproduceunreliableresultswhenapplied grams of a typical back-gated 2D FET with metal- to ultra-thin 2D layered materials. For example, lic source and drain contacts and hexagonal boron room-temperature electrical conductivity in a bulk nitride (hBN) encapsulation [36]. Unlike conven- semiconductor is directly related to charge carrier tional bulk semiconductor FETs, the presence of density. However, conventional implanted substitu- metallicelectrodesatthesource–drainjunctionsres- tional doping cannot be performed on 2D materials ults in Schottky contacts due to a lack of efficient duetotheiratomicthinness.Instead,differentmeth- doping techniques. Moreover, back-gated 2D FETs ods, such as charge transfer doping, are predomin- currently in the research stage consist of thick gate- antly used to generate electron and hole carriers in oxides(e.g.~300nm)thatrequirelargegatevoltages 2Dmaterials[31–33],andinfew-layermaterials,the (e.g. >10 V) to switch the device from the OFF to charge density falls off rapidly away from the sur- ONstates.Besides,backgatingaffectsboththechan- face, rather than being uniform as in conventional nel and contact regions in a convoluted manner that semiconductormaterials. complicates the gating characteristics of 2D FETs. In Furthermore, the pristine surface of 2D materi- thissection,wediscusstheoutputandtransferchar- als forms weak van der Waals bonds with adjacent acteristicsofback-gated2DFETsandprovideinsights materials and presents challenges to the creation of intotheextractionoffundamentaldeviceparameters. low-resistancecontacts,byintroducingatunnelbar- rier for charge carrier transport, whereas the form- 2.2.Current–voltagecharacterization ation of stronger bonds requires disruption of the I–V measurementisthefundamentalelectricalchar- 2D crystal structure, which introduces defect states. acterization technique for understanding the work- Therefore, it is important to accurately characterize ingprincipleofFETs.Also,I–V measurementsallow the properties of metal contacts, e.g., contact resist- for qualitative and quantitative understanding of anceandmetal-semiconductorSchottkybarrier[34]. intrinsic semiconductor properties such as mobility Interfacesbetween2Dsemiconductorsandmetalsare and carrier density, along with external properties subject to Fermi level pinning due to the tunnel bar- such as interface states and contact resistance. Here, rier at the interface, defect-induced interface states, wediscusstypicalI–V measurementofa2DFET;the and orbital overlap between adjacent heterogeneous performanceoftheFETischaracterizedprimarilyby materials, requiring precise characterization of the measuring the output (I as a function of V ) and SchottkybarrierandFermilevelpinning,whichcould D DS transfer(I asafunctionof V )characteristics. severely increase the contact resistance at the inter- D GS faces[35]. In this review, conductivity, carrier density, 2.2.1.Outputcharacteristics mobility,Schottkybarrierheight(SBH),contactres- To measure the output characteristics of a FET, the istance (R ) and trapped charges are discussed as drain current is measured as a function of V at DS key parameters for the electrical characterization of differentV .Theoutputcharacteristicswithasmall GS 2D devices, constituting the main sections below. V (figure 2(b)) allow the extraction of important DS Figure1illustratestherepresentativeparametersthat FETparametersasthedeviceactsasalinearresistorin can be extracted by various electrical characteriza- this region. Assuming channel-dominated behavior, tion methods, including current–voltage (I–V), Hall theI forann-type2DFETinthelinearregimecan effect,capacitance–voltage(C–V),and4-pointprobe beexpressedas (4PP)measurements,aswellasthetransmissionline method (TLM). Moreover, we also address the cor- µ WC n ox I = [(V −V )V ], (1) D GS TH DS relation between these macroscopic device paramet- ers and the nanoscale properties of 2D materials, visualized using scanning probe microscopy (SPM) where L, W, µ , C , and V are the channel n ox TH techniques. length, channel width, channel electron mobility, 2 2DMater.8(2021)012002 SBMittaetal Figure1.Keyparametersof2DFETsandrelevantelectricalcharacterizationmethods. oxidecapacitance,andthethresholdvoltage,respect- presenceofaglobalbackgate(V )in2DFETsresults BG ively.Wediscusstheuseofequation(1)toextractthe in simultaneous gating of the contact region, mak- channelmobilityandcarrierdensityinthefollowing ingR ,afunctionofV andV .Thus,thelinearity C GS DS sections. of the output characteristics can be used as a simple Inthepresenceof R ,onlyaportionofV drops yet important check to determine the effect of con- C DS acrossthechannel;thus,equation(1)needstobefur- tactresistanceonFETperformance.Notethat,dueto ther modified to address this issue. The effect of R the simultaneous gating of the contact and channel can be included straightforwardly by replacing V regions,contactscanshowdifferentbehavior(Ohmic DS with or Schottky) at different gate voltages. However, the linear behavior does not provide any information µ WC n ox I = [(V −V )(V −I ·2R )] (2) regarding the mechanism behind the Ohmic nature D GS TH DS D C of contacts as doped (gated) Schottky contacts can Here, 2R refers to the contact resistance for the resemble Ohmic characteristics due to enhancement sourceanddrainjunctionatsmallV .However,the of the tunneling component at the source junction DS 3 2DMater.8(2021)012002 SBMittaetal [37]. Thus, proper extraction of µ ,V , and R is efficiency of tuning the energy barrier at the source n TH C essential to understanding current flow in 2D FETs. terminal. A small SS over a wide range of current is Theextractionoftheseparametersisdiscussedinthe requiredtoachieve,sinceitindicatesalargeI /I ON OFF followingsections. ratioforsmallsupplyvoltages. For use of 2D FET in analog, digital, and high In the subthreshold regime or OFF state power applications, observations of current satura- (V <V ), the subthreshold current is limited by GS TH tion over a large V window is crucial [39, 40]. The thermal injection of carriers at the source junction DS current saturation region is characterized by a con- andcanbeexpressedas: stant I independent ofV , as shown in figure2(c); D DS q V −V ( ) GS TH k T I initiallyincreaseslinearlywithV (linearregime) D DS I ∼e (3) and then saturates at higherV . Although several DS where q is the elementary charge, k is Boltzmann’s reportshavedemonstratedcurrentsaturationinvari- constant, and T is temperature. The SS can be ous transition metal dichalcogenide (TMDC) (e.g. obtainedfrom(3),asfollows: MoS , WSe , WS ) FETs [28, 41–44], obtaining sat- 2 2 2 uration in 2D devices at desirable values of V DS dV k T C GS B CH SS = =ln(10) 1 + (4) still remains elusive due to large contact resistance, d(logI ) q C D ox low channel mobility, and high-field scattering. The k T applicationofhighelectricfieldwithoutthoseeffects where is the thermal voltage, C is the channel CH was realized by employing ionic gated transistors capacitance and C is the oxide capacitance. For an ox [45,46], although it is difficult to use the ionic tran- ideal 2D FET, C ≪C in the subthreshold region CH ox sistorsforpracticalpurposes.Lackofbandgap,weak and thus SS is ~60 mV/decade at room temperat- electrostatic control, and interfacial phonon scatter- ure. However, most 2D FETs are fabricated on thick ing in graphene are responsible for the poor cur- SiO substratewithlargeinterfacetrapdensity,yield- rentsaturationseeningrapheneFETs(showninfig- ing large SS values (> a few hundred mV/decade). ure 2(d)), which limits their usability in radio fre- Although unrealistic in practical applications, large quencyapplications[38,47,48]. C can be realized by using ionic gated transistors ox −1 that results in SS values very close to 60 mV dec 2.2.2.Transfercharacteristics despite using 2D Schottky devices [46, 50] and also Theotherwaytoassesstheelectricalperformanceofa mobility values close to the limitation by phonon FETisbyutilizingthetransfercharacteristicsthatcan scattering [51], making the ionic transistors efficient be obtained by measuring I as a function of V at D GS to quantitatively characterize the electronic proper- constantV ,asillustratedinfigure2(e).Thesechar- DS ties of 2D materials. The interfacial traps between acteristics are used to extract the parameters, such 2D channels and SiO also induce unwanted hys- dI as transconductance (g = ), threshold voltage m teresis in the transfer characteristics [52, 53]. This dV GS (V —the gate voltage at which the FET turns on), TH can be improved by stacking or encapsulating of the andsubthresholdswing(SS—thevalueindicatingthe 2D materials with an insulating 2D material such as sharpness of switching behavior of the 2D FET), as hBN[54–58].Moreover,asub-thermionic transistor showninfigure2(f).Forann-channelFET(n-FET), mechanism such as quantum mechanical band-to- the transfer characteristics display ON-state current band tunneling can exhibit a steep turn-on with low (I ) for V = V > V (V is the maximum ON GS DD TH DD SSvaluesfarbelowthethermioniclimit[59,60]. voltage supplied to the device) and OFF-state cur- rent(I )forV <V ,andviceversaforap-FET. 3.Conductivity(resistivity) OFF GS TH Various methods are employed to extract the V TH fromthetransfercharacteristics,suchaslinearregion 3.1.Conductivityin2Dmaterialsanddevices extrapolation,transconductancelinearextrapolation In an isotropic three-dimensional (3D) material, the (V versus g ), second-derivative of transconduct- electrical resistivity (ρ) and conductivity (σ) are GS m 1 A ance,andGhibaudo’smethod(interceptofV versus defined as ρ = =R× [Ω·cm], where R, A, GS σ L 0.5 I /g ) [49]. The right y-axis in figure 2(f) displays and L are the total resistance, cross-sectional area theg curveasafunctionof V . (=W×t,whereWisthewidthandtisthethickness m GS Scaling down the power supply voltage is critical of the material), and distance between the measur- for energy-efficient electronics, and one of the most ing points, respectively. Conductivity measurements effectivewaystocontrolthepowerdensityistolower in bulk semiconductors can be made without fab- the supply voltage. To reduce power consumption, ricating any electrical contacts using standard mul- it is necessary to overcome the abruptness (thermi- tipoint resistance measurements; however, the very oniclimitof60mV/decade)thatoriginatesfromthe nature of 2D materials necessitates the formation of thermalcarrierinjectionmechanism,i.e.,thermionic electrical contacts in 2D devices to determine res- emission (TE). The abruptness of a FET is measured istivity or conductivity [61]. Several studies on thick by SS, which is defined as the inverse of the slope of 2Dmaterials-baseddeviceshavedemonstratedsuper- −k log(I )versusV curve.TheSSdeterminesthegate linearbehavior(σ ∝ t )ofelectricalconductivityas D GS 4 2DMater.8(2021)012002 SBMittaetal Figure2.(a)Schematicdiagramofatypicalback-gatedbilayerWSe devicewithPttransferredviacontacts(TVCs).(b)2-probe outputcharacteristicsmeasuredatdifferentgatevoltages.ThelineartrendindicatesthepresenceofOhmiccontactsathighergate voltages[36].(c)Illustrationoftheidealoutputcharacteristics(withincreasingV )ofann-typeFETdisplayingdraincurrent GS saturation.(d)I asafunctionofV fortopgatevoltage(V ) = −0.3V, −0.8V, −1.3V, −1.8V, −2.3V,and −2.8Vat D DS TG V = −40VforthegrapheneFETshownintheinset[38].(e)TransfercharacteristicsoftheWSe deviceshowinggood BG 2 subthresholdswingandlowdrain-inducedbarrierlowering[36].(f)Transfercurve(left)andtransconductance(g )(right) characteristicsofanidealn-typeFETwithrespecttoV .ForabetterFETswitch-oncharacteristic,theslopeinthesubthreshold GS region(V <V )shouldbesharp.ThetransistorisswitchedonwhenV isequaltothemaximumvoltagesuppliedtothe GS TH GS device,V . DD a function of sample thickness [62, 63]. The super- appliedbythesameterminals.Overtime,2PPmeas- linearbehaviorinsuchstructuresisattributedtothe urement has become a standard method of obtain- non-uniformcurrentdistributioninthick2Dmater- ing the output and transfer characteristics of a 2D ials that results from gate-dependent carrier density FET. Figure 3(a) displays the individual compon- profile and interlayer resistance [37]. This is further ents of the total resistances (R ) in a ReS -based Total 2 accentuatedatthelimitof2Dmaterials(~10layersin 2D FET; the corresponding 2PP output character- the study cited here) where conductivity is observed istics at different V are illustrated in figure 3(b) GS toexhibitnon-monotonicthicknessdependencedue [69].AssumingR >R alongwithlinearI vs.V CH C D DS to the interplay between mobility and carrier dens- characteristics,R ,R ,and σ canbedeterminedby CH SH ity [64]. Besides, conductivity in 2D materials also usingthefollowingrelationship: shows a large degree of inter-sample variation due to unintentional doping from substrate , ambient L 1 L R = R = (5) surroundings,andsamplepreparationmethods[65– CH SH W σt W CH 68]. Therefore, the conductivity/resistivity of few- layer 2D devices is determined in terms of chan- where t refers to the thickness of the 2D semicon- CH nel resistance (R ) or sheet resistance (R ), which CH SH ductingchannel.Thepresenceofbackgateresultsin is a more straightforward way to evaluate current gatevoltage-dependentR valuesindicatingthegat- CH flow in 2D materials. Typically, R and R can CH SH ing behavior of channel conductivity. Similar results be determined by fabricating 2D FETs and measur- canalsobeobtainedfromthetransfercharacteristics, ingtheoutput/transfercharacteristicsatvaryingV GS which provide gate-dependent R at constantV . CH DS usingeithera2-pointprobe(2PP)or4PPtechnique, However, in many cases, the contact resistance in asdiscussedinthefollowingsections. back-gated2DFETsiseithercomparabletoorhigher than the channel resistance, resulting in significant errorsintheR valueextractedusing2PPmeasure- CH 3.2.2-pointprobemeasurements ments [72]. This issue can be resolved by using 4PP Standard 2PP measurements refer to measurements method, which can deconvolute the effect of R on in which the current and voltage are assessed and theextractedR andR values[73,74]. CH SH 5 2DMater.8(2021)012002 SBMittaetal Figure3.Differencesbetween2PPand4PPmeasurements.(a)SchematicillustrationoftheR inthe2Dtransistors,which Total consistsoftheR ,R ,andresistanceofthemetal(R ).(b),(c)Comparisonbetween2PPand4PPmeasurements,respectively, SH C m ofI asafunctionoftheV forafew-layeredReS -FETdevice[69].(d)SchematicofamonolayerMoS devicewith4PPcontact D DS 2 2 configuration.(e)2PPand4PPconductance,whichshowsdifferentV readingsduetodifferencesinchannelandcontact TH gating.(f)Highermobilityin4PPmeasurementsillustratingtheimpactofcontactresistance[70].(g)Schematicofamultilayer MoS devicewithvanderPauwcontactconfiguration[71].(h),(i)DifferentvanderPauwconfigurationsformeasuringthesheet resistanceofthesameMoS deviceatdifferentgatevoltages. 3.3.4-pointprobemeasurements 3.3.1.4PPmeasurementswithhallbargeometry Asdiscussedabove,2Ddevicessufferfromlargecon- Generally, 4PP measurements in 2D materials-based tact resistances, which make it difficult to explore devices are done on devices in which the contacts channel-dominated behavior and result in wrong and channel region are patterned in a Hall bar geo- inferences. Here, 4PP measurements are used to metry, as shown in figure 3(d) [70]. In this struc- measure R independent ofR . Figure 3(c) shows ture, the voltage probes (other than the source and CH C the output characteristics of a ReS device obtained drain contacts) minimally affect the current flow in using 4PP measurements, which reveal a higher the channel material and thus act like perfect volt- device current at the same V when compared to meters. The source and drain (S/D) probes are used DS 2PP measurements. The inset in figure 3(c) illus- tosource/measure I ,andV andV betweenS/Dare D 1 2 tratestheschematicandequivalentcircuitofthe4PP usedtosensethevoltagedifference(V = |V −V |); 12 2 1 structure used for the measurement. Accurate con- in turn, these measurements are used to evaluate ductivity measurements using the 4PP method are the intrinsic transport properties of 2D materials by typically enabled by the Hall bar and van der Pauw deconvolutingtheeffectsofR .Comparedtothe2PP geometry, as addressed below, which can be exten- measurements,the4PPmeasurementsresultinsmal- dedfurthertodeterminecarrierdensityandmobility lerR asonlyaportionofappliedV dropsacross CH DS frommagneto-transportmeasurements. the channel region. Here, R can be extracted from CH 6 2DMater.8(2021)012002 SBMittaetal the 4PP I–V characteristics by using the following resistances: relation: V V 34 43 SetA(horizontal):R = ,R = , 12,34 21,43 V L I I 12 21 R = (6) CH V V I L D 12 12 21 R = ,R = 34,12 43,21 I I 34 43 (7) V V where L is the distance between voltage probes in 12 24 42 SetB(vertical) :R = ,R = , 13,24 31,42 themiddleofthedevice.Consequently,R -corrected I I C 13 31 R and σvaluescanbecalculatedfromequations(5) V V SH 13 31 R = ,R = 24,13 42,31 and (6). Finally, the 4PP characteristics can also be I I 24 42 usedtocalculateR bysubtractingtheextractedR C CH Then,anaverageresistanceiscalculatedforsetsA value from R . Thus, 4PP measurements provide Total andB,whichcanbeexpressedas: an easy and efficient means of extracting both R CH (R + R + R + R ) and R . 12,34 21,43 34,12 43,21 R = , The 2PP and 4PP measurements of the trans- 4 (8) (R + R + R + R ) fer characteristics of a 1L-MoS device are shown 13,24 31,42 24,13 42,31 R = . in figure 3(e). These measurements provide differ- 4 ent values of V (using the linear extrapolation TH Finally, sheet resistance and conductivity are calcu- method), which implies different gating properties latedusingthefollowingrelation: of the channel and the contact regions due to dif- −πR /R −πR /R A SH B SH ferences in the band movements in the channel and e +e =1andσ = (9) R ·t SH CH contact regions [75]. Figure 3(f) shows higher 4PP- than 2PP-mobility due to the presence of substantial Similar expressions can be obtained for other chan- contact resistance. The results show that 4PP meas- nel shapes [77]. Since contact resistance is usually urements are necessary to accurately calculate the large in TMDC 2D FETs, accurate extraction of R CH intrinsic conductivity, unveiling true channel mobil- and R using van der Pauw measurements becomes ity,carrierdensity,andcontactresistanceasdiscussed highlydifficultevenafterreshapingtheflakesinregu- inlatersections. larforms.Thus,the4PPmeasurementsusingHallbar geometryaremoreprevalentinthe2Dcommunity. 3.3.2.4PPmeasurementswithvanderPauwgeometry Because exfoliated 2D materials come in irregular 3.4.Challengesof4PPmeasurements shapes, 4PP measurements with Hall bar geometry Although 4PP measurements are a powerful tool for generally require reshaping of the channel material; the electrical characterization of 2D materials-based this involves fabrication steps that could alter their devices (electrical conductivity in this section), cer- intrinsic properties as 2D materials are highly sens- tain experimental considerations need to be satisfied itive to surface treatments. In this respect, the van toensureaccuratemeasurementsanddataextraction. der Pauw method is advantageous for measuring the (i) Accurate 4PP measurements require the chan- sheet resistance of graphene and 2D materials as it doesnotrequirechannelpatterninginregularshapes nel region to be patterned (reshaped) in a way that avoids the impact of voltage probes on the [76]. In van der Pauw measurements, four contacts currentflowinthechannelregion,e.g.Hallbar or van der Pauw (square, circle, cloverleaf, etc) are placed at the edges (periphery) of a flake as shown in figures 3(g)–(i); a constant current flows structures [78]. This requirement is especially criticalforfew-layer2Ddevices,wherethepres- between adjacent pair of contacts (1–2 or 2–4), and thevoltagedropsaremeasuredbetweenanotheradja- ence of voltage probes directly on the channel (as in the case of TLM) can severely affect the cent pair of contacts (3–4 or 1–3). Although van derPauwmeasurementsforbulksemiconductorsdo current flow in the underlying channel. Sim- ilarly, in 4PP measurements with a non-Hall not require channel reshaping, typical Van der Pauw measurements for 2D materials often utilize regular- bar patterned channel, the intrusion of voltage probes into the channel region affects the local shaped flakes (or flakes patterned in regular shapes, e.g.square,rectangular,orcircularshapes)duetothe electric field and current flow in the channel regionandthuscanresultinerroneousextrac- convenience in analyzing experimental results. For a square channel geometry, two sets of measurements tionofR ,R ,andR [79]. CH SH C (ii) Another consideration in measuring a 2D FET areperformedtoincludeverticalandhorizontalcon- ductionintheflake,resultinginthefollowingsetsof using differential measurements (such as lock- 7 2DMater.8(2021)012002 SBMittaetal in amplifier-based measurements) is under- solid solubility, thickness, and binding energy of the standing the role of the common-mode rejec- 2Dmaterials[85].Forexample,althoughahighsub- 14 −2 tionratio(CMRR)[80].In4PPmeasurements, stitutionalNbdopantconcentrationupto10 cm the drain voltage is often biased at high drain (10%Nbconcentration)hasbeenachievedinmono- bias(V >1V)comparedtothesource,which layer CVD grown WS , the estimated active dopant DS 2 is often held at ground voltage. In the pres- densityaccordingtotheelectricalpropertieswasonly 12 −2 ence of large R , this leaves the middle voltage ~6 ×10 cm (approximately0.06chargesinduced probesmeasuringasmalldifferentialvoltageon per dopant), as evidenced by non-degenerate beha- top of a large background common voltage of vior of transfer curves [86]. Furthermore, charge DS .Thus,therejectionofthiscommonvoltage transfer doping of 2D materials, which is based on is crucial for accurate 4PP measurements. This their interaction with adlayers, atoms, or molecules, limitstheutilityofthe4PPmeasurementsin2D hasalsobeenwidelystudiedasanalternative[31–33, devicesbiasedatlowgatevoltages.Forexample, 41,44,87–96]. atypicalCMRRof100dBwithV =1Vresults Generally, in conventional semiconductors, DS in ±5 µV of common mode voltage. This lim- the doping concentration at room temperature is itsthevoltagerangeforthemiddleprobesto,at assumed to be the same as the free carrier concen- minimum, ±100 µVtoachieve>95%accuracy. tration, because free carriers such as electrons or (iii) Alogicalyetoftenignoredconsiderationin4PP holesaregeneratedfromfullyionizeddopantatoms, measurementsistheextremelysmallmagnitude which are embedded in the semiconductors by an of the voltage drops across the voltage probes ion implantation process followed by an activation duetothepresenceoflargeR atthesourceand process using high-temperature annealing. There- drain junctions, especially when the device is fore, doping concentration in bulk semiconductors in the OFF state. In the OFF state, both source can be estimated by various methods, e.g. secondary and drain regions are completely depleted and ion mass spectroscopy, X-ray photoelectron spectro- thusthecontactresistanceissubstantiallyhigh. scopy,andI−V (C−V)characterization.Bycontrast, Almost all of the source–drain bias is dropped doping density in 2D materials is either induced by across the source and drain regions, so the electrostatic gating or charge transfer, which directly voltageprobeshavetomeasureextremelysmall modulatesthefreecarrierdensityinthematerialand voltages.Thesevoltagesaredifficulttomeasure therefore is primarily determined by electrical char- withmoststandardsourcemeasuringunits.As acterization. a result, contact and channel resistance meas- urementsintheOFFstateareoftenerroneous. 4.2.Dopingdensityfromcurrent–voltage (iv) Since Ohmic contacts are essential for calcu- characterization lating accurate sheet resistance using van der The carrier density of a semiconductor can be mod- Pauw measurements, a reciprocity check needs ulatedbyelectrostaticgatinginaFETconfiguration. tobeconductedtoensurepropervanderPauw Inthisconfiguration,thetwometalelectrodes(source measurements in the case of 2D Schottky con- anddrain,S/D)areusedtomonitoritsconductivity, tact devices. The ratio is often calculated to while the third electrode (gate, G) induces free car- determinethereliabilityofvanderPauwmeas- riers in the channel material across a gate dielectric urements[81,82]. material. Here, the carrier density above V can be TH estimatedby 4.Carrier(doping)density V − V GS TH n = C , (10) ox 4.1.Dopingin2Dmaterialsanddevices q Electricalconductivityisfurtherrelatedtoextracting charge carrier density using the relation σ =1/qnµ, where C is the oxide gate capacitance per area (for ox −2 where q is the elementary charge, µ is the carrier example, 11.5 nF cm with 300 nm SiO [84]). mobility, and n is the carrier density. Carrier dens- Note that equation (10) assumes that the device ity in a semiconductor can be tuned with substitu- is channel-dominated for V >V ; however, it GS TH tionaldoping;however,substitutionaldopingisvery is not operated in a quantum-capacitance domin- difficultin2Dmaterialsduetotheirnanometer-scale ated regime. For a channel-dominated WSe device thickness. Despite this limitation, there have been a with low R , good linearity in the transfer curve for fewreportsonsubstitutionaldopingin2Dmaterials. a WSe FET is observed for V >V and thus 2 GS TH Forexample,group-Velementssuchasniobiumand the carrier density extracted from the equation at 12 −2 group-VII elements such as rhenium can be substi- high V (1.6–4.3 × 10 cm ) is in good agree- GS tutionally incorporated during growth into the crys- ment with that measured using the Hall effect (1– 12 −2 tal lattice of group-VI TMDCs, yielding p-type and 6 × 10 cm ) [36]. For 2D materials, the dop- n-type semiconductors, respectively [83, 84]. How- ing density is nearly equal to the free carrier dens- ever,thedopingdensityissignificantlylimitedbythe ity, since it is mainly induced by the application of 8 2DMater.8(2021)012002 SBMittaetal Figure4.Halleffectmeasurementsofabridge-typeHallbarstructure.(a)IllustrationoftheHalleffectofanelectron.(b)Circuit configurationofatypicalbridge-typeHallbarstructuredevice.(c)V versusB-fieldofagraphenedevicedependentonV .(d) H GS SdHeffectingrapheneshowingoscillatorybehaviorof ρ and σ inthepresenceofB-fields[3]. xx xx gate biases without external doping. When the dop- measurement of 2D materials. ASTM International ingisgeneratedbyexternalprocessinginsteadofgate providedaguidelineforthedevicegeometryofasix- biasing, the induced doping density can be determ- contact device: L ≥ 5 W, W ≥ 3 a, b ≥ 2 W [100]. ined by the shift in charge-neutral points (CNPs) or It requires that 1.0 ≤ L ≤ 1.5 cm, although it is 2p threshold voltages in the transfer curve according to verydifficulttoachieveacentimeter-sizeddevicewith ∆n =C (∆V )/q[97,98]. gooduniformitywhenworkingwith2Dmaterials. ox CNPorTH Hall effect measurements are usually conducted with a sinusoidal AC or DC drain current, I , flow- 4.3.Halleffectmeasurements D ing through the channel of the device (figure 4(b)), Hall effect measurements are widely carried out to andV is measured while B-field is swept at a fixed extract the intrinsic material properties of a semi- H V , as shown in figure 4(c). It should be noted that conductor such as carrier density, type, and mobil- GS the use of AC measurement with lock-in amplifiers ity.Figure4(a)illustrateshowanelectronmovesina often has a significant advantage over the DC meas- conductive channel under applied longitudinal elec- urement,sinceV isusuallyintherangeof1–10 µV tricand perpendicularmagneticfields. The underly- H with a current of 100 nA and a B-field of 1 T, which ingprincipleoftheHalleffectisbasedontheLorentz cannot be observed with conventional DC source force [99]. An electron flows (in the opposite direc- measuringunits.TomaketheDCmeasurementspos- tiontothecurrent)alongthechannelinthepresence sible,ahighercurrentisrequiredatthesameB-field, of an electric field E with drift velocity υ. When a which in turn results in many unfavorable effects perpendicular magnetic field B is applied, the elec- due to threshold voltage shift, Joule heating-induced tron experiences Lorentz force, resulting in a voltage breakdown,andphasetransition[101–103].Further- difference(Hallvoltage,V )transversetotheflowof more, the sheet carrier density is calculated from the the electron. The sign of V depends on carrier type followingequation: (electronorhole),andthevalueofV variesdepend- ingonthecarrierdensity,current,andmagneticfield. I ∆B D z Two typical device structures are used for Hall n = . (11) 2D q ∆V effect measurements: (1) van der Pauw structure (see figures 3(g)–(i)), and (2) Hall bar structure. This is a simplified equation by taking the Hall Figure4(b) shows a typical bridge-type Hall bar scattering factor (r, generally between 1 and 2) as structure device, which is widely used for Hall unity; it should be multiplied by r to the equation 9 2DMater.8(2021)012002 SBMittaetal depending on the type of scattering (see section 5.2) otherhand,comesinmanyflavors—effectivemobil- [30].Itshouldbenotedthatn canalsobedeterm- ity, field-effect mobility, and saturation mobility— 2D ined from the van der Pauw structure by measur- depending on how it is extracted. Its main advant- ingdifferentialvoltagesalongdiagonaldirection(e.g. ageisthatMOSFET mobilityisextractedin a region V and V in figures 3(h) and (i)) under the pres- of operation that more closely resembles true device 14 23 ence of a magnetic field. Without the Hall scattering operation; however, much care must be taken to factor, the extracted n for undoped 2D semicon- ensure that the model used for mobility extraction 2D 12 -2 ductorstypicallyrangesfrom0.5–6 ×10 cm with correctly models the device current and the carrier backgatevoltagesappliedacross300nmSiO atroom densityofthechannel. temperature[36,104].Theadvantageofthismethod is that any geometric non-uniformity in the devices 5.1.Halleffectmobility can be eliminated by extracting the inverse of the The standard procedure to measure the µ is to pat- slopeofalinearcurve.Asshowninfigure4(c),non- ternthesemiconductorintoaHallbarstructurewith zeroV atzeroB-fieldduetothenon-symmetricgeo- contactsplacedonthefingers,asshowninfigure4(b). metry, carrier inhomogeneity, and contact resistance In the typical approach for measuring the µ in 2D can be observed in typical measurements, which can devices, a constant current is flowed between the varydependingontheappliedV .TheR andHall source and drain contacts, while a magnetic field is GS SH mobility (µ ) values extracted from the Hall effect applied normal to the plane of the semiconductor. measurementsaredescribedinsection5.1below. Hall effect mobility measurements benefit from the Apart from Hall effect measurements, the carrier independent extraction of the carrier concentration density in 2D materials can also be determined by in the channel. In quasi-equilibrium, zero current observingtheShubnikov-deHass(SdH)effectwhere flows along the width of the device. Therefore, the theoscillatorybehaviorof ρ isobservedinthepres- total force along the width must be zero, satisfied xx ence of magnetic fields, as shown in figure 4(d). For whentheLorentzforceiszero,whichgivesE = υ B , y x z 2D devices with moderate electron/hole mobilities, where x is along the length, y is along the width, SdH oscillations are usually observed at ultra-low and z is perpendicular to the 2D semiconductor temperatures (a few kelvins) and in the presence of channel. The general expression for current flow is a large magnetic field [2, 3]. Over the years, tech- given byI =qWυ n . By defining the Hall voltage D x 2D I B D z niques such as van der Waals-based assembly [105], asV ≡ E W, we find thatV = , (see equation H y H qn 2D full device encapsulation, and clean contact fabric- (11)forn ).FromthemeasurementofV shownin 2D xx ation have enabled the observation of SdH oscil- figure4(b),theR ofthechannelcanbedetermined SH lations at moderate magnetic fields (<5 T) from by graphene [106, 107] and other 2D semiconductor- V W xx based devices [108, 109]. In this regard, the SdH R = . (12) SH I L D 4p effect has become an important measurement tool to determine important material parameters: (i) UsingR = ,wefindtheHalleffectmobil- 1 SH qµ n n 2D Quantum mobility (µ ) from the relation, µ ≈ q q itytobe whereB isthemagneticfieldreferringtotheonsetof SdHoscillation[57];and(ii)carrier(electron)dens- V 1 H 4p µ = , (13) ityfromtheslopeof1/BversusindexofSdHminima V W B xx z 2q bytherelationn = ,whereB isthemagnetic h∆ ( ) where the value of n is given by equation (11) and 2D fieldatminimum ρ andhisPlanck’sconstant.Thus, xx µ = µ is assumed (which is only valid for a Hall n H the Hall effect measurement along with SdH oscilla- scatteringfactorof1).Thisassumptionisfurtherdis- tionisaverypowerfulandeffectivetechniquetochar- cussed in the following section. As discussed in the acterizecarrierdensityin2Dmaterials. previous section, the quantum mobility can also be obtained from the onset of SdH oscillations by Hall 5.Mobility effectmeasurements(e.g.theonsetofSdHoscillation 2 −1 occursatB =1T, µ =10000cm V·s )[57]. Two forms of mobility are typically extracted in 2D devices—HalleffectmobilityandMOSFETmobility. 5.2.ChallengesofHalleffectmeasurement Bothextractiontechniqueshavetheirprosandcons. In principle, the measurement of µ is straightfor- µ extraction has an advantage in that it independ- ward, but in practice, several difficulties arise, com- entlymeasuresbothresistivityandcarrierconcentra- plicating the measurement on 2D materials. The tion.Itskeydisadvantageisthatitrequiresaspecial- first challenge is that the Hall effect measurement ized Hall bar structure (or other suitable geometries requires a specialized structure, ideally following the withsmallcontactsattheedgesofthestructure)and guidelines of ASTM Standard F76 [100]. The struc- the Hall scattering factor (r), is often unknown and ture should be designed such that the contacts lie as simplyassumedtobeone.MOSFETmobility,onthe closetotheedgeofthesampleaspossible.Theflakes 10 2DMater.8(2021)012002 SBMittaetal can be etched into the desired geometry, but doing measurementisapowerfultechniquetomeasurecar- so has a negative consequence that the lithography riermobilityin2Dmaterials;however,thetechnique and etch process may adversely decrease the mobil- isnotwithoutchallengesandcomplications. ity from its value in a pristine state. This is espe- cially concerning for the mobility measurement of 5.3.MOSFETmobility ultra-thinsamples,wheresurfacecontaminationcan Incontrasttoµ ,MOSFETmobilitiescanbeextrac- greatlyaffectthematerial’smobility. ted from the measured transistor characteristics. Another practical challenge for measuring Hall MOSFET mobilities come in two flavors: effective mobility in 2D materials is that V can be quite mobility and field-effect mobility. Figure 5 illus- small, making measurement difficult. V is propor- tratestheMoS MOSFETcharacteristicsemployedto H 2 tional to current per unit width, which is often less extracttheeffectiveandfield-effectmobilities[114]. −1 than1 µA µm forultra-thinsamples.V canhave anoffset(i.e.V ̸=0forB =0asshowninfigure4(c)) H 5.3.1.Effectiveandfield-effectmobilities due to asymmetry in a Hall bar geometry so the dif- Effective mobility is extracted from the drain con- ference in Hall voltage at different B-fields must be ductanceofaMOSFETbiasedinthelinearregime.A used instead of a single B-field measurement. A spe- generalexpressionforthedraincurrentofaMOSFET cialized probe station is typically required to obtain withanegligiblediffusivecurrentatsmallV canbe DS a large B-field, often involving the use of a cryostat writtenas with a cryogenic superconducting magnet. The AC Halleffectmeasurements,whereacoilisusedtogen- I ≈ µ Q V ,forV > V and D eff n DS GS TH erate the AC magnetic field, which is advantageous V ≪ (V − V ), (16) DS GS TH overDCmeasurementasitenablesfastandlowfield measurements<0.1T,canalsobeused[110]. where Q = C (V − V ) is the sheet charge n ox GS TH Although it is not often done for 2D materi- density of the channel, µ is the effective mobility, eff als, the sample (mostly graphene) can also be meas- and kT is the thermal energy. Ideally, Q is determ- ured while placed atop a permanent magnet that ined through independent capacitance or Hall effect is flipped between measurements to give a positive measurements of the MOSFET structure; however, andnegativeB-field[111,112].Unfortunately,many given the small size of many exfoliated samples, the back-gated devices that are pervasive across the 2D- capacitance of 2D MOSFETs is not typically meas- materialscommunityshowsignificanthysteresis[52, ured as the signal is much too small and complex to 113](orevenworse,devicedegradation)frommeas- reliably detect using conventional techniques. For an urement to measurement, which makes the differ- idealdevice,effectivemobilityisthengivenby ential extraction between the positive and negative B-field measurements prone to hysteretic error. A g L solution to overcoming this problem is to perform µ = , (17) eff Q W repeated measurements, switching back and forth between +B and-B ,toverifythatthedataisstable. z z where g is the drain conductance given by g ≡ d d Another, often overlooked, error in the measure- ∂I , as shown in figure 5(a). If the out- ∂V DS ment of µ arises from the assumption of energy- constantV GS putcharacteristicsdonotexhibitalineardependence independent scattering in the semiconductor, which on V around the bias point for which the mobil- is generally only valid at very high magnetic fields DS ityisextracted,theextractedmobilityissuspectsince (≫1 T) or for neutral impurity scattering. Energy- thedevicecharacteristicsdonotfollowequation(16) dependentscatteringiscapturedintheHallscattering ⟨ ⟩ from which µ is derived. Similarly, if the transfer eff factor,r = (1<r <2),where τ isthemeantime ⟨τ⟩ characteristicsdonotexhibitalineardependenceon between carrier collisions and ⟨τ⟩is the average over V around the bias point for which the mobility is GS energy. The Hall scattering factor can be determined extracted, the use of the equation to determine Q is R (B ) H z at a specific B-field by r = . Including this R (B =∞) H z highly suspect since the device behavior does not fit factor,thecarrierconcentrationbecomes thechargemodel. Field-effect mobility is derived from the I B D z ∂I n =r , (14) 2D transconductanceg = of a MOSFET ∂V GS qV constantV DS biased in the linear regime as shown in figure 5(b), andtheconductivitymobilityequals whichisgivenby µ g L H m µ = . (15) µ = . (18) n FE C V W ox DS Therefore, the µ can over-predict the conductivity ForconventionalMOSFETs,extractedµ isoften H FE mobility by up to a factor of 2. All in all, Hall effect lessthanthe µ duetoeffective-fielddependenceof eff 11 2DMater.8(2021)012002 SBMittaetal Figure5.Effectivemobilityandfield-effectmobility.(a)Effectivemobilityisextractedfromthedrainconductancenearthe originoftheoutputcharacteristics.Forbothmobilityextractiontechniques,boththetransferandoutputcharacteristicsshould showlinearbehavioraroundtheextractionbiaspoint.(b)Field-effectmobilityextractedfromthetransconductanceofa MOSFET,biasedinthelinearregime[114]. themobility.Whenconsideringthisdependence,the structures similar to those used for Hall effect meas- transconductancebecomes urementsasshowninfigure4(b).Insuchastructure, thevoltagedropbetweenthemiddlecontactsismeas- ∂µ eff g = C V µ + (V −V ) . (19) ured (V ), while V is applied between the source m ox DS eff GS TH xx DS L ∂V GS and drain contacts. This four-probe drain conduct- ∗ ∂I Since µ decreases with increasing effective field, anceisdefinedasg = .Themeasured eff d ∂V xx constantV ∂µ GS eff is negative and the measured transconductance potential is changed by varying the appliedV . In ∂V GS DS is less than what would ideally be expected. The this way, the effect of the contacts is removed from dependence of the µ on V is often expressed in eff GS theextractionprocedure. termsoftheeffectiveverticalfield, The measured potential across the channel may µ bequitesmallandperturbationofpotentialdistribu- µ = , (20) eff tion due to the device geometry (e.g. size of voltage 1 + αε γ eff sensingprobes[115])mayaffecttheabilitytoaccur- where µ , α, and γ are constants, and ε is the o eff atelydeterminethemodifieddrainconductance.The effective(vertical)fieldinthesemiconductorchannel. dual-gate structure makes it more complicated due However, the change in µ with V is proportional eff GS to the contact turn-on effect tending to overestimate tothechangein ε with V ,whichissmallforback- eff GS mobilityunlessthoroughcharacterizationtominim- gated2Ddeviceswiththickoxides.Furthermore,for ize measurement artifacts and systematic simulation ultra-thin few-layer 2D MOSFETs, the majority of are considered [116]. Nevertheless, due to the often the channel charge is already present near the chan- large and variable R in 2D MOSFETs, four-probe nelsurface[37],whichfurthersuggeststhatthegate- measurement presents the best technique to accur- dependence of µ will be less than that of conven- eff atelydeterminechannelmobilityforbothHalleffect tionaldevices. andMOSFETmobilitymeasurements. 5.3.2.Errorsduetocontactresistance Largecontactresistanceisacommonproblemin2D 6.Contactresistance(R )andSchottky devices that limits the accurate extraction of MOS- barriers FETmobilities.InconventionalMOSFETs,R isoften determined from TLM structures, and the extrac- 6.1.Contactresistancein2Ddevices ted mobilities can be corrected for degradation due Lack of simple, efficient, and controllable doping toR . In principle, the same TLM can be applied to techniques for 2D materials results in large R at the C C 2D MOSFETs; however, often large device-to-device metal-semiconductor junction. R depends on the variations make it difficult to achieve reliable and nature of the barrier, i.e., its width and height, since trustworthy results when applied to 2D materials. barrier sensitively affects carrier transport across it. Moreover, the mobility extraction from the contact- For the conventional semiconductors, e.g. Si and limited devices can be problematic since V is not GaAs, R is known to approach near the quantum TH C theonsetvoltagewherethechannelisdepletedwhich mechanicallimit[117].Also,therewasanearly-stage gives inaccurate charge density Q . One way to cir- experimental report on R in graphene devices by n C cumventtheproblemofR istofabricatefour-probe varying contact lengths, in which R much larger C C 12 2DMater.8(2021)012002 SBMittaetal than quantum limit was consistently obtained from Equation(22)isthefundamentalrelationshipthatis variousdeviceconfigurationsincluding2PPand4PP used to extract R in TLM. Note that the term R W C C measurements [118]. However, 2D semiconducting issometimesusedtorefertoR inliterature,whereit materials with a sizable bandgap in the range of representswidth-normalizedR .Several2-proberes- 0.5~2eV,e.g.,TMDCs,showveryhighR >10times istancemeasurementsaremade betweenan adjacent that of the conventional semiconductor materials pair of contacts with different channel lengths and [117, 119]. The large R at the metal-semiconductor R is plotted as a function of channel length. Fig- C Total interface is attributable to the formation of Schottky ure 6(b) shows a typical plot of R versus L from Total barriers due to mid-gap Fermi level pinning arising which R can be extracted by finding the y-intercept from intrinsic material defects and processing con- using a linear fit. Other relevant parameters are also ditions [36, 120]. These Schottky barriers not only highlighted in the plot. Furthermore, low source– limittheONcurrentofthe2DFETs,butalsodeterm- drainvoltages(<1V)arerecommendedforaccurate inetheirpolarity[121,122].Moreover,weakVander TLMtoavoidJouleheating[103]andimpactioniza- Waals bonding between high work function metals tion[129]inchannel2Dmaterials. suchasgold(Au)andpalladium(Pd)and2Dmateri- Figure 6(c) shows a schematic of a typical TLM als results in additional tunnel resistance and there- structure with a 2D material as the channel material fore higher R . In addition, typical back-gated 2D and conventional back-gated geometry. Unlike bulk devices allow simultaneous gating of contact and semiconductors, 2D materials generally do not con- channel regions, which convolutes the underlying ductwellwithoutgatingduetolargeR .Thus,equa- physics. Since R in 2D devices is often much lar- tion (22) needs to be modified to show the effect of ger than R , the output and transfer characterist- globalbackgating,inwhichcaseboththechanneland CH ics of such FET devices represent contact properties contactregionsaremodifiedsimultaneously,i.e. rather than channel properties, as discussed in the conductivity section [61, 123–127]. This limits the R (V )W =R (V )L +2R (V )W (23) GS SH GS C GS Total performance of scaled 2D FETs and affects extrac- tion of important device parameters such as field- Figure 6(d) illustrates the use of TLM to extract effectmobilityand V ,asdiscussedintheprevious TH contact resistance for Au contacts on a bilayer MoS sections. Thus, accurate estimation of R is critical C where the channel length was varied from 200 forunderstanding,improving,andbenchmarking2D to 1000 nm [130]. The measured total resistance devices. (R W)wasplottedasafunctionofchannellength; Total In this section, we discuss the widely employed the corresponding y-intercept provides the contact TLM technique used to estimate contact resistance resistance (R W). As discussed earlier, the contact in 2D FETs. We discuss the advantages and dis- resistanceshowscleargatevoltagedependence(high- advantages of the method and highlight important lighted by carrier density in the channel using equa- considerations that should be taken into account tion (10)), as contact resistance decreases with an when applying it to 2D materials. We also discuss increaseingatevoltage. the temperature-dependent Arrhenius method for extractingSBHsin2Ddevices. 6.2.1.Transferlengthandcontactresistivityextraction TLM also provides a simple way to study the scal- 6.2.Transmissionlinemethod ingpropertiesofcontacts,whichiscrucialtodeterm- The TLM/transfer length method is conventionally inethefundamentallimitstoscalingof2Dmaterials- used to determine R for metal contacts on bulk based FETs. As the channel length is scaled to enable semiconductors, such as Si and Ge [78, 128]. In this better electrostatics and achieve higher device dens- method, multiple devices are fabricated with TLM ity, a large portion of total resistance corresponds to geometry (shown in figure 6(a)), where the chan- thecontactresistanceresultingincontact-dominated nel length/spacing (denoted by L1, L2, etc) is varied behavior of scaled devices. Using a distributed res- between different contacts, while the contact length istive network model for the contact region (fig- iskeptconstant.Asshownintheinsetoffigure6(a), ure7(a)),analyticalexpressionsforcontactresistance R between any two contacts can be expressed as Total canbeobtainedintermsofspecificcontactresistivity alinearcombinationofR andthelength-dependent (ρ ),sheetresistanceundercontact(R ),andtrans- c SK R ofthesemiconductorinbetweenthecontacts,i.e. CH ferlength (L ): R =R (L) +2R (21) L Total CH C C R W = ρ R coth ; (24) C c SK which,usingequation(5),canbefurtherrewrittenas L = ρ /R . (25) R W =R L +2R W. (22) T c SK Total SH C 13 2DMater.8(2021)012002 SBMittaetal Figure6.(a)TopviewoftheTLMconfigurationshowingdifferentchannellengths(L ,L ,...).Theenlargedviewshowsthe 1 2 distributionoftotalresistanceintermsofR andR .(b)AlinearfitoftheplotofR versuschannellengthgivingriseto C CH Total R ,R ,andL .(c)SchematicofaMoS -basedTLMdevicewithbackgatingthroughSiO .(d)SchematicofabilayerMoS C SH T 2 2 2 deviceandtheTLMplotforthedeviceshowingthelineartrendofR versuschannellengthasafunctionofcarrierdensity Total (gatevoltage).TheinsetshowstheextractedR valuesasafunctionofcarrierdensity,demonstratingcontactregion gating[130]. Figure7.ExtractionofR andL .(a)SideviewshowingtheresistivenetworkusedtocalculateL .(b,c)Extracted ρ andL ina C T T c T bilayerMoS asafunctionofcarrierdensity(gatevoltage)atdifferenttemperatures[130]. Here,L is the physical contact length and Experimentally, these parameters are extracted from L represents the current crowding at the metal- TLM by assuming that R =R and L ≫ L T SK SH C T semiconductorjunctionandisdefinedastheeffective which allows us to extract L by finding the x– length over which a majority of charge transfer/cur- intercept of the curve of R versus L. Once L is Total T rent transport occurs beginning at the edge of the determined, ρ canbedeterminedbyeitherequations junction (x = 0). Further insight can be gained by (26)or(27).Figures7(b)and(c)showtheextracted consideringtwolimitingcases: ρ andL values,respectively,forthedevicepresented c T infigure6(d). (i)L ≫ L : R W = ρ R = L R (26) C T C c SK T SK 6.3.ChallengeswithTLM Overtime,theTLMhasbecomethemostcommonly employed method of determining R and R in 2D C SH (ii)L ≪ L : R W = (27) C T C materials-baseddevicesduetotheeaseofdevicefab- 14 2DMater.8(2021)012002 SBMittaetal rication and straightforward nature of the analysis. 6.4.SchottkybarrierheightsandFermilevel Moreover, the method is generally material agnostic; pinning it does not require any prior knowledge of effective Asdiscussedabove,thelargecontactresistancein2D mass,dielectricconstant,bandgap,etc..Furthermore, devices can be attributed to the presence of Schottky theTLMhasanadvantageover4PPascurrenttrans- junctions at the metal-2D semiconductor interfaces. port is not disrupted by the presence of inner elec- SchottkyjunctionsarecharacterizedbySBHs,therel- trodes,whichareusedasvoltageprobesintypical4- ative values of which determine the current trans- probemeasurements,asdiscussedintheprevioussec- port at the metal-semiconductor interface affecting tions[115,131,132].However,afewpotentialpitfalls the polarity, magnitude, and switching characterist- must be considered when applying TLM to 2D FET ics of the injected charge carriers. Figure 8(a) shows analysis: theSBHandconceptualbanddiagramofametal-2D semiconductorinterface.Foranidealmetal-2Dsemi- conductor junction, the SBH for n-type (ϕ ) or p- Bn (i) Reliable TLM requires linear dependence of type(ϕ )semiconductorsisgivenby: Bp channel resistance on channel length and low spatial variation of contact resistance. Fabric- Forn-type: ϕ = ϕ − χ, (28) Bn m ation issues such as irregular device geometry due to non-patterned 2D flakes, inhomogen- eous non-laminar current flow due to poly- Forp-type: ϕ = χ +E − ϕ , (29) Bp g m mercontamination,lithography-induceddam- age, and unknown contributions from sample where ϕ istheworkfunctionofametal, χistheelec- edges,cancausedeviationfromlinearscalingof tronaffinityandE isthe2Dsemiconductorbandgap. channel resistance and therefore result in erro- Forsuchidealsystems,theSBHforelectronsincreases neouscontactresistancemeasurements[120]. linearly with the metal work function, thus satisfy- (ii) TLM is also problematic when contact resist- ing the Schottky–Mott rule as shown in figure 8(b). ance is substantially higher than channel res- However, non-ideal states such as interface and gap istance, since a small amount of inter-device statesatthemetal-semiconductorinterfacecancause variation in contact resistance can cause large severe deviation from the Schottky–Mott rule, mak- errors in the linear fit. Moreover, for Schot- ing it difficult to control electron/hole SBH by vary- tky contacts with non-linear I–V characterist- ing the metal work function. Quantitatively, we can ics, R becomes bias-dependent, which needs C interpret this deviation by introducing a pinning tobecarefullyconsideredwhenexaminingscal- factor (S) and charge neutrality level (CNL, ϕ ) CNL ingbehavior.Theimpactofnon-linearityinthe [134,135]: plotofR versusLisseverewhentheextrac- Total n−type: ϕ =S(ϕ − ϕ ) + (ϕ − χ) Bn m CNL CNL tedtransferlengthsaresmall.TLMismostsuc- =Sϕ +b, (30) cessful at high back gate voltages, where the channel resistance is substantially larger than the contact resistance and it is clear that total p−type: ϕ =S(ϕ − ϕ ) + E + χ− ϕ Bp CNL m g CNL resistance scales linearly with channel length (31) [130]. ∂ϕ Bn (iii) Extracting transfer length and specific contact Here, S is defined as the slope S = and can be ∂ϕ resistivity requires that R =R holds true, SK SH calculated from the linear fit of ϕ versus ϕ plot. Bn m which is hard to justify for few-layer devices. S =1representsanidealmetal-semiconductorinter- Unlike conventional semiconductors, in which face whereas S = 0 represents almost no variation lateraltransportoccursfar(~10–100nm)from in SBH with a change in the metal work function, the metal-semiconductor interface, transport indicatingacompletelypinnedinterfaceatthecharge in 2D materials occurs right at the interface neutralitylevel.TheCNLforn-typecanbeestimated and the material properties are substantially bytherelation changedbythemetalcontacts(e.g.contactdop- χ +b ing, fabrication-induced damage, and change ϕ = . (32) CNL 1−S in bandgap). Recent studies have shown signi- For S < 1, the semiconductor Fermi level is fixed ficant differences in R and R , which calls SK SH foruseofcomplementarymethodsforaccurate near the CNL, which results in similar SBHs for different metal contacts, that is, ‘Fermi level pin- extractionofL , ρ andR suchascontact-end T C SK and cross-Kelvin bridge methods [133]. Future ning’, as shown in figure 8(c). Fermi level pinning is often attributed to metal-induced gap states (MIGS) work on modeling and analysis of metal con- tacts on 2D materials needs to take this into and defect-induced gap states (DIGS); however, the exact physical mechanism still remains an open consideration, helping to come up with accur- atemethodsofextractingL , ρ andR . question. T C SK 15 2DMater.8(2021)012002 SBMittaetal Figure8.SchottkybarrierheightandFermilevelpinning.(a)Banddiagramofametal-semiconductorjunction.(b)SBHversus metalworkfunctionshowingtheSchottky–MottruleandFermilevelpinning.(c)SchematicimageofFermilevelpinning[35]. 6.4.1.SBHextractionin2Ddevices duetoitsexponentialdependenceontheseparamet- Accurate extraction of SBH for any metal-2D semi- ers.Atacertaingatevoltage,termedflat-bandvoltage conductor junction is essential for understanding (V ), the conduction band is perfectly aligned with FB the underlying physics of 2D devices and dedu- theSBHatthesourceend,i.e. ϕ = ϕ .ForV > B,eff Bn GS cing the pinning factor and CNL. Generally, for V , the tunneling current starts to dominate the FB bulk semiconductors, SBH is determined by fab- overall current transport resulting in weaker tem- ricating Schottky diodes with different metal con- peraturedependence.Thus,theactualbarrierheight tacts; however, the large contact resistance at the can be extracted by identifying the effective barrier metal-2D semiconductor interface makes it almost corresponding to the flat band voltage by analyzing impossibletoconstructaproperSchottkydiode.For thetemperature-dependenttransfercharacteristicsas this reason, the standard back-gated FET structure showninfigure9(b). is more commonly used to extract SBH. The most To extract the SBH, the temperature-dependent prevalent method of determining SBH is the Arrhe- transfercharacteristicsaremodeledwiththethermi- nius technique, which depends upon analyzing the onic current equation and replotted in an Arrhenius temperature-dependenttransferoroutputcharacter- manner, shown in figure 9(c). From here, the effect- isticsofaback-gated2DFET[34,61]. ivebarrierforcurrentflowcanbeextractedbylinearly As shown in figure 9(a), current transport at the fittingtheArrheniuscurves,andcanbeexpressedas reverse-biased source junction of a 2D FET consists 2 3 ∆ln I (V )/T D GS of two distinct components: (i) TE, where charge 4 5 ϕ (V ) = . (34) B,eff GS −1 injection occurs over the barrier, and (ii, iii) tun- q ∆T neling transport, where the charge injection occurs through the barrier [136, 137]. Tunneling transport Finally, as shown in figure 9(d), ϕ is plotted B,eff canbefurtherdividedintothermionicfieldemission as a function of applied gate bias, and the actual (TFE) and field emission (FE), where TFE denotes SBH(ϕ )canbedeterminedbyidentifyingthegate Bn tunneling at an energy level higher than the source voltageatwhichthecurveof ϕ versusV deviates B,eff GS Fermi level and vice-versa. The relative contribution fromitsinitiallinearslope[34,61].Thisgatevoltage ofthesethreecomponentscanbetunedbychanging corresponds to the flat band voltage and the corres- theappliedgatebias.IntheOFFstate,theconduction ponding ϕ isrecognizedasϕ . B,eff Bn bandedgeishigherthantheactualSBHandiscom- 6.5.ChallengeswiththeArrheniusmethodofSBH pletely dominated by TE. In this regime, the current extraction canbeexpressedas EventhoughtheArrheniusmethodiswidelyusedto qϕ (V ) B,eff GS 2 extract SBH in 2D materials, its applicability is often I (V ) =WA T exp − 2D GS 2D k T questioned, because it requires several assumptions −qV DS that are not generally satisfied in 2D devices. Here, 1−exp (33) k T we discuss the assumptions and their impact on the extractedSBH. where ϕ (V ) is the gate voltage-dependent B,eff GS q 8πm k ∗ B effective barrier height, A = is the mod- (i) Needforacleartransitionfromthethermionic 2D ified Richardson constant, T is temperature and m regime to the tunneling regime: Since the is the effective mass. In TE regime the current is Arrhenius method depends upon proper strongly influenced by temperature and gate voltage identificationoftheflatbandvoltage,thedevice 16 2DMater.8(2021)012002 SBMittaetal Figure9.ExtractionofSBHfromatemperature-dependenttransfercurve.(a)Differenttransportregimesatthesourcecontact asafunctionofgatevoltage.ThermionicemissiondominatesintheOFFstate(V < V ),andtunnelingcurrentbeginsto GS FB dominateintheONstate.Here,qϕ isequivalenttothen-typeSBH(qϕ )atflat-bandcondition[61].(b)Transfercurveof B0 Bn 1.5 monolayerMoS witha1L-hBN/Cocontactinthetemperaturerangefrom100Kto240K.(c)Richardsonplot(lnI/T versus 1000/T)of(b).(d)SBHasafunctionofgatevoltage[104]. needs to show a clear transition from a ther- materials involves temperatures below 100 K. mionically dominated regime to a tunneling At such temperatures, the thermionic com- regime.However,thistransitionisoftenpoorly ponent is substantially smaller than the defined in 2D devices due to the presence of usual leakage floor for any considerable SBH non-idealities such as traps, non-homogenous (ϕ > 100 meV). For example, a contact- Bn doping due to surface contaminants, and van dominated 2D FET with an SBH of 0.3 eV der Waals gap [138–140]. Moreover, for doped should result in a maximum thermionic cur- contacts,deviceswiththick(>2nm)tunnelbar- rent of 6 nA at flat band condition at 300 K, riers, and few-layer (>5) devices, the assump- whichisreducedtolessthan1fAforT<77K. tion of pure thermionic current is difficult to Thus, it is extremely difficult to measure any verifyduetothehightunnelingcurrentarising thermionic current at low temperatures below fromthechannelregionunderneaththecontact 100 K. This means that the currents observed [121,137,141–144]. at such temperatures usually come from TFE (ii) Weaker thermionic current at lower tem- orFEcomponentsthatshowweaktemperature peratures: More often than not, the Arrhe- dependence [35, 145] and therefore leading to nius method for SBH extraction in 2D erroneousSBHextraction. 17 2DMater.8(2021)012002 SBMittaetal Figure10.(a)Schematicillustrationofa2DMOScapacitor.(b)IdealC–V characteristicsofaMOScapacitoratlowandhigh frequenciesindicatingdifferentregimes(accumulation,depletion,andinversion). 7.Trappedchargesanddielectricconstant is often used to mechanically exfoliate the 2D crys- tals and to transfer them to desirable substrate. But 7.1.Capacitance–voltagecharacterization thepolymerresiduesfromPDMSstampdegradethe C–V measurementisarobustelectricalcharacteriza- properties of transferred 2D materials via the form- tion method used to assess the properties of defects ation of interfacial bubbles and wrinkles, which res- in insulating and semiconducting materials and to ultsincontaminantstrappedattheinterfacebetween probethevariationinthespacechargedistributionin thesubstrateandthe2Dmaterial.Toavoidandmin- a semiconductor with applied gate voltage. It can be imize the formation of residues at the interface dur- usedtomeasurevariousparameters,suchasinsulator ing the stacking of such materials, alternative poly- capacitance(C)oroxidecapacitance(C ),flatband mers,suchaspoly(propylene)carbonate,canbeused i ox voltage, dopant concentration, interface traps, and [146].Afterfabricatingclean2DMOScapacitors,the dielectric border traps, which are typically analyzed electricalmeasurementsareconductedusingasemi- from metal-oxide-semiconductor (MOS) or metal- conductor parameter analyzer and an LCR meter. insulator-semiconductor(MIS)structures.Thebasic Care should be taken to ensure that the instruments structureofaMOScapacitorconsistsofmetal,oxide, areusedwiththelowestpossibleexternalimpedance and a 2D semiconductor material (n- or p-type) as to minimize the parasitic capacitances. Although 2D shown in figure 10(a). When performing the C–V materials have attracted a great deal of interest for measurementsof2Dmaterials,alargegatedarea(i.e. advancedelectronicapplicationsduetotheirtunable channelarea)withhighsignal-to-noiseratioandlow bandgaps and high surface-to-volume ratios [147– parasiticresistancesisrequiredtoensurethereliabil- 149], the device performance is strongly affected by ity of the measurements and analysis. From a device various 2D materials-related processing issues, such perspective, a 2D material-based MOS capacitor has as the adsorption of H O molecules from the envir- two distinct interfaces: metal/semiconductor inter- onment, structural defects (vacancies, grain bound- face (top) and semiconductor/oxide interface (bot- aries,dislocations,etc.),andtheinterfacechargetraps tom). Both interfaces are crucial to examine as they due to the interactions with dielectric materials (e.g. arecoupledtoeachother.TheidealC–V curveofdif- SiO ,Al O ,HfO ),whichresultsinhysteresisinC–V 2 2 3 2 ferentregionsofaMOScapacitorisillustratedinfig- (I–V)characteristicsanddegradationofelectronand ure10(b).TheworkingconditionofaMOScapacitor holemobilities[150–154].Zhuetalstudiedtheinter- depends on the applied V and can be divided into facialpropertiesofaHfO /monolayerMoS usingC– GS 2 2 three different regimes: (i) accumulation, in which V measurements and observed a double-hump fea- majoritycarriers(electrons)areaccumulatednearthe ture in the C–V curve characterized to different gate 2Dsemiconductor-dielectricinterface;(ii)depletion, voltages and frequencies, revealing traps in CVD- in which majority carriers become depleted at the grownMoS [155]. interface; and (iii) inversion, in which the density of When working with 2D materials, due to their majority carriers continues to decrease while that of inertsurfacesandtheabsenceofdanglingbonds,itis minoritycarriersincreases. difficulttoformauniformandhigh-qualitydielectric When attempting to fabricate the 2D MOS film,butthisgoalcanberealizedwithpropersurface (or MIS) vertical capacitors, various issues can be functionalization [156, 157]. Pretreatment of the 2D encountered. For vertical stacking of 2D materials, materialsurface(e.g.MoS )withoxygenplasma(O ) 2 2 a polymer, e.g. polydimethylsiloxane (PDMS) stamp or ultraviolet/ozone (UV/O ) has been considered 18 2DMater.8(2021)012002 SBMittaetal −1 −1 1 1 1 1 to enhance reactivity before high-k deposition to C = − − − , (35) it decreasethedensityofinterfacetraps[158–161].Pre- C C C C LF ox HF ox viously, the quartz substrates were used for the fab- rication of MIS capacitors to eliminate the parasitic it D = , (36) capacitances between the metal pads and the sub- it strates [162]; the C–V measurements of intermedi- where C is the capacitance of interface traps when ate(WSe ,1.2eV)andnarrowbandgap(blackphos- it all the traps react with AC signal at low frequency, phorus, ~0.3 eV) materials showed high-frequency and C and C are the capacitances measured at (unipolar) and low-frequency (ambipolar) behavior, LF HF low and high frequencies, respectively [158, 172]. respectively. 13 −2 −1 Liu et al evaluated D (10 cm eV ) in BP and it 7.2.Trappedchargesin2Dmaterials WSe -basedMIScapacitorswithAl O asadielectric 2 2 3 High-quality interfaces are crucial for high- usingtheparallelconductance(G ),whichisextrac- performance 2D devices due to the large surface- tedfromcapacitanceandconductancemeasurements to-volume ratio of 2D materials [163–166]. Charges [162],givenas trapped in the interface, either positive or negative, 2 2 ω G C m ox originate from structurally induced defects at the G = , (37) 2 2 G + ω (C −C ) ox m gate-dielectric and dielectric-semiconductor inter- m faces that are capable of trapping and de-trapping where ω is the measurement frequency, C is the charge carriers. The trapped charges in 2D device capacitanceofthedevice,andG istheconductance. structures have been quantitatively analyzed using D iscalculatedusing[155,162,170], it the capacitance and AC conductance measurements 2.5 G [155, 163, 167].Thedensity ofinterfacetrapscanbe D = . (38) it −2 −1 q ω determined by D = ∂N /∂E (cm eV ), where it it peak D is the interface trap density, N is the number it it AsignificantdecreaseinD wasreportedina2DhBN it of interface traps per unit area, and E is the energy. capacitor [162]. A low-temperature high-k depos- Figure11(a) illustrates various origins of interface itionmethodledtotheformationoftrapsassociated statesinahigh-k/MoS /oxidestructure[168]. with the dielectric known as border traps or near- Researchershaveemployeddifferentmethodsfor interfacialoxidetraps[173].Thesedefectsresponded interface analysis and extracted different types of to a change in V in the gate dielectric at some dis- GS trapped charges, such as interface trapped charges tance from the interface, and therefore induce hys- and dielectric border trapped charges (or oxide teresisinC–V measurementsandareresponsiblefor charges) [158, 161, 168–170]. For example, the thefrequencydispersionintheaccumulationregion. band diagrams of the interface and border traps in There have also been studies that determined the HfO /MoS are shown in figure 11(b). The inter- 2 2 density of border traps, as distinct from interface face traps in MoS bandgap dominate the C–V traps, using multi-frequency C–V characteristics of responsein the depletion region, whereas the border HfO /MoS and HfO -Al O /MoS top-gate stacks 2 2 2 2 3 2 traps in HfO dominate in the accumulation region. (figure11(d))[159,160]. The interface traps were investigated and theD was it extracted using frequency-dependent C–V measure- 7.3.Dielectricconstantsof2Dmaterials ments. The typical mid-gap D at the SiO gate The dielectric constant (ε) of a material is a fun- it 2 10 −2 −1 dielectrics/Siinterfaceis~10 cm eV ,whilethe damental electrostatic property that can be used to D of the high-k dielectric/Si interface ranges from determine the capacitance, charge screening, and it 11 12 −2 −1 10 to 10 cm eV [171]. One study examined energy storage capacity of electronic devices. ε also the density distribution and dynamics of trap states plays a significant role in defining the active inter- in CVD-grown MoS using capacitance measure- actions that take place between charged particles in ments;thetrapswereshowntocolonizethemid-gap thematerialandcontainsinformationaboutthecol- (Type M trap) and band edge (Type B trap) regions lectiveoscillationsofelectrongas,plasmons,excitons, (figure11(c))[155]. and quasiparticle band structures [174, 175]. The TheinfluenceofhighinterfacestatedensityD on unique structure of 2D layered materials leads to it high-k/2Ddevicecharacteristicshas inspired extens- anisotropic physical properties between the in-plane iveresearchonpassivationofthehigh-k/2Dinterface and out-of-plane directions, e.g. inhomogeneous to reduce D [158–161]. D most likely originates dielectricstrengthandCoulombinteractionstrength it it from the oxygen atoms that fill the sulfur vacan- characterized by ε; this is unlike conventional iso- ciesduringUV/O functionalizationtreatment[160]. tropicmaterialssuchassilicon.Thetheoreticaldielec- D can be calculated with the conventionalhigh-low tric property of 2D materials such as graphene and it frequency and multi-frequency methods using the MoS is anisotropic owing to the different nature followingequations of bonds in the in-pane and out-of-plane directions 19 2DMater.8(2021)012002 SBMittaetal Figure11.Interfaceandbordertrappedcharges.(a)Representationofvariousoriginsofinterfacestatesinahigh-k/MoS /oxide structure,whereV issulfurvacancies.(b)Schematicillustrationoftheenergybanddiagramsofinterfaceandbordertraps distributedinHfO /MoS .(c)D andtimeconstantoftrapstates(τ )asafunctionofV ofCVD-grownMoS onaSiO /Si 2 2 it it GS 2 2 substrate[155].(d)Comparisonofhigh-lowfrequencyandmulti-frequencymethodsofmeasuringbordertrapdensity(N ) bt andD .Thedifferenceintrapdensityshownbetween0and0.5Viscausedbythebordertrapresponseatlowerfrequencies.The it leftandrightinsetfiguresshowtheequivalentcircuitincludingC andtheextracted τ ,respectively[159]. it it (ε and ε ) [176–178]. Chen et al experimentally time-domain reflectometry, where the ε of hBN || extracted the ε of MoS from C–V measurements decreaseswithanincreaseinfrequency(figures12(b) based on vertical MIS capacitor structures by using and(c))[180].Theconfinednatureofatomicallythin thefollowingrelation: 2D crystals associated with the anisotropic dielectric screening has created long-term debates whether the MoS dielectric constant truly represents the dielectric fea- ε = , (39) MoS −1 −1 C −C min tures of such low-dimensional systems. The ε values accounted for by both theoretical and experimental approachesvarybymorethananorderofmagnitude −1 d 1 MoS [181].Therefore,futuredevelopmentsthatallowreli- C = + (40) min ε C MoS g ableandprecisemeasurementsof εareneeded. whereC istheminimumcapacitancemeasuredat min 8.Correlatingdeviceparametersto V <0V,d isthethicknessofMoS , ε isthe GS MoS 2 MoS 2 2 −1 nanoscalematerialproperties 1 1 dielectric constant of MoS , C = + 2 g C C BN in is the geometric capacitance, C is the geomet- Untilthissection,wehavedescribedtheextractionof BN ric capacitance of hBN, and C is the interlayer electricalparametersinthemacroscopictransportof in capacitance originating from the interlayer spacing 2D devices, mainly focusing on FET structures. The betweenhBNandMoS (figure12(a))[179]. devicepropertiesandperformancearelargelyaffected The ε as a function of the frequency (dielectric by both intrinsic (vacancies, anti-sites, substitutions, dispersion) of an hBN-based metal-insulator- and grain boundaries in polycrystalline samples) metal (MIM) capacitor was demonstrated using and extrinsic (strains due to surface roughness 20 2DMater.8(2021)012002 SBMittaetal Figure12.Extractionofthedielectricconstants(ε).(a)The εofMoS (ε )with(bluedots)andwithout(greendots) 2 MoS countingtheinterlayercapacitanceasafunctionofMoS thickness(d )[179].(b)Aschematicillustration(top)andanoptical 2 MoS microscope(OM)image(bottom)ofa32nm-thickhBN-basedMIMcapacitor(scalebarofintheOMimage:20 µm).(c)The extracted εofhBNasafunctionofappliedfrequency. εremainsstableatlowfrequencies(regionI),whereas εappearssmallerat higherfrequencies(regionII)sincethechargesareallowedlesstimetoorientthemselvesinthedirectionofthealternatingfield. TheinsetshowsthedispersioncharacteristicsofhBNflakeswithdifferentthicknesses[180]. and ripples, electron-hole puddles caused by charge density can be calculated using the following equa- impurities in a SiO substrate, chemical adsorbates, 2 E 1 F tion, n = , where ℏ is the reduced Planck π ℏv polymer residues, etc) disorder [105]. For example, constant, and v is the Fermi velocity of graphene thegrainboundaryinagraphenedevicecanaffectthe [191, 192]. A space charge region in a 2D semicon- sheet resistance depending on the grain size accord- ρ ductor,whichcanbecapacitivelycoupledwiththeair G GB G ingtotheequationR =R + ,whereR isthe SH SH SH gap between the tip and sample, should be carefully averagesheetresistanceofthegraphenegrains, ρ is GB considered for the measurements. Scanning capacit- the average grain boundary resistivity, and l is the ance microscopy, which measures local differential average grain diameter [182]. The charge inhomo- capacitance, allows for mapping of the carrier (dop- geneityinducedbytheSiO substrategivesrisetocar- 11 2 ing)densityandpolarityprofile,aswellasthemeas- rier density fluctuation of up to ~4.5 × 10 #/cm urementoftrappedchargesandquantumcapacitance at the sub-10 nanometer-scale length, as shown in [187,193,194]. figure13(a)[183,184].Mechanicalandsurfacemor- Scanning tunneling microscopy (STM) has phology (e.g. a crested substrate)-induced strain can become a core technique for exploring the emer- engineerthelocalbandgapandmobilityof2Dmater- gent physics of newly discovered materials. Since the ials[185,186].Theinfluencesofthedisorderarevery discovery of 2D materials, this technique has been difficult to characterize solely by macroscopic trans- widely employed to locally map the atomic struc- portunlessnanoscalecharacterizationtechniquesare ture and electronic properties of various 2D materi- utilized. In this section, we introduce various SPM als [198–200]. Due to the wide application of STM, techniques as supporting methods that enable local it has become an ideal tool to reveal the intrinsic characterization of 2D materials correlated with the atomicdefectsin2Dmaterialsduetothelowenergy electrical parameters discussed in the previous sec- of the tunneling electron, which should leave the tions.DetailedreviewsonSPMsofnanomaterialsand intrinsic defect structure to remain unaffected. Fig- nanoelectronicsarealsoprovidedin[187,188]. ure 13(d) shows the basic working principle of the Kelvinprobeforcemicroscopy(KPFM)isawidely STM technique, in which the STM tip (platinum- used SPM technique for nanomaterials and nano- iridium blend) scans the surface of a sample and electronics.KPFMmeasurescontactpotentialdiffer- measures the tunneling current as a function of the ences (V ) to provide a quantitative measure of CPD distance (d) between the tip and the surface of the the work function difference between a sample and sample. The equation of governing tunneling cur- a probe tip. Figure 13(b) shows a schematic illus- 2d 2m∆ϕ tration of a KPFM measurement setup for graphene rent is written as I(d) ∝eV ×e , where m inwhichAC(V )voltagegeneratesoscillatingelec- is the electron mass, ∆ϕ is the work function dif- AC trical forces and DC (V ) voltage is applied to nul- ference, ℏ is the reduced Planck constant and V is DC b lify the oscillating electric forces when V = V the offset bias voltage. The STM imaging technique DC CPD [189, 190]. The ∆V (contact potential difference has been applied on various 2D materials, includ- CPD between electrode and sample) is used to obtain the ing graphene, black phosphorus and TMDCs, to work function of graphene, which is correlated with reveal the electronic nature of intrinsic defects such the Fermi energy (E ) of graphene, a relative energy as point defects, surface defects, dopant impurities, levelwithrespecttothechargeneutralpoint(CNP), dislocation,andgrainboundariesinbulkaswellasin as shown in figure 13(c). For graphene, the carrier atomicallythinmonolayers[201–206].Anexampleof 21 2DMater.8(2021)012002 SBMittaetal Figure13.(a)ChargedensitymapobtainedfromanSTMdI/dV spectrumrevealingchargefluctuationingrapheneinducedbya SiO substrate[183].(b)SchematicillustrationofKPFMmeasurementsetupand(c)theextractedE ofgraphenedependingon 2 F theappliedgatevoltages[189].(d)SchematicmodeloftheworkingprincipleoftheSTMsystem.(e)AtomicallyresolvedSTM imageofintrinsictungsten(W)vacanciesinmultilayerWSe .Insetshowsanenlargedimage.(f)LogarithmicdI/dV spectrafor K/W (red)andintrinsicW (black)inmultilayerWSe [195].(g,h)Deviceschematicandresistancedistributioninthe vac vac 2 CAFMmeasurementofthelocalconductivityofgrapheneonSiCduetodifferencesinSiCtopography[196].(i)SBH measurementofmetal-MoS contactsusingtheCAFMtechnique.ThetechniqueallowsnanoscalemappingofSBH[197]. anSTMimageofWSe isgiveninfigure13(e)andthe of epitaxial graphene on a SiC substrate [196]. The corresponding dV/dI spectra showing the bandgap device structure is shown in figure 13(g); epitaxial and defect-induced mid-gap states are depicted in graphene was grown on a 4H-SiC substrate using figure13(f). sublimation and then scanned with a Pt-coated Si Anotherimportant surfaceand electrical charac- tip. The local current in this device differs on the terizationmethodologyusedinthefieldof2Dmater- (112n) facets compared to the (0001) basal plane ials is conductive atomic force microscopy (CAFM). terraces, which indicates that the local conductivity ThelateralresolutionofCAFMsitsrightbetweenthat of graphene can vary significantly depending on the of STM and conventional electrical probes. CAFM facetsofSiC,asshowninfigure13(h).Anothernovel uses an ultrasharp conductive tip to apply electrical application of CAFM is to investigate current trans- stress on the sample of interest. Typical CAFM sys- port at nanoscale metal-TMDC interfaces, as shown tems can provide a lateral resolution of ~10 nm, infigure13(i)[197].TheCAFMtipmakessmallarea which is adequate for characterizing small chan- contacts with TMDCs such as MoS , the surface of nel (sub-100 nm) 2D devices. In the field of 2D whichcanbethenscannedonthesurfacetoproduce materials, CAFM is generally used to map the lat- a map of the nanoscale contact resistance and SBHs. eral inhomogeneity in current transport that arises Given the difficulty in fabricating high-quality con- from several intrinsic and extrinsic factors, such as tacts in 2D materials, CAFM offers a simpler means charge puddles, polymer residues, grain boundar- of characterizing current transport at the metal-2D ies, and trap states. Giannazzo et al used CAFM materialinterfaceandhastheadditionaladvantageof to determine the substrate-dependent conductivity producingareascans[207]. 22 2DMater.8(2021)012002 SBMittaetal 9.Outlookandconclusion fundedbytheNationalResearchFoundationofKorea (NRF). Electrical characterization methods for atomically thin2Delectronicdevicesmustberevisitedsincethe ORCIDiDs techniquesusedforconventional3D-basedsemicon- ductorsdonotproperlymodel2Ddevices.Also,chal- MinSupChoi https://orcid.org/0000-0002-8448- lenges remain concerning the characterization of the 4043 electricalpropertiesofanisotropic2Dlayeredmater- WonJongYoo https://orcid.org/0000-0002-3767- ials, which show different carrier transport beha- 7969 vior between the in-plane and out-of-plane direc- References tions due to the tunnel barrier formed only along theout-of-planedirection.Electricalcharacterization [1] NovoselovKSetal2016Electricfieldeffectinatomically techniquesuniquetosurface-dominant2Dsemicon- thincarbonfilmsScience306666–9 ductors with layered materials need to be developed, [2] ZhangY,TanYW,StormerHLandKimP2005 which are separate from the techniques used for ExperimentalobservationofthequantumHalleffectand Berry’sphaseingrapheneNature438201–4 conventionalsemiconductors.Forexample,electrical [3] NovoselovKS,GeimAK,MorozovSV,JiangD, response-based surface characterization techniques KatsnelsonMI,GrigorievaIV,DubonosSVand suchasSPMscandetectlocalizedchargedistribution, FirsovAA2005Two-dimensionalgasofmasslessDirac doping density, defects, SBHs, mid-gap states, and fermionsingrapheneNature438197–200 [4] LiXetal2009Large-areasynthesisofhigh-qualityand bandgap,asdiscussedinthelastsection.Thesemeth- uniformgraphenefilmsoncopperfoilsScience3241312–4 ods can also be advantageous in analyzing charge [5] KimKS,ZhaoY,JangH,LeeSY,KimJM,KimKS,Ahn traps, which give rise to Fermi level pinning and J-H,KimP,ChoiJ-YandHongBH2009Large-scale leaky device performance. 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Journal
2D Materials – IOP Publishing
Published: Nov 24, 2020