We introduced a novel high-frequency source based on interband tunneling. A polarization-induced oscillation of trapped-hole-charge occurs in an AlGaSb/InAs/ AlGaSb resonant tunneling device. Rate equations for Zener tunneling, polarization, and electron-hole recombination is used to analyze the nonlinear dynamics of this device structure. The nonoscillatory state is unstable against the limit-cycle operation. The amplitude of trapped hole oscillation increases with bias, but the time-averaged values can be approximated by a step function. These lead to the hysteresis of the averaged trapped hole charge in AlGaSb barrier, and to the experimental intrinsic bistability in AlGaSb/InAs/AlGaSb resonant tunneling device. Large-scale time-dependent simulation of quantum transport with interband-tunneling dynamics is needed for the design optimization of this novel class of oscillator useful for high-bandwidth applications.