  Over the last few years, group IV hexagonal-diamond type crystals have
acquired great attention in semiconductor physics thanks to the appearance of
novel and very effective growth methods. However, many questions remain
unaddressed on their extrinsic doping capability and on how it compares to
those of diamond-like structures. This point is here investigated through
numerical simulations conducted in the framework of the Density Functional
Theory (DFT). The comparative analysis for group III and V dopant atoms shows
that: i) in diamond-type crystals the bulk sites symmetry ($T_d$) is preserved
by doping while in hexagonal crystals the impurity site moves towards a higher
($T_d$) or lower ($C_{3v}$) symmetry configuration dependently on the valence
of the dopant atoms; ii) for Si and Ge, group III impurities can be more easily
introduced in the hexagonal-diamond phase, whose local $C_{3v}$ symmetry better
accommodates the three-fold coordination of the impurity, while n-type
impurities do not reveal any marked phase preference; iii) for C, both n and p
dopants are more stable in the hexagonal-diamond structure than in the the
cubic one, but this tendency is much more pronounced for n-type impurities.
