The high-gain photomultiplier tube (PMT) is the most popular method to detect weak ultra-violet signals which attenuate quickly in atmosphere, although the vacuum tube makes it fragile and difficult to integrate. To overcome the disadvantage of PMT, an AlN/GaN periodically–stacked-structure (PSS) avalanche photodiode (APD) has been proposed, finally achieving good quality of high gain and low excessive noise. As there is a deep г valley only in the conduction band of both GaN and AlN, the electron transfers suffering less scattering and thus becomes easier to obtain the threshold of ionization impact. Because of unipolar ionization in the PSS APD, it works in linear mode. Four prototype devices of 5-period, 10-period, 15-period, and 20-period were fabricated to verify that the gain of APD increases exponentially with period number. And in 20-period device, a recorded high and stable gain of 104 was achieved under constant bias. In addition, it is proved both experimentally and theoretically, that temperature stability on gain is significantly improved in PSS APD. And it is found that the resonant enhancement in interfacial ionization may bring significant enhancement of electron ionization performance. To make further progress in PSS APD, the device structure is investigated by simulation. Both the gain and temperature stability are optimized alternatively by a proper design of periodical thickness and AlN layer occupancy.