  We show that an instability may be present in resonant tunneling through a
quantum well in one, two and three dimensions, when the resonance lies near the
emitter Fermi level. A simple semiclassical model which simulates the resonance
and the projected density of states by a nonlinear conductor, the Coulomb
barrier by a capacitance, and the time evolution by an iterated map, is used.
The model reproduces the observed hysteresis in such devices, and exhibits a
series of bifurcations leading to fast chaotic current fluctuations.
