  We show how a proper radial modulation of the composition of core-multi-shell
nanowires critically enhances the control of the free-carrier density in the
high-mobility core with respect to core-single-shell structures, thus
overcoming the technological difficulty of fine tuning the remote doping
density. We calculate the electron population of the different nanowire layers
as a function of the doping density and of several geometrical parameters by
means of a self-consistent Schr\"odinger-Poisson approach: Free carriers tend
to localize in the outer shell and screen the core from the electric field of
the dopants.
