  B[e] stars are hot stars surrounded by circumstellar gas and dust responsible
for the presence of emission lines and IR-excess in their spectra. How dust can
be formed in this highly illuminated and diluted environment remains an open
issue. HD 62623 is one of the very few A-type supergiants showing the B[e]
phenomenon. We obtained nine calibrated visibility measurements using the
VLTI/MIDI instrument in SCI-PHOT mode and PRISM spectral dispersion mode with
projected baselines ranging from 13 to 71 m and with various position angles.
We used geometrical models and physical modeling with a radiative transfer code
to analyze these data. The dusty circumstellar environment of HD 62623 is
partially resolved by the VLTI/MIDI even with the shortest baselines. The
environment is flattened and can be separated into two components: a compact
one whose extension grows from 17 mas at 8 microns to 30 mas at 9.6 microns and
stays almost constant up to 13 microns, and a more extended one that is
over-resolved even with the shortest baselines. Using the radiative transfer
code MC3D, we managed to model HD 62623's circumstellar environment as a dusty
disk with an inner radius of 3.85+-0.6 AU, an inclination angle of 60+-10 deg,
and a mass of 2x10^-7Mo. It is the first time that the dusty disk inner rim of
a supergiant star exhibiting the B[e] phenomenon is significantly constrained.
The inner gaseous envelope likely contributes up to 20% to the total N band
flux and acts like a reprocessing disk. Finally, the hypothesis of a stellar
wind deceleration by the companion's gravitational effects remains the most
probable case since the bi-stability mechanism does not seem to be efficient
for this star.
