We present a novel spectroscopic technique that is based on the ballistic injection of minority carriers from the tip of a scanning-tunneling microscope into a semiconductor heterostructure. By analyzing the resulting electro-luminescence spectrum as a function of tip-sample bias, both the injection barrier height and the carrier relaxation rate Gamma(s) after injection can be determined. At 4.2 K we found Gamma(s) = 5 x 10(13) s(-1) and at 77 K we found Gamma(s) = 8 x 10(13) s(-1). From current-dependent measurements we find that, at room temperature, a large fraction of the carriers is trapped prior to radiative recombination. At high currents or low temperatures the traps become saturated. We tentatively identify the Be acceptors in the structure as trapping centers.