Letter pubs.acs.org/NanoLett
Theoretical Demonstration of the Ionic Barristor Yifan Nie,† Suklyun Hong,‡ Robert M. Wallace,† and Kyeongjae Cho*,† †
Department of Materials Science and Engineering, The University of Texas at Dallas, Richardson, Texas 75080, United States Department of Physics and Graphene Research Institute, Sejong University, Seoul 143-747, Korea
‡
ABSTRACT: In this Letter, we use first-principles simulations to demonstrate the absence of Fermi-level pinning when graphene is in contact with transition metal dichalcogenides (TMDs). We find that formation of either an ohmic or Schottky contact is possible. Then we show that, due to the shallow density of states around its Fermi level, the work function of graphene can be tuned by ion adsorption. Finally we combine work function tuning of graphene and an ideal contact between graphene and TMDs to propose an ionic barristor design that can tune the work function of graphene with a much wider margin than current barristor designs, achieving a dynamic switching among p-type ohmic contact, Schottky contact, and n-type ohmic contact in one device. KEYWORDS: Ionic barristor, graphene, transition metal dichalchogenides, Schottky contact, density functional theory
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ZrS2,14 an n-type ohmic contact should be observed for the graphene−ZrS2 interface. As the Fermi level of graphene lies in the middle of the band gap for both MoS2 and WSe2, they will form a Schottky contact when brought into contact. The “barristor” is a novel device structure that makes use of the Schottky contact.15 Different from traditional Schottky field effect transistors, which fix the Schottky barrier height and function by tuning the thickness of the Schottky barrier and hence controlling tunneling current,16 barristors change the Schottky barrier height to achieve logic functionality. Graphene, being a single layered material, has a far lower density of states compared to metals. Thus, the graphene work function is very susceptible to a wide variety of tuning methods12,13 and is typically chosen to play the metal contact role in barristor designs. The tuning methods include static field effect,15,17 ionic liquid polarization,18 and so forth. The tuning margin of current barristor designs is about 0.2 eV. In this paper we use first-principles calculations with density functional theory to study the contact behavior of graphene and TMD, in which we show that no gap state is formed and hence there is no Fermi level pinning between TMD and graphene. As typical semiconducting TMDs, MoS2, and WSe2 are chosen because they show the most promising potential for transistor applications and hence have been studied most actively. ZrS2 is also chosen to further demonstrate the absence of any kind of Fermi level pinning, because it is predicted to have ohmic contact with graphene.10 Then we show that by inducing Li atoms or PF6 groups onto graphene, the work function of graphene may be tuned up and down to a very wide margin, without substantial changes to its band structure. Such a wide range can enable graphene to establish both n-type and p-type ohmic contact with a variety of semiconductors. Finally we use
ingle layered transition-metal dichalcogenides (TMDs) have received great research attention because of their outstanding mechanical and electrical properties which show great potential in transistor engineering.1,2 However, recent device studies have found that real devices behaviors are far inferior to the theoretical expectations.1,3,4 One of the major limiting aspects of the device performance is the contact between metal and the TMD, which is very sensitive to scaling.4 It has been confirmed by both experimental 5−8 and theoretical4,9−11 studies that a partial Fermi level pinning exists between the metal and the TMD, which will always pin the work function of metals to the gap states of TMDs induced by a metal-TMD interaction, resulting in high contact resistance and inability to establish p-type contact. Previous theoretical studies have revealed the cause of the partial Fermi level pinning.9,10 Apart from extrinsic and material imperfection (intrinsic defects) reasons, the cause of such partial Fermi level pinning lies in the charge transfer and chemical bonding at the interface resulting in metal work function modification and interface gap state formation. The high reactivity of the dangling bonds on metal surface causes strong orbital overlapping and hybridization between states of chalcogen and metal atoms on the surface, resulting in semicovalent or covalent bonds.9 Graphene, another 2D material in the spotlight, possesses semimetallic electric properties and molecular mechanical properties.12,13 Graphene has strong bonding in only two dimensions, which behaves similarly to the TMDs family. In absence of interlayer dangling bonds, graphene can form weak interlayer bonding with TMD compared to metal, thus providing a compatible and therefore less reactive interface. If this assumption is true, the Fermi level of graphene will not be modified by the contact and thus partial Fermi level pinning will not happen. In this case, as the work function of graphene is above the conduction band edge of group 4 TMD such as © XXXX American Chemical Society
Received: January 15, 2016
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DOI: 10.1021/acs.nanolett.6b00193 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters the graphene−TMD system as an example to propose a design of an ionic barristor. By exploiting the reversible nature of ionic adsorption and desorption, one side of graphene is used to form a high quality contact with the TMD, and the other side is used to reversibly tune the work function of graphene to establish and break an ohmic contact, realizing logic functionality. The density functional theory (DFT) calculations are performed by Vienna ab initio Simulation Package (VASP)19 with the projector-augmented wave (PAW) method.20 The local density approximation (LDA)21 is used to describe the exchange-correlation functional with the partial core correction included. Spin polarization and spin−orbit coupling are applied. The stable phase of MoS2 and WSe2 are H and T for ZrS2.14 A mismatch of the lattice constant exists between graphene and these TMDs. In order to fit the two layers into one super cell, different numbers of unit cells of graphene and the TMD are included in one super cell, and graphene is strained to match the optimized lattice constant of the TMD. A typical super cell
Figure 1. A typical super cell used in this study (green: Li, brown: C, yellow: S, and mauve: Mo).
Figure 3. Change of the band offsets when a layer of graphene approaches MoS2 (a) and WSe2 (b).
opposite side of ion adsorption is selected for work function alignment. The local density approximation (LDA) is found to be appropriate for studying the metal−TMD contact.9,14 The generalized gradient approximation (GGA)22 with the DFT-D2 method for van der Waals (vdW) corrections23 is also used to cross-check the structural accuracy and overall trends. We find that GGA results with vdW corrections are in overall agreement with LDA results. The optimized planar lattice constants for MoS2, WSe2, and ZrS2 are 3.12, 3.25, and 3.61 Å, respectively. The optimized planar lattice constant for monolayer graphene is 2.45 Å. In the supercell, the unit cells of the TMD and graphene are duplicated by different factors to roughly reach their least common multiple, which agrees well with observed behavior.24 Strain is induced in graphene to finely match the lattice constants, as the electronic behaviors of TMD are very much susceptible to lattice strain. The maximum strain induced into graphene is 2%. The electronic behaviors of graphene under this condition were examined. The work function of graphene shifts within ±0.15 eV after strain (Figure 2). Electron affinity and ionization energy vary within the same margin. Both the LDA method and the GGA+vdW method result in a similar structure and distance between graphene and the TMDs, indicating a secondary bond interaction. Our comparison also
Figure 2. Fermi level of graphene before and after strain, and band edges of the monolayer TMDs used in this study, in isolation. The possible tuning range of the graphene Fermi level is shown by the shaded column.
used in this study is shown in Figure 1, and the band offset of graphene and TMD is shown in Figure 2. The wave functions are expanded in plane waves with a kinetic energy cutoff of 500 eV, and the convergence criteria for the electronic and ionic relaxation are 10−4 eV and 0.05 eV/Å, respectively. Integration over the Brillouin zone is performed with a Γ-centered 6 × 6 × 1 Monkhorst−Pack k-point mesh for ionic and electronic optimization. A vacuum region of about 25 Å normal to the surface is added to minimize the interaction between adjacent slabs. Dipole correction on the stacking direction is applied to correct the sloped vacuum level caused by charge transfer between the layers. Vacuum level on the B
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Figure 4. Band structures of (a) monolayer graphene, (b) monolayer MoS2, (c) graphene in contact with MoS2, (d) graphene in contact with WSe2, and (e) graphene in contact with ZrS2. In the figures, the y-axis is the energy offsets in eV relative to the system’s Fermi level. Black dotted lines are the states that carbon atoms provide major contribution. The weight is represented by dot sizes.
shows that a distance of 3.5 Å is accurate enough to simulate the optimized contact system. Figure 3 shows that, when a layer of graphene is brought into close proximity of a monolayer TMD, the band offset does not change substantially, compared to the case when a metal approaches the monolayer TMD.10 The small change is due to the repulsion effect of wave functions on the interface. When the more significant effect of Fermi level pinning is absent, this effect stands out as the dominating influence on the band alignment. A more detailed band structure with two layers in contact is shown in Figure 4. Although in contact, there is little difference between the coupled system’s band structure (Figure 4c) and the simple overlapping of the bands of two isolated monolayers (Figure 4a,b). The Fermi level lies at the electric neutral point of graphene, and neither the work function of graphene nor the valence band edge (Ev) and conduction band edge (Ec) of MoS2 is changed significantly before and after contact (cf. Figure 5a,b). This indicates that graphene will form a Schottky contact with MoS2 and has recently been demonstrated by experimental and theoretical works.5,6,25,26 A similar case is observed for the graphene/WSe2 system, as shown in Figure 4d, since the work function of graphene is also between the Ev and Ec of the TMD. In both of these cases, the work function of graphene is retained, unlike a metal−TMD contact, in which the work function of metal is modified by the TMD. This results in a Fermi level “unpinning”, which is recently experimentally demonstrated.18 The band structures shown in Figure 4 also indicate that there are no gap states formed after contact formation, which is different from simulation results for metal−MoS2 contacts.10 In the absence of a pinning mechanism, the band structure of the layers are fixed before and after contact, and electrons will tunnel from one layer to the other through a Schottky barrier. Such an ideal interface makes the graphene−TMD interface a
good candidate for a barristor design, since it is suggested that any modification on the Fermi level of graphene may cause little interference to the underlying TMD. Different from MoS2 and WSe2, the conduction band edge of ZrS2 lies 1.2 eV below the Fermi level of graphene. Upon contact, as shown in Figure 4e, electrons will tunnel through from graphene to ZrS2 despite the relatively large distance and secondary bonding nature. As a result, the Fermi level of the coupled system will intersect the conduction band edge of ZrS2, indicating an n-type ohmic contact (Figure 5c). Despite the fact that no Fermi level pinning is present within the band gap edges of TMDs, the band alignment between graphene and MoS2 or WSe2 still results in a high Schottky barrier. The low current density in the contact has been the major impedance to applications of devices with graphene/ TMD contacts. However, the fact that there exists no pinning mechanism also suggests that the work function of graphene is insensitive to contact (Figure 4), which makes it possible to tune the work function of graphene on one side, and make ideal contact between graphene and TMD on the other side. Such tuning has been proved to be achievable by the electrostatic field effect and a polarizing ionic liquid.15,17,18 However, neither of them have been proved to establish real ohmic contact between graphene and the semiconductor, due to the high voltage required in these designs. Here we show that ion adsorption has the ability to tune the work function of graphene with a wider margin than the field effect or an ionic liquid, so that the tuned graphene work function can form both n-type and p-type ohmic contact with TMDs. LiPF6 has been widely used as an electrolyte in lithium battery technology, and graphene is a candidate for the anode material.27 In the following lithium, and hexafluorophosphate group (PF6) adsorption are taken as examples of tuning graphene’s work function to achieve ohmic contacts. C
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Figure 6. Fermi level of graphene doped with different concentration of Li atom or PF6 group.
doping limit of Li in graphite (1:6), it is found that the Fermi level can be tuned up by as much as 1.22 eV. Due to the large size of the PF6 group, the maximum doping concentration of PF6 cannot be comparable to that of Li; however, reaching a high doping concentration on the surface (1PF6:25C), the Fermi level can be tuned downward by 1.66 eV (Figure 6). Such a wide range of work function tuning (from 3.30 to 6.18 eV, as is shown in Figure 2) enables graphene to have an ohmic contact with a wide range of semiconductors including TMD monolayers, in the same manner as undoped graphene has an ohmic contact with ZrS2 described earlier. When in ohmic contact with a TMD, the Fermi level of graphene with ion adsorption will be fixed to the edge of conduction or valence band of the TMD before reaching the extrapolated tuning limit of Li or PF6 on graphene. Figure 7a shows the band structure of Li-doped graphene on monolayer MoS2. It is shown that by adding Li atoms at a Li:C ratio of 0.02, n-type ohmic contact is predicted. Doping with a PF6 group at an appropriate concentration (PF6:C ratio being 0.04) will enable the layers to have a p-type ohmic contact. Lower doping concentration (1 PF6 per 50 C atoms) can still shift the Fermi level, but not enough to reach the valence band of MoS2, leaving a Schottky barrier of 0.18 eV, as indicated in Figure 5a. Similarly, as shown in Figure 7c, doping at a concentration of 1 Li per 16 C atoms will enable graphene and WSe2 to have an n-type ohmic contact. Doping at 1 PF6 group per 32 C atoms is able to realize p-type ohmic contact between graphene and WSe2 (Figure 7d). This tuning mechanism is the same as that of a graphene-MoS2 contact. Figure 5 also shows that the position of the band gap edges of the TMDs with respect to the vacuum level are changed only slightly by ion adsorption, which confirms our assumption that ion adsorption does not strongly interfere with the underlying TMD layer while modifying the Fermi level of the graphene. It is noteworthy that, unlike implantation, ion adsorption is reversible. This indicates that the tuning of the work function of graphene can be performed reversibly, repetitively, and thus controlled dynamically. In addition, once ions have adsorbed onto graphene, the energy required to maintain the adsorption is small. Such properties can be used for a wide range of applications. Here we propose an improved barristor design with ionic adsorption and desorption.
Figure 5. Energy diagram for the Fermi level of graphene, strained graphene to match the TMD lattice constant, the valence and conduction band edges of TMDs (a. MoS2, b. WSe2, c. ZrS2) and the contact systems. Energy levels are measured from the vacuum level (E = 0).
Adsorption (or charge transfer “doping”) of a Li atom onto graphene will bring an electron into the material system without significant changes onto the associated band structure, causing its Fermi level to rise above the Dirac point. Doping with PF6 has the reverse effect. We have studied the relation between raising the Fermi level and doping concentration (as captured by the Li:C ratio) by adding one Li atom onto the graphene supercell with different sizes. By extrapolating to the D
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Figure 7. Band structures of the combined system of (a) Li-doped graphene and MoS2, (b) PF6-doped graphene and MoS2, (c) Li-doped graphene and WSe2, and (d) PF6-doped graphene and WSe2. In all four cases, an ohmic contact, n-type for a and c, p-type for b and d are predicted.
In graphene−semiconductor junction FET devices, the work function of either graphene or the semiconductor is tuned by the electrostatic field. In the case of 2D TMD materials, the thickness limits the size of depletion region, which in turn limits device performance. In addition, good interlayer quality is required on both sides of the thin layers, which makes it more difficult to fabricate devices while tuning the work function of TMD materials. The technique to grow, transfer and modulate graphene, has been well-established. In an “ionic barristor”, the work function of graphene is dynamically tuned, and switching on and off is realized by building and breaking ohmic contact with semiconductor. A possible structure for an ionic barristor is shown in Figure 8a. The source and drain electrodes are set on graphene and the TMD (in the example, WSe2), respectively, and a layer of electrolyte and a source gate is places on top of the graphene. The circuit design is shown in Figure 8b. In the off condition, the Schottky barrier between conduction band edge of TMD and Fermi level of graphene is high, effectively stopping electrons from tunneling. One side of graphene forms an ideal contact with the TMD, with no Fermi level pinning, and the other side is in contact with electrolyte with Li+ and PF6− ions. A gate electrode is set on top of the electrolyte. By changing the gate−source voltage (VGS), cations or anions in the electrolyte can adsorb on or desorb from graphene, changing the work function of graphene with a margin as much as ±1.5 eV. The completed ohmic contact will result in a high on/off ratio. For example, in a graphene-WSe2 device, the work function of the graphene can be tuned from midgap to the conduction band edge (or valence band edge for hole injection), with a range of 0.6 eV. Theoretically, at room temperature the on/off ratio can reach as much as 1014. One setback of the standalone ionic barristor design is that its application is limited by the inherent slow response time of ionic devices. In addition, hysteresis is present when swapping the switch. This serves as a severe disadvantage when the device is required to switch at a high frequency; on the other hand, it is an advantage when the status of the switch is required to
Figure 8. Device structure of the ionic barristor. (a) The topologicalal structure of a standalone ionic barristor, (b) circuit design for the ionic barristor, (c) an example of an ionic barristor integrated in the source site of a TMD based TFET.
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(9) Chen, W.; Santos, E. J. G.; Zhu, W.; Kaxiras, E.; Zhang, Z. Nano Lett. 2013, 13, 509−514. (10) Gong, C.; Colombo, L.; Wallace, R. M.; Cho, K. Nano Lett. 2014, 14, 1714−1720. (11) Kang, J.; Liu, W.; Sarkar, D.; Jena, D.; Banerjee, K. Phys. Rev. X 2014, 4, 031005. (12) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197−200. (13) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183−191. (14) Gong, C.; Zhang, H.; Wang, W.; Colombo, L.; Wallace, R. M.; Cho, K. Appl. Phys. Lett. 2013, 103, 053513. (15) Yang, H.; Heo, J.; Park, S.; Song, H. J.; Seo, D. H.; Byun, K.-E.; Kim, P.; Yoo, I.; Chung, H.-J.; Kim, K. Science 2012, 336, 1140−1143. (16) Bardeen, J.; Brattain, W. H. Phys. Rev. 1949, 75, 1208−1225. (17) Tian, H.; Tan, Z.; Wu, C.; Wang, X.; Mohammad, M. A.; Xie, D.; Yang, Y.; Wang, J.; Li, L.-J.; Xu, J. Sci. Rep. 2014, 4, 5951. (18) Chuang, H.-J.; Tan, X.; Ghimire, N. J.; Perera, M. M.; Chamlagain, B.; Cheng, M. M.-C.; Yan, J.; Mandrus, D.; Tománek, D.; Zhou, Z. Nano Lett. 2014, 14, 3594−3601. (19) Kresse, G.; Furthmuller, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169. (20) Kresse, G.; Joubert, D. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758. (21) Ceperley, D. M.; Alder, B. J. Phys. Rev. Lett. 1980, 45, 566−569. (22) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (23) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (24) Eichfeld, S. M.; Hossain, L.; Lin, Y.-C.; Piasecki, A. F.; Kupp, B.; Birdwell, A. G.; Burke, R. A.; Lu, N.; Peng, X.; Li, J.; et al. ACS Nano 2015, 9, 2080−2087. (25) Komsa, H.-P.; Krasheninnikov, A. V. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 085318. (26) Jin, C.; Rasmussen, F. A.; Thygesen, K. S. J. Phys. Chem. C 2015, 119, 19928−19933. (27) Dunn, B.; Kamath, H.; Tarascon, J.-M. Science 2011, 334, 928− 935.
remain static for a relatively long time. Therefore, another application of ionic barristor is proposed, where it is integrated into the source and/or the drain contact of another TMD based device, as shown in an example in Figure 8c. In this example, an ionic barristor is integrated into the source site of a tunneling field effect transistor, and the source gate voltage is set static to establish an ohmic contact with TMD. In this case, logic functionality is realized by the TFET. As Fermi level pinning is avoided at the source site, the electron injection efficiency is predicted to be increased. In conclusion, we have demonstrated separately that Fermi level pinning is absent between TMD and graphene and that ion adsorption is able to change the work function of graphene from 3.30 to 6.18 eV. Then by putting them in contact, we have shown that both n-type and p-type ohmic contact can be achieved by tuning the work function of graphene with ion adsorption. Then we proposed a design of the ionic barristor, which can be switched among three states, being off (Schottky contact), n-type ohmic contact and p-type ohmic contact. This Fermi level “unpinning” phenomenon between graphene and the TMD is due to the van der Waals interaction between them. In this sense, the Fermi level of graphene is not pinned to all other families of semiconductors that interact only weakly with graphene, in addition to the TMDs. This predicted ohmic contact between metals and semiconductors in contact with only van der Waals interaction is subject to experimental demonstration and its applications are open to a limitless possibility of creative device designs.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +1 (972)883 2845. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Center for Low Energy Systems Technology (LEAST), one of six centers supported by the STARnet phase of the Focus Center Research Program (FCRP), a Semiconductor Research Corporation Program sponsored by MARCO and DARPA. This work is also partially supported by Nano Material Technology Development Program (2012M3A7B4049888) through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning, and Priority Research Center Program (2010-0020207) through NRF funded by the Ministry of Education.
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REFERENCES
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