  We develop a semiclassical approach for the statistics of the time delay in
quantum chaotic systems in the presence of a tunnel barrier, for broken
time-reversal symmetry. Results are obtained as asymptotic series in powers of
the reflectivity of the barrier, with coefficients that are rational functions
of the channel number. Exact expressions, valid for arbitrary reflectivity and
channel number, are conjectured and numerically verified for specific families
of statistical moments.
