DOI:
10.1039/C4RA15218B
(Communication)
RSC Adv., 2015,
5, 20538-20544
Effect of vacancies in monolayer MoS2 on electronic properties of Mo–MoS2 contacts†
Received
25th November 2014
, Accepted 13th February 2015
First published on 13th February 2015
Abstract
Revealing the influence of intrinsic defects in monolayer MoS2 on the electronic nature of metal–MoS2 contacts is particularly critical for their practical use as nanoelectronic devices. This work presents a systematic study toward electronic properties of Mo metal contacts to monolayer MoS2 with vacancies by using first-principles calculations based on density functional theory. Upon Mo- and S-vacancy formation in monolayer MoS2, both the height and the width of the tunnel barrier between Mo metal and monolayer MoS2 are decreased. Additionally, the Schottky barrier of 0.1 eV for the perfect Mo–MoS2 top contact is reduced to zero for defective ones. The partial density of states near the Fermi level of defective Mo–MoS2 top contacts is strengthened and electron densities at the interface of defective Mo–MoS2 top contacts are increased compared with those of the perfect one, suggesting that Mo- and S-vacancies in monolayer MoS2 have the possibility to improve the electron injection efficiency. Mo-vacancies in monolayer MoS2 are beneficial to get high quality p-type Mo–MoS2 contacts, whereas S-vacancies in monolayer MoS2 are favorable to achieve high quality n-type Mo–MoS2 contacts. Our findings provide important insights into future design and fabrication of nanoelectronic devices with monolayer MoS2.
1. Introduction
Monolayer transition-metal dichalcogenides (mTMD), a family of 2D semiconductor layers arranged in a hexagonal lattice, have drawn tremendous attention as promising channel materials for digital electronic applications due to their nonzero band gap, small thicknesses, and pristine interfaces without out-of-plane dangling bonds.1–10 Among various mTMD materials, monolayer MoS2 has emerged because of its atomically thickness of ∼7 Å per layer,11 considerable band gap of 1.8 eV,12 planar nature, and pristine surfaces. Most recently, monolayer MoS2 has been used to construct field-effect transistors (FETs), which can offer lower power consumption than classical transistors.1,13 New phototransistor based on monolayer MoS2 has been demonstrated to have a better photoresponsivity as compared with the graphene-based device.14 Moreover, FET based biosensors with mTMD semiconductor as the channel material have been fabricated and exhibit highly advantageous over all other nanomaterial-based FET biosensors.15
However, low-resistance metal contacts to monolayer MoS2 remain a critical issue for its transistor applications because several factors, such as large band gap, pristine surfaces and lack of proper doping approach, may mask the innate exceptional electronic and magnetic properties of monolayer MoS2.16,17 In order to overcome this issue, many studies have been performed to reduce the tunnel barrier and Schottky barrier in metal–MoS2 contacts.16–20 Popov et al.20 have studied Ti–MoS2 and Au–MoS2 top contacts by density functional theory, indicating that the most common contact Au metal is rather inefficient for electron injection into monolayer MoS2. Kang et al.16 have evaluated In, Ti, Au, Pd, and Mo, contacts to monolayer MoS2 by density functional theory calculations, implying that Ti and Mo have great potential to form favorable n-type top contacts to monolayer MoS2. Nevertheless, the Schottky barrier for Ti–MoS2 contact is about 0.33 eV,17 which is still very high. Mo–MoS2 contact has ultra-low Schottky barrier of 0.1 eV at source/drain-channel junction, and high-performance FETs based on Mo–MoS2 contact have been demonstrated.17 Hence, Mo has been proposed as a promising contact metal to monolayer MoS2.
Vacancy defects were found to exist in monolayer MoS2 when monolayer MoS2 was prepared through sonochemical deposition21 and exfoliated method.22 Several literatures have reported the effect of vacancies on properties of monolayer MoS2. Ataca et al.23,24 have calculated the formation energy of neutral vacancies in monolayer MoS2 and studied the influence of vacancies on magnetic properties of monolayer MoS2, implying that vacancy creation appears to be a promising way to extend the applications of MoS2. The formation energies of charged vacancies in monolayer MoS2 under different atmospheric conditions have been investigated.25,26 Feng et al.27 have indicated that structural, electronic, and optical properties of monolayer MoS2 depend greatly on its intrinsic vacancies.
It should be noted that vacancy defects in monolayer MoS2 not only influence the properties of monolayer MoS2 but also affect the interfacial and electrical properties of metal–MoS2 contacts. However, to the best of our knowledge, effects of vacancies in monolayer MoS2 on electronic structure and electronic properties of Mo–MoS2 contact are not well understood yet. It is well known that the knowledge of electronic properties of Mo–MoS2 contact is very important for the practical applications of monolayer MoS2 as well as for the designing and analyzing of optoelectronic devices. Therefore, this work is focused on investigating the effect of vacancies in monolayer MoS2 on electronic structure and electronic properties of Mo–MoS2 contacts using first-principles calculations.
2. Computational details
In the present calculations, the exchange correlation of the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional as implemented in CASTEP code28 was employed. In order to consider the van der Waals interactions in TMD materials, DFT-D2 is adopted in this work, where the potential is described via a simple pairwise force field and is optimized for popular DFT functionals.29 The electron–ion interactions were described by norm-conserving Troullier–Martins pseudopotentials30 with partial core corrections. The plane-wave cutoff energy was set to be 200 Ry after extensive convergence analysis. The Brillouin-zone of Mo–MoS2 top contact region was performed over the 8 × 8 × 1 k-point grids using the Monkhorst–Pack method,31 where the self-consistent convergence of the total energy is 1.0 × 10−6 eV per atom. Conjugate gradient scheme was used to relax supercell until the component of the forces on each atom was less than 0.01 eV Å−1.
Mo–MoS2 top contact was modeled by a supercell slab, which is periodic in the x and y directions and separated by 20 Å vacuum region in the z direction to minimize the interactions between adjacent image cells. The supercell slab of Mo–MoS2 top contact contains 4 × 4 unit cells of monolayer MoS2 and the close-packed surface of Mo (001) extending to the 6th layer, which is the most probable orientation to be found in experiments. The supercell geometry of perfect Mo–MoS2 top contact is shown in Fig. 1(a), and geometries of defective Mo–MoS2 top contacts with single Mo and S vacancy are presented in Fig. 1(b) and (c), respectively. When optimizing these models by using conjugate gradient technique, atoms except the 3rd to 6th layers of Mo metal from the interface were allowed to relax so as to evaluate the effect of interfacial layers.17 Although in real situations, the contact metals consist of many layers, the situation restricted to 6 layers of metal atoms is thick enough to accurately model the electronic properties of metal–MoS2 contact17,20,32 because the obtained results do not change appreciably beyond this thickness. A similar approach had been successfully used to characterize mTMD and their contacts to metal electrodes.20,27
![image file: c4ra15218b-f1.tif](/image/article/2015/RA/c4ra15218b/c4ra15218b-f1.gif) |
| Fig. 1 The supercell geometry of Mo–MoS2 top contacts. (a) Bottom view and side view of perfect Mo–MoS2 top contact, (b) bottom view of defective Mo–MoS2 top contact with Mo vacancy in monolayer MoS2 and amplified sketch of monolayer MoS2 with Mo vacancy, and (c) bottom view of defective Mo–MoS2 top contact with S vacancy in monolayer MoS2 and amplified sketch of monolayer MoS2 with S vacancy. | |
3. Results and discussion
3.1 Tunnel barriers
The tunnel barrier between a metal and mTMD is characterized by its height and width, which are evaluated by the effective tunnel barrier height (ΦTB,eff) and physical separation (dp), respectively. The ΦTB,eff is defined as the minimum effective potential (Veff) difference between the Mo–MoS2 interface and monolayer MoS2. According to Kohn–Sham equations33 and Kang et al.16 reports, the effective potential of an electron (Veff(n)) represents the electron interaction with other electrons and external electrostatic field, and Veff(n) can be expressed by16,33 |
Veff(n) = VKS = VH(n) + Vxc(n) + Vext(n)
| (1) |
where VH(n) is the mean-field electrostatic interaction, Vxc(n) is the exchange–correlation potential, Vext(n) represents external electrostatic interactions, and VKS is the Kohn–Sham potential in Kohn–Sham equations. Fig. 2(a), as an example, shows the Veff versus position on z axis for perfect Mo–MoS2 top contact and denotes the ΦTB,eff of perfect Mo–MoS2 top contact. To evaluate the tunnel barrier height, the ΦTB,eff of perfect and defective Mo–MoS2 top contacts are plotted in Fig. 2(b). Obviously, ΦTB,eff value of perfect Mo–MoS2 top contact is about 0.12 eV, which is lower than those of Ti–MoS2 (0.45 eV (ref. 20)), Au–MoS2 (1.03 eV (ref. 20)) and Pd–MoS2 (0.15 eV (ref. 16 and 32)) top contacts, implying that perfect Mo–MoS2 top contact has higher carrier injection efficiency than Ti–, Au– and Pd–MoS2 top contacts.16 When a Mo- or S-vacancy is formed in monolayer MoS2, defective Mo–MoS2 top contacts have negligible ΦTB,eff value of 0.01 eV, indicating that carrier injection efficiency of defective Mo–MoS2 top contacts is further improved. It should be mentioned that these estimates of ΦTB,eff can be affected by a sizeable Self-Interaction Error (SIE),34–37 owing to the use of the non-SIE free PBE functional. The SIE can be estimated to contribute an additional 0.18–0.27 eV to the calculated barriers.
![image file: c4ra15218b-f2.tif](/image/article/2015/RA/c4ra15218b/c4ra15218b-f2.gif) |
| Fig. 2 (a) Minimum effective potential height (Veff) versus z position for perfect Mo–MoS2 top contact. The effective tunnel barrier height (ΦTB,eff) can be defined as the Veff difference between the Mo–MoS2 interface and monolayer MoS2. Color key is Mo metal = blue and monolayer MoS2 = green. (b) The ΦTB,eff and physical separation dS–Mo for perfect and defective Mo–MoS2 top contacts. | |
In order to evaluate the tunnel barrier width, physical separations of perfect and defective Mo–MoS2 contacts are calculated and presented in Fig. 2(b). The physical separation dS–Mo and average separation dMo–Mo are defined as shown in Fig. 1(a). It is clear from Fig. 2(b) that dS–Mo value of perfect Mo–MoS2 contact is about 1.34 Å, which is consistent with previous theoretical value (1.27 Å (ref. 16)) and smaller than those of other metal–MoS2 top contacts (2–3 Å).20,32 This small physical separation is lower than the sum of S and Mo covalent radii.20 Furthermore, the average separation dMo–Mo between the bottom Mo layer and the Mo layer in monolayer MoS2 is about 3.02 Å, which is shorter than those of Ti–MoS2 (3.57 Å) and Au–MoS2 (4.21 Å)20 top contacts. The small dS–Mo and dMo–Mo indicate strong orbital overlaps and thin tunnel barrier.
When Mo-vacancy is formed in monolayer MoS2, dS–Mo value of defective Mo–MoS2 top contact is reduced to 1.29 Å as shown in Fig. 2(b). There are two factors may lead to the decrease of the dS–Mo value. On one hand, S ions surrounding Mo-vacancy undergo an outward relaxation.27 On the other hand, dangling bonds of S ions, which induced by Mo-vacancy, can rebind with the Mo atoms in bottom Mo layer to shorten dS–Mo. When S-vacancy is formed in monolayer MoS2, dS–Mo value of defective Mo–MoS2 top contact is decreased to 1.25 Å because the Mo atoms around S-vacancy move toward to the vacancy.27,38 Moreover, the average separation dMo–Mo between the bottom Mo layer and the Mo layer in monolayer MoS2 is reduced from 3.02 to 2.92 Å, which is close to the diameter of Mo atom. Therefore, compared with perfect Mo–MoS2 contact, defective Mo–MoS2 top contacts are favorable to get stronger orbital overlaps and thus thinner tunnel barrier.
3.2 Density of states
The band structure and PDOS of monolayer MoS2 are shown in Fig. 3(a) and (b), respectively. It can be seen that an obvious band gap of 1.78 eV is observed for monolayer MoS2, which is consistent with the theoretical values of 1.73 eV (ref. 39) and 1.90 eV (ref. 40) obtained using GGA, but lower than the values of 2.12–2.78 eV obtained by HSE06 (ref. 41 and 42) and GW23,43 (see ESI Table 1†). The experimental value of 1.80 eV (ref. 12) may be rather an optical band gap because of the experimental methods used and the approximations applied in the treatment of the data. Hence, the band gap of monolayer MoS2 obtained by the higher-level functionals of HSE06 (ref. 41 and 42) and GW23,43 may be more close to the true experimental data. This is consistent with the expectation that the PBE Kohn–Sham gap usually underestimates the true band gap.
![image file: c4ra15218b-f3.tif](/image/article/2015/RA/c4ra15218b/c4ra15218b-f3.gif) |
| Fig. 3 (a) Band structure of intrinsic monolayer MoS2, (b) PDOS of intrinsic monolayer MoS2, (c) PDOS of perfect Mo–MoS2 top contact, (d) PDOS of defective Mo–MoS2 top contact with Mo-vacancy in monolayer MoS2, (e) PDOS of defective Mo–MoS2 top contact with S-vacancy in monolayer MoS2. | |
Fig. 3(c) presents the PDOS of perfect Mo–MoS2 top contact. It is obvious from Fig. 3(c) that the band gap vanishes, indicating a metallic contact between Mo metal and monolayer MoS2. According to the previous reports,16,20 the n-type or p-type can be determined from the PDOS of monolayer MoS2 in the Mo–MoS2 contact. If the position of Fermi level (EF) is shifted upwards the original conduction bands (Ec) of monolayer MoS2, indicating that monolayer MoS2 is doped n type. In contrast, if EF is close to the original valence bands (Ev) of monolayer MoS2, showing that monolayer MoS2 is doped p type. In Fig. 3(c), the EF of perfect Mo–MoS2 top contact is shifted upwards, to 0.25 eV above the bottom of conduction bands of monolayer MoS2, suggesting that monolayer MoS2 is doped n-type by Mo. The shift of EF is due to the fact that doping causes significant distortion to the band structure around the band gap. In order to comparatively study the PDOS of monolayer MoS2 under different conditions, it is necessary to lineup the band structures of intrinsic monolayer MoS2 and monolayer MoS2 in Mo–MoS2 top contacts. For this purpose, the valence bands maximum (EVBM) of Mo–MoS2 top contacts can be obtained by the following equation:44,45
|
EVBM = EVBM(intrinsic) + Vav(interface) − Vav(intrinsic)
| (2) |
where
EVBM(intrinsic) is the valence bands maximum of intrinsic monolayer MoS
2,
Vav(intrinsic) and
Vav(interface) represent the average potential of intrinsic monolayer MoS
2 and monolayer MoS
2 in Mo–MoS
2 top contacts, respectively. As a result, the band structures of Mo–MoS
2 top contacts are obtained (see ESI Fig. 1
†). The borders of the valence and conduction bands of intrinsic monolayer MoS
2 are marked as vertical dot lines in the PDOS of Mo–MoS
2 top-contacts, as shown in
Fig. 3(c). The dash line in
Fig. 3(c) represents the
EF of the Mo–MoS
2 contact system. According to the previous reports,
16,46 the n-type (p-type) Schottky barrier is the difference between the bottom of conduction bands (the top of the valence bands) of intrinsic monolayer MoS
2 and the
EF of the Mo–MoS
2 top contact, as exhibited in
Fig. 3(c). Like In–, Ti–, and Au–MoS
2 top contacts,
16,20,47 the
EF is pinned near the original conduction bands of intrinsic monolayer MoS
2. The Schottky barrier of perfect Mo–MoS
2 top contact is about 0.1 eV, which is in good agreement with previous theoretical results (0.13 eV,
16 0.1 eV (
ref. 17)) and lower than those of Ti–MoS
2 (0.33 eV,
17,32 0.35 eV (
ref. 16)), Au–MoS
2 (0.62 eV (
ref. 16 and 32)) and Pd–MoS
2 (0.90 eV (
ref. 16 and 32)) top contacts despite metal Mo has a high work function. In addition, high PDOS spread all over the original band gap of intrinsic monolayer MoS
2 implies the formation of Ohmic contact between Mo metal and monolayer MoS
2, which is consistent with previous theoretical and experimental report for Mo–MoS
2 top contact.
17,32 Furthermore, the broadening of the peaks in the PDOS near
EF reflects the formation of delocalized states with low effective electron mass allowing more electrons to be transferred between the metal and the mTMD layer.
20,32
PDOS of defective Mo–MoS2 top contacts with single Mo and S vacancy are presented in Fig. 3(d) and (e), respectively. In the case of Mo-vacancy, as shown in Fig. 3(d), a high PDOS near EF eliminates the band gap, indicating that Mo-vacancy has no effect on Ohmic contact and the metallic character of Mo–MoS2 system. In addition, PDOS near EF of defective Mo–MoS2 top contact are much higher than those of perfect one because the dangling bonds of S atoms surrounding Mo-vacancy can form covalent bonding with Mo atoms in the bottom Mo layer, which almost like the covalent bonding formation for Mo–MoS2 side contact.16 The higher PDOS near EF suggests the lower effective carrier mass and the higher efficiency of carrier transport. Hence, upon Mo-vacancy forming in monolayer MoS2, the Schottky barrier of defective Mo–MoS2 top contact vanishes. Moreover, in contrast to perfect Mo–MoS2 top contact, the EF of defective Mo–MoS2 top contact is shifted downwards, to 0.17 eV under the top of valence bands of monolayer MoS2. Therefore, Mo-vacancy in monolayer MoS2 is beneficial to achieve high quality p-type Mo–MoS2 top contact.
In the case of S-vacancy, as shown in Fig. 3(e), high PDOS near EF are also observed. Previous studies27,38 have shown that S-vacancy in monolayer MoS2 can induce defective states in the band gap. Thus, it can be found that some new peaks of PDOS appear near EF due to strong hybridization of d orbitals between Mo metal and monolayer MoS2. Additionally, the Schottky barrier of defective Mo–MoS2 top contact disappears, implying the efficiency of electron transport is further improved. Similar to perfect Mo–MoS2 top contact, the EF of defective Mo–MoS2 top contact is shifted upwards, to 0.62 eV above the bottom of conduction bands of intrinsic monolayer MoS2. It should be noted that the position of the EF of defective Mo–MoS2 top contact is higher than that of perfect one. Therefore, in contrast to Mo-vacancy, S-vacancy is beneficial to achieve high quality n-type Mo–MoS2 top contact.
3.3 Electron density
Average electron density of perfect and defective Mo–MoS2 top contacts are calculated and shown in Fig. 4. The minimum x–y plane average electron density of Mo–MoS2 interface and monolayer MoS2 is marked ρi and ρm, respectively. Usually, high electron density at the interface of metal–mTMD contacts allows sufficient injection of charge into mTMD layer.20 In Fig. 4(a), the ρi value of perfect Mo–MoS2 top contact is about 0.042 bohr−3, which is higher than those of other metal–MoS2 top contacts (0.013–0.033 bohr−3),16,20 implying that Mo metal has advantage to achieve strong orbital overlaps with monolayer MoS2, leading to low contact resistant and high electron injection efficiency.32 The previous studies17,27 have indicated that strong covalent bonds are formed at the interface of perfect Mo–MoS2 top contact. From Fig. 4(a), the ρi value of 0.042 bohr−3 is close to the ρm value of 0.051 bohr−3, indicating the formation of covalent bonds at the interface. This result is consistent with the previous reports.17,27
![image file: c4ra15218b-f4.tif](/image/article/2015/RA/c4ra15218b/c4ra15218b-f4.gif) |
| Fig. 4 Average electron density value in the x–y planes normal to the z axis: (a) perfect Mo–MoS2 top contact, (b) defective Mo–MoS2 top contact with Mo-vacancy, (c) defective Mo–MoS2 top contact with S-vacancy. Ball with a virtual edge in the panels represents Mo- or S-vacancy in monolayer MoS2. The ρi and ρm in each panel indicate the minimum x–y plane average electron density at interface and monolayer MoS2, respectively (in units of bohr−3). | |
Average electron densities of defective Mo–MoS2 top contacts with single Mo and S vacancy are presented in Fig. 4(b) and (c), respectively. It can be seen that the average electron densities at the interface region of defective Mo–MoS2 top contacts become higher compared with those in perfect Mo–MoS2 system, showing that the covalent bonds between the Mo metal and monolayer MoS2 are enhanced due to stronger orbital overlap, which are consistent with the above PDOS analysis. Consequently, Mo- and S-vacancy in monolayer MoS2 have possibility to decrease the contact resistant and improve the electron injection efficiency. In addition, the ρi value of 0.047 bohr−3 for Mo–MoS2 top contact with S-vacancy is slightly larger than the ρi value of 0.044 bohr−3 for Mo–MoS2 top contact with Mo-vacancy, indicating that S-vacancy is more favorable to improve the electronic transport of Mo–MoS2 top contacts. After introduction of Mo- or S-vacancy in monolayer MoS2, the difference between ρi and ρm for defective Mo–MoS2 top contacts is decreased.
3.4 Mulliken population
The electron density can also be confirmed by Mulliken population analysis. The calculated Mulliken populations of atoms in Mo metal layer and monolayer MoS2 for perfect and defective Mo–MoS2 top contacts are listed in Table 1. For perfect Mo–MoS2 top contact, 0.042 e of Mo atoms in metal layer are transferred to interfacial S atoms in top sulfur layer, suggesting strong interactions between the Mo and S atoms. Simultaneously, interfacial S atoms accept 0.079 e from Mo atoms in monolayer MoS2. As a result, the electron density at the Mo–MoS2 interface region is lower than that of Mo–S bond in monolayer MoS2. For defective Mo–MoS2 top contacts, the electrons transferred from Mo atoms in metal layer to interfacial S atoms are increased whereas the electrons moved from Mo atoms in monolayer MoS2 to interfacial S atoms are decreased compared with those in perfect Mo–MoS2 top contact, as shown in Table 1. Accordingly, the electron density at the Mo–MoS2 interface region increases whereas the electron density of Mo–S bond in monolayer MoS2 reduces. Therefore, the difference between ρi and ρm for defective Mo–MoS2 top contacts is decreased, which is consistent with above electron density analysis.
Table 1 Mulliken population of Mo atoms in metal layer as well as Mulliken population of Mo and S atoms in monolayer MoS2 for perfect and defective Mo–MoS2 top contacts. The atoms' serial number is indexed in Fig. 1(b) and (c)
|
Mo metal layer |
MoII |
MoIV |
SI |
SIII |
Perfect |
5.958 |
5.921 |
5.921 |
6.073 |
6.073 |
Mo-vacancy |
5.946 |
5.940 |
— |
6.082 |
— |
S-vacancy |
5.943 |
— |
5.941 |
— |
6.119 |
4. Conclusion
The effects of intrinsic vacancies in monolayer MoS2 on electronic structure and electronic properties of Mo–MoS2 top contacts have been investigated using the first-principles plane-wave pseudopotential method based on density functional theory. Tunnel barrier, Schottky barrier, and electron density of perfect and defective Mo–MoS2 top contacts were analyzed. Results show that the height and width of the tunnel barrier of Mo–MoS2 top contacts are decreased when Mo- or S-vacancy is formed in monolayer MoS2. Additionally, Schottky barriers are found to be 0.1 and 0 eV for perfect and defective Mo–MoS2 top contacts, respectively. PDOS near Fermi level of defective Mo–MoS2 top contacts are much higher than those of perfect one, implying the lower effective carrier mass for defective Mo–MoS2 top contacts. Average electron density at interface of defective Mo–MoS2 top contacts are increased compared with those in perfect Mo–MoS2 top contact, showing that contact resistant and electron injection efficiency are further improved by vacancies. Moreover, Mo-vacancy in monolayer MoS2 exhibits p-type Mo–MoS2 top contact, whereas S-vacancy in monolayer MoS2 shows n-type Mo–MoS2 top contact.
Acknowledgements
We acknowledge the National Natural Science Foundation of China under grant no. 61376091, the National Aerospace Science Foundation of China under grant no. 2014ZF53070, the Fundamental Research Funds for the Central Universities under grant no. 3102014JCQ01033 and the 111 Project under grant no. B08040.
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Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra15218b |
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