Exact solutions of the linearized equation for current flow in negative differential mobility elements

Space- and time-dependent perturbations of position-dependent stationary electric field profiles within negative differential mobility (NDM) elements are found as exact solutions of a linearized current density equation. The solutions, more general than those discussed previously, explicitly show the perturbation to be an accumulation of propagating disturbances. The solutions are used to demonstrate the nucleation of a cathode-adjacent high-field Gunn domain at current densities below the threshold current density for negative differential mobility.