Analysis of Bulk Negative Differential Mobility Element in a Circuit Containing Reactive Elements

The time and space evolution of the electric field in an inhomogeneous bulk negative differential mobility (NDM) element with a high n0l product, and the response of the surrounding lumped-element circuit, is theoretically investigated. We consider a circuit in which an NDM element of low-field resistance R0 and intrinsic capacitance C0 is in parallel with a parasitic capacitor Cp and in series with a load resistor, inductor L, and a battery. Exact numerical and approximate analytic solutions are obtained and discussed in terms of a damping parameter A [=(LC)1/2/R0C, where C=C0+Cp] and the ratio C0/C. Various oscillatory modes can all occur in the same NDM element for appropriate values of the circuit parameters. The dominant mode of circuit-controlled oscillation in a series L-parallel C circuit is the quenched multiple-dipole relaxation mode. LSA relaxation oscillations occur only for a narrow range of circuit parameters and LSA sinusoidal oscillations are excluded because of domain domination, even for NDM elements with small doping fluctuations. This produces an upper frequency limit for circuit control which must be considered in addition to that imposed by finite intervalley relaxation times.