Characterization of Single Defects inUltrascaled MoS2 Field-Effect TransistorsBernhard Stampfer,*,† Feng Zhang,‡ Yury Yuryevich Illarionov,†,¶ Theresia Knobloch,† Peng Wu,‡

Michael Waltl,† Alexander Grill,† Joerg Appenzeller,*,‡ and Tibor Grasser*,†

†Institute for Microelectronics (TU Wien), Gusshausstrasse 27-29, 1040 Vienna, Austria‡Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, United States¶Ioffe Physical-Technical Institute, Polytechnicheskaya 26, 194021 St-Petersburg, Russia

*S Supporting Information

ABSTRACT: MoS2 has received a lot of attention lately asa semiconducting channel material for electronic devices, inpart due to its large band gap as compared to that of other2D materials. Yet, the performance and reliability of thesedevices are still severely limited by defects which act astraps for charge carriers, causing severely reducedmobilities, hysteresis, and long-term drift. Despite theirimportance, these defects are only poorly understood. Onefundamental problem in defect characterization is that dueto the large defect concentration only the average responseto bias changes can be measured. On the basis of such averaged data, a detailed analysis of their properties andidentification of particular defect types are difficult. To overcome this limitation, we here characterize single defects onMoS2 devices by performing measurements on ultrascaled transistors (∼65 × 50 nm) which contain only a few defects.These single defects are characterized electrically at varying gate biases and temperatures. The measured currents containrandom telegraph noise, which is due to the transfer of charge between the channel of the transistors and individualdefects, visible only due to the large impact of a single elementary charge on the local electrostatics in these small devices.Using hidden Markov models for statistical analysis, we extract the charge capture and emission times of a number ofdefects. By comparing the bias-dependence of the measured capture and emission times to the prediction of theoreticalmodels, we provide simple rules to distinguish oxide traps from adsorbates on these back-gated devices. In addition, wegive simple expressions to estimate the vertical and energetic positions of the defects. Using the methods presented in thiswork, it is possible to locate the sources of performance and reliability limitations in 2D devices and to probe defectdistributions in oxide materials with 2D channel materials.

KEYWORDS: random telegraph noise, MoS2, SiO2, transistor, single defects, charge trapping, dichalcogenides

Molybdenum disulfide (MoS2) is one of the mostpromising semiconducting transition metal dichalco-genides and is considered for applications in beyond-

CMOS electronic devices. The direct electronic bandgap ofsingle-layer MoS2 can be as high as 2.6 eV,1,2 which makes thismaterial an interesting candidate for digital device applications.In addition, there is some understanding that MoS2 field-effecttransistors (FET) are suitable for high-frequency applications3

and circuit integration.4−6 In particular, numerous realizationsof MoS2 FETs can be found in recent literature reports.7−14

However, these studies mostly deal with the analysis of theperformance of these devices, as well as the exploration offabrication techniques allowing them to realize their theoreticalperformance potential predicted by simulations.15

One of the most important performance limitations is due todefects which can arise from both nonoptimized deviceprocessing and fundamental properties of insulators with their

unique defect bands.16−18 These defects can exchange chargeswith the channel, thus strongly affecting the device performanceand reliability.18,19 Although these problems are not oftendiscussed in the current 2D literature, they are of utmostimportance for industrial integration of these new technologiesand the transition from device prototypes to commercial 2Ddevices.The reliability of previously investigated MoS2 FETs, as well

as of 2D devices in general, is typically reduced by chargetrapping in oxide traps20−23 with very broad distributions oftime constants24 and trapping sites on top of the channel, forexample, adsorbates and water molecules.19,25 Charge trappingdecreases the mobility, and results in a hysteresis of the gate

Received: January 11, 2018Accepted: June 7, 2018Published: June 7, 2018

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transfer characteristics,18,19,25−28 as well as in partiallyrecoverable threshold voltage shifts which appear whenever abias is applied to the gate,10,19,29,30 conventionally known asbias-temperature instabilities (BTI).31−36

Although some understanding of these issues for different 2Dtechnologies has been achieved in our previous works,18−20,23

all these studies have been performed on large area deviceprototypes with micrometer dimensions. Since the defectdensities in these devices are considerable (we obtained valuesof ∼1012 cm−2 in our studies mentioned before, whichcorresponds to 106 traps for, e.g., a 10 μm × 10 μm device),the observed drifts of the transistor characteristics are thecollective response of a large number of defects.However, a considerably improved understanding of the

physical mechanisms of charge trapping and the nature of theinvolved traps can be obtained via the characterization ofindividual defects. Such a characterization is possible inultrascaled devices which contain merely a few defects withinthe channel area.36 As the channel area of a device is reduced,the number of defects in the devices decreases, but at the sametime their individual influence on the channel of the deviceincreases.37 This leads to an increase in the noise level of thedrain current as compared to bigger devices. In particular,charging and discharging of single defects can be observed assteps in the drain current.This issue is known as random telegraph noise (RTN)38 and

can be observed only in scaled devices. Statistical character-ization of RTN signals caused by every particular defect allowsthe extraction of the capture and emission time constants (τcand τe, respectively), trap level, activation energy, and verticalposition of this defect,39 thus giving insights into theunderstanding of the microscopic defect properties.Typically, RTN analysis is possible if only a handful of

defects are present. This implies that for a given defect densityD, the device area has to be scaled A = 5/D. On the basis of ourprevious studies, in which we extracted a D of about 1012/cm2,an area of 50 nm × 50 nm would be required to reach this singledefect limit (see Figure S1 in the Supporting Information (SI)).Therefore, we fabricated MoS2 FETs and report sub-100 nm

devices which contain only individual discrete defects withinthe channel area.By performing statistical analysis of a number of RTN traces

measured on different devices, we extract defect levels andvertical positions of these defects and discriminate betweenoxide traps and adsorbates on top of the MoS2 channel. Thispresents a considerable breakthrough in the overall under-

standing of the reliability and microscopic defect properties inMoS2 FETs.

RESULTS AND DISCUSSIONDevice Fabrication and Measurement. In total, about 30

ultrascaled MoS2, Schottky barrier (SB)-FETs with channellengths of about L = 50 nm and widths of about W = 65 nmwere fabricated on a 20 nm thick SiO2 gate dielectric. For thechannel, MoS2 flakes with thicknesses from 5 to 15 nm wereexfoliated onto the SiO2 substrate, masked using an e-beamlithography step and dry etched. Finally, Ni electrodes weredeposited on top of the channel material. Additional details onthe manufacturing process can be found in the methodssection. The devices are three-terminal structures with sourceand drain on top controlled by a highly doped Si back-gate (seeFigure 1a). A scanning electron microscopy (SEM) image of adevice can be found in Figure S2 in the SI.The band gap of MoS2 depends on the number of layers and

neighboring materials. It ranges from as high as 2.6 eV for asingle-layer and decreases rapidly with the number of layers,down to 1.29 eV for bulk material. Its nature changes fromdirect (for a single layer material) to indirect (for multilayermaterial). With the flake thicknesses of the investigated devices(>8 layers for the thinnest flakes), the band gap will be close tothe bulk value. Transfer characteristics (Figure 1b, recordedfrom 10 V to −15 V in steps of −0.2 V with an integration timeof 640 μs) support the notion that these devices behave asnormally on SB-MOSFETs. This is a result of the choice of gatestack and the unintentional doping of the MoS2 channel. Theapparent high level of electron injection is a consequence of thesource/drain Fermi level pinning for the Ni-contacts to MoS2close to the conduction band edge.40,41 The rather large valueof the subthreshold swing (∼900 mV/dec) and the observedon−off ratio of around 105 are well understood consequencesof the Schottky barrier operation of the devices in conjunctionwith a high interface trap density in the 1013 cm−2 range and thelarge oxide thickness of the devices (see the device modelingsection in the SI for details). The device shows rather linearoutput characteristics (Figure 1c, recorded from 0 to 2 V insteps of 0.02 V with an integration time of 640 μs) for the lowdrain bias used during the RTN measurements. This is a resultof the small body thickness of these devices and should not beinterpreted as “ohmic” contact behavior.41

All RTN measurements were performed in completedarkness and in a vacuum (5 × 10−6 to 10−5 Torr) at differenttemperatures ranging from 100 to 373 K. For each device wefirst measured gate transfer (ID−VG) characteristics at different

Figure 1. Device schematics (a), transfer characteristics ID−VG with fitted subthreshold slope (b), and output characteristics ID−VD (c). Thedevice behaves as normally on nMOS transistor as expected for MoS2.

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temperatures to find current fluctuations caused by charging/discharging of single defects, and determine the VG rangeaffected by the defect. After this a number of ID(t) traces weremeasured for several voltage points in the interesting range,with VG varied in 50−100 mV steps. The latter was necessary toproperly resolve the VG dependence of τc and τe.Taking into account that time constants of the defects are

widely distributed, the recording time intervals for the ID(t)traces were varied from 0.1 s for faster traps to 1000 s forslower traps. This was necessary to capture as many discretecurrent steps as possible. To maintain a reasonable time-resolution of the measured ID steps, the number of measure-ment points was increased for longer traces. At the same time,the number of traces measured for each gate bias point waslarger for smaller time intervals, in order to obtain betterstatistics. Finally, defects were characterized at several temper-atures for the extraction of the energy barriers of the chargetransfer reactions.In Figure 2 we show measurements of single defects in MoS2

devices. During initial characterization, discrete steps inrecorded ID−VG sweeps were regularly observed, as shown inFigure 2a. This impact of individual defects on the transfercharacteristics is known from studies on silicon devices42 as theresult of a single defect capturing and emitting a charge. Withincreasing gate bias, this defect’s likelihood to capture anelectron from the conduction band increases as the energy levelof the defect shifts below the Fermi level. Once in its chargedstate, the defect causes a threshold voltage shift due to the

presence of the electric charge close to the channel, affecting itsconductivity. From silicon devices it is known that defects arealso visible in stationary drain current measurements if they areclose to the Fermi level at the applied gate bias. As such a defectrandomly charges and discharges, the measured drain currentshows discrete steps to a lower or higher value, respectively, aneffect called RTN.38 A number of RTN traces with defectsbehaving in a different manner are shown in Figure 2b−d. Thetime constants of the defects depend on their energetic andspatial position relative to the channel, the temperature, and thenumber of carriers in the channel. Thus, extracting their timeconstants under various conditions allows us to acquireimportant information on the defects and their surroundings.In Figure 2b we show a defect with time constants that are

independent of gate bias. In contrast, Figure 2c shows a defectwith a strong gate bias dependence. At a gate bias of −5 V, thebias dependent defect is mostly unoccupied, as indicated by thehigher current state. Already at −4 V, the drain current ismostly in the low state, as the average capture time decreasesand the emission time increases. The bias range where thedefect shows RTN corresponds to the bias range wheretrapping is visible in the ID−VG measurements, although therange might be shifted depending on the sweep rate anddirection of the ID−VG measurement. This microscopicbehavior is what is visible in larger devices as hysteresis, causedby the superpositioned effects of many different traps. A morecomplicated case called anomalous RTN (aRTN) is shown in

Figure 2. Impact of single defects is clearly visible in the drain current of our nanoscale devices. (a) ID−VG characteristics measured on deviceD at 335 K. A single trap changes its charge state during the VG sweeps and causes a Vth shift of about 300 mV. In large devices many of suchevents cause the hysteresis. (b) Drain current at stationary gate biases showing RTN. A single trap that captures and emits an electron causesdiscrete steps in the drain current. The time constants are widely distributed and for this trap independent of gate bias. (c) A similarmeasurement, but showing a defect with bias dependent time constants. (d) A defect producing anomalous RTN. Periods of fast switchingalternate with periods of inactivity. The insets of panels d and b show the Markov chains for these two and three state defects, which are partof the HMMs used to extract the time constants. The neutral state is denoted as (1), the charged state (2), while (1′) is a metastable neutralstate.

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Figure 2d, where normal RTN behavior is interrupted byrandom periods of inactivity.Extraction of Time Constants. To gain more insight into

the physical properties of the defects, it is necessary to extractthe time constants from the measured traces. The moststraightforward method to extract the capture and emissiontime for each bias point is to measure the duration of the high-and low-current states, and average the recorded times asindicated in Figure 2b. This method, however, is quitesusceptible to the noise observed on the very low currentsmeasured and typically only successful for simple RTN signalswith a single active trap.To extract the time constants of the defects in our more

complicated signals, we used hidden Markov models (HMMs)and the Baum-Welch algorithm, which are commonly used alsoin speech processing and the analysis of DNA.43 This methoduses a Markov chain as a model for the defect, as shown in theinsets of Figure 2b and d. The algorithm then iterativelyoptimizes the time constants of the model to most likelyrepresent the measured data (see the methods section fordetails).This allowed us to extract the time constants of a number of

defects. Four representative examples, termed A to D, areshown in Figure 3: Three of the defects (A, C, D) showednormal RTN behavior which can be described by a two-stateMarkov model. In contrast, defect B showed random periods ofinactivity (Figure 2d), indicating that it has an additionalmetastable state between the stable charged and dischargedstates. This is called aRTN and is known from measurements inSi/SiO2 devices.44 Anomalous RTN is usually explained by aconfigurational change at the defect site.36 Of the four defectspresented, two show a bias dependence of their characteristiccapture and emission times, while the other two exhibit no gatebias dependence. The latter is not observed in Si/SiO2 devicesand most likely due to adsorbates on top of the device.For the interpretation of the gate bias dependence we start

with a trap located in the oxide between the backgate and thechannel (i.e., an oxide defect) or just under the channel(dangling bonds or processing residue). Applying a gate biaswill result in a change of the energetic position of the traprelative to the energies of the carriers in the channel, which willin turn affect the time constants. A defect located within theMoS2 (e.g., an S vacancy), at the edge of the channel (e.g.,etching induced defects45) or an adsorbate on its top surface(moisture, processing contaminations), on the other hand, will

exhibit little to no shift in energy relative to the channel, andthus no gate bias dependence. To illustrate the dependence ofthe time constants on the position of the defect in the device,numerical simulation results for the time constants of a trappositioned at varying distances below and above the MoS2 layerare shown in Figure S3 in the SI. From the extracted timeconstants, it is already possible to estimate its vertical (d) andenergetic (Et) position for bias-dependent defects via therelations39 (see the SI for details on these estimations.)

τ τ≈d t k T

Vd ln( / )

dox Be c

g (1)

≈ +E E V qVd

t( )i it f G, G,

ox (2)

Here, tox is the oxide thickness, kB is the Boltzmann constant, Tis the temperature, τc,e is the capture and emission times, Ef isthe channel Fermi level, VG,i is the gate voltage at theintersection τc = τe, and q is the elementary charge.For bias-independent defects, however, not much can be said

about the defect level except that it is close to the Fermi level.Defects above the Fermi level spend more time in the morepositive charged state, while defects below spend more time inthe more negative state. In this case, measurements at morethan one temperature may be used to extract capture andemission barriers using the Arrhenius law. The differencebetween the barrier heights is equal to the difference betweentrap- and channel-levels.

Theoretical Considerations. A more sophisticatedapproach to extract trap parameters is to fit the extracteddata using numerical device simulation. This has the advantagethat all available data can be used to gather information aboutthe traps, and no estimations have to be made regarding theprefactors or the electric field.To simulate the time constants of individual traps, as a first

step the electrostatics of the simulated devices have to becalibrated to the measurements. To calibrate the simulateddevices, we first averaged the ID−VG curves recorded betweeneach RTN measurement to obtain proper reference curves.This was necessary as the charging and discharging of individualdefects has a large influence on the threshold voltage of theseultrascaled devices, as shown earlier in Figure 2a. The same canbe achieved by choosing a proper time constant and integrationtime when employing the Agilent HP parameter analyzer. With

Figure 3. Extracted capture and emission times (symbols) of four defects found in four separate devices. Each pair (quadruple for trap B) ofpoints represents the ID traces measured at a specific bias and temperature. The defects A and D show a rather large dependence on gate biaswhile defects B and C show no clear bias dependence. Defect B has an additional metastable state with large time constants (aRTN). The linesare simulation fits for traps B−D, linear fits for trap A.

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the reference curves, we could then fit the device parameters tothe measurement results.Calibration results for device D are displayed together with a

more detailed discussion of the extraction method in the SI(see Figure S4 and Table S1) and show excellent agreementbetween the measured transfer characteristics and the analyticalmodel. Additional details on the device modeling can also befound in the Methods section.The second step is to simulate the individual traps together

with the calibrated devices. Popular choices for charge trappingmodels are the simple Shockley−Read−Hall (SRH) and thephysically more accurate nonradiative multiphonon (NMP)models.36 These models differ in the calculation of the energybarriers for the transition, as illustrated in Figure 4a. NMPtheory is closely related to Marcus theory, which is the standardway of dealing with charge transfer reactions in physicalchemistry.46

In the SRH framework, it is assumed that the electronicenergy is sufficient to describe charge transfer reactions. Assuch, a thermal barrier for the charge carriers exists only fromthe energetically lower to the higher state. Depending on trapposition and gate bias this can be either charge capture from thechannel to the defect or charge emission from defect tochannel. The reverse barrier is always zero and the rate in thisdirection is determined solely by the prefactor k0.In the more accurate NMP framework, the structural change

at the defect site following a charge capture or emission event istaken into account. This structural change is typically describedassuming parabolic adiabatic potential energy surfaces along theconfiguration coordinates of the reaction. In a simplesemiclassical approximation, the energy barriers are takenfrom the difference between the intersection point of thepotential energy surfaces and the ground state energies of thesystem. This model has two additional parameters, namely R

(ratio of parabola curvatures) and S (Huang−Rhys parameter).Furthermore, additional energy barriers are required ifmetastable states are present and energetically accessible.47

Since the SRH model does not account for structural changesat the defect site, it can neither explain the voltage nor thetemperature dependence seen in the experimental data (seeFigure 4b). Thus, in the following we use the more completeNMP defect model.

Defect Properties. Using the calibrated device simulationsand the time constants extracted from the measured RTN, weextract defect parameter sets using the NMP defect model.An exemplary band diagram of one of the devices at two bias

points displaying the extracted positions of the four defects isshown in Figure 5. The extracted parameter sets are given inTable 1. For comparison we have also estimated the locationsand trap levels using eqs 1 and 2 and obtained reasonableagreement.For the four defects studied, the gate bias dependences of the

capture and emission times indicate a position above thechannel for bias independent defects B and C, and positionsbelow the channel for defects A and D.For defect A, eq 1 yields a distance to the channel of only

about 8 Å. Together with the very fast time constants in themillisecond range even at 100 K, this points to a SiO2/MoS2interface defect.Defects B and C are most likely located on top of the channel

as both the low bias dependence and the simulation resultsindicate. Possible defect candidates include adsorbed watermolecules and processing contaminants. Water molecules arethe most probable candidate, and have already been linked tothe hysteresis in large area transistors,25 although for defect Bthe high measurement temperature and complex behaviorcould indicate a more complex type of defect (e.g., an etchingrelated defect). Adsorbates were visible on the surface of the

Figure 4. Shockley−Read−Hall (SRH) and nonradiative multiphonon (NMP) trap models in comparison. (a) Charge transfer reactions in theSRH (top) and NMP (bottom) models with the model parameters in bold letters. Energy barriers in the NMP model are calculated from theintersection of two parabolas while the energy barrier in the SRH model is the difference in ground state energies. (b) Capture and emissiontimes of a defect in dependence of its temperature below and above the channel for SRH (top) and NMP (bottom) defect models. In the SRHmodel, only one of the time constants exhibits a meaningful temperature dependence at any given bias. The remaining temperaturedependence is a result of the prefactor in the Arrhenius equation, which is proportional to the carrier density in the channel. Bothtemperature and bias dependence of the SRH model are in contradiction with the measured data.

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device at the temperatures at which defect C was measured (seeFigure S5 in the SI). Energetically, both defects are locatedclose to the Fermi level. This is a necessary condition,otherwise either capture or emission time would lie outside themeasurement range and no RTN could be observed.Finally, defect D most likely is a bulk SiO2 defect. These

defects have been extensively studied using density functionaltheory (DFT) calculations,49 and the most likely defectcandidates seem to be hydroxyl-E′ centers. The simulationyields a distance to the channel of about 17 Å for this defect,about half of the result from the estimation formula (Equation1). This is an error in the estimation, because part of the bias-dependence results from the prefactors, which are not constantin this bias range. The large change in carrier density in thechannel leads to an overestimation of the distance as comparedto the results of the simulation.Plots of the fits for the individual defects, of the extracted

potential energy surfaces, and activation energies can be foundin the SI.

CONCLUSIONSWe have studied single defects in nanoscale (65 nm × 50 nm),few-layer MoS2 devices. We showed the effect of individualdefects on the drain current in dynamic (ID−VG) and static(RTN) measurements, and extracted time constants from themeasured traces. We found that part of the defects in thesedevices show time constants independent of gate bias, unlikethe defects commonly found in silicon devices. We argue thatthis is likely due to the position of these defects in the devices,and give equations to estimate spatial and energetic positions.We compared the SRH and nonradiative multiphonon trapmodels to find that the simple SRH model is unable to explain

the temperature and bias dependences of the measured dataandjust like in Si technologiesthe NMP model should beused. Using detailed TCAD simulations we have extractedphysical parameter sets of the measured defects. From theobtained defect parameters, we made claims as to the physicalnature of the studied defects. Using the presented methods, it ispossible to pinpoint defects in 2D-devices, and thus learn moreabout the feasibility of certain oxide and channel materialcombinations for microelectronic devices.

METHODSFabrication. MoS2 (SPI Supplies) flakes were exfoliated onto a 20

nm silicon dioxide (SiO2) substrate with underlying highly dopedsilicon using standard adhesive tape techniques. The 20 nm SiO2 layerwas used in the following as the gate dielectric. After the flake transfer,e-beam lithography was used to define the channel width (W ≈ 65nm) of the active device region, followed by plasma dry etching (SF6,10 sccm; Ar, 10 sccm; pressure, 3 Pa; RF source power, 50 W; RF biaspower, 50 W; time, 17 s). Next, Ni (65 nm) electrodes were depositedacting as source/drain contacts. This step defined the channel length(L ≈ 50 nm) of the back gated three-terminal structures. Flakethicknesses varied between 5 and 15 nm.

Measurement. Basic electrical characterization (Figure 1b,c) ofthe devices was performed at room-temperature in air using acommercial parameter analyzer (Agilent 4156C). RTN measurementswere performed in the vacuum chamber of a LakeShore probestationwhich is able to reach a minimum pressure of 5 × 10−6 Torr. Thevacuum chamber was connected to a dewar with liquid nitrogen, whilethe temperature was varied between 100 and 373 K and controlled bya LakeShore temperature controller. Electrical defect characterizationwas performed using measurement equipment built at TU Wien,which allows a wide range of current measurements down to themicrosecond range.50 Depending on the time constants of theobserved defects, measurement time intervals for each single tracewere varied from 0.1 s for faster traps to 1000 s for slower traps, withthe number of measurement points adjusted accordingly. To obtainenough data for statistical analysis, at each bias point we measured 50−100 traces for smaller time intervals and 5−20 traces for larger timeintervals. Where possible, defects were characterized at differenttemperatures, typically ranging within an 40−80 K interval.

Parameter Extraction. To extract the capture and emission timesof individual defects from the recorded data, we statistically analyzedtraces in the bias range where RTN was visible. For each bias pointand temperature we trained HMMs composed of two- or three statetraps to the traces with software developed at TU Wien using theBaum−Welch algorithm.43 The Baum−Welch algorithm is used on thedrain current measurements to give the most likely set of parameters(transition times, step heights) for the measured data given theMarkov model of the trap. The Markov model itself consists of anumber of nodes (the hidden states of the defect, e.g., 1, 1′, 2), theallowed transitions between these states (1 ⇋ 1′ ⇋ 2) and theobservables of the hidden states (e.g., states 1, 1′ → high current level,state 2 → low current level, measurement noise σ).

Simulations. The current flowing in a thin-body Schottky-barriertransistor, in the below or near threshold regime−which is where the

Figure 5. Simulated band diagram for 1.2 V (opaque) and −4.2 V(semiopaque) with extracted defect positions marked. The biasdependent traps A and D are located below the MoS2 layer, whilethe bias independent traps B and C are on top of it. The gray barsmark the well-known SiO2 defect bands.

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Table 1. Extracted Trap Parameters, Calculated with the Analytical Expressions 1 and 2 (Left), and from TCAD DeviceSimulation (Right). Energies Are Relative to the Conduction Band Edge

type approximation fit parameter

defect E1′,approx zapprox E1a ε1′1

a E1′ R1′2 S1′2ℏω zsimulated

16 (A)b 0.003 eV −0.8 nm25 (B) ≲0.010 eV ≈8.0 nm −0.149 eV 0.99 eV −0.017 eV 0.80 1.60 8.5 nm26 (C) ≲−0.018 eV ≈8.0 nm −0.016 eV 0.69 1.38 8.0 nm28 (D) −0.843 eV −3.2 nm −0.640 eV 0.52 0.33 −1.7 nm

aParameters for three-state defects only. bNo TCAD fit.

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defects in our study are located−is mainly determined by thetransmission of the Schottky barriers at the source and draincontacts.41 Thus, to model the characteristics of these devices andto translate the gate voltage axis into an energy scale, we used theanalytical Schottky-barrier model from Penumatcha et al.51 as the basisto extract the relevant device parameters and band movement from themeasured ID−VG curves. Moreover, since the transmission probabilityfrom source to drain for the ultrashort channels used in this study isimpacted little by scattering inside the MoS2 channel, the onlyadditional correction to the above model in the device on-state madehere is through the introduction of the density of states (DOS)dependent quantum capacitance CQ.

52 In this way not only a moreprecise extraction of energy levels of the defects near threshold isachieved, but this approach also eliminates the need to speculate aboutthe details of the impact of scattering inside the FET channel andintroduces no additional fitting parameters. Following this, we used theNMP trap model together with calibrated device structures to performthe single-trap simulations of the capture and emission times. Furtherdetails of the simulations are discussed in the Supporting Information.

ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acsnano.8b00268.

Single-defect limit for different 2D technologies; SEMimage of a device; dependence of capture and emissiontimes on trap position; device modeling; adsorbates onthe MoS2 surface; estimation of trap position and energy;detailed results for individual defects (PDF)

AUTHOR INFORMATIONCorresponding Authors*E-mail: stampfer@iue.tuwien.ac.at.*E-mail: appenzeller@purdue.edu.*E-mail: grasser@iue.tuwien.ac.at.ORCIDBernhard Stampfer: 0000-0001-5424-7488NotesThe authors declare no competing financial interest.

ACKNOWLEDGMENTSThe authors acknowledge the financial support through theFWF Grant No. I2606-N30.

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