  Hot electrons injection in carbon nanotubes (CNTs ) where in addition to
applied dc field ($\mathbf{E}$), there exist simultaneously a quasi-static ac
electric field (i.e. when the frequency $\omega$ of ac field is much less than
the scattering frequency $v$ ($\omega\ll v$ or $\omega\tau\ll 1$, $v
=\tau^{-1}$, where $\tau$ is relaxation time) is considered. The investigation
is done theoritically by solving semiclassical Boltzmann transport equation
with and without the presence of the hot electrons source to derive the current
densities. Plots of the normalized current density versus dc field
($\mathbf{E}$) applied along the axis of the CNTs in the presence and absence
of hot electrons reveal ohmic conductivity initially and finally negative
differential conductivity (NDC) provided $\omega\tau\ll 1$ (i.e. quasi- static
case). With strong enough axial injection of the hot electrons , there is a
switch from NDC to positive differential conductivity (PDC) about $\mathbf{E}
\geq 75 kV/cm$ and $\mathbf{E} \geq 140 kV/cm$ for a zigzag CNT and an armchair
CNT respectively. Thus, the most important tough problem for NDC region which
is the space charge instabilities can be suppressed due to the switch from the
NDC behaviour to the PDC behaviour predicting a potential generation of
terahertz radiations whose applications are relevance in current-day
technology, industry, and research.
