## 2 Samples and Measurement Techniques  
Commercial AlGaN/(AlN)/GaN HEMT structures grown along the polar c-axis using the metalorganic chemical vapor deposition (MOCVD) method were selected for this study. The detailed description of the growth and characterization of alike structures can be found elsewhere [39; 40]. In particular, layers for the AlGaN/AlN/GaN sample were grown on a 500 \(\upmu\)m thick 6H-polytype SiC substrate as follows: a 90 nm thick AlN nucleation layer, a 1300 nmthick high resistivity GaN:C buffer, a 900 nm thick UID GaN layer and a 0.8 nm thick AlN spacer. Then, a 19 nm thick Al\({}_{0.25}\)Ga\({}_{0.75}\)N barrier layer was grown capping it with a 2 nm thick GaN and a 1 nm thick SiN\({}_{x}\) passivation layers. A similar structures, but without an AlN spacer (AlGaN/GaN) was developed on a semi-insulating 4H-polytype SiC substrate where a nominally undoped 20 nm thick Al\({}_{0.25}\)Ga\({}_{0.75}\)N barrier and 2.5 \(\upmu\)m thick GaN buffer were capped by a 1.5 nm thick GaN layer. Figure 1b illustrates only top part of the unintentionally doped (UID) GaN layer and AlGaN barrier required for 2 DEG formation. The ohmic contacts were fabricated of a Ti/Al/Ni/Au metal stack with a respective thickness of 30/90/20/100 nm annealed in nitrogen ambient for 30 s at 850 \({}^{\circ}\)C. The mesas were formed either by inductively coupled plasma reactive ion etching (ICP-RIE) using Cl plasma or by implantation of 700 keV energy Al ions into a depth of about 650 nm. More details about the device processing have been reported elsewhere [11; 41]. The TLMs were used to evaluate the performance of ohmic contacts [22]. Values for the contact resistance \(R_{c}\) and specific contact resistivity \(\rho_{c}\) at low electric fields were minimized to 1 \(\Omega\)mm and 2 \(\times\) 10\({}^{-3}\)\(\Omega\)mm\({}^{2}\), respectively, [11; 41; 42]. The Hall effect experiments in Van der Paw geometry at temperature of 300 K revealed the density \(n_{\text{2 DEG}}\) and mobility \(\mu_{\text{2 DEG}}\) values of 2 DEG in used samples to be of 8.3 \(\times\) 10\({}^{12}\) cm\({}^{-2}\) and 9.3 \(\times\) 10\({}^{12}\) cm\({}^{-2}\) and of 1.9 \(\times\) 10\({}^{3}\) cm\({}^{3}\)/Vs and 1.9\(\times\)10\({}^{3}\) cm\({}^{3}\)/Vs, respectively. Usually, GaN device fabrication is completed with the deposition of dielectric layers to passivate the surface states minimizing their influence on the device/transistor performance [43]. However, good performance of unpassivated HEMTs has also been reported [44; 45], exposing issues of the selection and usage of the surface passivants which might deteriorate the performance. In this work, the surfaces of all heterostructures after device processing were left unpassivated. A microscope photograph of the TLM samples, an illustration of the cross-section of AlGaN/GaN heterostructures with two metal contacts annealed on the surface, and the connection between the sample (device under test (DUT)) in the electronic scheme are shown in Figure 1a-c, respectively. The 2 DEG channel formed at the interface of the AlGaN and GaN layers is indicated by the blue line. Different length channels are selected for the pulsed I-V and microwave noise measurements by placing the two-pin microwave probe on top of the selected two nearby electrodes. The width \(W\) and the length \(D\) of rectangular electrodes were 250 \(\upmu\)m and 100 \(\upmu\)m, respectively. The distance between electrodes \(L\) for different TLM resistor samples were 6, 12.5, 25, 35, 45, 55, and 65 \(\upmu\)m. We assumed that the length of the 2 DEG channel is the same as \(L\) and is independent of the applied voltage. The current distribution under the right-hand side and left-hand side electrodes is considered to be the same. The current crowding phenomena is illustrated by the set of arrows (vectors which roughly show the direction and the magnitude of the current flow) parallel and perpendicular to the plane of 2 DEG.