  Primordial black holes (PBHs) are predicted in many models via different
formation mechanisms. Identifying the origin of PBHs is of the same importance
as probing their existence. We propose to probe the asteroid-mass PBHs
[$\mathcal{O}(10^{17})~{\rm g}\lesssim M\lesssim\mathcal{O}(10^{22})~{\rm g}$]
with gamma-rays from Hawking radiation and the stochastic gravitational waves
(GWs) from the early Universe. We consider four concrete formation mechanisms,
including collapse from primordial curvature perturbations, first-order phase
transitions, or cosmic strings, and derive the extended PBH mass functions of
each mechanism for phenomenological study. The results demonstrate that by
combining gamma-rays and GW signals we can probe PBHs up to
$\mathcal{O}(10^{19})~{\rm g}$ and identify their physical origins.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology