Reinterpreting Low Resistance in Sb–MoS2 Ohmic Contacts by Means of Ab Initio Transport Simulations

By using an in-house nonequilibrium Green’s function (NEGF)-based ab initio simulator, we investigate the physical mechanisms driving the Sb(<inline-formula> <tex-math notation="LaTeX">${01}\overline {{1}}{2}$ </tex-math></inline-formula>)–MoS2 system to exhibit the lowest reported contact resistance, <inline-formula> <tex-math notation="LaTeX">${R}_{C}={42} \Omega \cdot \mu \text{m}$ </tex-math></inline-formula>, to the 2-D semiconductor MoS2. We can find that the transport from the hybridized bands in the Sb–MoS2 heterojunction is quite ineffective and that the back-gate-induced doping of MoS2 in the contact region is crucial to explain the experiments. In fact, by accounting in our ab initio simulations for the presence of a back gate according to the experiments, it is possible to match the band structure of the MoS2 in the Sb–MoS2 heterojunction with that of the external MoS2 layer, which drastically increases the electronic transmission throughout the contact, and ultimately pushes <inline-formula> <tex-math notation="LaTeX">${R}_{C}$ </tex-math></inline-formula> close to the quantum limit. Furthermore, we extend the applicability of our previously demonstrated simulation methodology and thus investigate a field-effect transistors (FETs)-like device including an ab initio description of the carrier injection at the Sb–MoS2 contact.

Abstract-By using an in-house nonequilibrium Green's function (NEGF)-based ab initio simulator, we investigate the physical mechanisms driving the Sb(0112)-MoS 2 system to exhibit the lowest reported contact resistance, R C = 42 • µm, to the 2-D semiconductor MoS 2 .We can find that the transport from the hybridized bands in the Sb-MoS 2 heterojunction is quite ineffective and that the back-gateinduced doping of MoS 2 in the contact region is crucial to explain the experiments.In fact, by accounting in our ab initio simulations for the presence of a back gate according to the experiments, it is possible to match the band structure of the MoS 2 in the Sb-MoS 2 heterojunction with that of the external MoS 2 layer, which drastically increases the electronic transmission throughout the contact, and ultimately pushes R C close to the quantum limit.Furthermore, we extend the applicability of our previously demonstrated simulation methodology and thus investigate a field-effect transistors (FETs)-like device including an ab initio description of the carrier injection at the Sb-MoS 2 contact.Index Terms-Antimony, contact resistance, MoS 2 , quantum transport, vertical heterojunction (VHJ).

I. INTRODUCTION
I N THE quest for aggressively scaled and highly perform- ing field-effect transistors (FETs), 2-D semiconductors are playing an ever-increasing role [1], [2].However, their promising intrinsic potentials are often hindered by the high contact resistance (R C ) [3], [4].This is one of the biggest challenges for 2-D-based FETs, that is unlikely to be solved by resorting to traditional approaches used for 3-D semiconductors.Indeed, the ultrathin nature of monolayer 2-D materials makes them vulnerable to dopant implantation [5], and also techniques for chemical doping based on surface adsorbates are deemed not reliable and effective enough [4], [6].
Among various solutions devised and tested to reduce the R C to 2-D semiconductors, the use of semimetals with low work function (WF) is arguably the most promising option to reduce R C in n-type FETs with 2-D semiconductors [7], [8], [9], [10], [11], [12].This is attributed to a combination of low WF and low density of states (DoS) at the Fermi level (E F ), which leads to a suppression of metalinduced-gap-states (MIGS) close to the MoS 2 conduction band (CB) [12].
The lowest experimentally reported R C extracted in a 2-D FET device using semimetallic Bi to contact MoS 2 is 123 • µm [7].However, despite the encouraging progress, the low Bi melting point of 271 • C jeopardizes its CMOS process integration.Further steps toward CMOS compatible devices have been achieved using Sb with (0001) surface to contact MoS 2 , demonstrating FETs operational after 400 • C thermal treatment, and reporting an R C of 660 •µm [9].Density functional theory (DFT) simulations extracted the barrier height between Sb and MoS 2 ; however, no transport simulations were conducted to calculate R C [9].An even lower R C to MoS 2 has been very recently obtained by using Sb contacts with (01 12) surface orientation, reaching a minimum R C = 42 • µm at a channel carrier density n 2-D ≈ 3 × 10 13 cm −2 [13], thus approaching the quantum limit resistance of the 2-D semiconductor, namely, 29.6 • µm at the above carrier density.Such a low R C was attributed to the strong overlap between Sb and MoS 2 orbitals in the vertical heterojunction (VHJ), resulting in spatially delocalized hybrid bands with a significant projection onto the MoS 2 orbitals [13].Upon inspection of DFT calculations for the band structure in the VHJ, Li et al. [13] identified such hybridized states as the crucial aspect enabling a high electronic transmission toward the MoS 2 layer external to the VHJ, ultimately leading to the low R C .No attempts to calculate R C in Sb-MoS 2 systems have been reported to date.In this work, for the first time, we present an ab initio transport study of the Sb(01 12)-MoS 2 system as shown in Fig. 1(a), based on an in-house developed simulator [10], [12], [14], [15].This article is organized as follows.In Section II, we present the simulation methodology that allows us to perform nonequilibrium Green's function (NEGF) based, quantum transport simulations over large structures and still retain the accurate description of the band structure enabled by ab initio DFT calculations discussed in Section III.In Section IV, we reinterpret the origin of the experimentally obtained low R C value by inspecting not only the DoSs in the VHJ but also the vertical transmission inside the VHJ (from the Sb to MoS 2 ), and the lateral transmission from the VHJ to the external MoS 2 layer.
Our results reveal that R C observed in experiments can only be explained by having MoS 2 -type states in the VHJ that match the CB minimum of the external MoS 2 layer, with both minima being close to the Fermi level.We also show that the back-gate biasing (BGB) of the contact region is paramount to attain these conditions.Finally, in Section IV, we use selfconsistent simulations, coupling the NEGF equations with the 3-D Poisson's equation, to analyze a FET structure resembling those reported in [13], and comprising an ab initio description of the Sb-MoS 2 contact.The conclusion is drawn in Section V.

II. SIMULATION METHODOLOGY
The Sb(01 12)-MoS 2 VHJ is simulated with Quantum ESPRESSO (QE) [16], [17] and with an orthorhombic topological symmetry of the VHJ, which is a natural choice for transport calculations [15].Given the noncommensurate Sb and MoS 2 lattices, we defined a commensurate cell for the VHJ resorting to a procedure well established in the literature [12], [18].Namely, we matched a strained Sb 2 × 2 unit cell onto an unstrained MoS 2 [Fig.2(a)] layer, that leads to a mean absolute strain of 4.56% in Sb.To suppress the effects of the spurious replica of the VHJ along z, we introduced a ∼2-nm-thick vacuum region [see Fig. 2(b)], together with the appropriate dipole corrections [17].The relaxation of atomic positions was reached when the forces acting on each atom were less than 2.5 meV/Å and by setting an energy convergence criteria of 10 −7 eV.The kinetic energy cutoff was set to 612 eV (45 Ry) and a 12 × 12 × 1 Monkhorst-Pack k-point grid was used to sample the Brillouin zone (BZ).We used scalar, relativistic norm-conserving pseudopotentials with generalized gradient approximation (GGA) exchangecorrelation approximation.Grimme's DFT-D3 scheme was employed to include the van der waals (vdW) interactions.After the relaxation procedure, the extracted distance between MoS 2 and Sb is 0.33 nm [Fig.2(b)], which matches with the value obtained on a supercell larger than ours (see Fig. 1 in the extended data of [13]), and it is slightly larger than the ∼0.29-nm value experimentally obtained for the same VHJ by using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) [13].
Quantum transport simulations are performed by means of the NEGF method.Starting from the plane-wave Hamiltonian matrices computed by QE, we extracted Hamiltonian matrices with a reduced order by using a basis set consisting of unit-cell restricted Bloch functions (URBF) [15].The effectiveness of the URBF basis set in reproducing the band structure of the VHJ obtained with the QE plane-wave Hamiltonians is verified in Fig. 1(b), where it is shown the band structure of the Sb-MoS 2 VHJ close to E F and along the to X path of Fig. 1(c).For the VHJ used in this work, moving from a plane wave to a URBF basis set allowed us to reduce the Hamiltonian rank by a factor larger than 10 2 .
The overall transport simulations used to determine R C involve three regions [i.e., Sb, VHJ, and MoS 2 , as shown in Fig. 1(a)], whose Hamiltonian matrices were first individually extracted.Then, in order to enable transport through the transport direction x, the overall Hamiltonian matrix in the URBF basis was built by using the Hamiltonian matrices coupling the three regions [10], [12].III.DFT SIMULATIONS OF THE Sb(01 12)-MoS 2 SYSTEM Fig. 3(a) shows the band structure along the high-symmetry points of the orthorhombic VHJ as shown in Fig. 1.The CB minima (CBM) of MoS 2 , that in the primitive unit cell are located in the K -points of the first BZ, are back folded at the point of the first BZ of the supercell, as it is indicated by the green arrows in Fig. 2(c).Fig. 3(a) shows that such a minimum (E VHJ CBM,MoS 2 ) is ≈400 meV above E F , Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.so that its contribution to the conductance across the overall heterostructure is negligible in close-to-the-equilibrium bias conditions.The interaction between Sb and MoS 2 also results in the formation of hybridized bands with a significant projection on MoS 2 orbitals that touch or cross E F .This is in qualitative agreement with the findings in [13], also obtained by means of DFT simulations.However, the band plots cannot be directly compared because of different super cells employed in this work and in [13], leading to different bands folding.

IV. SIMULATIONS AND COMPARISON WITH EXPERIMENTS
We used ab initio simulations to investigate R C for the Sb-MoS 2 system in Fig. 1(a), by employing the in-house developed Green-Tea tool [14], [15].Experimental results for a single layer MoS 2 FET with Sb contacts show an average R C of about 209 • µm at an MoS 2 channel electron density n 2-D ≈ 3 × 10 13 cm −2 , with the lowest reported value being R C = 42 • µm [13].By considering the MoS 2 external to the Sb-MoS 2 heterojunction, we analytically converted n 2-D ≈ 3 × 10 13 cm −2 into a band alignment (E F − E CBM,MoS 2 ) ≈70 meV, where E CBM,MoS 2 denotes the corresponding MoS 2 CBM.To this purpose, we used an effective mass approximation model with an MoS 2 effective mass, m = 0.44 m 0 , and a nonparabolicity coefficient, α = 0.94 eV −1 , extracted by fitting DFT calculations in a range of ∼200 meV above the CBM.
In Sections IV-A and IV-B, we calculate the close-toequilibrium R C in the best case scenario, where, if not  3) is also shown.(c) LDOS for the system shown in Fig. 1 for a contact length L C = 15 nm.The alignment with E F of the CBM for the external MoS 2 layer corresponds to an electron density n 2-D = 3 × 10 13 cm −2 , which is consistent with the n 2-D value reported in [13].
otherwise stated, we neglect the band-bending outside the VHJ region and we use the band alignment (E F − E CBM,MoS 2 ) ≈ 70 meV for the MoS 2 external to the VHJ.

A. R C Simulations Neglecting Back-Gate Biasing (BGB)
Fig. 4(a) shows the calculated electronic transmission spectrum at equilibrium for energies close to E F and for different transverse k y values.Then, we used the Landauer formula to calculate the linear conductance spectrum G k y (E) as follows: where q is the electron charge, h is Planck's constant, and f 0 (E) is the Fermi-Dirac distribution function.The ballistic equilibrium transmission spectrum T k y (E), for a given k y , is computed by using the retarded Green's functions and the contacts self-energies as follows [15]: where k y subscript is omitted to lighten the notation.Here, the broadening functions are defined as ] is the self-energy of the left (L) or right (R) contact, [G] is the retarded Green's function of the system, and Tr{• • • } denotes the trace of a matrix.Finally, by accounting for the contributions from different transverse k y values, we obtain R C as follows: As it can be seen, the transmissions in Fig. 4  reported in experiments [13].The availability of states around E F , both in the VHJ and in the external MoS 2 layer [see LDOS plot in Fig. 4(c)], appears insufficient to achieve a low R C , because the transmission from the hybridized states in the VHJ to the external MoS 2 CBM states is poor.
In order to further test the results of Fig. 4, we considered possible uncertainties in the experimental estimate of n 2-D in the MoS 2 channel region [13].Fig. 5 reports the calculated R C by increasing n 2-D up to 7.5 × 10 13 cm −2 , but R C can only be modulated in a range of values that remain much larger than the experimental value [13].This can be attributed to the fact that even though the CBM of the MoS 2 outside the VHJ (located at the point of the supercell first BZ) is degenerate by several tens of millielectron volts (Fig. 5), there are no similar states close to E F in the hybridized bands of the VHJ, where the states resembling the CBM of MoS 2 are instead located at much higher energy, namely, about 400 meV above E F .

B. Influence of BGB on VHJ Region and on R C
The vast discrepancy between the simulated and experimental R C values shown in Figs. 4 and 5 that mainly stems from the fact that the CBM of the MoS 2 external to the VHJ located at the point (in the first BZ of the supercell) has no counterpart states at E F in the VHJ [see Fig. 5(b)], has prompted us to re-examine the experimental framework.In the experiments, the back-gate electrode extends under the Sb-MoS 2 contact as shown in Fig. 6(a) and the quoted R C values for an n 2-D ≈ 1 ÷ 3 × 10 13 cm −2 correspond to back-gate biases up to 10 ÷ 15 V [13].Thus, an electrostatic doping of the MoS 2 in the VHJ should be also expected.Therefore, we performed DFT simulations including a charged plate as a back gate in the VHJ supercell, as illustrated in Fig. 6(b).
By assuming that most of the back-gate voltage drops across the HfO 2 , the charge can be estimated as Q = ε 0 ε r V GS /t ox .By taking ε r = 25 for the 14-nm-thick HfO 2 [20], and dividing by the area of the supercell (1.04 nm 2 ), a 10-V back bias translates into ∼1 electron charge/supercell (e./s.c.).The effect of the gating is shown in Fig. 6(c), where the charged plate is  located in A, and a linear average potential drop is observed between the charged plate and the MoS 2 layer (triangular and square symbols).In contrast, a flat potential was observed in the case with no back gating (circles).In these DFT calculations, in order to prevent the electrons from spilling out from the MoS 2 due to the large electric field and the close proximity of the charged plate to the MoS 2 , we included a potential barrier between the charged plate and the MoS 2 [17], [21] [not shown in Fig. 6(c)].Fig. 7(a) shows that the BGB can reduce E VHJ CBM,MoS 2 by about ≈400 meV, reminding that E VHJ CBM,MoS 2 is here defined as the CBM at the point for the electronic states of the VHJ projected on the MoS 2 orbitals [see green line in Fig. 3(a)].The energy shift of Sb states is smaller (∼100 meV) compared Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.It is worth noting that, despite the very similar LDOS in Figs.4(c) and 8(c) (same color scales), the electronic transmission is very different in Figs.4(a) and 8(a).This is because the available DOS close to E F is a necessary but not sufficient condition to reduce the contact resistance, which ultimately requires to have, close to E F , states of the VHJ that match those in the external MoS 2 region.In this latter respect, Fig. 3(a) shows that the projection onto the MoS 2 orbitals of the states in the VHJ close to E F is small and, in particular, much smaller than in Fig. 7(a).Clearly, the back gating can pull down to E F the states of the VHJ that have a good wave function matching to MoS 2 , thus resulting in the much better electronic transmission displayed in Fig. 8(a) compared with Fig. 4(a).
To further investigate the R C dependence on the BGB, that ultimately sets (E VHJ CBM,MoS 2 − E F ), in Fig. 9  aspects could help explain the spread the experimentally obtained R C values [13], besides additional extrinsic effects such as possible MoS 2 defects and trap states.

C. Self-Consistent, 3-D Simulations for a FET Structure
Compared with our previous studies [10], [12], we have extended our ab initio simulator to include a self-consistent coupling between the NEGF and the 3-D Poisson's equation, which allowed us to simulate the monolayer MoS 2 FET with a 20-nm channel length sketched in Fig. 10(a), that resembles the FET shown in Fig. 6(a) [13].In the device simulations, the semimetallic source contact is described as shown in the previous sections whereas, in order to lighten the heavy computational burden, the drain region is simulated by using a chemical doping of MoS 2 resulting in the same alignment between the Fermi level and the MoS 2 CBM as in the source.
The length of the ab initio simulated source contact is 10 nm, which is twice the transfer length of 5.1 nm estimated from TLM measurements [13].Given the semimetallic nature of Sb, we neglected the penetration into the source region of the electric field.In other words, we did not solve Poisson's equation in the Sb-MoS 2 VHJ and set Dirichlet-type boundary conditions for Poisson's equation at the source end of the channel [see shaded area in Fig. 10(b)], enforcing the band alignment (E VHJ CBM,MoS 2 − E F ) = −20 meV.Fig. 10(b) and (c) shows, respectively, the CBM profile along the channel and the spectrum of the current density for a V GS of 0 V and V DS = 0.1 V, which is then integrated over the energy to obtain the ballistic I DS current.
Finally, in Fig. 11, we compare the I DS simulations of this work with the experimental data [13], for a V DS = 0.1 V.The comparison is performed by subtracting from V GS the threshold voltage V T , obtained from a linear fitting of the I DS versus V GS curve.We did not attempt a comparison in the subthreshold region because experiments exhibit a subthreshold swing exceeding 200 mV/dec [13], most probably I DS versus (V GS − V T ) characteristics at V DS = 0.1 V. Simulated ON-currents for the device shown in Fig. 10(a) agree well with experimental results from Fig. 8(c) in the extended data of [13].Experiments are plotted versus (V GS − V T ) by using V T = −4 V, extracted from a linear fitting of the I DS versus V GS experimental curve.due to traps in the bandgap of MoS 2 or border traps in the HfO 2 layer [22], whose description goes beyond the scope of this article.Fig. 11 shows that the simulated I DS in the ON state is in good agreement with experiments.

V. CONCLUSION
The origin of the close to quantum limit resistance of Sb-MoS 2 contacts has been investigated by means of ab initio transport simulations.Our results suggest that the hybridized states in the VHJ are not sufficient to explain the low R C value that requires to have MoS 2 -type states in the VHJ that match the CB minimum of the external MoS 2 layer.This, in turn, can be only attained by accounting for the back-gate biasing, which emphasizes the added value of the ab initio approach to the device modeling that we have embraced in this study.
Finally, we used self-consistent simulations, coupling the NEGF equations with the 3-D Poisson's equation, to analyze a FET structure resembling that reported in [13], and comprising an ab initio description of the Sb-MoS 2 contact at the source.
The simulation results agree quite well with experiments in the ON-state operation of the transistor.

Fig. 1 .
Fig. 1.(a) Overall structure used for DFT and NEGF transport simulations consisting of three regions: the central Sb-MoS 2 VHJ region (having a length L C ), the leftmost Sb region (extending the Sb region of the VHJ), and the rightmost MoS 2 region (extending the MoS 2 region of the VHJ).(b) Band structure of the VHJ along the high-symmetry points shown in (c), and obtained with the reduced URBF basis (symbols)[15], and, compared with the results by QE for a plane waves basis set (dashed lines).

Fig. 2 .
Fig. 2. (a) Top view of the primitive unit cell for MoS 2 (green dashed lines) and the orthorhombic super cell for the VHJ (black dashed lines).(b) Side view of the simulated VHJ, where d is the distance between MoS 2 and Sb with (01 12) surface orientation.Vacuum is added along the z-direction to reduce the interaction between the periodic replicas of the VHJ in QE calculations.(c) Corresponding first BZs, where the arrows indicate the back folding of the K-points of MoS 2 (for the primitive unit cell) at the Γ point of the first BZ of the supercell.

Fig. 3 .
Fig. 3. (a) Band structure of the VHJ along the high-symmetry points shown in Fig. 1(c).Circles indicate the projection on MoS 2 orbitals, and the size of circles is proportional to the weight of the projection.The green line identifies the states in the VHJ corresponding to the CBM of MoS 2 alone, which is back folded at the Γ point in the super cell, as it is shown in Fig. 2(c).(b) Electronic structure of the VHJ projected on MoS 2 orbitals and plotted throughout the first BZ of the supercell.(c) PDOS for MoS 2 (blue line) and Sb (red line).The hybridization between MoS 2 and Sb results in gap states for MoS 2 .The semimetallic nature of Sb is identified by the V-shaped DOS near E F .

Fig. 3 (
b) reports a 3-D plot throughout the first BZ of the projection onto MoS 2 orbitals of the electronic states in the VHJ that reveals the hybridized states within the MoS 2 energy bandgap.Hybridized states are clearly even in the projected DoS (PDOS) in Fig.3(c) (blue line), where, moreover, the Sb PDOS (red line) confirms the semimetallic nature of Sb that is identified by the typical V-shaped DOS close to E F[19].

Fig. 4 .
Fig. 4. (a) Electron transmission T ky (E) versus energy for different transverse wave-vectors k y that cover almost the entire first BZ.k y values are in units of 2π/a y .(b) Calculated values of the integral over the energy defined in (1) for the conductance spectrum.The R C value resulting from (3) is also shown.(c) LDOS for the system shown in Fig.1for a contact length L C = 15 nm.The alignment with E F of the CBM for the external MoS 2 layer corresponds to an electron density n 2-D = 3 × 10 13 cm −2 , which is consistent with the n 2-D value reported in[13].
(a) are much smaller than 1.0 close to E F , and Fig. 4(b) reports k y resolved contributions to R C .The overall calculated R C is about 28 k • µm, namely, much larger than the average 209 •µm

Fig. 5 .
Fig. 5. (a) Calculated contact resistance from NEGF ab initio simulations.Results are obtained by modulating the CBM of the rightmost MoS 2 with respect to E F , as pictorially shown in (b), thus also modulating the MoS 2 charge density to test the sensitivity to uncertainties in the n 2-D experimental estimate in [13].The band alignment in the VHJ is fixed by the results from DFT calculations in Fig. 3.

Fig. 6 .
Fig. 6.(a) Sketch of the experimental device in [13], where an HfO 2 back-gate oxide extends under the Sb-MoS 2 VHJ.(b) Simulation setup used in QE to describe the BGB effect to reproduce the VHJ in the dashed region in (a).The charge plate in A is positively charged and red arrows depict the electric field in the MoS 2 and Sb regions.The dipole correction in B allows us to zero the electric field in the vacuum region above Sb, as required by the periodicity along z by the planewave basis.(c) Average in-plane electrostatic potential + bare potentials) either with no gating effect (blue circles) or with increasing values of the charge in the charged plate (squares and triangles).The plot does not show the energy barrier introduced in the vacuum region to prevent electrons spilling from the MoS 2 to the charged plate [17].Point B indicates the abscissa where the dipole correction is enforced in DFT calculations (see Section II).

Fig. 7 .
Fig. 7. (a) Influence of the BGB on the band structure of the VHJ.The BGB can effectively pull E VHJ CBM,MoS 2 at the Γ point toward E F (see the text and the green line in Fig. 3(a) for the definition of E VHJ CBM,MoS 2 ).(b) Difference between E VHJ CBM,MoS 2 and E F versus the charge density in the charged plate, which mimics the BGB.

Fig. 8 .
Fig.8.Same results as shown in Fig.4, where (a) is the electron transmission T ky (E) versus energy, (b) is the energy integral of the conductance spectrum defined in (1), and (c) is the LDOS of the system shown in Fig.1, but here accounting for the BGB effect in the VHJ and for a back-gate voltage of 10 V (corresponding to a charge density of 1 e./s.c. in Fig.7), which brings E VHJ CBM,MoS 2 ≈ −20 meV below E F .
(a) we show the R C behavior for different gate voltages by keeping fixed the value n 2-D ≈ 3 × 10 13 cm −2 in the external MoS 2 region.This is shown in the sketch of Fig. 9(b), where the band alignment of the MoS 2 in the VHJ is varied while keeping fixed the one of the MoS 2 external to the VHJ.Simulations can reproduce quite well the experimental R C values with a BGB compatible with experiments, i.e., close to 10 V. A closer inspection of Fig.9(a) for a BGB ∼10 V reveals a large sensitivity of the simulated R C on the E VHJ CBM,MoS 2 value, which depends on the BGB but also on possible uncertainties about the MoS 2 to Sb distance, as it has been reported for the MoS 2 -Bi system[12].These

Fig. 9 .
Fig. 9. (a) Calculated contact resistance values obtained from NEGF simulations versus the back-gate voltage or, equivalently, versus the E VHJ CBM,MoS 2 alignment to E F .(b) CBM of the MoS 2 external to the VHJ [see Fig. 1(a)] is fixed at 70 meV below E F , consistently with the experimental estimate of n 2-D = 3 × 10 13 −2 .The blue solid and dashed lines the lowest and average R C experimental values reported in [13].

Fig. 10 .
Fig. 10.(a) Sketch of the ab initio simulated short channel MOSFET having a 20-nm channel length and 10-nm contact length (not in scale), where transport calculations include also the Sb-MoS 2 VHJ at the source.An idealized lead is used at the drain to reduce the computational burden.(b) CB minimum profile along the device structure.(c) Current spectrum for V GS = 0 V and V DS = 0.1 V.
Reinterpreting Low Resistance in Sb-MoS 2 Ohmic Contacts by Means of Ab Initio Transport Simulations Daniel Lizzit , Member, IEEE, Marco Pala , Senior Member, IEEE, Francesco Driussi , Member, IEEE, and David Esseni , Fellow, IEEE