In the phenomenon of superfluorescence (SF), a macroscopic polarization spontaneously builds up from an initially incoherent ensemble of excited dipoles and then cooperatively decays, producing giant pulses of coherent radiation. SF arising from electron-hole recombination has recently been observed in semiconductor quantum wells, but its observability conditions have not been fully understood. Here, by fully mapping out the magnetic field (B), temperature (T), and electron-hole pair density (n) dependence of SF intensity and linewidth, we have constructed a ‘phase’ diagram, showing the B-T-n region in which SF is observable. In general, SF can be observed only at low enough temperatures, high enough magnetic fields, and high enough laser powers with characteristic threshold behaviors. These results lay the foundation of our understanding of electron-hole SF and provide guidelines for our search for a Bardeen-Cooper-Schrieffer state of excitons.