Emitter quantization and double hysteresis in resonant-tunneling structures: A nonlinear model of charge oscillation and current bistability

The effects of emitter quantization on the current-voltage $\mathrm{}(I-V)\mathrm{}$ characteristics of conventional double-barrier resonant tunneling structures (RTS’s) are investigated by numerical, graphical, and analytical methods. Different stability and degrees of emitter quantization can lead to a host of different I–V characteristics in the negative differential resistance (NDR) region. Among these are simple NDR, NDR with a rising plateaulike region and well-separated double hysteresis, and NDR with a falling plateaulike region and well-separated double hysteresis. The ratio of the main hysteresis width to the secondary hysteresis width can vary between 1 and ∞. The use of large enough spacer layers can eliminate the hysteresis and plateaulike behavior. Our numerical results for RTS’s are analyzed by employing graphical (based on simulated quantum-well charge) and analytical methods, and compared with experiments. We introduce a nonlinear physical model which is solved analytically for the limit cycle solution. The limit cycle predicts a rising average current, whereas the nonoscillatory solution predicts a falling current in the plateau region as a function of bias. The limit cycle also predicts a monotonically decreasing amplitude of the current oscillation as a function of bias in the plateau region. The fundamental frequency increases, reaches a maximum, and sharply decreases to zero as a function of bias in the plateau region. These analytical results agree with experiments and numerical simulations. The origin of inductive delay in RTS’s is further clarified. We believe we have resolved in fine detail the controversy about the $I-V$ characteristics of conventional RTS’s. A prescription for this structure to operate as an all solid-state THz source is also given.