  In this paper the two-dimensional structure of protoplanetary disks around
Herbig Ae/Be stars is studied. This is done by constructing a self-consistent
model based on 2-D radiative transfer coupled to the equation of vertical
hydrostatics. As a simplifying assumption a grey opacity is used. It is found
that the disk can adopt four different structures, dependent on the surface
density distribution Sigma(R) as a function of radius, i.e. on radial- and
vertical optical depth of the disk. For the case of high to intermediate
vertical optical depth, the temperature and density structures are in agreement
with the simple ``disk with inner hole'' model of Dullemond, Dominik & Natta
(2001, henceforth DDN01). At large radii the disk adopts a flaring shape as
expected, and near the dust destruction radius (located at about 0.5 AU for
most Herbig Ae stars) the disk is superheated and puffs up. The region directly
behind this ``puffed-up inner dust wall'' is shadowed, as predicted by DDN01.
For the case of intermediate to low vertical optical depth, but still high
radial optical depth, the 2-D models show that the shadow can cover the entire
disk. The disk is then no longer flaring. When the disk is optically thin even
in radial direction, it becomes unshadowed again because the inner rim can no
longer block the stellar light. Finally, for disks that flare at intermediate
radii, but become too optically thin at large radii, the outer parts once again
become shadowed. But this time the shadowing is caused by the flaring part of
the disk instead of the inner rim. Observational consequences of these four
geometries are discussed.
