  I show that the MacColl-Hartman effect, namely, the saturation of the group
delay time of sub-barrier quantum tunneling as a function of the barrier width,
comes from the saturating behavior of a more fundamental concept - the phase of
the stationary wave function. The explanation of saturation is given based on
the decomposition of the stationary wave function into the spectrum of wave
numbers and formulation of the initial condition for the direction of
propagation of the incident matter wave. It is also shown that the saturation
plateau of MacColl and Hartman actually doesn't continue indefinitely, but has
a finite length. After the plateau, the sub-barrier tunneling time
monotonically increases with increasing width of the potential, and this
applies both to the maximum's of the wave packet and to the average tunneling
time.
