  A one dimensional Vlasov Poisson simulation code is employed to investigate
the plasma sheath considering electron induced secondary electron emission
(SEE) and backscattering. The SEE coefficient is commonly treated as constant
in a range of plasma simulations, here improved SEE model of a charged
dielectric wall is constructed which includes the wall charging effect on SEE
coefficient and the energy dependency of SEE coefficient. Pertinent algorithms
to implement above SEE model in plasma simulation are studied in detail. It is
found that the SEE coefficient increases with the amount of negative wall
charges, which in turn reduces the emissive sheath potential. With energy
dependent SEE coefficient, the sheath potential is a nonlinear function of the
plasma electron temperature, as opposed to the linear relation predicted by
classic emissive sheath theory. Simulation combining both wall charging effect
and SEE coefficient energy dependency suggests that the space charged limited
sheath is formed at high plasma electron temperature levels, where both sheath
potential and surface charging saturate. Additionally, different algorithms to
implement the backscattering in kinetic simulation are tested and compared.
Converting backscattered electron to secondary electron via an effective SEE
coefficient barely affects the sheath properties. The simulation results are
shown to be commensurate with the upgraded sheath theory predictions.
