Insight on the Characterization of MoS 2 Based Devices and Requirements for Logic Device Integration

MoS 2 basedtransistorsarebeingexploredasapromisingcandidatefordifferentapplications.Thetechniquesemployedtocharacterize these devices have been directly adapted from 3D semiconductors, without considering the validity of the assumptions. In this work, we discuss the limitations of two-probe (2P), four probe (4P) and transfer length methods (TLM) for extracting electrical parameters. Based on ﬁnite-element modeling, we provide design considerations for 4P structures to measure more accurately. Extracting the parameters from these techniques in the appropriate regimes, we identify contact resistance R C to be critical for scaled MoS 2 devices. Using 4P and TLM measurements along with temperature dependent measurements, we derive further insights into the behavior of the R C in the subthreshold and linear regime. Additionally, we propose an empirical model for the on-state contact resistance.

The ever-growing demand in semiconductor industry for faster, denser, efficient and robust technology has been driving the need for innovative solutions. Though, scaling was very effective in this regard, in recent years there are growing challenges for the conventional three-dimensional (3D) semiconductors. 1 One limitation is the reduced electrostatic control of the gate over the device channel as the channel length (L CH ) get smaller. To overcome this problem multigate technologies evolved and FINFET structures has become the de facto standard for high performance devices. However, even these devices face problems due to, among other things, the 3D nature of these devices. 2 Another possible solution is to use 2D planar technologies with ultra-thin body semiconductors to allow for better electrostatic control without losing the two-dimensional (2D) nature of the processing and the device. Nevertheless, this cannot be achieved with conventional 3D semiconductors due to performance degradation on thinning below 100 nm. Breaking the out of plane covalent bonds increases the dangling bonds on the surface, resulting in mobility degradation due to surface scattering of electrons. 3 In this context, the family of 2D crystals such as graphene and transition metal dichalcogenides (MX 2 ) offer an interesting case to investigate as alternate ultra-thin body channels. The layers being weakly bonded to each other only by Van der Waals forces and no out-of-plane covalent bonds, there are less dangling bonds than in case of thinning down 3D semiconductors. This enables better electrostatic control while avoiding degradation of transport properties. Among the 2D material crystals, MX 2 are specially interesting due to their semi-conductive properties. [4][5][6] They have also been predicted to have robust performance for channel lengths down to 15 nm. 7 Molybdenum disulfide (MoS 2 ), is commonly used as a representative of the MX 2 family. It has been demonstrated to be an interesting candidate for different applications such as low power logic devices, spintronic, valleytronic and also photo-voltaic devices. [8][9][10][11][12] It is imperative to evaluate certain parameters of MoS 2 and compare them to the actual requirements of industry. Some of the most relevant parameters are (1) the ratio between the on and the off current (I O N/O F F ), (2) the parasitic resistance (R C ), (3) the field effect mobility of the carriers (μ F E ), and the (5) carrier concentration (n 2D ).
Several methods have been used to characterize these parameters for MoS 2 devices. 4,9,13 In this work, we discuss the extraction of = These authors contributed equally to this work.
* Electrochemical Society Fellow. z E-mail: lockhart@imec.be aforementioned parameters by using two probe (2P), four probe (4P), and Transmission Line Measurements (TLM), clarifying the underneath assumptions and their effect on the MoS 2 device measurements. Extracting the relevant parameters from the techniques, we identify the potential problems in introducing MoS 2 in the industry. Further, we give some insight into the electron transport between the metal-MoS 2 interface with temperature measurements and characterization of effective thermionic emission barrier. Finally, we conclude with comparisons of the extracted parameters with respect to the present requirements from industry and suggestions for improvement.

Technique Discussion and Parameter Extraction
For the measurements and property extraction MoS 2 back-gated 4P-FETs and TLM structures were built. Sketches, optical images and additional information of the devices can be seen in Figure 1. For the fabrication, mechanically exfoliated MoS 2 flakes were transferred to a highly doped Si covered with 55 nm SiO 2 . The thickness of the flakes was assessed by atomic force microscopy (AFM) and they ranged between 3.2 nm and 5.91 nm. In Figure 1b a sample of an AFM height profile is shown. The contacts were fabricated using E-beam lithography and lift-off of 70 nm Au metal. After fabrication, the devices were annealed at 140 • C for 2 hr in vacuum. For the 2P characterization the device L1 from the TLM set D was used (L CH = 400 nm).
Two probe field effect transistors (2P-FET).-These are the easiest to implement and correspond directly to the final transistor to be used. The two probes refer to the source and drain contacts which act as both voltage and current probes. A potential difference (V DS ) is applied across these probes and the circulating current (I DS ) is measured. I DS is modulated with the gate potential with respect to the source (V GS ) by changing the induced carrier concentration in the MoS 2 film. The resulting transfer curve (I DS vs. V GS ) can be seen Fig. 2a. The upper axis of the graph is the displacement field (D = r × V GS /T O X ), This allows for comparison of the transfer curve with a different gate stack. In this device the total resistance is given by, Where R CH is the channel resistance and the parasitic resistance (R P ) contains all the other undesired resistances as contact resistance (R C ) and the resistance of any un-gated region (R A ) before accessing where L CH is the channel length, W CH is the channel width, C O X = /T ox = 6.28e −8F/cm 2 is the gate stack capacitance for 55 nm SiO 2 and q e is the electron charge. Thus from these equations it can be seen that the transconductance (Eq. 4) in the linear regime will be constant (Eq. 5) and in the saturation regime it will be linearly depending on V GS − V T H (Eq. 6). In Fig. 2b, a plot of the transconductance (gm) obtained from numerical differentiation of I DS can be seen. The plateau in gm, corresponds to the linear operation regime of the FET and mobility is extracted from this peak value using Equation 7. Further, V T H is the V GS value obtained by extrapolating the linear fit of the saturation regime to zero transconductance. The extracted parameters are listed in Table I.
In the case of overlapping back-gated MoS 2 device (as is the case for device D-L1 used in this work and most MX 2 literature), both of the previous assumptions (low R P and gate independent R P ) for 2P are invalid. First, the value of the parasitic resistance can be considerably higher than in conventional semiconductors and secondly because R C shows a strong gate-field modulation (demonstrated later with other techniques). This renders the above extraction inaccurate and additional test structures (such as 4P and TLM) are required to de-couple a) b) c) Figure 2. a) Transfer characteristics for device L1 from TLM set D (L CH = 400 nm). b) Transconductance of the same device. Line fitted to determine V TH and peak used to extract peak transconductance and mobility. c) Fitting to total resistance of the device for the regime where transconductance is mostly constant (linear regime). The data clearly fit to the model and the extracted mobility (22.71 cm 2 V −1 s −1 ) is higher than the original mobility obtained without excluding the effect of R C (14.5 cm 2 V −1 s −1 ).
) unless CC License in place (see abstract However, in this work, we provide an empirical relationship for R C that would still allow us to reliably extract parameters from 2P measurements and give a good estimation of R P as a function of V GS . We observe from other measurement techniques and fittings discussed in future sections, that gate-dependent R C in MoS 2 FETs exhibit a 1/V GS dependency in the linear operation regime to a good approximation as shown in Figure 10a. Thus the 2P R T in the linear regime is modeled with Equation 1 and R P and R CH are fitted as follows, For the case of overlapping gates as the whole channel is gated the access resistance (R A ) can be considered zero, and thus the R C is the main contributor to R P (Eq. 9). From the observations on the behavior of R C extracted in the next section R C can be empirically expressed as Equation 9. R CH is obtained from Equation 2 for the case when the absolute value of |V GS -V T H | |V DS /2|. The intrinsic mobility (without the effect of R C ) and the pre-factor of R C are obtained by least-square fitting to the 2P experimental data. V T H is still extracted by the methodology suggested above because the position for the onset of accumulation is not expected to be drastically affected by R C . Figure 2c shows that the aforementioned fitting method provides a good fit to the data. The extracted parameters are shown in Table  I. The mobility obtained from the fit is higher compared to previous extraction without the R C correction indicating that neglecting R C could lead to underestimation of the field mobility, specially for scaled devices where the R CH is in the same order of R C . Additionally, the fitting also allows to evaluate R C (4.4K ohm @VGS = 30V) for different gate bias without the need to build complicated test structures. Note that for back-gated devices, assuming constant R C in Equation 1 it yields poor fit with unrealistic values for both the mobility and contact resistance.

Four probe field effect transistors measurements (4P-FET).-
Unlike 2P, provide a direct way to measure R CH and extract mobility without the effect of contact resistance. It also provides an advantage over TLM (discussed later) for contact resistance determination, by allowing to examine source and drain resistances independently. The measurement setup is similar to 2P configuration except that the channel potential is now sensed with two additional probes P1 (V P1 ) and P2 (V P2 ) as shown in Figure 1a. By doing some the channel potential can be directly measured excluding the effects of R C . No potential drop is assumed in the contact between probes P1 and P2 due to the low current drawn by the high impedance voltmeter (>1E + 12 ohm) connected to them.
For a constant V DS (V GS -V T H ), I DS is modulated by varying V GS and the channel potentials (V P1 and V P2 ) are measured for each V GS . The sheet resistance and field mobility can then be extracted using Equations 12 and 14 respectively from the extracted channel potential (Eq. 11).
As V DS V GS -V T H , the accumulation layer can be considered to be uniform along the channel and hence the sheet resistance should also be uniform throughout. Then, by linear extrapolation the contact resistances at the source (R C S ) and drain (R C D ) are determined independently from the measured potentials in P1 and P2 respectively as shown in Equations 16 and 17.
where L S P1 and L D P2 are the distances from the source and drain contacts to the center of P1 and P2 probes, respectively. Nevertheless, the accuracy of the measured potentials and subsequent extrapolations depend sensitively on the device geometry. This is mainly because the 4P approach relies on the assumption that the introduction of voltage probes does not alter the potential distribution of the FET and this consideration will not hold for all geometries.
In order to investigate the effect of geometry on the measurements, a 2D finite-element model was created to study the changes of the channel potential in the linear regime for different potential probe configurations. The design investigated has source and drain contacts placed at the edge of a rectangular flake. Source and drain contacts were treated as ohmic and conductivity of the channel was assumed to be spatially uniform and varying only with gate-bias. The probes P1 and P2 of equal lengths (L P ) are centered at one-third and two-thirds of the channel length (L CH = 2.5 μm) respectively. Three different L P (100 nm, 300 nm and 500 nm) were simulated with 6 different levels of intrusion into the channel from non-invasive (Y = 0 μm) to completely invasive (Y = 1.4 μm) to understand the potential profile perturbation. Figure 3a shows the simulated equipotential lines in the device under bias conditions V DS = 1 V and V GS = 30 V for L P = 300 nm (L P ≈ L CH /10) with an intrusion length of 100 nm from the flake edge. The equipotential lines are slightly altered around P1 and P2 as marked (Fig. 4a). As the probes intrude into the channel, electrons can flow from the source to the drain through the parallel path of the metal probes P1 and P2 if this resistance is less than that through the channel. This will cause an increase of the total current and further uncertainty with respect to the measured V P1 and V P2 . As a result the calculated sheet resistance using Equation 12 can be underestimated as shown in Fig. 3b. This difference in sheet resistance can also lead to overestimation of contact resistance when extrapolated to the contacts (from Equations 16 or 17). From the model it can be inferred that ideally voltage probes with length ten-times smaller than the channel length and with minimum intrusion are preferable for more accurate measurements.
In MoS 2 4P devices, in order to avoid a shaping step in the fabrication process, P1 and P2 are positioned in the perimeter of the naturally shaped flake. The previously mentioned considerations are taken into account. In our experiments, the probe intrusion are about 300 nm for device A and 280 nm for device B. Given the fact that the channel widths of the devices are 3.1 μm and 2.5 μm for A and B respectively, the aforementioned probe intrusions are comparable to an intrusion of about 100 nm in Figure 3a (W CH = 1 μm). Further, the length of the probes is 300 nm, for L CH = 2.5 μm. Thus, the underestimation of R S H for our devices are represented by the green dot on the red-line of Figure 3b. An error of 3.9% is then expected for the values extracted from these devices. In Figure 4, results of the 4P measurements for the device A can be seen and the extracted parameters are listed in Table I. The mobility of 26.75 cm 2 V −1 s −1 is higher than the mobility extracted from the 2P device without excluding R C (14.5 cm 2 V −1 s −1 ), but similar to the mobility extracted using Equation 9 to fit and exclude the effect of R C in the same 2P measurement (22.71 cm 2 V −1 s −1 ). This demonstrates that the empirical model is a good option to gain some understanding while using 2P devices. The threshold voltage is extracted similar to the 2P technique using Equation 6. Additionally the source contact resistance (R C S ) and drain contact resistance (R C D ) were extracted as shown in Figure  4c. We observe that for V GS > V T H the source and drain resistances are similar in magnitude and exhibit identical gate-field dependency.
Transmission line measurements (TLM).-These allows to evaluate sheet resistance, contact resistance and additionally contact resistivity and transfer length from a set of 2-P devices with varying channel-length adjacent to one another. A representative sketch of the setup and and optical image of the device can be seen in Figure 1c and Figure 1d. The voltage and current are sensed across the same contacts similar to 2P. In TLM, the contact region is modeled as a resistor ladder as shown in the inset of Figure 5a and when current flows from semiconductor to the metal it naturally chooses the path of least resistance. The potential drop along the contact according to 15,16 is given as, L T = ρ c /R S H [19] where I is the current through the contact, R S H is the sheet resistance of the semiconductor under the contact, ρ C is the specific contact resistivity, L C is the contact length and L T is the characteristic injection length or transfer length. L T is considered as the distance over which significant current injection happens under the contact. This phenomenon is generally termed as current crowding. Equation 18, the contact front resistance at x = 0 ( Figure 5a) is given as, With the approximation L C > 1.5 L T (Figure 5a), Equation 21 reduces to, From above equation, the total resistance (R T ) for each 2P device is given as, Note the final expression above assumes linear regime operation.
For our experiments, we fabricated two sets of TLM structure each with three different channel lengths. Each TLM set is built on a single flake to ensure minimum variability between the contacts of individual devices in the set. Details of device dimensions are provided in Figure 1d. Transfer curve for the TLM set D is shown in Figure 6a. Generally, a slight threshold shift is observed between the devices of a TLM set and this is corrected by aligning to a common V T H before using Equation 23 to evaluate the resistances for the same gate overdrive voltage across the devices. Plotting R T Vs L CH , as the method suggests, the sheet resistance, contact resistance and transfer length (and hence contact resistivity from Equation 24) can be obtained from the slope, R T intercept and L CH intercept, respectively, for each V GS . An example is shown in Figure 5b.
Mobility is extracted from the sheet resistance ( Figure 6b) using Equations 13 and 14 and the value ( ≈21 cm 2 V −1 s −1 ) is in good agreement with those obtained from previous techniques. We observe a strong gate modulated R C with magnitudes similar to the 4P measurement (Figure 6c). The current crowding model provides further insights on R C modulation. As Equation 22 demonstrates, even a constant transfer length would exhibit a gate-modulated Rc as charge is injected in MoS 2 film changing R S H . This dependence on R S H gives rise to the 1/V GS modulation for the contact resistance. Figure 6d shows that the transfer length is not constant during the whole regime but arrive to a plateau where it is rather constant. As a result, the extracted contact resistivity using Equation 24 (ρ C ) is also changing as 1/V GS (Figure 6e). The lowest contact resistivity for our device is about 2.4e-6 Ohm × cm 2 .
Additionally, the contact resistance is compared to the channel resistance of devices with L CH equal to 100 nm, 200 nm, 400 nm and 2500 nm. The result can be seen in Figure 6f. It is clear that for L CH smaller than 100 nm the contact resistance will be equal or even higher than the channel resistance, making R C the dominant resistance of the device. Therefore, scaling L CH below 100 nm requires that the problem of high R C and ρ C be addressed.
For more insights on R C and ρ C we have conducted temperature dependence studies to identify any thermally activated mechanism.

Thermionic emission in the the Metal/MoS 2 interface.-Schot-
tky Barrier is formed between MX 2 and the metal due to the work function difference between the two materials. Unlike conventional semiconductor, the ultra-thin body of MX 2 makes it difficult for doping via traditional methods and in the subthreshold regime where the accumulation layer under the contact is not completely formed, the barrier width could be significant. Hence transport mechanisms such as thermionic emission and direct or Fowler-Nordheim tunneling (Figure 8b) could determine the contact resistivity. Figure 8a, shows the band-diagram of MX 2 FET in the subthreshold regime. Two Schottky diodes are connected back to back with the channel in between. For a potential difference of V DS > 3 KT/q and V GS < V T H , the drain-diode is forward-biased and source-diode is reverse-biased. With increasing gate bias, the V DS is predominantly dropped at the largest of three sources of resistance -source junction, drain junction or the channel. If the Schottky barrier is presumed to limit the current, then the reverse-biased junction at the source will dominate. Then, 3D-thermionic emission Equation 25, where the barrier φ S B is replaced by an effective barrier φ ef f is used to model the current across the source junction and access the barrier modulation with VGS. 17 In this equation A is the area where current is flowing, A * * is the Richardson constant, T is the temperature in K, n is the ideality factor and K B is the Boltzmann constant.
Experimentally, a set of transfer curves I D -V GS for different V DS is measured for a range of temperatures (typically between 270 K . a) b) Figure 7. a) Fitting to R C extracted from TLM to demonstrate the behavor of R C modelled in Equation 9. b) Comparison of the contact resistance as obtained from TLM structures, 4P devices and 2P fitting. The minimum values for each method was 2.8 K ohm μm, 2.5 K ohm μm and 4.4 K ohm μm respectively. It can be clearly seen that the values extracted from 4P and TLM are very similar specially for the regions of V GS where the transconductance of the device remain constant. The extracted RC from fitting is about a factor of 1.6 higher than the extracted R C from TLM and 4P, nevertheless is a good estimation considering the simplicity of the setup. This fitting technique is suited to give a good estimation when working with scaled 2P devices.
The effective barrier decreases monotonically with increase in V GS but with two different slopes approximately around V GS = V F B . Furthermore, the effective barrier is reduced to 0 eV around V T H and this can also be noticed in the change of temperature coefficient for the total resistance (I D -V D ). For V GS < V F B , a positive temperature coefficient (conductivity decreases with decrease in temperature) is noticed, characteristic of thermionic emission over the barrier ( Figure  8e). For V GS > V T H , the barrier width is thin enough (indicated by 0 eV) and tunneling mechanisms could dominate at the contacts leading to the total resistance limited by the heavily doped channel, suggested by the negative temperature coefficient (conductivity increase with decrease in temperature- Figure 8f. Thus, the intrinsic barrier height can be defined as the value of φ ef f at the point when it deviates from its linear dependence with V GS . This point also defines the flatband state of the device. The flatband barrier height for different elemental metals to MoS 2 is reported in Table II. We noticed that the extracted barrier heights differ significantly from the  General observations of characterization techniques.-Consistently across the different measurement techniques, we note that the contact resistance is significantly modulated by gate overlap with the contacts. In the subthreshold regime, this gate dependency could be predominantly due to the modulation of φ S B by the gate bias and subsequent thinning of Schottky barriers at the source and drain contacts for V GS above flatband potential. This is substantiated by the change from positive to negative temperature coefficient of the total conductivity and the low or negative φ ef f as the gate is swept from subthreshold to accumulation regime. This was observed independently of the nature of the metal used. In the linear regime, the accumulation layer has sufficiently thinned down the barrier and the R C seems to depend only in the reduction of R S H , as explained by the current crowding model. The model also points out that contact resistivity is significantly modulated by V GS . The 4P analysis corroborates the observation on the transparency of Schottky barrier in the linear regime and shows that both the carrier injection (at source contact) and carrier extraction (at drain contact) exhibit similar resistance (within experimental errors) hinting at injection mechanism different from subthreshold region. Additionlly, we use the values of R C extracted from TLM set D and demonstrate that it fits to the model we state in Equation 9 to fit the total resistance and extract the parameters of a 2P devices excluding contact resistance ( Figure 7a). Also, the values of the contact resistance from all the methods we have used in order to compare were plotted and shown in Figure 7b. The values extracted from 4P and TLM are very similar as expected. However for the case of the value from 2P device fitting we see that there is an overestimation of R C with respect to the other techniques. Nevertheless, considering that a 2P device was used and that the device was 400 nm it is clearly an interesting option. From the above analysis, it is evident that R C and ρ C plays a significant role in the integration of MX 2 devices.

Technology Requirements
Following the projections of the International Technology Roadmap for Semiconductors (ITRS 2.0) the earliest that TMDC can be introduced to industry would be the period 2018-2023. 19 At 2019 the required half pitch (channel length) for high performing devices will be of 21 nm (14 nm) for hight performance devices. That will signify a contact area of only about 14 nm. These dimensions are sketched in Figure 10. Considering the electron mean free path of a perfect MoS 2 layer is about 15 nm 20 it is possible that mobility will not be our main concern. Even if in real devices due to natural defect this were not the case and the mean free path were smaller, the biggest problem will still be the R C . Not only because as the L CH is much smaller than the 100 nm specified in previous sections but also because the contact length (L C ) is smaller than the transfer length determined from TLM (Figure 6d). This will mean that we actually would be in the red region of Figure 5a and thus the actual approximation for coth(L C /L T ) in Equation 21 will be 1/L C instead of 1 and thus instead of Equation 22 the approximation for R C will be: And thus the contact resistance will increase by a factor of 1/L C with respect to the case where the contact was longer than the transfer length worsening even more the performance of the device for the specific case of 13 nm the measured contact resistance will increase from 2.8K ohm × μm to about 280 K ohm × μm while the channel resistance that at 100 nm was already very similar to the contact resistance ( Figure 6f) will decrease by a factor of 7. This will make the R C of the device almost 3 order of magnitude higher than the channel resistance. As it can be seen from Figure 11  Rc (ohm * µm) Figure 11. Different contact resistance reported in literature for optimization through Metal/MoS 2 interface engineering and through doping. 13,[21][22][23][24][25] has been done to reduce the contact resistance. 13,[21][22][23][24][25] These trials can be divided in two main fields: engineering the interface and doping the MoS 2 film. For engineering the interface, different metals has been used with Ni, Au, and Mo being the most popular choice and Mo and Au presenting the lowest R C . Other way of engineering the interface is by introducing a material in between the metal and the 2D material. The most successful strategy in this field was by introducing graphene layers in between. Furthermore, the lowest r C (200 ohm × μm) correspond to the case where one additional layer of patterned graphene is introduced in addition to the normal graphene layer. 21 The second strategy is to dope the MoS 2 film to reduce the sheet resistance. By doing so the R C has been reduced down to about 500 ohm × μm for the case of chloride doping. 22 Further decrease of R C could be achieved by combining both strategies. Nevertheless, even for the lowest reported R C to our knowledge (200 ohm × μm) 21 the R C will be at least 2 order of magnitude higher than the channel resistance for the required dimensions. Also from Figure 6e it can be seen that even for high V GS when thermionic emission is not expected to dominate the transport from the contact to the MoS 2 film the contact resistivity still remains very high (2.4E-6 Ohm ×cm 2 ) far from the ideal value of 1E-9 Ohm ×cm 2 desired in technology. A possible explanation could be a large direct tunneling barrier that the electrodes need to overcome or a fully depleted region under the contact limiting carrier injection. Nevertheless further research is required to reduce its value.

Conclusions
In summary, we have compared the validity of different electrical test structures in evaluating parameters such as field mobility, threshold voltage, contact resistance and contact resistivity. We have provided corrections such as gate bias-dependent empirical model for R C in case of 2P and recommendation for device geometries for 4P and TLM to reliably extract the above mentioned parameters for MoS 2 FETs. Particularly, we have modeled 4P setup and evaluated its accuracy for invasive and long voltage probes. The design considerations were further used in our experiments to evaluate the behavior of source and drain resistances independently in the linear regime. These results were in agreement with those from TLM structures and the following conclusions can be draw: In the linear regime, field effect mobility can be reliably extracted from the plateau in the gm curve for long channel devices. For shortchannel devices, the contact resistance is comparable or equal to the channel resistance and either 4p or TLM would be required to decouple R CH from R C . The contact resistance at source and drain are similar in magnitude and exhibit 1/V GS dependency. From the current crowding model, we can infer that improving sheet resistance can lead to a reduced contact resistance. Also, the contact resistivity exhibits a strong gate dependency and the underlying physics needs to be understood. In the subthreshold regime, temperature dependence measurement yield an effective barrier for the devices which can be reduced with increased gate-field. Finally we compare the extracted parameters with the technology requirements following the industry requirements and identified the contact resistivity and thus the parasitic contact resistance as the major challenges that need to be addressed before scaling the devices below 100 nm.