  We study the formation and evolution of HII regions around the first stars
formed at z=10-30. We use a one-dimensional Lagrangian hydrodynamics code which
self-consistently incorporates radiative transfer and non-equilibrium
primordial gas chemistry. The star-forming region is defined as a spherical gas
cloud with a Population III star embedded at the center. We explore a large
parameter space of host halo mass, gas density profile, and stellar luminosity.
The formation of the HII region is characterized by initial slow expansion of a
weak D-type ionization front near the center, followed by rapid propagation of
an R-type front throughout the outer gas envelope. We find that the transition
between the two front types is indeed a critical condition for the complete
ionization of halos of cosmological interest. In small mass (< 10^6 M_sun)
halos, the transition takes place within a few 10^5 yr, yielding high escape
fractions (>80%) of both ionizing and photodissociating photons. In larger mass
(> 10^7 M_sun) halos, the ionization front remains to be of D-type over the
lifetime of the massive star, the HII region is confined well inside the virial
radius, and the escape fractions are essentially zero. We derive an analytic
formula that reproduces well the results of our simulations. We discuss
immediate implications of the present results for the star formation history
and early reionization of the Universe.
