*3.2. Band Alignment Characteristics*

To assess the optical characteristics of the three various stacked gate dielectrics, UV-Vis spectroscopy was used to obtain the absorption spectra and the optical bandgap values (Figure 4) of samples S1, S2, and S3 were determined to be 5.49, 5.51, and 5.63 eV, respectively, based on the Tauc relationship [24]. Compared with pure Sm2O3 and pure Al2O3, the band gaps of three various stacked gate dielectrics showed a value balance [25]. Also, this section investigates the valence band maximum (VBM) of various stacked gate dielectrics, as the valence band alignment is crucial for assessing the interface quality. As shown in Figure 5a, the band gap values of InP substrates were derived from XPS measurements, while the valence bands of samples S1, S2, and S3 were deduced from the absorption spectra by linear extrapolation. Based on Kraut's method [26], we also calculated the valence band shift (ΔEV) to evaluate the valence band electronic structure of the samples. By using Sm 3d5/2 and In 3d core-level spectra, the ΔEV of high-k/InP gate stacks was determined based on the following formula:

$$
\Delta \mathbf{E}\_{\rm V} = (\mathbf{E}\_{\rm In\ 3d} - \mathbf{E}\_{\rm V})\_{\rm In\ } - (\mathbf{E}\_{\rm Sm\ 3d} - \mathbf{E}\_{\rm V})\_{\rm high-k} - (\mathbf{E}\_{\rm In\ 3d} - \mathbf{E}\_{\rm Sm\ 3d})\_{\rm high-k/In\ } \tag{3}
$$

where EIn 3d (InP) and ESm 3d (high-k) corresponding to the core-level positions are extracted to be 445.8 and 1084.3 eV. In addition, the Ev (InP) and Ev (high-k) represent the VBM (Valence-Band Maximum) of the bulk materials. The values of ΔEv are calculated as 1.87, 1.82, and 1.76 eV, respectively, based on the binding energy difference in the highk/InP structure. Meanwhile, the value of the conduction band offset (ΔEc) is obtained by subtracting the extracted ΔEv and the band gap of the InP (1.34 eV) from the band gap of dielectric layers [27].

$$
\Delta \mathcal{E}\_{\mathbb{C}} \left( \text{high}-\text{k}/\text{InP} \right) = \mathcal{E}\_{\mathbb{S}} \left( \text{high}-\text{k} \right) - \Delta \mathcal{E}\_{\mathbb{V}} (\text{High}-\text{k}/\text{InP}) - \mathcal{E}\_{\mathbb{S}} (\text{InP}) \tag{4}
$$

As shown in Figure 5b, the ΔEc values for the three samples were calculated as 2.28, 2.35, and 2.53 eV. According to previous reports in the literature, ΔEc is related with the tunneling leakage current. The higher ΔEc indicates that the leakage current of the Sm2O3/Al2O3/InP samples is smaller.

**Figure 4.** The determination of band gaps for sample S1, S2, and S3.
