  In direct dark matter (DM) detection via scattering off the electrons, the
momentum transfer plays a crucial role. Previous work showed that for
self-interacting DM, if the DM particle has a size (the so-called puffy DM),
the radius effect could dominate the momentum transfer and become another
source of velocity dependence for self-scattering cross section. In this work
we investigate the direct detection of puffy DM particles with different radii
through electron recoil. We find that comparing with the available experimental
exclusion limits dominated by the mediator effect for XENON10, XENON100 and
XENON1T, the constraints on the puffy DM-electron scattering cross-section
become much weaker for large radius DM particles. For small-radius DM
particles, the constraints remain similar to the point-like DM case.
