A general numerical method has been developed to solve the periodic time-dependent Schrödinger equation under a weak ac field where the quantum transmitting boundary method is employed to formulate boundary conditions of far-from-equilibrium open systems. Also derived are current components for ac small-signal analysis. We apply the method to a resonant tunneling diode (RTD) structure. Our calculations illustrate that the assumption of Lorentzian-like form of line shapes of the current functions is no longer valid at high frequencies. Thus a careful treatment to these integral functions is fundamental to obtain a physically reasonable result. Results of linear admittance, rectification coefficient, and second-harmonic generation coefficient are presented as a function of frequency and bias, at both positive differential resistance and negative-differential resistance (NDR) region. The calculations have shown that at high frequencies (several THz), the reactive feature of RTD, whether inductive or capacitive, depends on the bias and frequency. The capacitive feature, i.e., the positive imaginary part of the admittance, reaches maximum in the middle of the NDR region. This behavior can be ascribed to the confined electrons in the well. The characteristic of the transition from electron to optical behavior is observed when the frequency increases. The rectification coefficient and second-harmonic generation coefficient show a resonant enhancement at high frequencies. A comparison with the results obtained by the Wigner function is demonstrated. Different definitions of the ac reactive current component are discussed in order to clarify the confusion in the literature.

• Received 21 April 1995

DOI:https://doi.org/10.1103/PhysRevB.52.5092