## 5 Discussion
However, it would be difficult to explain why this resistance is so different (more than 10 times), as it is compared between three channels at a given current. An interesting correlation is observed in the dependencies of \(\rho_{\text{cf}}\) (inset of Figure 9) and \(R_{\text{c}}\) (Figure 4) on the current for different samples. In that case the increase in both starts earlier if low-field resistance \(R_{\text{c0}}\) is higher. For example, from Figure 4a it follows that the difference of \(R_{\text{c0}}\) between two samples (closed squares and circles) is \(\sim\)3 times, and that correlates with more than \(\sim\)12 times difference in \(R_{\text{c}}\) at an elevated current density of \(\sim\)700 mA/mm (Figure 4a). This makes sense, because \(P_{\text{c}}\) is higher for larger \(R_{\text{c}}\) at the same current, resulting in an increase in self-heating. In other experiments, when the change in sample temperature was realized by direct heating of the sample (instead of Joule heating), two distinct trends of the change in \(R_{\text{c}}\) and \(\rho_{\text{c}}\) versus temperature were found [26; 27; 28; 52; 53; 54; 55; 56; 57; 58; 59]. The decrease in \(R_{\text{c}}\) was attributed to the metal-semiconductor junction properties and the increase was due to metal-like behavior when electron transport is determined by the \"spike mechanism\"--metal protrusions directly contacting the 2 DEG channel under the electrodes  
As it was previously discussed, both \(R_{\text{c}}\) and \(R_{\text{ch}}\) increase due to self-heating (Figures 4 and 8). This is also observed in Figure 3a, where the dependence of the total resistance on the current is nonlinear. In terms of sheet resistance \(R_{\text{2D}}\), an increase is observed in Figure 3b, where the slope (which is proportional to \(R_{\text{2D}}\)) changes with the  
Figure 8: The dependence of channel resistance change \(\Delta R_{\text{2D}}=R_{\text{2D}}-R_{\text{2D0}}\) on dissipated power density in channel; AlGaN/GaN (closed squares), AlGaN/AlN/GaN (closed triangles and circles). The inset shows the dependence of the excess noise temperature \(\Delta T_{\text{n}}\) on the dissipated power per electron \(P_{\text{e}}\) in the 45 μm-long channel. The lines in the main panel and inset demonstrate the dependencies of \(\Delta R_{\text{2D}}\sim P_{\text{2D}}\) and \(\Delta T_{\text{n}}\sim P_{\text{e}}\), respectively. current. The increase in the resistance of the 2 DEG channel at the interface of AlGaN and GaN is widely acknowledged to be due to electron-phonon scattering, the intensity of which increases with the temperature of the device at a high current. The electron scattering is largely determined by the strong electron-LO-phonon interaction in the GaN and associated hot-phonon effect [25]. It is natural to expect that the 2 DEG channel properties of the area beneath the electrodes (which have a sheet resistance of \(R_{\rm c2D}\)) at least in part would preserve some features of the channel between the electrodes (which have a sheet resistance of \(R_{\rm 2D}\)). Therefore, we compare the self-heating of \(R_{\rm c}\) and \(R_{\rm 2D}\) by plotting \(R_{\rm c}(I)\) versus \(R_{\rm 2D}(I)\) in Figure 9. Here, \(R_{\rm c}\) is multiplied by \(W\) as in Figure 4. The channel sheet resistance \(R_{\rm 2D}\) is estimated from the \(R(L)\) slope \(\Delta R/\Delta L\) (see Figure 3b) and the channel width \(W\) as \(R_{\rm 2D}=(\Delta R/\Delta L)\times W\). In Figure 9, \(R_{\rm c}\) is nearly proportional to \(R_{\rm 2D}\) at lower currents (see solid lines), but then, it starts to increase faster than \(R_{\rm 2D}\) (see dashed lines). The threshold-like increase in \(R_{\rm c}\) is resolved, revealing the threshold position for all three samples at value of about \(\sim\)600 \(\Omega\)/sq. The increase in \(R_{\rm c}\) is not good news for those who fabricate devices with small \(R_{\rm c0}\) and those who believe that it will remain the same small at higher currents (electric fields).