  The definition of the intrinsic cut-off frequency ($f_T$) based on the
current gain equals to one (0 dB) is critically analyzed. A condition for the
validity of the quasi-static estimation of $f_T$ is established in terms of the
temporal variations of the electric charge and electric flux on the drain,
source and gate terminals. Due to the displacement current, an electron
traversing the channel length generates a current pulse of finite temporal
width. For electron devices where the intrinsic delay time of the current after
a transient perturbation is comparable to such width, the displacement currents
cannot be neglected and the quasi-static approximation becomes inaccurate. We
provide numerical results for some ballistic transistors where the estimation
of $f_T$ under the quasi-static approximation can be one order of magnitude
larger than predictions obtained from a time-dependent numerical simulations of
the intrinsic delay time (including particle and displacement currents). In
other ballistic transistors, we show that the gate current phasor can be
smaller than the drain one at all frequencies, giving no finite value for
$f_T$.
