  HfO$_2$-based ferroelectrics are one of the most actively developed
functional materials for memory devices. However, in HfO$_2$-based
ferroelectric devices, dielectric breakdown is a main failure mechanism during
repeated polarization switching. Elucidation of the breakdown process may
broaden the scope of applications for the ferroelectric HfO$_2$. Here, we
report direct observations of a breakdown process in HfO$_2$-based
ferroelectric capacitors, by \textit{in-situ} laser-based photoemission
electron microscopy (laser-PEEM). We have not only clearly visualized the hard
dielectric breakdown (HDB) spot, but also observed the regions responsible for
the soft dielectric breakdown (SDB) which is a precursor phenomenon to HDB. It
was found that the low-resistance region formed after SDB is wider than the
conduction path formed after HDB. Furthermore, our spectromicroscopic analysis
revealed that the photoelectron spectrum after SDB shows an enhancement in
intensity without spectral-shape modulation, interpreted that the initially
existed defects are increased. In the HDB spot, however, an additional shoulder
structure was observed. These results provide spectroscopic evidence that the
electronic states responsible for the conduction path after SDB are different
from those after HDB. Through this work, we propose this microscopic approach
as a versatile tool for studying buried materials as they are, accelerating the
development of material engineering for advanced electronic devices.
