  We demonstrate that the dynamic nuclear polarization (DNP) of phosphorus
donors in silicon can be very effective in a magnetic field of 4.6 T and at
temperatures below 1 K. The DNP occurs due to the Overhauser effect following a
cross relaxation via the forbidden flip-flop or flip-flip transitions. Nuclear
polarization values $P>0.98$ were reached after 20 min of pumping with 0.4
$\mu$W of microwave power. We evaluated that the ratio of hyperfine state
populations increased by three orders of magnitude after 2 hours of pumping,
and an extremely pure nuclear spin system containing $<10^{-11}$ of the other
spin state can be created. An inverted DNP has been obtained by pumping the low
field ESR line of P followed by the flip-flip cross relaxation. This transition
has much smaller relaxation rate and required substantially longer pumping
times. We found that the nuclear polarization dynamics deviates substantially
from a simple exponential function. The evolution of the polarization is
characterized by two time constants $T^{'}_{ac}\approx$15 s in the beginning,
and $T^{"}_{ac}\approx$1100 s for long pumping time. Temperature dependence of
the nuclear relaxation rate of $^{31}$P was studied down to 0.75 K, below which
the relaxation time became too long to be measured. The nuclear polarization
followed a bi-exponential time dependence during relaxation. We suggest that
the non-exponential behavior of DNP dynamics and the subsequent relaxation is
mediated by the nuclei of $^{29}$Si surrounding $^{31}$P donors, which affect
the transition probabilities of the forbidden cross-relaxation processes.
