In this paper we calculate the analytic expression of the phase time f
or the scattering of an electron off a complex square barrier. As is w
ell known the (negative) imaginary part of the potential takes into ac
count, phenomenologically, the absorption. We investigate the Hartman-
Fletcher effect, and find that it is suppressed by the presence of a (
non negligible) imaginary potential. In fact, when a sufficiently larg
e absorption is present, the asymptotical transmission speed is finite
. Actually, the tunnelling time does increase linearly with the barrie
r width. A recent optical experiment seems to be in agreement with our
theoretical expectation.