Faisal
Ahmed
ab,
Min Sup
Choi
ac,
Xiaochi
Liu
ac and
Won Jong
Yoo
*abc
aSamsung-SKKU Graphene Center (SSGC), SKKU Advanced Institute of Nano-Technology (SAINT), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea
bSchool of Mechanical Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea
cDepartment of Nano Science and Technology, SKKU Advanced Institute of Nano-Technology (SAINT), Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea. E-mail: yoowj@skku.edu
First published on 14th April 2015
This study illustrates the nature of electronic transport and its transition from one mechanism to another between a metal electrode and MoS2 channel interface in a field effect transistor (FET) device. Interestingly, measurements of the contact resistance (Rc) as a function of temperature indicate a transition in the carrier transport across the energy barrier from thermionic emission at a high temperature to tunneling at a low temperature. Furthermore, at a low temperature, the nature of the tunneling behavior is ascertained by the current–voltage dependency that helps us feature direct tunneling at a low bias and Fowler–Nordheim tunneling at a high bias for a Pd–MoS2 contact due to the effective barrier shape modulation by biasing. In contrast, only direct tunneling is observed for a Cr–MoS2 contact over the entire applied bias range. In addition, simple analytical calculations were carried out to extract Rc at the gating range, and the results are consistent with the experimental data. Our results describe the transition in carrier transport mechanisms across a metal–MoS2 interface, and this information provides guidance for the design of future flexible, transparent electronic devices based on 2-dimensional materials.
In this study, we have tried to bridge the gap by systematically elaborating the different carrier transport mechanisms that are involved along the interface. We carried out low temperature measurements on the contact properties of the MoS2 devices. As a result, different behaviors of charge injection across the interfacial barrier and their crossover were clearly visualized. In order to further elaborate the analysis, we measured the Rc of the metal–MoS2 junction as a function of the temperature to examine the competition between thermionic emission and tunneling transport at the interface. In addition, we also investigated the nature of the tunneling behavior by using the simplified mathematical models for Fowler–Nordheim (F–N) tunneling and direct tunneling. We found that for Pd–MoS2, an obvious transition is observed from direct to F–N tunneling. In contrast, only direct tunneling occurs for Cr–MoS2. Finally, we used the Landauer theory22,23 to analytically calculate Rc contributed by the current components and combined them to obtain the net Rc value, which we found to be consistent with the experimental results.
A semiconductor parameter analyzer was used to carry out the electrical measurements, and the low-temperature measurements were performed from room temperature down to 120 K by using liquid nitrogen. Rc was extracted at a given number of temperature points and the range of the gating to further detail its behavior as shown in Fig. 1(c). Further details about the calculation of Rc can be found in our previous study.24
Unlike metal–MoS2, the Rc at the metal (Pd)–graphene interface declines as the device cools.27 This contradictory temperature dependency is mainly a result of a difference in the origin of Rc along these two junctions. Graphene under a metal electrode is more responsible for Rc in the metal–graphene interface. When the temperature decreases, the carrier transport across the interface changes from diffusive to ballistic, mainly due to the coupling length and carrier mean free path that eventually suppress Rc. This explains why the Rc of pure edge-contacted graphene shows no variation with temperature.28 However, a metal–MoS2 contact, as explained in the previous paragraph, has an Rc that originates from the formation of the barrier, and its temperature sensitivity depends on the carrier transport across it.
Direct tunneling
(1a) |
(1b) |
Fowler–Nordheim tunneling
(2a) |
(2b) |
Here ϕB is the barrier height, m is the free electron mass, m* (0.46 m)31 is the effective mass of electrons in the MoS2 channel, q is the electron charge, h is Planck's constant and d is the width of the barrier.
Eqn (1b) and (2b) imply that direct and F–N tunneling differ in terms of I–V dependency. Therefore if the plot for ln(1/V2) vs. 1/V shows linearity, then F–N tunneling is expected to occur, whereas when the slope rises exponentially, direct tunneling is thought to occur. The main graph in Fig. 2(a) displays an almost exponential plot throughout the applied bias range, which indicates that direct tunneling is the dominant mechanism for the Cr–MoS2 contact. The inset in the same graph, which is plotted according to eqn (1b), shows a linear trend that further confirms the direct tunneling. In contrast, Fig. 2(b) shows that, for the Pd–MoS2 contact in the high bias region (left side of the graph), a linear decrease first reaches a specific point and then rises exponentially in the low bias region, which reveals a transition from F–N (colored area) to direct tunneling. In order to explain this anomaly, we investigate the band diagram along the interface of both contacts. The direct tunneling and the F–N tunneling are determined by the nature of the interfacial barrier, that is, the former occurs when the barrier is trapezoidal (wide) and the latter occurs when the barrier is triangular (thin).29,30 Generally, a MoS2 device has two contacts that induce their respective SBs: the source SB and the drain SB. The shape, width and height of these barriers are mainly modulated by the applied bias,10,20 affecting the carrier injection behavior. First, consider the Pd–MoS2 contact [Fig. 2b]. When a high drain bias is applied, the drain barrier reduces and eventually vanishes but the source barrier becomes thin. Therefore, at a low drain bias the carriers have to overcome two wide barriers so the direct tunneling is realized, whereas at a high drain bias they only experience a thin and triangular source barrier that favors F–N tunneling. As a result, the change in the transport mechanism from direct tunneling at the low drain bias to F–N tunneling at the high drain bias is realized at the Pd–MoS2 interface [Fig. 2(d)]. This crossover occurs at around 0.22 V (4.5 V−1), and it is worth noting here that as the temperature increases from 123 K to higher temperatures, the amount of F–N tunneling that occurs keeps decreasing and completely vanishes at around room temperature. This observation is consistent with our earlier discussion in that the tunneling current is dominant mainly in the low temperature regime. In addition, we also extracted the width of the Pd–MoS2 interface from the F–N tunneling equation. By substituting the slope of the linear portion of Fig. 2(b), the SB height and effective mass of 0.25 eV and 0.46 m respectively,31 in eqn (2b), the effective barrier width (d) of around 0.3 nm is obtained for the Pd–MoS2 junction.
However for the Cr–MoS2 contact, there is no sign of F–N tunneling throughout the applied bias sweep. One major difference between these two metals can be seen in their work functions. With respect to MoS2 (4.2–4.6 eV), Cr (4.6 eV) has a lower work function, whereas Pd (5.0 eV) has a higher work function, so they form a lower and a higher SB height with MoS2, respectively.6 Besides barrier height, tunneling depends more severely on its width since the charged carriers have to tunnel quantum mechanically throughout the barrier width. Therefore, this anomaly could not be explained simply by considering the differences in the work function and the SB height. As mentioned earlier, MoS2 contains the pristine surface without the dangling bonds. Therefore, when a metal is deposited over the surface of MoS2, a weak van der Waals interaction occurs between them, inducing a physical separation [tunnel barrier (TB)] along with the SB at the contacts. For example, the extent of TB depends partly on the difference of the lattice structures between the deposited metal and MoS2. It is reported that Cr and MoS2 have a large mismatch in their lattice structures, whereas this difference is very small between Pd and MoS2.11 Therefore, when MoS2 comes into contact with Cr, a weak overlapping occurs in their orbitals that induce a wide TB at their interface along with SB as shown in Fig. 2(c). On the other hand, the better orbital overlapping and a narrow TB are observed at the Pd–MoS2 junction [Fig. 2(d)]. Besides physical mismatch, the unique properties of metals with respect to MoS2 may also partly affect the nature of TB. We think that due to high chemical reactivity of Cr, the partial oxidation of Cr might occur due to uninvited surface contaminations introduced during the EBL process that may further induce a wide TB at the Cr–MoS2 interface. Moreover, Pd has better wetting ability towards the MoS2 surface and a uniform growth of Pd is also expected, that may also cause a narrow TB at their junction.32 As explained in the previous paragraph, by applying a high drain bias, the drain SB vanishes and the source SB gets thinned, but the TB may remain intact from these changes due to its physical nature. Therefore, at a high voltage the effective barrier width still remains wide for the Cr contact, but it is thinned for the Pd contact since it is mainly dominated by TB for the former and by SB for the latter contact. As a result, we observe only direct tunneling without realizing F–N tunneling at the Cr–MoS2 contact, but a clear transition is observed from one behavior to another at the Pd–MoS2 interface.
Generally, carriers along the metal–MoS2 interface are divided into three components, i.e. thermionic emission (ITH) over the top of the barrier and tunneling components (ITN-1 and ITN-2) along their respective regions as depicted in the energy band diagram of Fig. 3(a). The numerical equations of all three current components along with their detailed calculation procedures are illustrated in SI S2† and their results are shown in Fig. 3(b) in unit of A m−1. All the current components are gate dependent and can be explained by the barrier modulation theory. The thermionic emission (ITH) current component increases due to the decrease of the effective barrier height, and the tunneling components (ITN-1 and ITN-2) increase because of thinning of the effective barrier width, when higher gate bias is applied. Next, Rc of each current component is extracted by applying the simplified Landauer formula, i.e. Rc = 1/Iq, where I is the current component and q is the electron charge,22,23 to the current components, since the applied drain bias is 1 volt; therefore the chemical potential difference becomes unity. Their result is shown in Fig. 3(c) after normalizing to the standard unit of Rc, i.e. ohm mm. As expected, the current component with a smaller magnitude across the barrier contributes significantly to the Rc under the same bias conditions. As mentioned earlier the carriers across the interface split into three parallel paths (see band diagram) so we replace Fig. 3(a) with a parallel electrical resistor network shown in Fig. 3(d) to combine all Rc values. Finally, their net result is shown in Fig. 3(e) and compared with experimentally calculated results of Rc. Note that the ITN-2 current level is very low i.e. around 10−32 A m−1 at a gate bias of 70 V and its corresponding Rc is extremely large i.e. around 1031 ohm m (not shown in Fig. 3(c)) that is much higher than the acceptable range of Rc. Interestingly, after applying the proposed model the extracted total Rc value is within the acceptable range and agrees well with our experimental results. However at low gate bias where the device is near off-state, the difference between theoretical and experimental data is a little bit large and the gap is reduced as the device enters into the strong accumulation region.
However, the difference between the two results could be attributed to the assumption made during analytical calculations. Interestingly, despite this, the analytically calculated Rc values in our scheme sweep to several ohm mm depending on the gate bias which are close to the experimentally measured Rc for the metal–MoS2 interface by other groups.14,17–19 Conclusively, using the proposed model above one can easily calculate Rc across the range of gate bias for metal–MoS2 interfaces.
Currently, the lowest reported value for Rc in a metal–MoS2 contact is still several orders of magnitude higher than the acceptable levels for miniaturized electronics.34 However, by adopting the carrier transport techniques illustrated in this report, one can effectively reduce the Rc values to appreciable limits, such as by (i) selecting an appropriate metal, which will preferably have a lower work function and an effective orbital overlapping with MoS2, since this will reduce SB and TB and will enhance thermionic emission and tunneling across the barrier; (ii) doping the contact region since a degenerate and stable doping technique can induce a much thinner barrier that will facilitate carriers to tunnel through it; and (iii) using an edge contact since it has been theoretically proposed that an edge contact more efficiently injects the carriers than a surface contact for TMDCs due to their layered body.11 Carefully controlling the edge etching and the defects can produce a one-dimensional contact for MoS2. All the above techniques solely depend on carrier injection, thus fundamental knowledge on carrier injection will be helpful to achieve optimum contacts.
In summary, the temperature-dependent carrier transport in a metal–MoS2 interface was systematically investigated according to several charge injection mechanisms and their transitions. The transition from thermionic emission to tunneling was observed at around 248 K. In addition, an anomaly in terms of differences in the tunneling behavior was spotted for Cr–MoS2 and Pd–MoS2 contacts, which suggests a difference in the nature of their interfacial barrier. This work is a promising approach towards realizing optimized metal–MoS2 contacts for future devices using 2-dimensional materials.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr01044f |
This journal is © The Royal Society of Chemistry 2015 |