## 2 Experimental Section  
Figure 1 shows the device structure and the illustration of F incorporation. The wafers used in our study were molecular beam epitaxy grown by a vender. P-type (Zn-doped, 3 \(\times\) 10\({}^{18}\)/cm\({}^{3}\)) InP wafers were the starting substrates. P-type (Be-doped, 5 \(\times\) 10\({}^{16}\)/cm\({}^{3}\)) In\({}_{0.52}\)Al\({}_{0.48}\)As of 100 nm thick was grown as a buffer layer, followed by a 300 nm p-type In\({}_{0.53}\)Ga\({}_{0.47}\)As layer (Be-doped, 5 \(\times\) 10\({}^{16}\)/cm\({}^{3}\)), which was used as the channel layer. The native oxides were removed with 1% diluted HF solution, followed by 20% (NH\({}_{4}\))\({}_{2}\)S solution for sulfur passivation. To protect gate stack from the source and drain (S/D) activation annealing, the gate-last process was adopted: A 10-nm-thick atomic-layer-deposited (ALD) Al\({}_{2}\)O\({}_{3}\) was deposited at a substrate temperature of 200 \({}^{\circ}\)C as an encapsulation layer. S/D regions were selectively implanted with a Si dose of 2 \(\times\) 10\({}^{14}\)/cm\({}^{2}\) at 35 keV. The S/D activation annealing was performed in nitrogen ambient at 700 \({}^{\circ}\)C/10 s. The encapsulation layer was then removed using buffered oxide etch solution. A 5 nm-thick ALD HfO\({}_{2}\) film was deposited after the same surface preparation (HF and (NH\({}_{4}\))\({}_{2}\)S). Some samples were treated _ex situ_ with CF\({}_{4}\) plasma with varied RF wattages and treatment times. A mixed flow of CF\({}_{4}\) and O\({}_{2}\) gas (ratio \(\sim\)10:1) was introduced into the chamber with pressure of 100 mTorr. The purpose of O\({}_{2}\) flow was to avoid carbon contamination. Control samples without CF\({}_{4}\)/O\({}_{2}\) plasma treatment were also fabricated as references. Post-deposition annealing was then performed for all the samples at 500 \({}^{\circ}\)C for 60 s in a nitrogen ambient. Subsequently, a 200 nm TaN was sputtered and patterned as gate electrode. AuGe/Ni/Au alloy was deposited by E-beam evaporation and a liftoff process to form S/D Ohmic contacts; backside contact was made by E-beam evaporation of Cr/Au, followed by annealing at 400 \({}^{\circ}\)C for 30 s in nitrogen ambient. Figure 2: X-ray photoelectron spectroscopy (XPS) analysis of the Hf 4\(f\) electronic spectra for the samples with and without fluorine (F) incorporation. Figure 3: XPS analysis of the F 1\(s\) electronic spectra for the control sample and fluorinated sample. Figure 1: The device cross-sectional structure of HfO2/In0.53 Ga0.47 As gate stack. Samples were treated in a mixed flow of CF4 and O2 gas (ratio \(\sim\)10:1) with varied RF power and treatment time. Figure 2: X-ray photoelectron spectroscopy (XPS) analysis of the Hf 4\(f\) electronic spectra for the samples with and without fluorine (F) incorporation. Compared to the control sample, the fluorinated sample has an increased binding energy by 0.2 eV and 0.3 eV for the Hf 4/\(f_{7/2}\) and Hf 4/\(f_{5/2}\) signal, respectively. This suggests that parts of the oxygen vacancies were terminated by the incorporated F atoms to form stronger Hf-F bonds with higher binding energy. In Figure 3, the peak signal located at \(\sim\)685 eV corresponds to the F bonds in the bulk HfO\({}_{2}\), indicating that F was incorporated into the HfO\({}_{2}\) after CF\({}_{4}\)/O\({}_{2}\) plasma treatment. In order to search the F distribution in the HfO\({}_{2}\)/In\({}_{0.53}\)Ga\({}_{0.47}\)As gate stack, the secondary ion mass spectrometry (SIMS) technique was examined, as shown in Figure 4. A considerable amount of F was incorporated into the HfO\({}_{2}\) gate stacks with CF\({}_{4}\)/O\({}_{2}\) plasma treatment while the oxygen concentration remained similar. Due to sudden structural transition at the HfO\({}_{2}\)/In\({}_{0.53}\)Ga\({}_{0.47}\)As interface, the density of defective bonds at the interface is much higher than that in the HfO\({}_{2}\) bulk.