Depending on the technology you might have options such
as stacking Nem on Nbase on Nsink on NBL to maximally
drive down sheet rho. This might be in the library as a
"crossunder" element (or not - more popular in the days
of single level metal). Such a critter would have more variability
than a single-shot resistor.
Surprising that a Nem or Pem resistor would be high sheet
resistivity, I am used to emitters in the 10-20/sq and base
in the 100-300/sq ranges.
Seems to me that an emitter (N or P) resistor ought to come
in about 1/3 - 1/5 square. Maybe these are not "approved"
in the externally-released PDK but with some negotiation,
could be allowed / quantified / support provided.
Metal is an option, probably 0.1 /sq range so you would be
looking at 20-40 squares and fat enough to carry the current.
Could be that, at low currents, a serpentine could be sensible.
If this is an emitter ballast resistor, consider that each of the
N emitter "fingers" wants its own resistance and the 3.8 ohms
might be the "parallel sum" (like maybe 16, 60 ohm resistors,
one per emitter stripe) and a lot more fortunate local aspect
ratio? See whether the resistor can be made "spatially diffuse"
and maybe non-layout-impacting, or even layout-improving
by (say) using the resistor(s) as crossunders (for example,
emitter current through 16 resistors-as-crossunders, means
room above for the gang base feed routing...).