  We report a comprehensive study of the energy response to low-energy recoils
in dual-phase xenon-based dark matter experiments. A recombination model is
developed to explain the recombination probability as a function of recoil
energy at zero field and non-zero field. The role of e-ion recombination is
discussed for both parent recombination and volume recombination. We find that
the volume recombination under non-zero field is constrained by a plasma
effect, which is caused by a high density of charge carriers along the
ionization track forming a plasma-like cloud of charge that shields the
interior from the influence of the external electric field. Subsequently, the
plasma time that determines the volume recombination probability at non-zero
field is demonstrated to be different between electronic recoils and nuclear
recoils due to the difference of ionization density between two processes. We
show a weak field-dependence of the plasma time for nuclear recoils and a
stronger field-dependence of the plasma time for electronic recoils. As a
result, the time-dependent recombination is implemented in the determination of
charge and light yield with a generic model. Our model agrees well with the
available experimental data from xenon-based dark matter experiments.
