  We study the incandescence of a semiconductor system characterized by a
radiatively broadened material excitation. We show that the shape of the
emission spectrum and the peak emissivity value are determined by the ratio
between radiative and non-radiative relaxation rates of the material mode. Our
system is a heavily doped quantum well, exhibiting a collective bright
electronic excitation in the mid-infrared. The spontaneous emission rate of
this collective mode strongly depends on the emission direction and, uncommonly
for a solid-state system, can dominate non-radiative scattering processes.
Consequently the incandescence spectrum undergoes strong modifications when the
detection angle is varied. Incandescence is modelled solving quantum Langevin
equations, including a microscopic description of the collective excitations,
decaying into electronic and photonic baths. We demonstrate that the emissivity
reaches unity value for a well-defined direction and presents an angular
radiative pattern which is very different from that of an oscillating dipole.
