## 2 Heterostructure Growth and Sample Fabrication  
The commercial HEMT structures for the research were provided by TopGaN Ltd., Warsaw, Poland. The heterostructures were grown using the metal organic chemical vapor deposition method on c-plane of a 500 \(\upmu\)m thick 6H-polytype SiC substrate with a 90 nm thick AlN nucleation layer. The 1300 nm-thick high resistivity GaN:C buffer was followed by the 900 nm-thick UID GaN layer and 0.8 nm AlN spacer. On the top, a 19 nm thick Al\({}_{0.25}\)Ga\({}_{0.75}\)N barrier was grown capping it with 2 nm GaN and 1 nm SiN\({}_{\text{x}}\) passivation layers. The Al mole fraction and strain states of the layers were calculated by fitting the experimental X-ray diffraction (XRD) curves with computer simulations. Sketch of the whole structure (WS) is shown in Figure 1. The values of the 2 DEG density and the electron mobility were obtained from the Hall effect measurements in a Van der Paw geometry. The results are summarized in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(T_{0}\) & \(N_{\text{S}}\) & \(\mu\) \\ (K) & (\(10^{12}\) cm\({}^{-2}\)) & (\(10^{3}\) cm\({}^{2}\)/V\(\cdot\)s) \\ \hline
77 & 6.9 & 1.7 \\
300 & 8.3 & 1.9 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hall data on two dimensional electron gas (2 DEG) performance.  
Figure 1: A layer sketch of the whole sample (WS) and the three samples prepared for the research. Thickness of each layer is indicated in nanometers obtained from XRD and SIMS (for WS) and surface profilometry (for other samples) measurements.  
The composition and strain/relaxation state of the epilayers were observed in detail by reciprocal space mapping (RSM) employing the Malvern Panalytical, Empyrean X-ray diffractometer system. The asymmetric (105) RSM of grazing incidence and exit geometry was carried out on the WS sample. The results are shown in Figure 2. Typical almost relaxed peaks from SiC, AlN nucleation layer, thick GaN buffer are clearly visible, while the AlGaN barrier is fully strained to GaN (shares the same x-axis coordinates of reciprocal lattice units). The rocking curve measurements revealed very good structural quality of deposited nitride layers. Namely, the full width of half maximum (FWHM) of rocking curve (RC) of symmetric (002) reflection was 0.036 deg, the FWHM RC of asymmetric (204) and (114) reflections were of 0.067 and 0.056 deg, respectively. For GaN, the lattice parameters were measured to be of \(a=3.1897\) and \(\delta a/a=0.00012\), demonstrating almost relaxed layers.  
The three mesas each of 4 \(\times\) 4 mm\({}^{2}\) area but of various depth were processed on the same piece of the AlGaN/AlN/GaN HEMT structure. We used UV photolithography and chlorine-based reactive ion etching methods to this end. These mesas were purposed for an accurate investigation of the high-frequency characteristics of individual UID GaN and GaN:C buffer with AlN nucleation layers. Figure 1 shows the sketch of layers in the processed mesas without cap and barrier layers, i.e., the quantum well removed (QWR), the half buffer removed (HBR), and only the substrate (SUB) left. The etch depth and the surface morphology of processed zones were controlled with the surface profilometer (VeecoDektak 150), scanning electron (Horriba SU70), and optical microscopes.  
In addition, the selected HEMT structure sample was characterized by secondary ion mass spectroscopy (SIMS) in order to determine concentration of impurities in all epitaxial layers down to the substrate. Special surface-cleaning procedures were used before the SIMS measurement enabling a determination of the doping level well below \(10^{17}\) cm\({}^{-3}\). The averaged concentration of C atoms was found to be of about \(1.5\times 10^{16}\) cm\({}^{-3}\) and \(1.2\times 10^{18}\) cm\({}^{-3}\) in the top UID GaN and bottom GaN:C parts of the buffer layer, respectivel  
Figure 2: Asymmetric (105) reciprocal space map of the WS sample.