Henderson's Dictionary of Biological Terms (Science Reference
QH302.5 .H65 1995) offers these entries:
Archaea
n. organisms found in the oldest Precambrian rocks, i.e. rocks
of the Archaean era.
Archaean
a. appl. the earlier eon of the Precambrian, ending at about
2500 million years ago.
Archaebacteria
n. plu. class of prokaryotic microorganisms forming the
division Mendosicutes, including extreme thermophiles, extreme halophiles
and methanogens (methane producers). Typically found in extreme
environments, e.g. hot springs, salt lakes. They differ in many ways
from other bacteria, e.g. in the structure of their cell walls and
membrane lipids and posession of introns in some genes, and are thought
to represent a quite separate group from the true bacteria or
eubacteria.
And here's the result of a search for archaebacteria in Encyclopedia Britannica Online.