  The electron sheath is a particular electron-rich sheath with negative net
charges where plasma potential is lower than the biased electrode. Here an
improved understanding of electron sheath theory is provided using both fluid
and kinetic approaches while elaborating on its implications for plasma-surface
interaction. A fluid model is first proposed considering the electron presheath
structure, avoiding the singularity in electron sheath Child-Langmuir law. The
latter is proved to underestimate the sheath potential. Subsequently, the
kinetic model of electron sheath is established, showing considerably different
sheath profiles in respect to the fluid model due to the electron velocity
distribution function and finite ion temperature. The model is then further
generalized involving a more realistic truncated ion velocity distribution
function. It is demonstrated that such distribution function yields a
super-thermal electron sheath whose entering velocity at sheath edge is greater
than that prescribed by the Bohm criterion, implying a potentially omitted
calibration issue in the probe measurement. Furthermore, an attempt is made to
incorporate the self-consistent presheath-sheath match within the kinetic
framework, showing a necessary compromise between realistic sheath entrance and
the inclusion of kinetic effects. In the end, the consequent secondary electron
emission due to sheath-accelerated plasma electrons in electron sheath are
analyzed, providing a sheath potential coupled with the plasma and wall
properties.
