Resonant-tunnelling diodes (RTDs) are used for studies of fundamental aspects of tunnelling and also for realization
of oscillators at high frequencies, particularly in THz frequency range. Also, the RTDs can be considered
as the building blocks of different electronic structures, including optical, e.g., quantum-cascade lasers. It is generally
accepted that the inherent limitation of the operating frequency and the charge relaxation (response) time
of RTD is determined by the quasi-bound-state lifetime. The simple picture is not generally correct. Here we
show, first, that the Coulomb interaction between electrons can lead to large reduction/increase of the relaxation
time. Second, we demonstrate that the operating frequencies of RTDs are limited neither by quasi-bound-state
lifetime, nor by relaxation-time constants; particularly the differential conductance of RTDs can stay negative at
the frequencies far beyond the limits imposed by the time constants. Here we provide the experimental evidences
for both effects. We demonstrate negative differential conductance up to the frequency of 12 GHz in our RTDs
with the inverse quasi-bound-state lifetime of around 1 GHz. Also the relaxation time in our RTDs was shown
to be a factor of 2 shorter/longer (depending on the RTD operating point) than the quasi-bound-state lifetime.
According to our theory, the effects are not limited to the low frequencies and the same effects should persist
at higher frequencies also. Our results indicate not only that nowadays operating frequencies of RTDs could be
increased, but the results also elucidate the fundamental limitations of the whole class of resonant-tunnelling
structures: single-electron-transistor-like structures, multi-barrier structures, quantum-cascade lasers, etc.