New formulas for an exact and simple evaluation of the phase time associate
d with the passage of electrons or photons through a finite superlattice ar
e derived. This time, named here the superlattice-tunneling time tau(n), ex
hibits a resonant-band structure or a superluminal phase time behavior depe
nding on whether the particle's energy lies in a band or a gap. In the band
, tau(n) remains larger than the free motion time tau(f), while in the gap
it can be less than tau(f) (with strong substrate effects), but it is large
r than the single-cell phase time tau(l). Extremely good agreements with op
tical-pulse and superluminal delay times measured by Spielmann et al. and S
teinberg et al, are found, including the superlattice-tunneling-time limit
and the substrate effects. Conditions for measurements of earlier electron
arrival are also analyzed.