High-frequency behavior of quantum-based devices: Equivalent-circuit, nonperturbative-response, and phase-space analyses

The high-frequency response of resonant tunneling devices (RTD’s), subjected to a time-dependent signal, is considered in two different situations when operating in the negative-differential-resistance (NDR) region: stable and unstable. The study of this behavior is considered from three different approaches, all based on the phase-space distribution-function formalism. In the stable case, the equivalent-circuit approach (ECA) is deduced from the published numerical results obtained by one of us (FB. and collaborators) dealing with the complex dynamical aspects in phase space of quantum transport in RTD, operating at dc bias in the NDR region of its ideal characteristic current-voltage (I-V) curve. The ECA is found to be very useful in resolving the various outstanding controversies concerning the dynamical quantum transport behavior of RTD. For unstable operation in the NDR region, nonperturbative approaches are more appropriate. Here, a time-dependent transformation of phase space is found which transforms the quantum distribution (QDF) transport equation to the same form as that in the absence of a time-dependent signal. This time-dependent transformation is useful when the applied time-dependent electric field is assumed to be position independent. In a more general and realistic situation, an applied time-dependent voltage at the drain will self-consistently lead to a time-dependent and position-dependent potential inside the device. For this general situation, we introduce two different representations of quantum transport, namely, the Liouville representation and the phase-space fluid representation. The QDF solution has inherent undesirable features for studying the dynamics of phase space, which can be eliminated by special processing. This processing yields the positive definite Husimi distribution. It is suggested that the use of the Husimi distribution enables a microscopic dynamical viewpoint of ECA as well as shedding further light on the dynamical nature of the quantum inductance.