  Electrostatic shielding is an important consideration for large area field
emitters (LAFE) and results in a distribution of field enhancement factors even
when the constituent emitters are identical. Ideally, the mean and variance
together with the nature of the distribution should characterize a LAFE. In
practice however, it is generally characterized by an effective field
enhancement factor obtained from a linear fit to a Fowler-Nordheim plot of the
$\text{I V}$ data. An alternate characterization is proposed here based on the
observation that for a dense packing of emitters, shielding is large and LAFE
emission occurs largely from the periphery, while well separated emitter tips
show a more uniform or 2-dimensional emission. This observation naturally leads
to the question of the existence of an emission-dimension, $D_e$ for
characterizing LAFEs. We show here that the number of patches of size $L_P$ in
the ON-state (above average emission) scales as $N(L_P) \sim L_P^{-D_e}$ in a
given LAFE. The exponent $D_e$ is found to depend on the applied field (or
voltage) and approaches $D_e = 2$ asymptotically.
