DFT investigations of the piezoresistive effect of carbon nanotubes for sensor application

Abstract

We investigate the piezoresistive effect of carbon nanotubes (CNTs) within density functional theory (DFT) aiming at application-relevant CNTs. CNTs are excellent candidates for the usage in nano-electromechanical sensors (NEMS) due to their small band gap at zero strain leading to a finite resistivity at room temperature. The application of strain induces a band gap-opening leading to a tremendous change in the resistivity. DFT with the LDA approximation yields reasonable results for pure carbon systems like CNTs and is applied to calculate the electronic structure of experimentally relevant CNTs. For the transport part, a simple ballistic transport model based on the band gap is used. We compare our DFT results for the band gaps of strained CNTs to results of tight binding (TB) models. By introducing a scaling factor of √ 2, an excellent agreement of the the DFT data with TB model published in [1] is obtained.Copyright line will be provided by the publisher 1 Introduction Carbon Nanotubes (CNTs) are very interesting systems from both, the physical and the technological, point of view. In addition to their outstanding mechanical properties like high stiffness and an enormous Young's modulus of about 1 TPa [2], their electronic structures show a rich variety of interesting effects.One of them is the huge piezoresistive effect (up to one order of magnitude per percent strain), which is the change of the resistivity due to a deformation, relying on the change of the band gap. This behavior is highly desirable for NEMS sensor applications. The effect is strongly dependent on the chiral angle -in the same way the electronic structure depends on the chirality. Therefore, atmoistic models are needed to build up device simulations.The modeling of the piezoresistive effect of CNTs using TB models is pioneered by Yang and Han [1] as well as Kleiner and Eggert [3]. The latter one tries to include curvature effects of CNTs by introducing another TB constant. Because its corrections are made using curvature effects, this model is most likely applied for semimetallic CNTs,

Empirical transport model of strained CNT transistors used for sensor applications

“…6) and thus, the analytical model fails. The inset shows the bandgap with respect to strain (already published in [4]), which agrees satisfyingly over the whole strain range. Above, a strain dependence has to be taken into account.…”

“…t 0 is the TB-hoppingparameter (≈ 2.66 eV), ν declares the Poisson's ratio, ε denotes the strain, and θ represents the chiral angle. This is exemplarily shown in figure 7 (inset) for the (8,4)-CNT in comparison to DFT data. Further theory and results concerning bandgaps are published in [4].…”

“…The basic sensor mechanism is the change of the bandgap of CNTs under strain, but also the strain dependence of the effective mass and the Fermi velocity play a role. The effect of strain on the bandgap can be described either analytically [1,2,4] or by electronic structure calculations [4,31,32]. The analytical expression for the bandgap change ∆E G /ε is the following:…”

“…Conventional silicon-based sensors suffer from a low signal-to-noise-ratio for mechanical high-frequency applications in the MHz regime -due to their stiff design in combination with a capacitive readout. CNTs have the abilitiy to change their bandgap upon strain [1,2,3,4]. This opens the possibility of strain-engineering in CNTs.…”

Electronic and optical properties of deformed graphitic and helical nanobutes

“…Medu njima, posebnu pažnju su privukle grafitne nanotube i mogućnost da nova generacija piezootpornih (nano)senzora bude bazirana na kompozitnim filmovima od grafitnih nanotuba [76,77,78]. Naime, zahvaljujući izuzetnim elektronskim osobinama (zavisnostširine energetskog procepa od kiralnih indeksa i tipa deformacije, balistička provodnost) i velikom Jangovom modulu, koji kod jednoslojnih nanotuba iznosi oko 1 TPa [79], moguće je dobiti nanosenzore sa dinamičkim opsegom znatno preko 60 dB i veličinom ispod 1 µm 2 [7].…”