Abstract
1. Introduction
Two-dimensional (2D) semiconductor has been a competitive candidate of channel material of transistors for the coming sub-10 nm generation field effect transistor (FET) as they offer several advantages over traditional silicon[
Directly contacting the 2D semiconductor channel with metal electrode is a feasible doping means in the absence of a sustainable substitution doping method[
In this paper, we explore the vertical and lateral interfacial properties of BL tellurene FETs by using ab initio electronic band calculation and quantum transport simulation, which takes FLP at the interfaces into counts and presents accurate predictions on the SBH[
2. Models and methods
A fully relaxed BL tellurene structure is shown in Fig. 1 with lattice constants of a = 4.32 Å and b = 5.81 Å, which is in accordance with the calculation results reported before[
Figure 1.(Color online) (a) Top-view and (b) side-view of bilayer (BL) tellurene structure. Brown balls represent the contact layer while the orange ones represent the noncontact layer. (c) Schematic diagram of the interface when the BL tellurene atoms contact with metal surface. Green balls stand for the contacting metal atoms.
Table Infomation Is Not EnableWe carry out density functional theory (DFT) calculations using Vienna ab initio simulation package (VASP) to complete geometric optimizations and electronic calculations[
A two-probe model is presented to simulate BL tellurene based transistor, as shown in Fig. 2. We adopt the optimized composite BL tellurene-metal systems for the source and drain regions and BL tellurene for the channel with length of 5 nm. Both electrodes are considered semi-infinite along the transport direction. Gate voltage is set to zero in our calculation. Transport simulations are carried out using DFT combining with non-equilibrium Green’s function (NEGF) method implemented in the Atomistix ToolKit (ATK) 2017 package[
Figure 2.(Color online) Schematic diagram of the BL tellurene FET. Schottky barriers may arise at the interfaces represented by dashed lines in two directions.
therein,
Generalized gradient approximation (GGA) of Perdrew-Burke-Ernzerhof (PBE) parameterization form is employed throughout the paper[
3. Results and discussions
3.1. BL tellurene–metal interface
Eight composite tellurene–metal systems have been brought up, and after structural optimization, the Al, Ag, Au, Cu and graphene interfaces are slightly distorted, while the Ni, Pd and Pt interfaces are strongly distorted, as shown in Fig. 3. The distortions are induced by the interactions between BL tellurene and metals. For the optimized system, dy is the minimal distance between the contact tellurene layer and the nearest metal layer along y direction according to Fig. 1(c), while dTe–M represents the minimal atom-to-atom distance between the Te atom and metal atom. The binding energy Eb of the composite system is estimated as
Figure 3.(Color online) Side-views of the calculated stable BL tellurene–Ag, Al, Ni, Au, Pd, Pt, Cu and graphene contacts. Brown balls are tellurene atoms, while other colored balls are metal and graphene atoms. The diagram of average potential distribution is inset in the black box, where the Fermi level is set to zero with the red dash lines and the tunneling barrier Δ
where
The distinction of the last two groups could be attributed to the different configurations of the valence electron of the metal atoms. Ag (4d105s1), Al (3s23p1), Au (5d106s1), and Cu (3d104s1) atoms possess one unpaired electron. It forms no more than one covalent bond with BL tellurene, and the remnant would form the metallic bond for the metal surface. It brings about a relatively small binding energy. On the other hand, Ni (3d84s2) and Pt (5d96s1) atoms possess two unpaired electrons, and at most two covalent bonds are formed with BL tellurene correspondingly. Despite of the 4d10 valence electron configuration of free-standing Pd atom, Mulliken population analysis indicates that the Pd atom approximately owns two unpaired electrons (4d95s1) when it interacts with tellurene. The reason lies in that the s–d orbit hybridization of Pd atom gives partially unoccupied d states that could strongly interact with p states of Te. Therefore, the Pd, Pt and Ni electrodes possess large binding energies.
We provide the energy band structures of free-standing BL tellurene and the eight interfacial systems in Fig. 4. Free-standing BL tellurene owns an indirect band gap of 0.96 eV without considering spin-orbit coupling, which keeps pace with the previous experiment result of 0.85 eV[
Figure 4.(Color online) (a) Band structure of the BL tellurene. (b)–(i) Band structure of the BL tellurene-metal systems (projected to the bilayer tellurene). The Fermi level is set at zero and represented by the dashed lines. Gray lines: the band structure of the composite system. The red lines reflect the band structure of the tellurene layer away from the metal surface (the noncontact tellurene layer), the blue ones reflect the band structure of the tellurene layer near the metal surface (the contact tellurene layer). The line width is proportional to its weight.
The distributions of the total potential of the interfacial systems, which contains Hartree potential with exchange potential and correlation potential, are presented in Fig. 3. The red dash line represents the Fermi level and the difference between the Fermi level and the vacuum level is the work function (
Partial density of states (PDOS) is also plotted to further expound the interactions between BL tellurene and the electrodes. The PDOS of free-standing BL tellurene is shown in Fig. 5(a), while those of the composite systems are shown in Figs. 5(b)–5(i) with the solid lines representing the contact tellurene layer ingredients and the dash lines representing the noncontact tellurene layer ingredients. For the bulk metallic electrodes, a large number of the states appear around the Fermi level of the contact layer, whereas a relatively small number of the states around the Fermi level of the noncontact layer. It further confirms a much stronger hybridization between the bulk metal electrodes with the contact tellurene layer compared with the noncontact tellurene layer. By contrast, there are no states at the Fermi level of tellurene for graphene electrode, indicating a weak vdW interaction between tellurene and graphene.
Figure 5.(Color online) (a) Part density of states (PDOS) of BL tellurene. (b)–(i) PDOS of each orbital for BL tellurene on the metal surface by the band calculations. Solid lines represent for the PDOS of the contact tellurene layer, while dash lines represent for the PDOS of the noncontact tellurene layer.
3.2. SBH of the BL tellurene transistors
Here a two-probe model with BL tellurene as the channel material is set up to examine the Schottky barriers in a transistor configuration, which might be formed at three interfaces as shown in Fig. 2. A vertical Schottky barrier (
The vertical Schottky barrier
As to the lateral Schottky barrier (
The QTS method is based on a two-probe model, where both the electrode and the channel parts are calculated as a whole. The method is confirmed to offer SBHs consistent with the experimental results[
Figure 6.(Color online) Localized density of states (LDDOS) of the BL tellurene FET devices with metals Al, Ag, Ni, Au, Pd, Pt, Cu and graphene as electrodes (left panel) with a 5-nm channel length as well as the zero-bias transmission spectrum of the FET devices (right panel). Metal-induced gap states at the interfaces are indicated by the black dashed lines, and the Fermi level is represented by white and red dashed lines.
The lateral SBHs obtained by the WFA and the QTS methods are compared in Fig. 7(a). Even though the QTS and WFA method provides the same contact polarity for Pt, Pd, Cu and Ni electrodes, the hole SBH differs (0.01, 0.08, 0.12 and 0.15 eV for Pt, Pd, Cu and Ni electrodes, respectively). Remarkably, the QTS and WFA methods provide opposite contact polarity for Ag, Al and Au electrodes. Opposite to the QTS method, the WFA method does not consider the interaction between the electrode and the channel. Therefore, the difference of the SBHs revealed by those two methods lies on the interaction between the electrode and channel parts. Here we state the interaction to two aspects. First, the contact between the channel and electrode gives rise to abundant interfacial states, which are indicated by the black dashed lines in the LDDOS diagram of Fig. 6. Considering that there is no termination of BL tellurene crystal structure at the interface and the flat surface of 2D semiconductor, those interfacial states are not induced by defects, dangling bonds or the termination of tellurene structure. Therefore, they are mainly induced by metal-induced interfacial states (MIGS) that exponentially damp when penetrating into BL tellurene from metals. The MIGS would bring about intense Fermi pinning effect, thus modulate the Fermi level of the system and the SBHs. Second, the contact between the drain/source and channel regions also gives rise to a charge transfer or a charge redistribution, which induces a dipole field. The built-in field makes a relative movement between the Fermi level of the electrode and the band structure of the BL tellurene and changes the SBH. Therefore, SBHs obtained by quantum transport simulation differ from the ones obtained by work function approximation due to the coupling between the channel and electrode.
Figure 7.(Color online) (a) Comparison of the electron and hole SBHs of the BL tellurene FETs obtained by work function approximation (
The transport energy gap Eg is defined as
The FLP effect is measured by the pinning factor S, which is the slope of the relationship between the lateral electron SBH and the work function of the bulk metal electrodes. S = 1 denotes a no FLP case while S = 0 denotes a full FLP case. Here we plot the lateral electron SBHs as a function of the metal work function, as shown in Fig. 7(b). The fitting lines are shown of the two methods leaving out the graphene cases. An extremely low pinning factor of Sa = 0.02 is obtained by the QTS method, that is much smaller that of the WFA method (Sb = 0.29). It indicates that the consideration of the interaction between the BL tellurene channel and the electrode will induce further FLP effect. What’s more, the pinning factor of BL tellurene is smaller than that of ML tellurene (S = 0.09), ML black phosphorene (S = 0.28) and ML MoS2 (S = 0.27) as well[
The ultralow S (0.02) could be inferred by the deep-into-channel MIGS in the narrow band gap. Here we plot the fitting line of the S and the band gap of the 2D channel material, as shown in Fig. 8. The calculated pinning factors of various 2D material containing blue phosphorene (0.42), arsenene (0.33), InSe (0.32), black phosphorene (0.28), MoS2 (0.1), Bi2O2Se (0.12), ML tellurene (0.09) and BL tellurene (0.02) are presented here[
Figure 8.(Color online) FLP factor (
Our study indicates that the BL tellurene based transistors favor p-type Schottky contacts for the lateral direction, and this is owing to the small work function (4.51 eV) of BL tellurene. Experimentally, a lateral p-type Schottky contact is generated for the 7.5 nm-thick tellurene based FET with Pd electrode, which is in line with our study[
4. Conclusion
To sum up, we explore the interfacial properties of the BL tellurene based transistors with eight common electrodes including 2D graphene by using ab initio electronic structure calculations and quantum transport simulations. Covalent interactions take place between BL tellurene and bulk metal electrodes. We find that both tellurene layers for Ni, Pt and Pd electrodes undergo metallization, while only the contact tellurene layer for Ag, Al, Au and Cu electrodes undergoes metallization, leaving the uncontact tellurene layer semiconducting. Therefore, no vertical Schottky barriers are formed for Ni and Pt and Pd electrodes but Schottky barriers are formed between the two tellurene layers for Ag, Al, Au and Cu electrodes. VdW interaction between the BL tellurene and graphene takes place and a vertical p-type Schottky contact for graphene electrode is formed. The Fermi level is tightly pinned in the band gap of BL tellurene with a pinning factor S = 0.02 owing to the deep-into-channel MIGS and work function modulation at the lateral interfaces for the bulk metal electrodes. As a result, lateral robust Schottky barriers are developed for the bulk metal electrodes. Besides, a lateral quasi-Ohmic contact is developed for graphene electrode. Our work offers a systematic investigation on the interfaces of the BL tellurene based transistors and also will guide electrode selections of few-layer tellurene based transistors.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 11674005, 11664026,11704406), the National Materials Genome Project of China (No. 2016YFB0700600), the Key Research and Development Program of Ningxia (No. 2018BEE03023), the Natural Science Foundation of Ningxia (No. 2018AAC03236), the Higher School Scientific Research Project of Ningxia Department of Education (No. NGY2018-130), the Key Scientific Research Project of Ningxia Normal University (No. NXSFZDA1807) and the Youth Talent Support Program of Ningxia, China (2016).
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