## 2 Samples and Measurement Techniques
The current-voltage characteristics were measured by applying voltage pulses of width \(\tau_{\text{P}}\) = 100 ns and a duty cycle \(\sim\) 10\({}^{-5}\). The current-voltage and the hot-electron noise temperature-voltage characteristics were measured by applying voltage pulses to the TLM samples with electric field values reaching up to \(\sim\)12 kV/cm. A voltage pulse generator (Generator AVL-2A-W-B-P-M, Avtech Electrosystems) was connected to the DUT through a coaxial current probe, a coaxial voltage probe, a microwave diplexer, and a microwave probe (Model 40A with a two-pin ground-signal configuration,  
Figure 1: Microscope image of the TLM samples of the AlGaN/GaN channel with electrodes (of width \(W\) and length \(D\)) (**a**) and intersection illustration of the AlGaN/GaN heterostructure with the 2 DEG channel, showing the active part of the epitaxial structure and involving only two electrodes (**b**). Arrows illustrate the current flow. An illustration of the DUT connection in the electronic scheme is presented in (**c**). 100 \(\upmu\)m pitch, GGB Industries), which was mounted on a high-precision probe station with vibration isolation (EPS150, Cascade Microtech). The coaxial voltage probe was realized as a pick-off tee giving 30 times attenuated replica of the voltage pulse. The coaxial current probe (Model 6027, Pearson Electronics) was inductively coupled giving the voltage replica of the current pulse (conversion ratio 1 Volt/Ampere). Signals from both probes were recorded by a digital oscilloscope (DSO1022A, Keysight Technologies). As the DUT is biased by the voltage pulse, the excess microwave noise \(\Delta T_{\text{n}}=T_{\text{n}}-T_{0}\) (where \(T_{\text{n}}\) is noise temperature and \(T_{0}\) is room temperature) of the DUT appears at the pins of the microwave coaxial probe. The microwave diplexer is used to route the microwave noise of the DUT to a noise analyzer, consisting of low-noise amplifiers, a diode detector, and a box-car averager with a gating function (SR250 with modules 240A, 245, Stanford Research Systems). The diplexer was connected in the close vicinity to the DUT; it was connected straight to the coaxial connector of the coaxial microwave (two-pin) probe. The total resistance of the DUT is a sum of contacts resistances and the resistance of the channel, \(R_{\text{c}}+R_{\text{ch}}+R_{\text{c}}\), while \(R_{\text{p}}+R_{\text{p}}\) is the resistance of the connections between the voltage probe and the DUT, including the resistance of the microwave probe. The description of experimental setups can be found elsewhere [46; 47]. In microwave noise temperature experiments, the module of complex \(S_{11}\) parameter (i.e., reflection coefficient in pulsed mode) of the DUT at \(\sim\)10 GHz also was measured and used for the proper estimation of the noise temperature [48; 49]. Mesa-isolated TLM electrodes (i.e., channel etched) were used for the leakage current test and for standard \(S_{11}\) parameter spectra measurements by vector network analyzer operating up to 40 GHz. Extracted parasitic capacitance (parallel to the channel) for the shortest channel was less than \(\sim\)50 fF. From \(S_{11}\) spectra measurements of normal TLM structures (i.e., channel not etched), a small serial inductance \(\sim\)30 pH was extracted. The results of the low-field total resistance measurements of the three heterostructure samples (with and without an AlN thin barrier layer) in the TLM configuration are shown in Figure 2. TLM measurements were conducted with conventional contact-front (two-terminal) method [22]. The total resistance of the DUT is the sum of the channel resistance and contact resistance (see Figure 1c):  
\[R=R_{\text{ch}}+2R_{\text{c}}=(R_{\text{2D}}/W)\times L+2R_{\text{c}} \tag{1}\]  
where the resistance of the 2 DEG channel (layer) \(R_{\text{ch}}\) is expressed in terms of sheet resistance \(R_{\text{2D}}\) of the 2 DEG channel between electrodes [22]. If the length \(L\) is reduced to zero, the total resistance approaches \(2R_{\text{c}}\).