  We perform the first three-dimensional radiation hydrodynamical simulations
that investigate the growth of intermediate-mass BHs (IMBHs) embedded in
massive self-gravitating, dusty nuclear accretion disks. We explore the
dependence of mass accretion efficiency on the gas metallicity $Z$ and mass
injection at super-Eddington accretion rates from the outer galactic disk
$\dot{M}_{\rm in}$, and find that the central BH can be fed at rates exceeding
the Eddington rate only when the dusty disk becomes sufficiently optically
thick to ionizing radiation. In this case, mass outflows from the disk owing to
photoevaporation is suppressed and thus a large fraction ($\gtrsim 40\%$) of
the mass injection rate can feed the central BH. The conditions are expressed
as $\dot{M}_{\rm in} > 2.2\times 10^{-1}~M_\odot ~{\rm yr}^{-1}
(1+Z/10^{-2}~Z_\odot)^{-1}(c_{\rm s}/10~{\rm km~s}^{-1})$, where $c_{\rm s}$ is
the sound speed in the gaseous disk. With increasing numerical resolution,
vigorous disk fragmentation reduces the disk surface density and dynamical
heating by formed clumps makes the disk thickness higher. As a result, the
photoevaorative mass-loss rate rises and thus the critical injection rate
increases for fixed metallicity. This process enables super-Eddington growth of
BHs until the BH mass reaches $M_{\rm BH} \sim 10^{7-8}~M_\odot$, depending on
the properties of the host dark-matter halo and metal-enrichment history. In
the assembly of protogalaxies, seed BHs that form in overdense regions with a
mass variance of 3-4$\sigma$ at $z\sim 15-20$ are able to undergo short periods
of their rapid growth and transits into the Eddington-limited growth phase
afterwards to be supermassive BHs observed at $z>6-7$.
