  Using the WKBJ approximation, and the Unruh method, we obtain semi-analytic
expressions for the absorption probability (in all energy regimes) for Dirac
fermions on a higher dimensional Schwarzschild background. We present an
analytic expression relating the absorption probability to the absorption
cross-section, and then use these results to plot the emission rates to third
order in the WKBJ approximation. The set-up we use is sufficiently general such
that it could also easily be applied to any spherically symmetric background in
$d$-dimensions. Our results lead to the interesting conclusion that for $d>5$
bulk fermion emission dominates brane localised emission. This is an example
contrary to the conjecture that black holes radiate mainly on the brane.
