  The extended $\gamma$-ray halos around pulsars are unique probe of
transportation of high-energy electrons (and positrons) in vicinities of such
pulsars. Observations of morphologies of several such halos indicate that
particles diffuse very slowly around pulsars, compared with that in the Milky
Way halo. The energy-dependent morphologies are expected to be very important
in studying the energy-dependence of the diffusion coefficient. In this work we
point out that the spectrum of high-energy electrons takes effect in shaping
the $\gamma$-ray morphologies at the ultra-high-energy bands, and thus results
in a degeneracy between the electron spectrum and the energy-dependence of the
diffusion coefficient. The reasons for such a degeneracy include both the
Klein-Nishina effect of the inverse Compton scattering and the curvature (if
any) of the electron spectrum. It it thus necessary to take into account the
spectral shape of electrons when deriving the energy-dependence of diffusion
coefficient using ultra-high-energy $\gamma$-ray measurements of extended
pulsar halos.
