## 6 Conclusions  
The infrared-terahertz spectroscopy method has been developed for the investigation of optical performance of 2 DEG and GaN:C buffer layers in the AlGaN/AlN/GaN heterostructures grown on SiC substrate. The high-frequency Drude conductivity of the 2 DEG layer and the single-phonon-resonance dielectric permittivity of the barrier, buffer and nucleation layers were taken into consideration in the transfer matrix method in order to describe the experimental data.  
Attenuation of the transmitted signals in the long-wavelength spectrum part at temperature of 77 K was associated with high-frequency Drude conductivity of 2 DEG. However, at room temperature, the simulation predicted a noticeably wider attenuation band than that observed in the experiment. The discrepancy between theory and experiment was eliminated assuming a 1.5-fold increase in the electron effective mass with the increase of temperature.  
Transmittance and reflectance of samples with sequentially removed UID GaN, GaN:C buffer and AlN nucleation layers by reactive removing allowed the investigation of the TO phonon damping factor in the frequency range of 380-720 cm\({}^{-1}\). It was demonstrated that the presence of a proper AlN nucleation layer on SiC substrate allowed the reduction of the phonon damping factor of GaN:C buffer by a factor of 2.5 in comparison to the buffers which were grown directly on Al\({}_{2}\)O\({}_{3}\) substrate. Therefore, the deposition of the nucleation layer significantly improves the crystal quality of epitaxial layers by growing them on foreign substrates.  
This work opens the way for the development of non-destructive test methods based on terahertz and infrared spectroscopies of high-frequency performance of epitaxial GaN and 2 DEG layers in the commercial AlGaN/GaN high-electron mobility transistor structures.  
Conceptualization, V.A.S. and I.K.; methodology, R.B.A., D.P., V.A.S. and I.K.; software, R.B.A. and D.P.; validation, M.D.M., M.Y.V., V.J. and I.K.; investigation, R.B.A., D.P., M.D.M., M.Y.V., V.J., J.J., S.T., P.P., M.K., M.S. and I.K.; writing--original draft preparation, R.B.A., V.A.S., P.P. and I.K.; writing--review and editing, V.A.S., J.J. and I.K.; visualization, R.B.A., D.P., M.Y.V., and I.K.; supervision, I.K.; funding acquisition, P.P., M.S. and I.K. All authors have read and agreed to the published version of the manuscript.  
This research received funding from the Research Council of Lithuania (Lietuvos molslo tartyba) under the \"TERAGANWIRE\" Project (Grant No. S-LL-19-1). The work at Warsaw was supported by the National Center for Research and Development (Grant No. WPC/20/DefeGaN/2018) and the National Science Centre (Grant No. UMO-2017/27/L/ST7/03283). The authors [PERSON], [PERSON] and [PERSON] are grateful for the support of the Ministry of Science and Higher Education of the Russian Federation (state assignment).  
The data that support the findings of this study are available on request from the corresponding author.  
The work was supported by the Research Council of Lithuania (Lietuvos molslo tartyba) under the \"TERAGANWIRE\" Project (Grant No. S-LL-19-1). The authors [PERSON], [PERSON] and [PERSON] are grateful for the support of the Ministry of Science and Higher Education of the Russian Federation (state assignment). The work at Warsaw was supported by the National Center for Research and Development (Grant No. WPC/20/DefeGaN/2018) and the National Science Centre, Poland (Grant No. UMO-2017/27/L/ST7/03283). The authors acknowledge access to the THz spectrometer T-SPEC 800 kindly provided by Teravil Ltd., Vilnius, Lithuania. The authors acknowledge [PERSON] for the help during sample fabrication and [PERSON] for enlightening discussions.