  The interstellar medium is known to be chemically complex. Organic molecules
with up to 11 atoms have been detected in the interstellar medium, and are
believed to be formed on the ices around dust grains. The ices can be released
into the gas-phase either through thermal desorption, when a newly formed star
heats the medium around it and completely evaporates the ices; or through
non-thermal desorption mechanisms, such as photodesorption, when a single
far-UV photon releases only a few molecules from the ices. The first one
dominates in hot cores, hot corinos and strongly UV-illuminated PDRs, while the
second one dominates in colder regions, such as low UV-field PDRs. This is the
case of the Horsehead were dust temperatures are ~20-30K, and therefore offers
a clean environment to investigate what is the role of photodesorption. We have
carried-out an unbiased spectral line survey at 3, 2 and 1mm with the IRAM-30m
telescope in the Horsehead nebula, with an unprecedented combination of
bandwidth high spectral resolution and sensitivity. Two positions were
observed: the warm PDR and a cold condensation shielded from the UV field
(dense core), located just behind the PDR edge. We summarize our recently
published results from this survey and present the first detection of the
complex organic molecules HCOOH, CH2CO, CH3CHO and CH3CCH in a PDR. These
species together with CH3CN present enhanced abundances in the PDR compared to
the dense core. This suggests that photodesorption is an efficient mechanism to
release complex molecules into the gas-phase in far-UV illuminated regions.
