  The quantum interference effect on the quasiparticle density of states (DOS)
is studied with the diagrammatic technique in two-dimensional d-wave
superconductors with dilute nonmagnetic impurities both near the Born and near
the unitary limits. We derive in details the expressions of the Goldstone modes
(cooperon and diffuson) for quasiparticle diffusion. The DOS for generic Fermi
surfaces is shown to be subject to a quantum interference correction of
logarithmic suppression, but with various renormalization factors for the Born
and unitary limits. Upon approaching the combined limit of unitarity and nested
Fermi surface, the DOS correction is found to become a $\delta$-function of the
energy, which can be used to account for the resonant peak found by the
numerical studies.
