## 2 Experimental Details  
LH-HEMTs were grown on InP (3-inch), and MHEMT were grown on larger GaAs (6-inch) substrates through molecular beam epitaxy (MBE). The epitaxial layer, arranged from top to bottom, consisted of the following components: a heavily doped 40 nm multilayer cap (comprising In\({}_{0.7}\)Ga\({}_{0.3}\)As, In\({}_{0.53}\)Ga\({}_{0.47}\)As, and In\({}_{0.52}\)Al\({}_{0.48}\)As), a 4 nm InP etch stopper, an 8 nm In\({}_{0.52}\)Al\({}_{0.48}\)As barrier, Si \(\delta\)-doping, a 3 nm In\({}_{0.52}\)Al\({}_{0.48}\)As spacer, a 10 nm In\({}_{0.53}\)Ga\({}_{0.47}\)As channel, and a 100 nm In\({}_{0.52}\)Al\({}_{0.48}\)As buffer. The N\({}^{+}\) type 10 nm In\({}_{0.7}\)Ga\({}_{0.3}\)As and 20 nm In\({}_{0.53}\)Ga\({}_{0.47}\)As capping layer was heavily doped with 5.00 \(\times\) 10\({}^{19}\)/cm\({}^{3}\). Also,the N\({}^{+}\)-type 10 nm In\({}_{0.52}\)As\({}_{0.48}\)As capping layer was doped with a doping density of \(3.00\times 10^{19}/\)cm\({}^{3}\). And the Si \(\delta\)-doping density between the InAlAs barrier and spacer was 5.0 \(\times\) 10\({}^{12}\)/cm\({}^{2}\) for both epitaxies. In LM-HEMTs epitaxy, the measured sheet carrier density (\(N_{S}\)) of the 2-dimensional electron gas (2 DEG) in the InGaAs channel layer was \(2.9\times 10^{12}/\)cm\({}^{2}\), and the electron hall mobility (\(\mu_{n}\)) was 10,060 cm\({}^{2}\)/V-s. The measured MHEMT \(N_{S}\) and \(\mu_{n}\) were 3.0 \(\times\) 10\({}^{12}\)/cm\({}^{2}\) and 8950 cm\({}^{2}\)/V-s, respectively. To check \(N_{S}\) and \(\mu_{n}\), van der Pauw Hall measurements were carried out. This was measured after etching the multi-capping layer. The epitaxy used in the experiment was a commercial epitaxy. InP substrates were utilized to form LM-HEMTs with this structure, whereas GaAs substrates were employed for growing MEHMT with a metamorphic buffer (graded). Figure 1a illustrates a schematic of the cross-sectional view of the InAlAs/InGaAs HEMTs. Transmission electron microscopy (TEM) was used to confirm the discrepancies in dislocation and rough surface morphology between LM-HEMTs and MHEMT. Figure 1b presents TEM images of LM-HEMTs, exhibiting a clean interface between the substrate and the In\({}_{0.52}\)Al\({}_{0.48}\)As buffer. MHEMT TEM images in Figure 1c confirm the existence of a significant dislocation density and rugged surface generated from the mismatch of lattice constants between the substrate and the metamorphic buffer. Figure 1c tries to clearly confirm the dislocation using a bright field TEM image. The purpose of this selection was to enhance the clarity in order to emphasize the discrepancies in dislocation between LM-HEMTs and MHEMT to make the observed variances more apparent and distinguishable. Figure 1: (**a**) This schematic depicts the cross-section view of HEMTs grown on two different substrates. Additionally, TEM images of the cross-section are provided, showing (**b**) LM-HEMTs and (**c**) MHEMT. The fabrication process for both MHEMT and LM-HEMTs included mesa isolation through phosphoric-acid-based wet chemical etching for device isolation. Additionally, non-alloyed Ohmic contacts were established using a Molybdenum (Mo, 10 nm)/Titanium (Ti, 10 nm)/Platinum (Pt, 30 nm)/Gold (Au, 350 nm)/Nickel (Ni, 5 nm) stack for the source and drain electrode formation. At this time, the Ni metal located at the top of the Ohmic metal stack was used to improve the adhesion between SiO\({}_{2}\) and the ohmic metal. SiO\({}_{2}\) passivation was achieved through sputtering. This improves adhesion during photoresist coating to form a T-gate, increases the stability of the T-gate structure, and helps to reduce the side etch length in the recess etch process before gate deposition. And then, sub-200 nm T-gates were formed using electron beam lithography. The SiO\({}_{2}\) passivation layer, which was applied to the active area, underwent reactive ion etching before the gate was deposited. Then, a multilayer cap with significant doping was subjected to etching through the utilization of an etchant based on phosphoric acid.