Computational Study of Metal Contacts to Monolayer Transition-Metal Dichalcogenide Semiconductors

Among various 2D materials, monolayer transition-metal dichalcogenide (mTMD) semiconductors with intrinsic band gaps (1–2 eV) are considered promising candidates for channel materials in next-generation transistors. Low-resistance metal contacts to mTMDs are crucial because currently they limit mTMD device performances. Hence, a comprehensive understanding of the atomistic nature of metal contacts to these 2D crystals is a fundamental challenge, which is not adequately addressed at present. In this paper, we report a systematic study of metal-mTMD contacts with different geometries (top contacts and edge contacts) by ab initio density-functional theory calculations, integrated with Mulliken population analysis and a semiempirical van der Waals dispersion potential model (which is critical for 2D materials and not well treated before). Particularly, In, Ti, Au, and Pd, contacts to monolayer ${\mathrm{MoS}}_2$ and ${\mathrm{WSe}}_2$ as well as $\mathrm{Mo}\text{−}{\mathrm{MoS}}_2$ and $\mathrm{W}\text{−}{\mathrm{WSe}}_2$ contacts are evaluated and categorized, based on their tunnel barriers, Schottky barriers, and orbital overlaps. Moreover, going beyond Schottky theory, new physics in such contact interfaces is revealed, such as the metallization of mTMDs and abnormal Fermi level pinning. Among the top contacts to ${\mathrm{MoS}}_2$, Ti and Mo show great potential to form favorable top contacts, which are both $n$-type contacts, while for top contacts to ${\mathrm{WSe}}_2$, W or Pd exhibits the most advantages as an $n$- or $p$-type contact, respectively. Moreover, we find that edge contacts can be highly advantageous compared to top contacts in terms of electron injection efficiency. Our formalism and the results provide guidelines that would be invaluable for designing novel 2D semiconductor devices.

Popular Summary

Semiconductors are used throughout the electronics industry in transistors and integrated circuits. Recently, a new class of thin, two-dimensional monolayer semiconductor materials known as monolayer transition-metal dichalcogenides (mTMDs)—with a chemical formula of $M{X}_2$, where $M$ is a transition metal and $X$ is O, S, Se, or Te—has shown exceptional promise for building next-generation energy-efficient digital switches and ultrasensitive biosensors because of their inherently large and uniform band gaps of 1–2 eV. Furthermore, mTMDs have inherent flexibility and transparency, rendering them attractive to display electronics. These materials additionally have pristine surfaces without any out-of-plane dangling chemical bonds, which help reduce the interface traps as well as scattering of charge carriers, thereby boosting device performance. Ensuring low-resistance metal contacts to mTMD semiconductors is the primary hindrance to using this technology, however. We conduct a systematic study of various metal-mTMD contacts with different geometries (top contacts and edge contacts).

Studies have shown that the contact resistance at the metal-mTMD interface is 1–3 decades higher than that of metal-silicon contacts. These high resistances hinder the performance of mTMD transistors, prompting research to explore different metals and contact configurations. We investigate the nature of the physical contacts between monolayer ${\mathrm{MoS}}_2$ and ${\mathrm{WSe}}_2$ and In, Ti, Au, Pd, Mo, and W contacts using an ab initio density-functional theory specifically designed for two-dimensional layered materials. We not only provide a pathway to identify the best contact metals for these semiconductors but also reveal some new physics of the interfaces that, in turn, determine the carrier transport across such interfaces. Our calculations also show that edge contacts are favored over top contacts.

The formalism and the results in this work provide guidelines for novel two-dimensional semiconductor device design and fabrication, a field that is on the rise because of limitations in scaling silicon semiconductor technology. Our results show how two-dimensional monolayer semiconductors can be optimally designed to yield the highest electronic efficiencies.

Figure 1

Schematic illustrating advantages of 2D materials: surfaces of (a) 3D (bulk) and (b) 2D materials. The pristine interfaces (without out-of-plane dangling bonds) of 2D materials help reduce the interface traps. Mobile charge distribution in (c) 3D and (d) 2D crystals used as channel materials. $V(x)$and $|\psi (x){|}^2$ represent the potential and the probability density of the electronic charges, respectively. The carrier confinement effect in 2D materials leads to excellent gate electrostatics.

Figure 2

(a) Band diagrams of silicon, some 2D materials, and selected contact metals. Graphene [1, 2] has a zero-band-gap electronic dispersion at so-called Dirac points, while $h$-BN has a large $E_g$ ($>5\mathrm{eV}$) and can be used as an extremely thin dielectric layer [3]. $E_c$, $E_v$, and $E_g$ represent conduction band edge, valence band edge, and band gap, respectively. $\chi$ and ${\varphi }_F$ represent electron affinities and metal work functions (WFs), respectively. (b),(c) Three views of lattice structures of (b) ${\mathrm{MoS}}_2$ and (c) ${\mathrm{WSe}}_2$. Red rhombuses represent primitive unit cells and $a$ is the lattice constant. Chirality is shown in (b) by armchair edge and zigzag edge. Lattice structures are relaxed using DFT with $8\times 8\times 1$ $k$ points sampled in the Brillouin zone (BZ). (d),(e) Energy dispersions of (d) ${\mathrm{MoS}}_2$ and (e) ${\mathrm{WSe}}_2$. $E_{\mathrm{Fi}}$ denotes the intrinsic Fermi level. Inset in (d) shows the first BZ of mTMDs containing the $M$, $K$, and $\mathrm{\Gamma }$ points.

Figure 3

Schematic of metal-mTMD (a) top contact, (b) edge contact, and (c) combined contact.

Figure 4

Flow chart of the framework for metal-mTMD contact computational study in four steps: (a) choosing metals, (b) interface modeling, (c) DFT calculations, and (d) contact evaluation. $E_{\text{vac}}$, $E_c$, $E_v$, and $E_F$ represent vacuum level, conduction band edge, valence band edge, and Fermi level, respectively. $E_{\mathrm{Fm}}$ and $E_{\mathrm{ch}}$ represent metal Fermi level and channel potential, respectively.

Figure 5

Schematics showing the impact of lattice mismatches in metal-TMD contact. (a) Small lattice mismatch that maximizes the orbital overlaps between metal and TMD. (b) Large lattice mismatch that prevents maximizing the orbital overlaps.

Figure 6

Schematic showing the electron probabilities on different atomic orbitals of contact metal and mTMD ($M{X}_2$). Metals with $d$ orbitals are preferred as contact metals due to the possible overlap with $d$ orbitals in mTMD, resulting in better electron injection.

Figure 7

(a) Schematic cross-sectional view of a typical metal-${\mathrm{MoS}}_2$ contact ($n$-type top contact). $A$, $C$, and $E$ denote the three regions while $B$ and $D$ are the two interfaces separating them. Red arrows show the pathway ($A\to B\to C\to D\to E$) of electron injection from contact metal ($A$) to the ${\mathrm{MoS}}_2$ channel ($E$). The inset shows the source and drain contacts and the channel region in a typical backgated FET. (b)–(d) The three possible band diagrams of (a): metal contacts with (b) very weak bonding, (c) medium bonding, and (d) strong bonding. $E_c$, $E_v$, $E_{\mathrm{Fm}}$, and $E_{\mathrm{ch}}$ represent conduction band edge, valence band edge, metal Fermi level, and channel potential, respectively.

Figure 8

Optimized geometries of top contacts to ${\mathrm{MoS}}_2$: (a) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ (in different views), (b) $\mathrm{In}\text{−}{\mathrm{MoS}}_2$, (c) $\mathrm{Pd}\text{−}{\mathrm{MoS}}_2$, (d) $\mathrm{Ti}\text{−}{\mathrm{MoS}}_2$, (e) $\mathrm{Mo}\text{−}{\mathrm{MoS}}_2$ (in different views). $d$ is defined as the physical separation (the $z$ component of the nearest core-to-core distance between the metal atoms and the chalcogenide atoms). Radii of the atomic spheres shown in (a)–(e) are fixed to the covalent radius of the elements, which is a measure of the size of an atom that forms part of one covalent bond. Hence, the touching of atomic spheres indicates the formation of covalent bonds [e.g., the Ti-S bond in (d)].

Figure 9

Optimized geometries of top contacts to ${\mathrm{WSe}}_2$: (a) $\mathrm{Au}\text{−}{\mathrm{WSe}}_2$, (b) $\mathrm{In}\text{−}{\mathrm{WSe}}_2$, (c) $\mathrm{Pd}\text{−}{\mathrm{WSe}}_2$, (d) $\mathrm{Ti}\text{−}{\mathrm{WSe}}_2$, (e) $\mathrm{W}\text{−}{\mathrm{WSe}}_2$ (in different views).

Figure 10

Evaluation of the tunnel barriers at the contacts. (a) Plot of minimum effective potential ($V_{\text{eff}}$) versus $z$ position for $\mathrm{In}\text{−}{\mathrm{MoS}}_2$ top contact. ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$ is the $V_{\text{eff}}$ of the Mo-S bond orbitals and thereby the effective tunnel barrier height (${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$) is defined as the minimum barrier height that an electron from the metal has to overcome if it has the same potential energy as ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$. Hence, ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ can be calculated as the $V_{\text{eff}}$ difference between the vdW gap (${\mathrm{\Phi }}_{\text{gap}}$) and ${\mathrm{MoS}}_2$ (${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$). ${\mathrm{\Phi }}_{\text{metal},\min }$ denotes the minimum $V_{\text{eff}}$ that an electron can have in the metal. It is worth noting that in some metals (such as Au) ${\mathrm{\Phi }}_{\text{metal},\min }$ can be higher than ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$ (thus, electron energy is always higher than that of Mo-S bond orbitals), in which case ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ is calculated as ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}={\mathrm{\Phi }}_{\text{gap}}-{\mathrm{\Phi }}_{\text{metal},\min }$. ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ vanishes to zero when ${\mathrm{\Phi }}_{\text{metal},\min }$ or ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$ is higher than ${\mathrm{\Phi }}_{\text{gap}}$. $d$ is defined as the physical separation (the $z$ component of the nearest core-to-core distance between the metal atoms and the chalcogenide atoms). (b) ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ versus $d$ plot for various top contacts.

Figure 11

Partial density of states (PDOS) [DOS on specified atoms and orbitals, for example, Mo-$d$ ($d$ orbital on Mo)] of top contacts to ${\mathrm{MoS}}_2$: (a) only ${\mathrm{MoS}}_2$, (b) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$, (c) $\mathrm{In}\text{−}{\mathrm{MoS}}_2$, (d) $\mathrm{Pd}\text{−}{\mathrm{MoS}}_2$, (e) $\mathrm{Ti}\text{−}{\mathrm{MoS}}_2$, (f) $\mathrm{Mo}\text{−}{\mathrm{MoS}}_2$. $E_F$ denotes Fermi level.

Figure 12

PDOS of top contacts to ${\mathrm{WSe}}_2$: (a) only ${\mathrm{WSe}}_2$, (b) $\mathrm{Au}\text{−}{\mathrm{WSe}}_2$, (c) $\mathrm{In}\text{−}{\mathrm{WSe}}_2$, (d) $\mathrm{Pd}\text{−}{\mathrm{WSe}}_2$, (e) $\mathrm{Ti}\text{−}{\mathrm{WSe}}_2$, (f) $\mathrm{W}\text{−}{\mathrm{WSe}}_2$. $E_F$ denotes Fermi level.

Figure 13

Band structures of (a) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ system, (b) $\mathrm{Ti}\text{−}{\mathrm{MoS}}_2$ system, and (c) $\mathrm{Mo}\text{−}{\mathrm{MoS}}_2$ system. The original band structure of ${\mathrm{MoS}}_2$ without contact is also plotted for reference (red curves), which is superimposed on the new band structure (gray curves) such that old and new subbands align. The Schottky barrier (${\mathrm{\Phi }}_{\mathrm{SB}}$) is marked in blue. Note that the symmetric points ($\mathrm{\Gamma }$, $X$, and $Y$) are different between (a), (b), and (c) due to different dimensions of the unit cells. PDOS of ${\mathrm{MoS}}_2$ after contact by Mo is also shown in (c).

Figure 14

${\mathrm{\Phi }}_{\mathrm{SB}}$ of all of the (a) ${\mathrm{MoS}}_2$ top contacts and (b) ${\mathrm{WSe}}_2$ top contacts. ${\mathrm{\Phi }}_{\mathrm{SB},N}$ (${\mathrm{\Phi }}_{\mathrm{SB},P}$) denotes $n$ type ($p$ type) SB for electrons (holes).

Figure 15

Valence electron densities (${\mathrm{bohr}}^{-3}$) of metal-mTMD top contacts: (a) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$, (b) $\mathrm{In}\text{−}{\mathrm{MoS}}_2$, (c) $\mathrm{Mo}\text{−}{\mathrm{MoS}}_2$, (d) $\mathrm{Pd}\text{−}{\mathrm{MoS}}_2$, (e) $\mathrm{Ti}\text{−}{\mathrm{MoS}}_2$, (f) $\mathrm{Au}\text{−}{\mathrm{WSe}}_2$, (g) $\mathrm{In}\text{−}{\mathrm{WSe}}_2$, (h) $\mathrm{Pd}\text{−}{\mathrm{WSe}}_2$, (i) $\mathrm{Ti}\text{−}{\mathrm{WSe}}_2$, (j) $\mathrm{W}\text{−}{\mathrm{WSe}}_2$. Panel (c) and the left-hand contours in (a) and (b) show average density along $x$ projected on the $y\text{−}z$ plane. Panels (d)–(j) and the right-hand plots in (a) and (b) show average electron density value in the $x\text{−}y$ planes normal to the $z$ axis (${\rho }_e$). ${\rho }_m$ in each panel indicates the minimum $x\text{−}y$ plane average electron density at each interface (in units of ${\mathrm{bohr}}^{-3}$).

Figure 16

(a) Maximum bond Mulliken populations (on a scale of 0 to 1) of top-contact interface bonds (colored numbers) compared to that of Mo-S (W-Se) bonds inside mTMDs (black numbers). (b) Bond Mulliken populations of the $\mathrm{Ti}\text{−}{\mathrm{MoS}}_2$ top contact. Population values are marked beside each interface bond. Population values of Mo-S bonds are also marked in ${\mathrm{MoS}}_2$.

Figure 17

Summary of metal-mTMD top-contact electron injection efficiency, in terms of orbital overlap, Schottky barrier, and tunnel barrier.

Figure 18

Optimized geometries of edge contacts: (a) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ (in different views), (b) $\mathrm{In}\text{−}{\mathrm{MoS}}_2$, (c) $\mathrm{Pd}\text{−}{\mathrm{MoS}}_2$, (d) $\mathrm{Ti}\text{−}{\mathrm{MoS}}_2$, (e) $\mathrm{Au}\text{−}{\mathrm{WSe}}_2$ (in different views), (f) $\mathrm{In}\text{−}{\mathrm{WSe}}_2$, (g) $\mathrm{Pd}\text{−}{\mathrm{WSe}}_2$, and (h) $\mathrm{Ti}\text{−}{\mathrm{WSe}}_2$. The large-volume overlaps of metal and chalcogenide atomic spheres exist in every edge contact [in (a)–(h)], indicating the formation of strong covalent bonds. Hence, physical separations in edge contacts (Table 1) are much smaller than that of top contacts in Figs. 8 and 9 due to the covalent bonds formed between mTMD and metals.

Figure 19

Minimum $V_{\text{eff}}$ of (a) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ edge contact and (b) $\mathrm{In}\text{−}{\mathrm{MoS}}_2$ edge contact. ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$ is the $V_{\text{eff}}$ of the Mo-S bond orbitals and thereby the effective tunnel barrier height (${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$) is defined as the minimum barrier height that an electron from the metal has to overcome, if it has the same potential energy as ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$. Hence, ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ can be calculated as the $V_{\text{eff}}$ difference between the vdW gap (${\mathrm{\Phi }}_{\text{gap}}$) and ${\mathrm{MoS}}_2$ (${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$). ${\mathrm{\Phi }}_{\text{metal},\min }$ denotes the minimum $V_{\text{eff}}$ that an electron can have in the metal. It is worth noting that in some metals [such as in (a)] ${\mathrm{\Phi }}_{\text{metal},\min }$ can be higher than ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$ (thus, electron energy is always higher than that of Mo-S bond orbitals), in which case ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ is calculated as ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}={\mathrm{\Phi }}_{\text{gap}}-{\mathrm{\Phi }}_{\text{metal},\min }$. $d$ is defined as the physical separation (the $z$ component of the nearest core-to-core distance between the metal atoms and the chalcogenide atoms). Though $d$ does not vanish, ${\mathrm{\Phi }}_{\mathrm{TB},\text{eff}}$ can vanish, when ${\mathrm{\Phi }}_{\text{metal},\min }$ or ${\mathrm{\Phi }}_{{\mathrm{MoS}}_2}$ is higher than ${\mathrm{\Phi }}_{\text{gap}}$, such as in (b).

Figure 20

PDOS of mTMD near $E_F$ of edge contacts to (a)–(d) ${\mathrm{MoS}}_2$ and (e)–(h) ${\mathrm{WSe}}_2$. Because of orbital overlaps (covalent bonds) at the interfaces, all the mTMDs in edge contacts have overlap states in the original band gaps and near $E_F$, so that mTMDs are metallized by edge contacts.

Figure 21

(a),(b) Minimum of average electron density values in the $x\text{−}y$ plane in Fig. 3 at the interfaces for all top and edge contacts. Ti, Pd, Mo, and W may form better top contacts due to higher interface electron density. Electron densities are significantly increased for edge contacts. (c),(d) Valence electron densities of $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ edge contact. (c) Average density along $y$ projected on the $x\text{−}z$ plane; (d) average density in the $x\text{−}y$ planes normal to the $z$ axis. The red number in (d) indicates the minimum electron density at the interface.

Figure 22

(a),(c) The cleaved $x\text{−}z$ planes (red rectangles) used to show electron localization functions (ELF) for (a) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ top contact and (c) $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ edge contact. (b),(d) ELF plots on the cleaved $x\text{−}z$ plane in $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ (b) top contact, (d) edge contact. Half-transparent dots indicate positions of atoms. High ELF (closer to 1) indicates high probability of finding an electron. For edge contact, $\mathrm{Au}\text{−}{\mathrm{MoS}}_2$ has overlapping electron orbitals (Au-S bonds, indicated by green dashes) resulting in the increasing of electron density as shown in Fig. 21. Thus, the contact resistance is reduced by using edge contacts.

Figure 23

Comparison of calculated (DFT-D2 with LDA) and experimentally measured (ARPES) [44] valence band structures of ${\mathrm{MoS}}_2$. The valence band maxima is set to zero energy.