  We present a theoretical analysis of mid-infrared radiative recombination in
InAs/GaSb superlattices (SLs). We employ a semi-analytical plane wave expansion
method in conjunction with an 8-band $\mathbf{k} \cdot \mathbf{p}$ Hamiltonian
to compute the SL electronic structure, paying careful attention to the
identification and mitigation of spurious solutions. The calculated SL
eigenstates are used directly to compute spontaneous emission spectra and the
radiative recombination coefficient $B$. We elucidate the origin of the
relatively large $B$ coefficients in InAs/GaSb SLs which, despite the presence
of spatially indirect (type-II-like) carrier confinement, are close to that of
bulk InAs and compare favourably to those calculated for mid-infrared type-I
pseudomorphic and metamorphic quantum well structures having comparable
emission wavelengths. Our analysis explicitly quantifies the roles played by
carrier localisation (specifically, partial delocalisation of bound electron
states) and miniband formation (specifically, miniband occupation and optical
selection rules) in determining the magnitude of $B$ and its temperature
dependence. We perform a high-throughput optimisation of the room temperature
$B$ coefficient in InAs/GaSb SLs across the 3.5 -- 7 $\mu$m wavelength range,
quantifying the dependence of $B$ on the relative thickness of the
electron-confining InAs and hole-confining GaSb layers. This analysis provides
guidance for the growth of optimised SLs for mid-infrared light emitters. Our
results, combined with the expected low non-radiative Auger recombination rates
in structures having spatially indirect electron and hole confinement,
corroborate recently observed high output power in prototype InAs/GaSb SL
inter-band cascade light-emitting diodes.
