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We demonstrate theoretically that in a spintronic diode (SD), having a free magnetic layer with perpendicular magnetic anisotropy of the first and second order and no external bias magnetic field, the out-of-plane regime of magnetization precession can be excited by sufficiently large (exceeding a certain threshold) RF signals with the frequencies ≲250 MHz. We also show that such a device can operate as a broadband energy harvester capable of converting incident RF power into a DC power with a conversion efficiency of ∼5%. The developed analytical theory of the bias-free SD operation can be used for the optimization of high-efficiency RF detectors and energy harvesters based on SDs.