Temperature dependence of the electrical transport properties in few-layer graphene interconnects
© Liu et al.; licensee Springer. 2013
Received: 29 May 2013
Accepted: 11 July 2013
Published: 25 July 2013
We report a systematic investigation of the temperature dependence of electrical resistance behaviours in tri- and four-layer graphene interconnects. Nonlinear current–voltage characteristics were observed at different temperatures, which are attributed to the heating effect. With the resistance curve derivative analysis method, our experimental results suggest that Coulomb interactions play an essential role in our devices. The room temperature measurements further indicate that the graphene layers exhibit the characteristics of semiconductors mainly due to the Coulomb scattering effects. By combining the Coulomb and short-range scattering theory, we derive an analytical model to explain the temperature dependence of the resistance, which agrees well with the experimental results.
KeywordsGraphene Graphene multilayer Short-range scattering theory Coulomb scattering effect
Graphene has been a subject of intense research since it was discovered in 2004 because of its intriguing band Structure [1, 2]. The energy-momentum relationship of graphene is found to be linear for low energies near the six corners of the two-dimensional (2D) hexagonal Brillouin zone [1–4], leading to a zero effective mass for electrons and holes [2–5]. Such behaviour can be described by the Dirac equation for spin 1/2 particles [1–6]. Furthermore, graphene is also an excellent electronic material as it can be either a metal or semiconductor depending on the edge states, zigzag or armchair . It exhibits superior mobility, with reported values in excess of 15,000 cm2 V−1 s−1, which is superior to that of III-V semiconductors for high-speed device applications. As such, graphene has been widely predicted to be a potential material for post-complimentary metal-oxide semiconductor technology, particularly for use as ballistic transistors or interconnects [8–12]. Most graphene studies have focused on monolayer structures . Recently, few-layer graphene (FLG) have received much attention because of its promising bandgap tunability. For instance, bilayer graphene is reported to have a tunable bandgap [13, 14] and trilayer graphene is a semimetal in the ideal case with a gate-tunable overlapped bandgap . As more graphene layers are added, the electrical properties of FLG also change, which can be further explored for the design of various devices . However, theoretical understanding and experimental investigations of FLG are still lacking for applications such as interconnect.
In this letter, we report a systematic investigation of the temperature dependence behaviour of the four-terminal electrical resistance in FLG interconnects. The resistance of tri- and four-layer graphene, under direct current (DC) electric fields and in a temperature range from 5 to 340 K was measured. The T-1/2 dependence shows the evidence of the electron–electron Coulomb interaction in FLG. Our temperature-dependent resistance results reveal that the FLG interconnects display semiconductor properties and further confirm that Coulomb interaction can play a dominant role.
Results and discussion
where E k is the wave vector energy and τ(E k ) is the transport scattering rate. For the low temperature limit, the scattering time averaged over energy can be written as 〈τ〉 ≈ τ(E F ) . The density of states D(E F ) in tri- and four-layer graphene is assumed to be a constant . Here, the Fermi energy is , and based on the Boltzmann equation of mobility as function of the scattering time: , we can obtain the mobility of graphene as . As such, at low temperatures, the Coulomb scattering is proportional to the carrier density in the tri- and four-layer graphene structures [21–23].
These considerations explain qualitatively why the resistance of tri- and four-layer graphene decreases with the increasing temperature. We note that due to the complexity of the FLG band structure, these anomalous electrical properties are believed to originate in the unusual band structures near the Fermi level of graphene [26–29]. More rigorous theoretical explanation of FLG intrinsic semiconductor behaviours would be interesting and requires further experimental investigations.
In conclusion, FLG interconnects were fabricated via a combination of mechanical exfoliation and photo lithography techniques. The temperature dependence of the electrical resistance of tri- and four-layer graphene was investigated. The observed I-V curve shows unique combination of the low threshold of linearity and manifestation of the second ohmic region for the strong DC electric field in the FLG interconnects. With the RCDA method, our experimental results suggest that Coulomb interaction plays an essential role. The non-metallic temperature-dependent resistance is observed in the temperature range of 5 to 340 K. In this case, even though the FLG band structure as semimetal with zero-band gap, tri- and four-layer graphene resistors behave more like semiconductors. By combining the Coulomb and short-range scattering theories, an analytical model was developed, which well explains the experimental results.
We would like to acknowledge support from Nanyang Technological University (NTU) (M58040017) and Ministry of Education, Singapore (MOE2011-T2-2-147 and MOE2011-T3-1-005). Y. P. Liu acknowledges Dr Cheong Siew Ann (NTU) for useful discussions. The authors also thank Sun Li and Li Yuanqing for their assistance in experimental measurements.
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