Bandgap Extraction and Device Analysis of Ionic Liquid Gated WSe2

Bandgap Extraction and Device Analysis of Ionic Liquid Gated WSe2 Schottky Barrier Transistors Abhijith Prakash* and Joerg Appenzeller School of Electrical and Computer Engineering & Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States S Supporting Information *

ABSTRACT: Through the careful study of ionic liquid gated WSe2 Schottky barrier field-effect transistors as a function of flake thicknessreferred to in the following as body thickness, tbodycritical insights into the electrical properties of WSe2 are gained. One finding is that the inverse subthreshold slope shows a clear dependence on body thickness, i.e., an approximate square root dependent increase with tbody, that provides evidence that injection into the WSe2 channel is mediated by thermally assisted tunneling through the gate-controlled Schottky barriers at the source and drain. By employing our Schottky barrier model, a detailed experimental plot of the WSe2 bandgap as a function of body thickness is obtained. We will discuss why the analysis employed here is critically dependent on the use of the above-mentioned ionic liquid gate and how device characteristics are analyzed in detail. KEYWORDS: WSe2, bandgap, subthreshold swing, Schottky barrier FETs

T

ransition metal dichalcogenides (TMDs) are an emerging class of semiconductors that have received considerable attention by the electronic device community, in particular due to their layered structure and inherent 2D nature, which provides excellent electrostatic integrity.1−10 In order to evaluate the full potential of TMDs for device applications, understanding their intrinsic properties is critical. One such intrinsic property is the transport bandgap as a function of layer thickness. Theoretical calculations predict that apart from the change in bandgap due to the choice of TMD material, energy gaps in TMDs11,12 and other ultrathin body materials such as black phosphorus (BP)13−15 strongly depend on the number of layers. Those predictions have been experimentally confirmed to some extent by optical methods16−21 and for MoS2 as well as BP using transport measurements.22−25 Here we report the determination of the transport bandgap in WSe2 for various thicknesses by employing an analysis that is believed to be more appropriate than the often applied analysis of transfer characteristics ID− VGS that require the transconductance gm = dID/dVGS to be constant over an appreciable gate voltage range, a situation that typically does not occur in our ionic liquid gated TMD fieldeffect transistor (FET) data.

of the other TMDs and more importantly due to the ambipolar nature of its electrical characteristics, that is, its ability to support the injection and transport of both electrons and holes.26 The latter property is essential for inverters,27 and both of the above-mentioned properties are useful for realizing energy efficient switches such as tunneling field-effect transistors (TFETs).28,29 For the extraction of the desired bandgap information as a function of thickness, we built socalled ultrathin body Schottky barrier (SB) FETs where the entire channel between the metallic source and drain electrodes is gated. Using a model developed by us25,30,31 we analyze WSe2 SB-FET characteristics quantitatively to gain insights into the bandgap dependence on the number of TMD layers involved in transport. In the following we provide a short synopsis how this analysis is performed. Figure 1 displays schematically the expected transfer characteristics of an ultrathin body SB-FET for different drain bias values when the metal source and drain Fermi levels are aligned with the middle of the bandgap, as illustrated on the right of Figure 1 for positive and negative drain voltages (i.e., an SB height for electrons, Φn, that is equal to the SB height for holes, Φp). This picture captures approximately the situation in WSe2.31 Furthermore, the figure assumes that bands are under

RESULTS AND DISCUSSION WSe2 is an important member of the TMD family due to its smaller effective electron and hole masses if compared to most

Received: November 1, 2016 Accepted: February 6, 2017 Published: February 13, 2017

© 2017 American Chemical Society

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Figure 1. Transfer characteristics and associated band diagrams of an SB-FET with Φn = Φp under ideal gate control.

to the geometric screening length λ and approaches 60 mV/dec for vanishing λ (λ = 0).31 A good approximation for SS as a function of λ32 is

ideal gate control between the threshold voltages VTp‑P and VTn‑N that denote the transition between the device on- and offstate for negative and positive drain voltages respectively. Under this condition, the bandgap can be immediately deduced from Eg = q(VTn ‐ N − VTp ‐ P)

⎛k T ⎞ 1 SS = ⎜ B ⎟ln(10) ⎝ q ⎠ 1 − e(−d / λ)

(1)

(2)

where d mainly depends on material parameters such as carrier effective mass, and λ itself is given by33

if the two threshold voltages are determined for vanishing drain voltage values or if VTn‑N is measured for positive drain voltages and VTp‑P for negative VDS. Under these conditions it is always the source sideeither through electron or hole injection that determines the current flow, and the threshold voltages are determined by the line-up of the conduction (VTn‑N) or valence band (VTp‑P) with the source Fermi level independent of the actual VDS value. Figure 1 also illustrates how changing the drain voltage (and its polarity) impacts the observed device characteristics and that the relative shift between characteristics for different drain voltages (VDS) is uniquely determined by the actual VDS value if the above assumption about one-to-one band movement with the gate voltage (VGS) applies. For example, the right branch of the subthreshold characteristics for VDS = −0.9 V is shifted by 0.9 V to the left relative to the red line that is labeled n-FET and that is obtained for positive VDS values. Furthermore, the two band diagrams on the right illustrate how carrier injection as a function of VGS is enabled for different VDS polarities through Schottky barrier tunneling. The characteristic tunneling distance is given by the geometrical screening length λ in this case.31 This implies that for the condition sketched in the main panel of Figure 1 the inverse subthreshold slopes (SS) of the two subthreshold regions (SS = d(VGS)/d(log(ID))) between the threshold voltages are identical and will always be larger than 60 mV/dec (the thermal limit) even if the above one-to-one band movement with VGS holds true.31 Note in this context that the above arguments are not impacted if the lineup of the source and drain Fermi levels is not perfectly in the middle of the bandgap, as long as the slopes of the subthreshold characteristics are evaluated near the threshold voltages VTp‑P and VTn‑N (Supplementary note 1). SS is roughly proportional

λ=

εbody − x εox

tbodytox

(3)

where tox denotes the gate dielectric film thickness, εox is the value of the dielectric constant of the gate oxide, and εbody−x captures the dielectric constant of the channel material in the direction of transport. tbody is the so-called body thickness, the thickness of the semiconducting channel that replaces the maximum depletion width (WDM) that is typically found in eq 3 instead of tbody. As long as tbody is smaller than WDM, the above equation that is independent of the doping level in the channel is a proper description. Experimental Analysis. WSe2 flakes were micromechanically exfoliated onto substrates with 90 nm SiO2 as the topmost layer and highly doped Si beneath the SiO2. Electron beam lithography followed by electron beam evaporation has been used to define source/drain terminals. Channel lengths are designed to be 1.5 μm. Ni is employed as the source/drain electrode metal with a Ti/SiO2 passivation on each electrode for protection from the ionic liquid gate that is used to impact the channel potential. Flake thicknesses were determined by optical contrast after proper calibration and atomic force microscopy (AFM). To ensure that the gate indeed controls the band movement in the device off-statethe gate voltage range between VTn‑N and VTp‑Pin a one-to-one fashion, a sufficiently large oxide capacitance (Cox) is required to compensate for the effect of any finite interface trap density that results in an interface trap capacitance (Cit). Lowest values for Cit in the case of TMDs are 1627

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Figure 2. (a) Schematic device structure (b) Experimentally obtained transfer characteristics and (c) output characteristics of an ionic liquid gated SB-FET with a bilayer WSe2 channel, when operated as an n-FET. (d) Output characteristics of the same device when operated as a pFET.

Figure 3. Experimental device characteristics for various WSe2 channel body thicknesses.

Figure 4. Inverse subthreshold slope (SS) as a function of channel thickness for (a) electron branches and (b) hole branches. Dashed lines are fits using eq 2 as mentioned in the text.

reported to be 4 × 10−2 μF/cm2,34 and frequently values between 0.1 and 1 μF/cm2 are observed. Noticing that Cox for a 1 nm SiO2 gate dielectric is around 3.5 μF/cm2, only devices with the most aggressively scaled gate dielectrics will allow for a bandgap analysis as described above. In order to achieve such a

gate control, the ionic liquid diethylmethyl-(2-methoxyethyl)ammonium bis(trifluoromethylsulfonyl)imide, which has been shown to exhibit Cox values of at least 5 μF/cm2,35,36 is used as the dielectric in our study. To create the desired electric field in the channel region, a Ti/Au electrode is utilized as shown in 1628

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Figure 5. (a) Experimentally obtained transfer characteristics for ±0.9 V. (b) Extraction of the transport bandgap after shifting to compensate for hysteresis.

for thicker bodies. Figure 4 also shows the respective fits for electrons and holes employing eq 2, assuming a Cox of 5 μF/ cm2 and εbody−x of 8 (Supplementary note 2). “d” values of 4.3 nm and 4.1 nm are extracted for electrons and holes respectively, with a standard error of ±0.3 nm in the fitted values of d. While this trend has been reported before for other materials such as silicon30,32,37 and carbon nanotubes,37,38 it is here quantitatively analyzed for a TMD-based device. In particular this key finding underlines the benefit of twodimensional layered material systems for improved electrostatics and aggressive channel length scaling since it proves that the body thickness dependent geometric screening length λ indeed mediates transport through a TMD SB-FET. Note that the respective inverse subthreshold slopes were extracted for the electron branch under positive drain voltage conditions and for the hole branch for negative VDS. As we will discuss below in the context of the bandgap extraction, some charging occurs over the course of the measurement, resulting in slightly different SS values depending on the scan direction and drain voltage polarity.39 So-called “pulsed measurements”, where (a) a voltage pair of VGS and VDS is applied to the device, (b) the current is measured, and (c) the sample is subsequently left without any applied bias for about 10 s before (d) the next data point is obtained, are found to be almost hysteresis free for many prototype devices currently explored in academia.40−42 By comparing various sweep conditions with this type of pulsed measurements, we have identified that under positive (negative) drain voltage conditions a scan from positive (negative) to negative (positive) gate voltages allows extracting SS values for the electron (hole) branch. Last, we turn our attention to the extraction of the electronic bandgap in WSe2 as a function of its thickness using eq 1. Extraction of the transport bandgap using the method described in the previous sections requires obtaining subthreshold characteristics for positive drain voltages for scans from positive to negative gate voltages (called in the following n-FETs) and for negative VDS from VGS-scans in the opposite direction (called in the following p-FETs). Figure 5a shows such a set of experimentally obtained transfer character-

Figure 2a. The complete device structure is very similar to that described in one of our earlier articles9 and can be thought of as a top-gated SB-FET with a gate dielectric having an equivalent oxide thickness (EOT) in the sub-nanometer regime. Such a small EOT in turn translates according to eq 3 into a very small scaling length λ. While the value of λ does not impact the band movement in the channel and thus leaves VTn‑N and VTp‑P unaltered, it does impact the injection of electrons and holes from the source and drain and, according to eq 2, the inverse subthreshold slope SS. Before evaluating the bandgap and SS values as a function of TMD body thickness, we need to ensure that the gate control indeed allows for a one-to-one translation between gate voltage and band movement; that is, the gate capacitance is sufficient to compensate for any Cit contribution. Figure 2b shows in this context exemplary transfer characteristics of a bilayer WSe2 transistor at 300 K with an inverse subthreshold slope of close to 60 mV/dec and an offset of 0.4 V between individual VDSdependent hole branches that is identical to the applied drain voltage change. This set of curves provides evidence for the validity of our simple model (Figure 1). Figure 2c and d show the respective output characteristics of the device with clear current saturation at higher drain voltages and an approximately linear current change with drain voltage for small VDS values. As discussed in detail elsewhere,31 this IDS−VDS dependence is consistent with highly transparent Schottky barrier contacts for small λ values according to eq 3. Last, the extremely small λ value in the sub-1 nm regime also gives rise to the almost ideal SS value of 60 mV/dec despite operation in the Schottky barrier regime according to eq 2. With this set of control experiments in place we are now in a position to study how the device characteristics of WSe2 SBFETs are impacted by the thickness of the channel, i.e., tbody. Figure 3 displays the dependence of device characteristics on body thickness showing two trends that are quantitatively analyzed in the following: (i) change of SS and (ii) change of VTn‑N and VTp‑P and thus bandgap. Figure 4 displays the extracted SS values for both electron and hole branches as a function of tbody, indicating a clear trend toward larger SS values 1629

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channel, is the best exponential fit from our data for N ≥ 2 that describes this trend. Including the standard errors in fitting, the above equation can be best represented as Eg = (1.02 ± 0.02)eV + (0.84 ± 0.15)eV exp(−N/(3.20 ± 0.64)). It is also worth noting that the extracted transport gaps as determined in the present study are in general smaller than those inferred from optical experiments,16−19,46,47 a curious observation that deserves a more detailed comparison between electrical and optical data analysis.

istics for a bilayer WSe2 SB-FET when operated as an n-FET for a drain bias of 0.9 V and as a p-FET for a drain bias of −0.9 V. In both these cases the gate voltage was swept from the onstate of the majority branch to its off-state, as that approach yields reliable SS values for the majority branches as explained in the last section. This means the gate voltage sweep directions were different for the n-FET and the p-FET, which resulted in a hysteresis shift. This extrinsic shift can then be calculated from a comparison between the experimentally observed difference between the current minima (here Δ = 1.42 V) and the expected difference (0.9 V) according to the model depicted in Figure 1. For the case in Figure 5a a value of 0.52 V can be extracted. Figure 5b displays the complete set of subthreshold characteristics after correcting for the extrinsic hysteresis shift. Note that one would expect that the light blue colored nbranch for vanishing VDS coincides with the red symbols labeled n-FET and that the light red colored p-branch for vanishing VDS coincides with the blue symbols labeled p-FET if NO stretching of the light-colored subthreshold branches would have occurred. However, the scan direction dependent “stretch” of the SS values is clearly visible and further supports the choice of approach for the bandgap extraction as presented here. Next, VTn‑N and VTp‑P are determined by carefully identifying the gate voltage at which the exponential dependence of ID on VGS no longer holds true (see Supporting Information). For any curve where the minimum current point in the ambipolar device characteristics could not be directly observed since it was below the noise floor, an extrapolation of the two branches was employed. Last, the extracted bandgap values determined from eq 1 by using the experimental threshold voltage values were already corrected by a constant value of +90 mV that accounts for the finite temperature impact on the extraction of VTn‑N and VTp‑P as explained in the Supporting Information. Figure 6

CONCLUSIONS In conclusion, we have experimentally demonstrated ionic liquid gated Schottky barrier FETs on WSe2 from various flake thicknesses. Excellent device characteristics with steep inverse subthreshold slopes close to the thermal limit of 60 mV/dec at room temperature have been obtained. Based on a simple Schottky barrier model a clear experimental dependence of SS values on tbody has been explained. Moreover, the same model has been successfully employed here to extract electronic bandgaps for WSe2 as a function of its thickness over a wide range of body thicknesses. METHODS A standard micromechanical exfoliation technique was used to obtain WSe2 flakes on top of the substrates having 90 nm SiO2 on the surface and highly doped Si underneath. Electron beam lithography was used to pattern source/drain contacts while maintaining a channel length, for all devices, of 1.5 μm. Electron beam evaporation was used to deposit both the contact metal (Ni) and the passivation layers (Ti/ SiO2). The ionic liquid diethylmethyl-(2-methoxyethyl)ammonium bis(trifluoromethylsulfonyl)imide was used as the gate dielectric, and a Ti/Au stack was employed as the gate electrode.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b07360. Determination of threshold voltage at 300 K, supplementary notes, and notes on the error bars (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Abhijith Prakash: 0000-0002-8169-677X Notes

The authors declare no competing financial interest.

Figure 6. Transport bandgap of WSe2 as a function of its thickness, as extracted from the experimental transport data. Dashed line represents an exponential fit to our data.

ACKNOWLEDGMENTS This work was supported in part by the Center for Low Energy Systems Technology (LEAST), one of six centers supported by the STARnet phase of the Focus Center Research Program (FCRP), a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

summarizes our findings for different devices with varying body thicknesses. It should be noted that each reported Eg value is an average of the extraction performed for three different drain voltage pairs (e.g., +0.5 and −0.5 V). The apparent trend of decreasing bandgap with increasing body thickness is consistent with theoretical expectations from density functional theory (DFT) and tight binding calculations11,12,43−45 and is reported here from experimental electrical transport measurements. Most of those calculations predict an exponential dependence of Eg on tbody, and the expression Eg = 1.02 eV + 0.84 eV exp(−N/3.20), where “N” is the number of layers in the

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