In this study, we focus on two options for the semiconducting TMD: WS2 (in its most stable 2H phase) and HfS2 (in its most stable 1T phase). WS2 is one of the most studied 2D materials and shows great promise with reasonably high theoretical predictions for both its n-type and p-type mobility.8 HfS2 is a relatively less known material, with fewer experimental results, but is predicted to have an exceptionally high mobility and a higher drive current, while maintaining good scalability down to 5 nm gate lengths.8 We investigate several device configurations depending on the type of metal-semiconductor contacts. For 2D-2D TC and SC we consider a single independent contact as well as a full transistor configuration. For the full transistor, both a dual-gate (DG) MOSFET and a Dynamically-Doped Field-Effect Transistor (D2-FET) device, i.e., an individually back-gated transistor that does not require a spacer and allows for dynamically doping the source and drain extension with its gate (Fig. 1.b and d),8 are simulated. For 2D-3D contacts, we are limited to a single contact configuration as the significant computational cost prohibits a full transistor simulation. All device structures simulated in ATOMOS are shown in Fig. 1. In all transistor simulations, the gate length is L = 14 nm. The gate oxide has a relative permittivity εR = 15.6, corresponding to HfO2, and thickness of 2 nm, resulting in an equivalent oxide thickness EOT = 0.5 nm. The work function of the metal gate is typically adjusted to shift the threshold voltage and achieve a fixed IOFF value at a gate voltage bias VGS = 0 V. The source-drain bias is set at VD = 0.6 V, unless specified otherwise. For single contact simulations, the source and drain are ill-defined and VD and VGS denote respectively the bias applied over the contact and the potential difference between the doping gate, if present, and the metallic part of the system. The metal contacts and source- and drain- (S&D) extensions are surrounded by a low-K spacer oxide with εR = 4.
2D-2D Top-contact configuration
For HfS2, HfTe2 (1T) was found to be an interesting n-type contact candidate with a low Schottky barrier. The results for a single contact and for the DG device with chemical doping are summarized in Fig. 2. Figure 2 (a) demonstrates the influence of the doping concentration on the contact resistance in a single TC configuration. The contact resistances for doping concentrations of 3×1020 cm-3 and 5×1020 cm-3 are respectively 90 Ωµm and 50 Ωµm and are largely independent of the bias. These values are comparable with the quantum limit of 20–30 Ωµm at these doping concentrations9. When the doping concentration is reduced, the value of the contact resistance rapidly increases. An average value of 370 Ωµm is observed at 1×1020 cm-3 and RC ~10 kΩµm at 1×1019 cm-3. Also the dependency of the contact resistance on the bias increases significantly. Figure 2 (b) shows the influence of the contact overlap length, LC. The contact resistance appears largely independent of LC, implying that injection happens through edge injection despite the low Schottky barrier height. Figure 2 (c) shows the current for a DG-MOSFET in comparison with a device with perfect ohmic contacts and a device with highly-doped HfS2 second layer regions acting as metallic TC. We find that the introduction of HfTe2 TC reduces the current by about 60% compared to the device with perfect ohmic contacts. From the density of states (DOS) of the device in equilibrium without doping, we can extract an estimate of the Schottky barrier height of nSBH = 40 meV. This SBH is further reduced at the source side under operating conditions, owing to the Fermi-level degeneracy in the conduction band induced by the high doping concentration, as can be seen in Fig. 2 (f) and (g). Hence, the reduction in current can mostly be attributed to the vdW gap. This is confirmed by the results on the HfS2 DG-nMOSFET with highly-doped HfS2 TC, that mimic ohmic vdW contacts. This reference case does not have a Schottky barrier but demonstrates a similar current reduction. Figure 2 (d) and (e) demonstrate the influence of doping concentration and the length of the TC overlap region. A doping concentration of 3×1020 cm-3 is required to preserve the ON-current (ION). Increasing the doping concentration beyond this value increases ION, but the benefits appear less significant than for the single contact and the effect saturates at NSD = 5×1020 cm-3. ION shows a peak around LC = 4.5 nm, but little dependency on LC for higher values of LC, affirming that injection happens through edge injection. We thus find that the conditions under which the transport simulations were performed were close to ideal. Consequently, doping concentration and contact overlap length do not provide a means to significantly alleviate the 60% reduction in ION imposed by the vdW contact.
For WS2, finding an adequate n-type TC has proven challenging. Three metallic TMDs were selected as possible TC candidates: WTe2 (1T’), MoTe2 (1T’) and NbS2 (2H). The results for a single contact are shown in Fig. 3 (a) and (b). LC was set to 4.5 nm based on our findings on the HfS2-HfTe2 TC. The contact resistances for n-type doped WS2 are all extremely high, even for the high doping concentration of NSD = 5×1020 cm-3. As a reference, also the contact resistance of a highly-doped WS2 layer as TC is shown, demonstrating that contact resistances as low as 45 Ωµm could be achieved for n-type WS2 by finding a vdW metal with the correct work function. For p-type contacts, NbS2 is found to be an interesting candidate, showing contact resistances of 150 Ωµm and 100 Ωµm for doping concentrations of respectively 3×1020 cm-3 and 5×1020 cm-3. Similarly to HfS2-HfTe2, the contact resistance increases rapidly when the doping concentration is reduced, showing average contact resistances of 370 Ωµm at NSD = 1×1020 cm-3 and ~ 5k Ωµm at NSD = 1×1019 cm-3.
Figure 3 (c)-(j) show the results for the DG-MOSFET. The device parameters were chosen based on our findings on HfS2-HfTe2 TC. NSD was set to 3×1020 cm-3, Lext to 4.2 nm and LC to 4.5 nm. The DOS in the simulation was used to extract an estimate of the SBH. The SBH for WS2-WTe2 and WS2-MoTe2 are found to be around 500 meV under operating conditions, as can be seen in Fig. 3 (e) and (f). The large contact resistances are attributed to the presence of a significant Schottky barrier height on top of the tunneling barrier imposed by the vdW gap. These lead to severe ION reductions by respectively a factor 1000 and 10 000, when compared to the reference case with perfect ohmic contacts of Fig. 3 (c). To provide an additional reference, we discuss a TC configuration with highly doped WS2 for the metal, which is also characterized by a vdW gap but does not have a Schottky barrier. As a result, ION is only reduced by 25%, complying with the low contact resistance found for these TC.
WS2-NbS2 is characterized by a negative value for pSBH and, hence, provides an ohmic p-type TC. Despite this ohmic contact, ION is reduced by 95% under normal operating conditions of VD = 0.6 V. When VD is lowered to 0.15 V, the reduction is found to be only 50%. An explanation of this phenomenon can be found in the DOS and current spectrum of the device. NbS2 is a cold metal with no high energy carriers, which is denoted by the gap in the DOS of the left-most and right-most parts of Fig. 3 (g) and (i). At low bias, this has little influence on the current. However, at high bias, the energy at which carriers are injected at the source is similar to the energy of the drain-side gap. Therefore, carriers cannot be ballistically extracted at the drain side and the current is reduced. A more in-depth discussion is provided in ref. 10. It should be noted that such behavior emerges only in full device simulations when both contacts are made of the same cold metal and not in the simulation of a single contact, or if a more complex device scheme with asymmetric source and drain contacts would be used.10 This shows the importance of full device simulations, where possible, as the extraction of contact resistances alone can neglect physics important for device performance. It is interesting to note that the contact resistances for the WS2-NbS2 TC are larger than the ones found for the HfS2-HfTe2 TC. However, the reduction of ION is slightly less severe for the WS2 device with NbS2 TC than for the HfS2 device with HfTe2 TC. This may be attributed to the better transport property of HfS2. This results in a lower channel resistance in serie with RC, and hence a greater influence of RC despite its lower value. A second thing to note is that HfS2 with HfTe2 TC showed a similar reduction in ION as the HfS2 reference case with highly doped HfS2 TC, implying that the contact resistance is mostly the results of the vdW gap. The WS2-WS2(n++) TC and WS2-NbS2 TC are also characterized by similar vdW gaps. Indeed, the interlayer coupling is found to be almost identical. Despite this, WS2-NbS2 shows a much greater reduction of ION than WS2-WS2(n++). A possible explanation can be found in the necessity of k-matching. This means that ballistic transmission through the contact or even the full device, does not only require states at the same energy at injection and extraction, but also requires states at the same k-point. This requirement is not exclusive to cold-metal based devices but can be more relevant for such transistors as the band structure of cold metals often consists of one band at the Fermi level. Hence, at a specific energy, states are only available at certain k-points. Additionally, in contrast to the cold-metal behavior discussed above which only arises in full devices, the requirement for k-matching is also relevant for single contacts. This explains the larger contact resistance for the WS2-NbS2 TC than for the WS2-WS2(n++) or HfS2-HfTe2 TC. A more in-depth discussion is provided in the supplementary material.
2D-2D Side-contact configuration
For the 2D-2D SC configuration, we limit ourselves to HfS2-HfTe2 and WS2-NbS2 as these provided low Schottky-barrier heights for the ideal case of vdW contacts. The results for the single contact simulations are shown in Fig. 4 (a) and (b). For both material combinations, the results strongly depend on the doping concentration. HfS2-HfTe2 SC show significantly lower contact resistances than the WS2-NbS2 SC. For doping concentrations of respectively 3×1020 cm-3 and 5×1020 cm-3, the contact resistance of the HfS2-HfTe2 SC is largely independent of the bias and has values of respectively 75 Ωµm and 38 Ωµm. For a doping concentration of 1×1020 cm-3, both the average value of the contact resistance and its susceptibility to the bias increase significantly, with an average value of around 500 Ωµm. Note that for low doping concentrations, the SC has a higher contact resistance than the TC, while for a high doping concentration the SC has a lower contact resistance. For WS2-NbS2 SC, the average value as well as the susceptibility to the bias is large, even in the case of high doping concentrations.
Figure 4 (c)-(h) shows the results for the HfS2 and WS2 DG-MOSFET with, respectively, HfTe2 and NbS2 SC. The S&D extensions have length Lext = 9 nm and are doped with a doping concentration of NSD = 3×1020. VD is limited to 0.15 V for the WS2 device to suppress any reduction effect related to the cold metallic nature of NbS2. Figure 4 (e) and (g) denote the DOS for both systems. The SBH’s are both around 100 meV. The formation of covalent bonds at the HfS2-HfTe2 or WS2-NbS2 interface gives rise to moderate Fermi level pinning, mildly increasing the SBH compared to the ideal vdW contact. In that regard, the 2D metals used here may have an advantage over other SC metals as they provide a very clean atomic interface, sharing either a same Hf or S atom for the HfS2-HfTe2 or WS2-NbS2 cases respectively. Despite the similar SBH, the current spectra, denoted in Fig. 4 (f) and (h), demonstrate significantly different behavior. For the HfS2-HfTe2 system, the current passes through the Schottky barrier quasi ballistically, while for the WS2-NbS2, the current is strongly scattered. The IV curves are shown in respectively Fig. 4 (c) and (d). For HfS2-HfTe2, the SC perform better than the TC, showing a reduction of ION of only 25% instead of 60% for the TC. For WS2-NbS2 the SC perform significantly worse than the TC, showing a reduction of ION of 85% instead of 50%. This complies with the contact resistances in Fig. 4 (a) and (b). The more severe ION reduction and the strong presence of scattering for WS2-NbS2 can be linked to the need for k-matching, discussed in further detail in the supplementary material.
Dynamic doping
The discussion on TC showed that sufficient doping concentration is required to allow for tunneling through the vdW gap. A high doping concentration is known to increase the number of available carriers and the electric field, and hence to promote tunneling.11 For SC, there is no vdW gap, but there is a significant SBH. Sufficient doping is required to thin the Schottky barrier. Figure 1 showed how a gate can be used to achieve dynamic doping8,12 in D2-FETs and single contacts. For both 2D-2D TC and 2D-2D SC, HfS2-HfTe2 contacts provided the lowest contact resistance and demonstrated good device performance. Figure 5 demonstrates how the contact resistances are influenced when a doping gate is used. The chemical doping concentration is set to the intrinsic doping concentration NSD = 1×1019 cm-3. Figure 5 (a) and (c) show how the carrier concentration increases, and hence, the contact resistance decreases, as the gate potential is increased. However, for the single contact case, the carrier concentration depends not on VGS, but on the difference between the gate potential and the potential in the TMD, i.e., VGS-VD. The contact resistance thus depends strongly on the bias even in the case of high carrier concentrations. Additionally, Fig. 5 (a) and (c) show that carrier concentrations of ~ 3×1020 cm-3 can be reached. The contact resistances can reach values as low as 50 Ωµm for TC and 55 Ωµm for SC. Note that these values are lower than the respective RC values obtained for the single contacts with chemical doping concentrations of 3×1020 cm-3. In addition to providing the required carrier concentration, the doping gate thus lowers the contact resistance through other methods, presumably through creating additional electric fields which are beneficial for tunnelling. The effect appears most pronounced for the TC as the RC value reached are even lower than the values found for NSD = 5×1020 cm-3. Fig. S2 in the supplementary material shows that these carrier concentrations and contact resistances are achieved for a bias of VGS-VD = 0.9 V. For a moderate bias of VGS-VD = 0.6 V, we find a carrier concentration of ~ 1.8×1020 cm-3 and contact resistances of 105 Ωµm and 115 Ωµm for respectively TC and SC. Figure 5 (b) and (d) demonstrate the importance of the overlap length of the doping gate, ΔL. For both SC and TC, the contact resistance deteriorates when the doping gate does not fully reach the metal contact, i.e., ΔL < 0. For the TC, it is found that the doping gate best extends beyond the metal, with RC decreasing up to ΔL = 2.5 nm. For the SC, the importance of ΔL is less severe, and a small extension below the metal of ΔL = 0.5 nm is found to be sufficient.
Figure 6 demonstrates the effect of adding a doping gate to a complete transistor. The D2-FET is compared to the DG-MOSFET for both HfS2-HfTe2 TC and SC. For both cases, the DG-MOSFET with intrinsic doping, NSD = 1×1019 cm-3, demonstrates a low ION. The discussion above showed that for both SC and TC, the contact resistance is very large for such low doping concentrations. Additionally, even with perfect contacts, a source extension with such low doping concentration would also suffer from source starvation and reduced ION values.8 For both types of contacts, the D2-FET manages to supply the required carrier concentration to lower the contact resistance and restore the current in ON state. It is interesting to note that for the TC, the D2-FET also shows significantly better performance than the DG-MOSFET for NSD = 3×1020 cm-3. However, our results in Fig. 2 (d) showed that increasing the doping concentration beyond NSD = 3×1020 cm-3 added little benefit. Hence, any additional carrier concentration increase by the doping gate should not influence the results significantly. Additionally, the D2-FET and DG-MOSFET with SC show very similar results for NSD = 3×1020 cm-3. Finally, the D2-FET with intrinsic doping slightly surpasses the performance of the DG-MOSFET with NSD = 3×1020 cm-3 for the TC. For the SC, however, the D2-FET with intrinsic doping does not reach the ION of the DG-MOSFET with NSD = 3×1020 cm-3. The explanation for this discrepancy is linked to the additional contact resistance lowering by the doping gate. Our results in Fig. 5 showed that the doping gate lowers the contact resistance through other methods than supplying the required carrier concentration and that this effect is more pronounced for TC. This explains why the D2-FET outperforms the DG-MOSFET for the TC configuration despite a higher doping concentration providing little benefit, and it explains why this is not true for the SC configuration. The reason for the different influence of the doping gate on TC and SC is linked to the different mechanism limiting the current, i.e., vdW tunneling for the top contact which is more sensitive to electric field enhancement and Schottky barrier tunneling for the side-contact which is more sensitive to doping though thinning of the SBH.
For TC, the top metal prevents the introduction of a second doping gate. For SC, a top doping gate can be introduced, by using, for instance, the compact doubled-forked (E2) dynamically-doped E2D2-FET architecture.12 The device configuration as well as the corresponding contact resistances and device currents are shown in Fig. 7. As expected, the introduction of a second doping gate doubles the carrier concentration to 6×1020 cm-3 reduces the contact resistance to a minimum value of 25 Ωµm. Fig. S2 in the supplementary material shows that this is for a bias of VGS-VD = 0.85 V. For a moderate bias of VGS-VD = 0.6 V, we obtain a carrier concentration of ~ 4×1020 cm-3 and a contact resistance of 42 Ωµm. Despite normalization by the gate perimeter (i.e., the current shown in Fig. 7 (d) is the current per gate), the E2D2-FET outperforms the D2-FET, demonstrating a higher value for ION.
2D-3D Top-contact configuration
For the 2D-3D TC configuration, we limit ourselves to WS2 for the TMD and Pt, Ru, Mo, Bi, Sb for the metal. The low melting temperature of Bi (~ 209°C)13 makes it unsuitable for direct use in fabrication. Therefore, Bi doped with Y and La (YBi and LaBi) are also considered here as alternatives, as their melting temperature is significantly increased (2020°C and 1615°C respectively)13,14. For 2D-3D systems, transport simulations are characterized by a large computational cost. Combined with the large number of combinations of metal and surface orientation, this makes an initial screening before performing transport simulations indispensable. We consider four parameters for screening: the vdW gap and the binding energy (EB), giving an indication of the interaction strength, and the n-type and p-type SBH (nSBH and pSBH). A more thorough discussion is presented in the methods section. The results are shown in Fig. 8. The numerical values, as well as those for several other parameters extracted from the DFT simulations, can be found in the supplementary material.
Figure 8 shows a clear correlation between the vdW gap and the binding energy, indicating that the vdW gap can indeed also be used as a measure for the interaction strength. A bimodal model is distinguished, corresponding to interfaces that are strongly interacting: Pt, Ru, Mo and YBi and LaBi with Y/La termination, and interfaces that show less interaction than a WS2 bilayer: Bi, Sb and most other YBi or LaBi surface orientations. Only one exception, YBi (10 − 1), with an intermediate interaction strength greater than the WS2 bilayer, is found. Additionally, it can be seen that, except for a few metal-surface combinations, the estimated Schottky barrier is always several 100 meV’s. From the discussion on 2D-2D interfaces, it is known that the combination of the vdW gap in a bilayer and a Schottky barrier of several 100 meV’s greatly reduces device performance. Even an ohmic vdW contact introduces a contact resistance that requires a relatively high doping concentration to be mitigated. To limit the additional contact resistance of this vdW gap, the interfaces exhibiting an interaction strength greater than the bilayer may be of interest. However, these strongly interacting interfaces tend to be strongly pinned, resulting in large SBH both for n-type and p-type. Three exceptions were found with adequate values for nSBH and strong to intermediate interaction strength: YBi (10 − 1) and LaBi and YBi (111) terminated on Y/La. Of these three interfaces, YBi (111) is predicted to be ohmic with a negative nSBH. However, YBi (111) shows a strongly corrugated structure, destroying the 2D nature of WS2, as shown in the supplementary material. One of the consequences is a severe reduction of the band gap to 1.4 eV and a very strong sensitivity of the SBH to the local strain level and microstructure, which is not desirable in practice, especially for edge-dominated injection, as also discussed just below. We therefore restricted the transport simulations to YBi (10 − 1) and LaBi (111) with respectively nSBH = 190 meV and nSBH = 15 meV. The DOS obtained from the transport simulations provides a second way to extract an estimate for the Schottky barrier height, resulting in respectively nSBH = 260 meV and nSBH = 540 meV. The difference between the estimates extracted from the DFT screening and from the transport simulation is explained as follows. As discussed in further detail in the methods sections, the pure TMD parts of the transport simulation use matrix elements extracted from a pure TMD DFT simulation with relaxed atomic positions. This is done to remove any effect of corrugation due to the metal in the parts that do not have any metal. However, the relaxation process changes the band alignment and, hence, changes the Schottky barrier height. The second estimate extracted from the DOS of the transport simulation corresponds to the Schottky barrier between the metal and the relaxed structure that is not under it, while the first estimate extracted during DFT screening corresponds to a Schottky barrier value between the metal and the corrugated TMD below the metal. For edge dominated-injection, as encountered here, the second and higher barrier is probably the most relevant. Figure 9 (a)-(c) show the contact resistance for the WS2-YBi (10 − 1) TC as a function of doping concentration and contact overlap length. Figure 9 (c) shows that the contact resistance is largely independent of the contact overlap length, implying edge injection. However, Fig. 9 (a) indicates that the dependency on the doping concentration is significant. The contact resistances for NSD = 5×1020 cm-3 and NSD = 3×1020 cm-3, are respectively RC = 50 Ωµm and RC = 95 Ωµm. Doping concentrations lower than NSD = 3×1020 cm-3 result in severe increases of the value of RC as well as its susceptibility to the bias. As references, contact resistances for a monolayer of WS2 with pure Schottky-barrier contacts of respectively 190 meV and 260 meV, as well as a WS2-bilayer vdW-limited but ohmic contact as a function of doping concentration are shown in Fig. 9 (b). Just like our previous results on 2D-2D contacts indicate, doping is important for tunneling through the vdW gap and thinning the Schottky barrier. However, both the absolute values of RC for the reference cases as well as their susceptibility to the doping concentrations are less than for the WS2-YBi (10 − 1) TC. This is an indication that the intermediate interaction strength of the WS2-YBi (10 − 1) TC does not fully mitigate the vdW gap, as the current is not only limited by the Schottky barrier. We infer that for the combination of a nonzero SBH and this vdW-like gap, a doping concentration of at least NSD = 3×1020 cm-3 is highly essential.
Figure 9 (d) shows the contact resistance for the WS2-LaBi (111) TC as a function of doping concentration. For a doping concentration of NSD = 5×1020 cm-3, sufficient to thin the Schottky barrier, the contact resistance is found to be 40 Ωµm, i.e., slightly lower than the YBi TC. This can be attributed to the stronger interaction strength for the LaBi TC. However, for lower doping concentrations, the contact resistance increases significantly, up to several 100 kΩµm for a doping concentration of NSD = 1×1020 cm-3. This is an indication that, despite the low Schottky barrier estimate between metal and the corrugated TMD underneath the metal, there is a significant Schottky barrier impeding the current when insufficient doping is provided. This Schottky barrier is present for edge injection between the metal and the relaxed free-standing TMD. A more in-depth discussion of the different types of TMD in the 2D-3D TC simulation is provided in the methods section.