# Modeling of NEMS Based on Carbon Nanotubes

##### Goals and Requirements

A variety of nanoelectromechanical systems (NEMS) employing carbon nanotube walls as movable elements are being developed. These devices include rotational and plain nanobearings, a nanogear, an electromechanical nanoswitch, a nanoactuator, a Brownian motor, a memory cell, a nanobolt–nanonut pair, and a gigahertz oscillator. It is important to realize that the design of such systems is associated with the development of non-contact methods for controlling the motion of nanotube walls. The crucial issue for the NEMS design is the possibility of predicting system behavior at macroscopic operation times (more than 1 s) depending on the microscopic structure of the whole device and its components. Thus, to study such systems, one should apply the multilevel approach in which system parameters determining its behavior at long operation times are found from detailed atomistic calculations.

##### Solution

Kintech Lab in cooperation with Moscow Institute of Physics and Technology, Institute of Spectroscopy, and RCC “Kurchatov Institute” have developed a multilevel approach for studying operation characteristics of nanotube-based NEMS. In this approach, the tribological properties of NEMS are investigated by molecular dynamics simulation. The results of this study are then used to describe the dynamic behavior of NEMS at long simulation times.

As a model system, we considered a gigahertz oscillator based on a double-walled nanotube (DWNT). The operation characteristics of the device were calculated using the macroscopic model of the oscillator depending on the Q-factor and the level of thermal noise. The Q-factor and the noise in the system are determined by the microscopic structure of the oscillator. These parameters were found on the basis of molecular dynamics simulations with the MD-kMC code developed in Kintech Lab.

##### Multilevel approach for studying NEMS characteristics

The nanooscillator Q-factor was found by molecular dynamics simulations of free oscillations. It was shown that the nanooscillator Q-factor is

- inversely proportional to temperature
- higher for incommensurate than for commensurate nanotubes
- strongly decreases if defects are incorporated into the nanotube

Moreover, significant thermodynamic fluctuations were revealed in the nanooscillator.

The possibility to control the motion of the NEMS components with an electric dipole moment by a non-uniform electric field was demonstrated at times up to few nanoseconds using molecular dynamics simulations. It was also found that thermodynamic fluctuations result in the instability (breakdown) of the stationary operation mode in the NEMS.

Based on the results obtained by molecular dynamics simulations, a macroscopic model of a non-linear oscillator was developed. This model was applied to the study of NEMS operation at simulation times up to 1 s. It should be mentioned that the results obtained with the macroscopic model at times of few nanoseconds agree with the results of molecular dynamics simulation. In particular, the macroscopic model was used to calculate the parameters of the control force *F**ex**(t)=F**0**cos(ωt+φ)* for which the stationary operation mode of the nanooscillator is possible.

Using the macroscopic model, it was also demonstrated that the stability of NEMS operation subjected to thermodynamic fluctuations can be achieved by increasing the amplitude of the control force *F**0* and the NEMS size.

Thus, on the basis of the multilevel approach we could calculate the operation characteristics of the NEMS and specify the restrictions imposed on the system size depending on its microscopic structure and temperature.

Details see in O.V. Ershova, Yu. E. Lozovik, A.M. Popov, O.N. Bubel’, E.F. Kislyakov, N.A. Poklonskii, A.A. Knizhnik, I.V. Lebedeva, “Control of motion of NEMS based on carbon nanotubes with electric field”, JETP, 134 (2008) 762.