  We analyse the optical properties of
InAs$_{1-x}$Sb$_{x}$/Al$_{y}$In$_{1-y}$As quantum wells (QWs) grown by
molecular beam epitaxy on relaxed Al$_{y}$In$_{1-y}$As metamorphic buffer
layers (MBLs) using GaAs substrates. The use of Al$_{y}$In$_{1-y}$As MBLs
allows for the growth of QWs having large type-I band offsets, and emission
wavelengths $> 3$ $\mu$m. Photoluminescence (PL) measurements for QWs having Sb
compositions up to $x = 10$\% demonstrate strong room temperature emission up
to 3.4 $\mu$m, as well as enhancement of the PL intensity with increasing
wavelength. To quantify the trends in the measured PL we calculate the QW
spontaneous emission, using a theoretical model based on an 8-band $\vec{k}
\cdot \vec{p}$ Hamiltonian. The theoretical calculations, which are in good
agreement with experiment, identify that the observed enhancement in PL
intensity with increasing wavelength is associated with the impact of
compressive strain on the QW valence band structure. Our results highlight the
potential of type-I InAs$_{1-x}$Sb$_{x}$/Al$_{y}$In$_{1-y}$As metamorphic QWs
to address several limitations associated with existing heterostructures
operating in the mid-infrared, establishing these novel heterostructures as a
suitable platform for the development of mid-infrared light-emitting diodes.
