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rasmita sahoo

Why resistance of a metallic CNT is decreasing with increase of temperature?

I was trying to find out the resistance of an (10,10) armchair CNT which is metallic in nature using length sweep mode. The expected result is that the resistance should increase with increase in temperature but I am getting just the reverse result. Can you please clarify why this is happening?

Results detail: Length of the CNT = 100nm Resistances are 20.036KOhm and 12.2KOhm for temperatures 300K and 500K respectively.

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    Zlatan Aksamija

    It is indeed true that we expect the resistance to increase with increasing temperature. It is important to understand what is the physical process causing this behavior. Resistance arises due to the interaction between the electrons whos motion through the tube makes up the current with the phonons, or quantized lattice vibrations. Electrons scatter with phonons causing them to lose energy, thereby producing resistance. Phonons are heat, so higher temperature means there will be more phonons to scatter with, and consequently more resistance.

    In order to simulate this expected behavior in the CNT-BTE tool, we have to look at the simulator parameter list. There we will find the “relaxation time” which represents the average time it takes the electron distribution to “relax” or return to equilibrium. We can think of this parameter tau as the average lifetime of the electron, or the average time it can move freely without scattering with another phonon. As mentioned earlier, increasing temperature has the effect of increasing the number of phonons present in the tube, which leads to more scattering of electrons with phonons, or thermal lattice vibrations. Therefore, the electron relaxation time parameter also needs to be adjusted to reflect the temperature of the system. This was left as a user parameter on purpose so that the user can change this parameter and explore what the consequences of different choices for tau may be. In particular, the relaxation time will decrease with increasing temperature to reflect the increased scattering between electrons and phonons. It is up to the user to select an appropriate value of this parameter to reflect the desired simulation temperature. A good starting point is the default value at 300K. We expect the scattering rate to be proportional to temperature, the relaxation time, being the roughly inverse of the scattering rate, should be inversely proportional to temperature. For example, if a simulation at 500K is needed, one can choose the relaxation time to be 46fs(default)*300/500=27.6fs.

    A future version is planned which will compute the scattering rate and relaxation time automatically instead of allowing the user to choose this parameter.

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