Acoustoelectric direct current density in fluorine doped single-walled carbon nanotubes due to harmonic mixing of bichromatic fields with commensurate frequencies

Abstract

Herein, we theoretically report on the acoustoelectric direct current (ADC) generation in a non-degenerate fluorine doped single-walled carbon nanotubes (FSWCNTs), due to mixing of waves with commensurate harmonics in the hypersound regime, qℓ≫1 (where q is the acoustic wavenumber and ℓ is the carrier mean free path). The only restriction of the theory on the sound intensity was that, the interaction energy between the carrier and the acoustic phonons must be small in comparison with the characteristic carrier energy. It was observed that in this situation, the higher harmonics of the effective field of the acoustic wave can be neglected; the origin of the nonlinearity was due to the distortion of the distribution function for carriers moving in phase with the phonons, as a result of interaction with the acoustic wave; the nonlinear effects can then be very important. The ADC generated was highly nonlinear and non-ohmic and depended on the amplitude of the bichromatic fields (i.e., pump and probe field), overlapping integral for jumps (Δs and Δz), carrier concentration (no), Bloch frequency (Ω), photon frequency (ω) and acoustic phonon frequency (ωq). The strong nonlinearity and non-ohmicity of the I-V characteristic of the FSWCNTs may be associated with a number of nonlinear phenomena including the non-parabolic band relation, carrier heating due to distortion in carrier distribution function, Stark component, and Bloch oscillations of intraminiband carriers. It was possible to alter the magnitude and direction of the rectified ADC by adjusting the phase of the fields, and the generation of ADC corresponded to even instability zones in the FSWCNTs. Thus, based on the high ADC obtained, we propose FSWCNTs for ADC generation under bichromatic fields with commensurate harmonics.