  We demonstrate a chip-integrated semiconductor source that combines
polarization and frequency entanglement, allowing the generation of entangled
biphoton states in a hybrid degree of freedom without postmanipulation. Our
AlGaAs device is based on type-II spontaneous parametric down-conversion (SPDC)
in a counterpropagating phase-matching scheme, in which the modal birefringence
lifts the degeneracy between the two possible nonlinear interactions. This
allows the direct generation of polarization-frequency entangled photons, at
room temperature and telecom wavelength, and in two distinct spatial modes,
offering enhanced flexibility for quantum information protocols. The state
entanglement is quantified by a combined measurement of the joint spectrum and
Hong-ou-Mandel interference of the biphotons, allowing to reconstruct a
restricted density matrix in the hybrid polarization-frequency space.
