  The extreme mass ratio inspirals(EMRIs) are promising gravitational wave(GW)
sources for space-borne GW detectors. The signals of EMRIs usually have long
timescales, ranging from several months to several years, and their detection
requires accurate GW signal templates. In most waveform models, the compact
objects in EMRIs are considered test particles, which do not consider the small
bodies' spin, mass distribution, and tidal deformation. In this work, we
simulate the GW signals of EMRIs by considering the compact objects' spin and
mass quadrupole. We find that a compact object's spin can significantly
influence the GW signals, and the tidal-induced and spin-induced quadrupoles
matter only if the compact objects are white dwarfs, especially EMRIs of a
higher symmetric mass ratio. We can distinguish white dwarfs from other compact
objects in this case. The structures of black holes and neutron stars in EMRIs
do not have detectable effects on GW signals. Furthermore, compared with the GW
signals that use test particle approximation, the signal-to-noise ratios(SNRs)
of GW signals that consider extended bodies decrease slightly, which hints that
we can omit the spin and quadrupole of the compact object in the detection of
EMRIs.
