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## Boltzmann Transport Simulator for CNTs

Simulate Electron transport in Single-walled carbon nanotubes using an upwinding discretization of the Boltzmann transport equation in the relaxation time approximation.

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#### Abstract

This tool simulates electron transport in single-walled carbon nanotubes using an upwinding discretization of the Boltzmann transport equation in the relaxation time approximation. Users can select chirality and length of the nanotube, as well as the applied voltage across the tube and the temperature of the environment. The simulator can also be adjusted by setting the number of points in the discretization. Simulation is performed in both space and momentum, represented by the number of points Nx and Nk in the x-direction (space) and k-direction (momentum). The length of the simulation depends on the size of the time step, and the number of steps taken in the simulation. The maximum size of the time step is limited by stability criteria, and the tool will warn the user and adjust the step to achieve stability if it is set too large.

The simulator can be run in three distinct modes: single voltage, voltage sweep, and length sweep. The first mode produces the transient current, as well as the final steady-state potential, field, and charge density profiles after a single run at a user-specified value of applied voltage at the endpoint of the tube. The tube should stay charge-neutral (zero charge throughout), so the charge density can serve as a check on the stability of the simulation. If non-zero or oscillating charge appears, the time step should be decreased.

In voltage sweep mode, the simulation is repeated over a range of points for the applied voltage up to the value specified by the user. This produces a typical I-V curve (current-voltage relationship) for the given nanotube. This simulation can then be repeated for various lengths of tube to obtain a set of IV curves for a given chirality.

The last mode is a length sweep, which runs the simulation repeatedly with a fixed applied voltage, but ranging over a number of different tube lengths up the the value specified by the user. This simulation produces a resistance vs. length plot at a given voltage, from which the tube's resistivity can be extracted. The simulation can be repeated at high and low values of applied voltage in order to compare high-field and low-field resistivity of a particular tube.

This tool will work for semi-conducting tubes, but it is really intended for metallic tubes only. The user can select the value of relaxation time, as well as the details of the discretization grid to learn about the stability of the explicit upwind discretization scheme. Relaxation time can be varied to learn about the effect of scattering on the IV curves and high- and low-field resistivity of single-walled carbon nanotubes.

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