Abstract: In this paper, we present a reliable measurement method to study the influence of the GaN buffer layer on phonon-escape time in comparison with commonly used Si substrates and, in consequence, on the IF bandwidth of HEBs. One of the key aspects is to operate the HEB mixer at elevated bath temperatures close to the critical temperature of the NbN ultra-thin film, where contributions from electron-phonon processes and self-heating effects are relatively small, therefore IF roll-off will be governed by the phonon-escape.Two independent experiments were performed at GARD and MSPU on a similar experimental setup at frequencies of approximately 180 and 140 GHz, respectively, and have shown reproducible and consistent results. The entire IF chain was characterized by S-parameter measurements. We compared the measurement results of epitaxial NbN grown onto GaN buffer-layer with Tc of 12.5 K (4.5nm) with high quality polycrystalline NbN films on Si substrate with Tc of 10.5K (5nm) and observed a strong indication of an enhancement of phonon escape to the substrate by a factor of two for the NbN/GaN material combination.