  A great number of metal and semiconductor photocathodes, which are of high
practical importance for photoinjector applications, closely follow the 1/3
gradient Dowell-Schmerge (DS) law describing the spectral dependence of the
mean transverse energy ($MTE$), $viz.$ $MTE$ as a function of the incident
laser photon energy. However, some (rare) semiconductor photocathodes show
$MTE$ trends that are significantly different. For example, spectral $MTE$
measurements on PbTe, BaLaSnO or Hf/HfO$_2$ have clearly demonstrated trends
that can differ from DS law being non-monotonic, slower growing, or displaying
constant $MTE$ versus laser photon energy. We have discovered that $n$-type
ultra-nano-crystalline diamond (UNCD) and single crystal diamond are anti-DS
photocathodes in that their $MTE$ decreases with the incident photon energy. It
was previously established that UNCD is a highly emissive material in the near
UV such that quantum efficiency ($QE$) grows with the laser photon energy. The
unique and novel combination of high increasing $QE$ and low decreasing $MTE$
of UNCD may pave the way to desired high brightness electron beams, through
operation well above its work function which fundamentally differs from
'Boltzmann tail' operation near the photoemission threshold. One other
remarkable result followed: As UNCD is a $sp^2$ grain boundary diluted $sp^3$
diamond matrix, control over grain boundary/grain engineering in the material's
synthesis allowed for the production of different kinds of UNCD. The resultant
tuning of the $sp^3$-to-$sp^2$ ratio in different UNCD photocathodes allowed
for switching between canonical +1/3 DS and approximate --1/3 gradient
'anti-DS' behavior.
