  We study analytically quantum tunneling of relativistic and non-relativistic
particles at both Killing and universal horizons of Einstein-Maxwell-aether
black holes, after high-order curvature corrections are taken into account, for
which the dispersion relation of the particles becomes nonlinear. Our results
at the Killing horizons confirm the previous ones, i.e., at high frequencies
the corresponding radiation remains thermal and the nonlinearity of the
dispersion does not alter the Hawking radiation significantly. In contrary,
non-relativistic particles are created at universal horizons and are radiated
out to infinity. The radiation also has a thermal spectrum, and the
corresponding temperature takes the form, $T^{z}_{UH} = 2\kappa_{UH}
(z-1)/(2\pi z)$, where $z$ denotes the power of the leading term in the
nonlinear dispersion relation, $\kappa_{UH}$ is the surface gravity of the
universal horizon, defined by peering behavior of ray trajectories at the
universal horizon. We also study the Smarr formula by assuming that: (a) the
entropy is proportional to the area of the universal horizon, and (b) the first
law of black hole thermodynamics holds, whereby we derive the Smarr mass, which
in general is different from the total mass obtained at infinity. This
indicates that one or both of these assumptions must be modified.
