Investigation of the excitations of plasmons and surface exciton polaritons in monoclinic gadolinium sesquioxide by electron energy-loss spectroscopy and plasmon spectroscopic imaging

The monoclinic gadolinium sesquioxide (denoted as m-Gd2O3) with its lower crystal symmetry exhibits larger dielectric permittivity (κ) than the cubic Gd2O3 (denoted as c-Gd2O3). Recently, a few nanometers thick m-Gd2O3 thin film has been successfully epitaxially grown on a GaN substrate as a promising candidate gate oxide in metal-oxide-semiconductor field-effect transistors (MOSFETs). Thus, it is important to understand the electronic excitations in m-Gd2O3 and investigate them by electron energy loss spectroscopy (EELS) performed with aloof electron beams and electron diffraction to gain the spatial and momentum resolutions. In this study, using scanning transmission electron microscopy combined with EELS (STEM-EELS) in the aloof electron beam setup, we observed low-loss spectral features at 13 eV and 14.5 eV at the specimen edge in a grazing incidence and the material interior, which can be interpreted as a surface plasmon (SP) and a volume plasmon (VP), respectively. Surface exciton polaritons (SEPs), which represents surface resonances associated with excitonic onsets above the bandgap, were also observed at about 7, 10.2, and 36 eV energy loss. Their surface excitation character was confirmed by energy-filtered transmission electron microscopy spectrum imaging (EFTEM-SI) and using relativistic energy versus-momentum (E–k) map calculations. The momentum (q)-dependent EELS indicates that the SEP features near the bandgap represented a function of q and revealed a nondispersive behavior for VP and SEP at 36 eV. The oscillator strengths for VP and SEP at 36 eV dropped at different q values along with different q directions, revealing the anisotropic electronic structures of m-Gd2O3.


Introduction
Gadolinium oxide (Gd 2 O 3 ) with a large bandgap of about 5.3 eV (ref. 1) and high-permittivity constant (3 r or k ¼ 14 to 20) 2,3 has attracted much attention in the microelectronic community as a potential high-k dielectric material for applications in complementary metal-oxide-semiconductor (CMOS) and metaloxide-semiconductor eld-effect transistors (MOSFETs). The k values ranging from 14 to 20 suggest a $4 nm thickness to satisfy the requirement of a 1 nm equivalent oxide thickness (EOT). Here, the EOT is equal to t high-k (k SiO 2 /k high-k ), where t high-k is the thickness of high-k dielectrics and k SiO 2 ¼ 3.9 is the dielectric constant of SiO 2 . The growth of Gd 2 O 3 lms on various semiconductor substrates with abrupt interfaces and single domain structure is required to prevent the leakage and decrease the capacitance induced by grain boundaries and interfacial layers formed under annealing during the fabrication of CMOS and MOSFET devices. The cubic phase Gd 2 O 3 (c-Gd 2 O 3 , space group Ia 3) lm with a single domain structure has been successfully epitaxially grown on GaAs, 2,4 Si, 3,5 and Ge 6 substrates when the lm thickness was less than 5 nm. However, aer increasing the lm thickness above 8 nm, depending on the substrates, to improve the gate capacitance, the epitaxial c-Gd 2 O 3 lms tend to transform from the cubic phase to the monoclinic phase. 6,7 Most recently, monoclinic phase Gd 2 O 3 (m-Gd 2 O 3 , space group of C2/m) was stabilized in the thin lms and the bulk form via epitaxial growth on a GaN substrate 8 and by doping during the fabrication processes. 9 Most importantly, the k value of m-Gd 2 O 3 was higher than 20 due to its crystal symmetry, 10 which leads to an essential improvement of the EOT values. Therefore, a deeper understanding of the electronic band structure, including bandgap and band offset for m-Gd 2 O 3 lm/semiconductor heterostructures, becomes crucial for further CMOS and MOSFET microelectronic technology applications.
It was found that 10 nm-thick Gd 2 O 3 lms minimize the effect of moisture absorption on the electrical performance. 8,11 However, technologies beyond the 16 nm CMOS require the combination of high-carrier-mobility semiconductors and high k gate dielectric for further reducing the EOT to less than 1 nm. 11 The thickness of the m-Gd 2 O 3 lms on various semiconductor substrates is restricted in the range of 4 to 8 nm when considering an EOT value less than 1 nm. Furthermore, the restricted thickness makes it even more challenging to investigate the electronic excitations in m-Gd 2 O 3 thin lms and exclude the effects of interface plasmons generated in the heterostructures. [12][13][14] Thus, it is rst necessary to understand the electronic excitations in bulk m-Gd 2 O 3 material.
The information about electronic excitations, particularly concerning transitions between valence and conduction bands in m-Gd 2 O 3 , studied by electron energy loss spectroscopy (EELS) and theoretical band structure calculations, are lacking in the literature in contrast to c-Gd 2 O 3 . 14-16 Shu et al. investigated the core-level electronic excitations of c-and m-Gd 2 O 3 by EELS. 14 No distinguishable difference for the Gd N 4,5 -edge excited from the occupied 4d orbital states to the unoccupied 4f orbital states was observed in both c-and m-Gd 2 O 3 . In contrast, the O K-edge exhibited distinct differences in both the spectral features and energies due to the different Gd and O coordination and Gd-O bond lengths. 14 Furthermore, Shu et al. also reported some differences in the low-loss region between c-and m-Gd 2 O 3 , however, without detailed analysis for m-Gd 2 O 3 . 14 Besides, Gd 2 O 3 has a larger bandgap of about 5.3 eV and the interband transitions generating weakly bound delocalized excitons presumably of the Wannier-Mott type readily build up collective resonances at the material surface. Furthermore, the surface resonances associated with transverse excitonic onsets could be assigned to surface exciton polaritons (SEPs). 13,14,17 Indeed, the surface-related excitations will dominate if the material thickness is continuously decreased. Thus, the SEPs modes would be much more easily observed in the thinner thickness of m- In this work, the electronic excitations in m-Gd 2 O 3 were systematically studied by low-loss EELS with nonpenetrating incident electron beam (aloof excitation) in scanning transmission electron microscopy (STEM) mode and electron diffraction mode to gain both spatial and momentum (q) resolution.
Experimental c-Gd 2 O 3 powders (99.99% purity, ACROS*) were used as the starting material, pressed as a pellet, and then calcined in air at a temperature above 1200 C to form the m-Gd 2 O 3 . 9,14 A Bruker D8 X-ray diffractometer was used to determine the phase purity and crystallinity for the synthesized m-Gd 2 O 3 pellets. TEM specimens were prepared using a tripod polishing technique and then thinned by Ar + ion milling operated at 5 kV until a hole formed, and then operated at 0.3 kV to remove the surface amorphous layers. 13,14 Microstructures and electronic excitations were examined using a Thermo Fisher Themis 300 [(S) TEM] equipped with an electron monochromator and Gatan Image Filter (GIF, model Quantum 965) operated at 200 kV. The energy resolution with electron monochromator was 0.2 eV throughout the STEM-EELS experiments. The momentum (q)dependent EELS experiments were carried out in the diffraction mode with q resolution of 0.015Å À1 . Real-space energy-ltered TEM (EFTEM) spectrum-imaging (EFTEM-SI) with a tunable energy-selection slit was performed on a JEOL 2100F (S)TEM equipped with a Gatan Image Filter (GIF, Tridiem 863), which was operated at 197 kV accelerating voltage. The singlescattering EELS distributions were derived by deconvolution from the raw EELS data, which was performed by removing the zero-loss peak either by tting a pre-measured zero-loss peak from vacuum or removing plural scattering with the Fourier-log method. Then, the subsequent Kramers-Krönig analysis (KKA) was conducted using a DigitalMicrograph soware package (Gatan Microscopy Suite, Gatan-AMETEK) as described elsewhere. [18][19][20] The scattering probabilities of energy versusmomentum (E-k maps) and aloof STEM-EEL spectra as a function of impact parameter were calculated by Kröger's equation 21 and equations within ref. 22 and 23 in MATLAB scripts. The dielectric data of m-Gd 2 O 3 was taken from the KKA result.

Results and discussion
Both phase purity and crystallinity of the synthesized m-Gd 2 O 3 were conrmed by X-ray diffraction (XRD) in the previous report. 14 Because the b angle between the (100) and (001) planes for m-Gd 2 O 3 is $100.13 , it is essential to obtain electron diffraction (ED) patterns and related TEM and STEM images along the [010] orientation, which displays this characteristic b angle. Fig. 1(a) shows a representative high-resolution TEM (HRTEM) image of m-Gd 2 O 3 recorded from the edge of the grain with the size of a few mm. It is a clean edge without any amorphous or damaged area caused by Ar + bombardment. Fig. 1(b) presents the corresponding selected-area electron diffraction (SAED) pattern of m-Gd 2 O 3 collected along the [010] zone axis from the area shown in Fig. 1(a). The d-spacings of the (200) and (001) indexed diffraction spots nearest to the central transmitted spot were 0.67 nm and 0.851 nm, respectively, which is in agreement with the earlier reported XRD data for m-Gd 2 O 3 . 14 The angle between the two oriented axes was measured at about 100 , which is close to the expected value of the b angle for m-Gd 2 O 3 . Furthermore, to examine the material structure at the atomic scale, the high-resolution high-angle annular dark-eld (HAADF) STEM imaging of m-Gd 2 O 3 was performed along the [010] projection [ Fig. 1(c)]. The contrast of the HAADF STEM images usually follows the atomic number (Z) dependence, Z n , where n is usually between 1.3 and 2, the so-called Z-contrast. 24 Although the Gd and O atomic columns along the [010] zone axis are well-separated from each other [see illustrated atomic structure in Fig. 1(d)], it is hard to observe a clear contrast is generated from the O atomic columns due to the large atomic number difference between Gd (Z ¼ 64) and O (Z ¼ 8). Thus, the bright dots in Fig. 1(c) represent the Gd atomic columns, and their arrangements are consistent with the illustrated atomic structure from the same orientation [see Fig. 1(d)]. The corresponding intensity prole measured along the red dot line in Fig. 1(c) is shown in Fig. 1(e). The average distance between the two Gd atomic columns was 0.36 nm [ Fig. 1(e)], which is consistent with the expected distance in Fig. 1(d). These results unambiguously conrm the monoclinic symmetry of the synthesized Gd 2 O 3 .
While performing EELS in the STEM mode (STEM-EELS), it is possible to preserve the spatial resolution and operate with nonpenetrating electron beam setups when the electron probe is sequentially positioned at the different positions along a chosen direction from the material interior to vacuum. Signal delocalization enables in this case the acquisition of the EELS spectra even when the electron beam is located at 2 nm or farther from the grain surface. Such an aloof setup can eliminate knock-on damage and signicantly reduce the beaminduced ionization damage. 18,25 Fig. 2(a) shows the EELS spectra of m-Gd 2 O 3 recorded using the aloof beam at the different positions from the material interior to vacuum, as indicated by the circles in the HAADF STEM image inset in Fig. 2(a). The low-loss EELS spectrum of c-Gd 2 O 3 (gray curve) is also shown in Fig. 2  suggests that the peak experimentally observed at 14.5 eV energy loss can be interpreted as a volume plasmon (VP). This value is close to 14.6-15 eV, which was reported earlier for VP in Gd 2 O 3 . 14, 18 The energy of the volume plasma resonance, ħu p , for the particular excitonic system can be approximated as follows. 18  Fig. 2(b)] unlike the interpretation of VPs suggested in the literature. 15,16 An assignment of this spectral peak will be discussed in more detail below. Fig. 2(d) shows the experimental EEL spectra recorded for various thicknesses at the accelerating voltage of 200 kV. The experimental EEL spectra indicate that both the VP at 14.5 eV and the peak at 36 eV energy loss increased their oscillation strength by increasing the thickness from 0.6l to 1.5l (l is the inelastic mean free path. The log-ratio (relative) method was considered to measure the sample thickness using the DigitalMicrograph soware package). The enlarged low-loss EEL spectra are redrawn [see inset in Fig. 2(d)] to illustrate the bandgap measurements.
Cherenkov radiation (CR) can be excited when the material has high dielectric constant or refractive index (n), and the TEM accelerating voltage is high enough to induce signicant relativistic effects. The differential scattering cross-section for the volume losses including CR losses is described by the following equation. 19 where 3(u) ¼ 3 1 (u) + i3 2 (u) is the complex dielectric function, U is the solid angle of scattering, E is the energy loss, D is the thickness of the specimen in units of the mean free path length for inelastic scattering, q E ¼ E/2gT is the characteristic scattering angle, n is the velocity of incident electrons, and c is the speed of light. In this study, the 3 1 value in m-Gd 2 O 3 was varied from 4.5 at u / 0 to 7 at the energy loss #5 eV [see Fig. 2 The accelerating voltage used for EELS measurement was 200 kV, yielding n of about 0.7c. The conditions satised the CR excitation criterion of (n/c) 2 3 > 1. 19,21,23,30,31 The CR excitation could therefore appear as a broaden feature at the energy loss #5 eV, and affect the KKA results and determination of the bandgap energy. In addition, the more intensive CR excitation generated with increasing specimen thickness tended to shi of the bandgap toward lower energies from 5.1 eV to 4.9 eV [see Fig. 2

(c)].
To evaluate the CR effect, we rst calculated the relativistic energy versus-momentum (E-k maps) for Gd 2 O 3 slabs of 50 nm, 100 nm, and 150 nm in thickness at different accelerating voltages varying from 30 kV to 200 kV, respectively, which were calculated using Kröger's equation, 21 as shown in Fig. 3. From the calculated E-k maps, the VP at 14.5 eV (marked by the purple arrows) enhanced its intensity by increasing both the accelerating voltages and thickness, thus indicating its nondispersive character. For the 50 nm-thick m-Gd 2 O 3 slab, CR excitation showed distinct dispersion features near the bandgap onset below 5 eV (marked by red arrows) when the accelerating voltage was 100 kV. For m-Gd 2 O 3 slabs of 100 nm and 150 nm in thickness, the CR excitations displayed dispersion features near the bandgap onset below 5 eV (marked by red arrows) at all the accelerating voltages. The related relativistic loss probabilities per unit electron path length along the electron trajectory and integrated over the k range up to 0.03Å À1 are shown in Fig. 4. Fig. 4(a), (c), and (e) present thickness-dependent EELS spectra calculated for different accelerating voltages. Similar to Fig. 3, the VP at 14.5 eV and the peak at 36 eV energy loss were observed regardless of the chosen thicknesses and used the accelerating voltages. However, the oscillation strength of the peak at 36 eV energy loss increased with the increasing accelerating voltages in agreement with the report. 32 The same EEL spectra shown in Fig. 4(a), (c), and (e) are redrawn in Fig. 4(b), (d), and (f) to illustrate the bandgap measurements. With increasing specimen thickness and accelerating voltages, the generated CR tended to shi the bandgap toward lower energies from about 4.95 eV to 4.9 eV. The discrepancy in the bandgap measurements between the experimental spectra (Fig. 2) and the calculated spectra (Fig. 4) could be due to different integrated k ranges. This will be discussed in more detail in Fig. 7. Thus, to minimize the CR effect, it is recommended to reduce the accelerating voltage to less than 60 kV. 20,31 Based on our calculations, the accelerating voltage should be less than 30 kV, when n is about 0.33 c, to satisfy the condition (n/c) 2 3 1 < 1. However, decreasing the accelerating voltage to 30 kV is practically difficult due to the limitations of available high voltage settings, stability, and tedious alignments in both TEM and Gatan GIF systems needed for such changes. Thus, the EEL spectra in Fig. 2 and 7 were recorded with a sufficient thickness of 50 nm to suppress the surface excitations by analyzing the material interior 33 and minimizing the CR excitation in the spectral region #5 eV. Furthermore, the KKA results in Fig. 2(b) were carefully processed to remove the zero-loss peak and iteratively remove the surface losses and other retarding effects as described in the literature. 20 To investigate surface-related resonances such as surface plasmons (SPs), the aloof electron beam was continuously positioned at the specimen edge at the grazing incidence and a few nanometers away from the specimen edge. The red spectrum in Fig. 2(a) obtained at the grazing incidence at the specimen edge, which shows that the VP peak was redshied from about 14.5 eV to 13 eV energy loss and the intensity of the spectral feature at about 36 eV energy loss was signicantly decreased. The spectral peak at about 13 eV energy loss can be interpreted as an SP because the small negative values of 3 1 in this energy range lead to a maximum in the energy loss function f Imf À1 3ðuÞ þ 1 g at 13 eV [see the red spectrum in Fig. 2(c)]. 13,14,18,25 Aer moving the electron beam from the specimen edge into the vacuum [e.g., see the blue, cyan, and pink spectra in Fig. 2(a)], the oscillation strength of the SP at about 13 eV decreased with the distances, indicating the presence of evanescent wave elds of SPs. 13,14,18,25 Interestingly, the broad shoulder at about 7 and 10.2 eV energy loss decreased much slower than the SP peak at 13 eV energy loss, and further showed a prominent spectral onset at about 7 eV energy loss [e.g., see the pink spectrum in Fig. 2(a)], conrming the surface character of the related excitations. The interband transitions generating weakly bound delocalized excitons presumably of the Wannier-Mott type readily build up collective resonances at the material surface. Furthermore, the surface resonances associated with transverse excitonic onsets could be assigned to surface exciton polaritons (SEPs) if the condition 3 2 > j3 1 j $ 0 is fullled. 13,14,17 Indeed, the excitonic and/or interband transitions from the O 2p to the Gd 5d states can contribute to the spectra in the low-loss range from 7 to 11 eV, 14 corresponding to the strong JODOS bands at about 6.5, 9.5, and 11.9 eV energy loss [ Fig. 2(d)]. Therefore, it is reasonable to suggest that the spectral features at about 7 eV and 10.2 eV energy loss can be interpreted as SEPs.
The interband transitions and plasmon losses can be visualized in real space using EFTEM-SI in the selected specic energy loss range. 14,17,18 EFTEM-SI was performed to examine the SEP, SP, and VP excitations in m-Gd 2 O 3 with a 2 eV energy window centered at 7, 13, 15 eV, and 36 eV energy loss [see in Fig. 5(b)], where the related spectral features were found. Fig. 5(a) shows the corresponding zero-loss TEM image of the oxide area where EFTEM-SI analyses were conducted. The intensity maximum in the EFTEM SI image representing the spatial location of the SEP at about 7 eV and the SP at 13 eV energy loss evidently visualizes the related surface excitations at the edge of an oxide grain with the evanescent wave eld decaying into the vacuum. In contrast, the intensity maximum of the VP at about 14.5 eV energy loss and of the broad band at about 36 eV energy loss was strongly localized within the bulk material interior, thus unambiguously indicating the volume character of the excitations.
To gain deeper physical insights into the aloof STEM-EEL spectra shown in Fig. 2(a) as a function of impact parameter b, the relativistic E-k maps 22,23 were calculated for a 50 nm thick m-Gd 2 O 3 layer and shown in Fig. 6(a). Fig. 6(b) shows related relativistic loss probabilities per unit electron path length along the electron trajectory and integrated over the k range up to 0.03 A À1 . The calculated E-k maps in Fig. 6 reveal the predominant VP at about 14.5 eV energy loss when the electron probe was positioned inside the slab at b ¼ À15 nm. For the electron probe sequentially located at the edge in a grazing incidence (b ¼ 0 nm) at b ¼ 6 and 15 nm away from the edge, the SP at about 13 eV energy loss was initially greatly enhanced at the b ¼ 0 nm and then its oscillation strength decreased with increasing b values, thus indicating its surface character in the presence of evanescent wave elds. The calculations also successfully reproduced the SEPs at about 7 eV and 10.2 eV energy loss at b $ 12 nm. Both calculated E-k maps in Fig. 6(a) and corresponding STEM-EELS spectra in Fig. 6(b) appear in good agreement with the experimental results presented in Fig. 2(a).
As far as the spectral feature at about 36 eV energy loss are concerned [the red spectrum in Fig. 2(a)], this peak appeared at the specimen edge and then increased its oscillation strength with increasing specimen thickness [see Fig. 2(c)]. Most importantly, contrary to the SP at 13 eV and the VP at 14.5 eV energy loss, this peak did not shi while the probe moved from the edge to the material interior. Furthermore, the peak also decayed into the vacuum at about 6 nm from the edge measured from the intensity prole in the corresponding EFTEM-SI image [ Fig. 5(b)]. This was consistent with the calculated relativistic loss probabilities spectra for b ¼ 6 nm [ Fig. 6(b)]. Interestingly, the decay length of about 6 nm is longer than the delocalization of about 1.5 nm calculated using the formula, 0.5l/(q E 3/4 ), where l is the wavelength and q E is the relativistic characteristic angle, 18 implying that the 36 eV peak might be associated with both bulk and surface excitations. Indeed, the onset of the peak at about 36 eV energy loss closely correlates with the broad 3 2 feature at about 33.2 eV energy loss and the corresponding oscillating 3 1 structure [ Fig. 2(b)]. This 3 2 feature signies the diffused oscillator strengths induced by the bulk transverse interband transitions from deep 5p states to 5d bands, 14 which are related to a broad feature at the same energy loss in the JODOS [ Fig. 2(d)]. Since the criteria condition of 3 2 > j3 1 j $ 0 discussed above is fullled, this spectral feature can also be interpreted as the excitation of SEPs in m-Gd 2 O 3 .
The momentum (q)-dependent EELS (q-EELS) is a powerful method to examine the excitations in solids varying both the relatively large momentum transfer (Dq) and the energy loss DE. 18,19,25 Fig. 7(a) and (b) show the q-EELS spectra acquired along the [001] and [100] directions up to the Brillouin zone (B. Z.) boundary for q values of about 0.35Å À1 and 0.45Å À1 , respectively. Fig. 7(c) presents the EEL spectra corresponding to the q values of 0.018Å À1 and 0.45Å À1 acquired along the [100] direction to enhance the observed differences. From the spectra in Fig. 7(a)-(c), a few interesting ndings have to be pointed out. At rst, the VP at about 14.5 eV energy loss displays a nondispersive behavior along the [001] and [100] directions probably due to conning the nearby interband transitions. 18,25 Meanwhile, the SEP at about 36 eV energy loss also exhibits a nondispersive behavior, resulting from its band structure with a relatively small curvature. 15,18,25 In the second, the plateau between 5 to 10 eV energy loss was observed [see the black color spectra in Fig. 7(a) and (b)] when the q was less than 0.2Å À1 and then increased the oscillator strengths to enhance the SEP features at about 7 eV and 10.2 eV energy loss when the q was larger than 0.2Å À1 [see the red color spectra in Fig. 7(a) and (b) and see the shadowed region I in Fig. 7(c)]. In the third, the measured bandgap energy varied from about 4.4 eV to 5.4 eV. In the fourth, the spectral features at about 17.8 eV energy loss and the Gd O 2,3 -edge (21 to 28 eV energy loss) enhanced their oscillator strengths with increasing q values [see shadowed regions II and III in Fig. 7(c)]. Finally, the oscillation strength of the SEP at about 36 eV energy loss increased with increasing q values and became more intensive than the VP peak at q > 0.25 A À1 as one can see on comparing the black and red spectra in Fig. 7(a)-(c).
In general, the excitation probability d 2 s dudU is inversely proportional to q 2 , according to the following the equation: 18,25 where q is momentum transfer. From eqn (3), the excitation probability should decrease with increasing q values, leading to a decrease in the oscillator strengths. In addition, the VP dispersion usually exhibits a parabolic dispersion upward to higher energies at larger q values accompanied with decreasing oscillator strengths and peak broadening in terms of the fullwidth at half maxima (FWHM, DE 1/2 ¼ ħ/s, where ħ is Planck's constant and s is relaxation time) beyond the cutoff wavevector (q c ). 18,25 Although both the VP and the SEP at about 36 eV energy loss display the nondispersive behavior with no distinct changes of the DE 1/2 [see Fig. 7(a) and (b)], this is hardly reconcilable with a plasmon behavior when the DE 1/2 should increase rapidly with q. 18,25 However, Fig. 7   indicating the anisotropy of the electronic structures of m-Gd 2 O 3 . The further inspection of the curves in Fig. 7(d) indicates different dropped slopes for the VP and the SEP at about 36 eV energy loss, suggesting the different damping mechanisms. The plasmons, as collective oscillations of valence band electrons, would induce the kinematically allowed single-electron excitations and then start damping because the plasmons transfer all of their energy to excite single-electron transitions and create the electron-hole pairs when the plasmon wavevector q exceeds the q c values. 18,25 On the contrary, the SEP at about 36 eV energy loss may be treated here as an intrinsic characteristic of interband transitions, which is a kind of single-electron excitation. This is because m-Gd 2 O 3 with a sufficient thickness of 50 nm was used for q-EELS measurements to suppress its surface character in the material interior. 29,33 Thus, it appears that the SEP at about 36 eV energy loss was only damped by the interactions between the excitons. Therefore, the rst step needed for the transfer of all the SEP energy to excite a single-electron transition and create an electron-hole pair was absent. This could reasonably explain the different damping rates observed in the study for the VP and the SEP excitations.

Conclusions
The electronic excitations of valence electrons in monoclinic Gd 2 O 3 were thoroughly studied using STEM-EELS with the aloof electron beam and electron diffraction to gain both the spatial and momentum resolutions. By positioning the electron probe at the specimen edge in a grazing incidence and in the material interior, the SP at about 13 eV and the VP at 14.5 eV energy loss were observed. Intriguingly, unusual surface-related excitations, SEPs, were observed at about 7, 10.2, and 36 eV energy loss with an evanescent wave eld decaying into the vacuum as it was conrmed by EFTEM SI in agreement with the relativistic energy versus-momentum (E-k) maps calculations. The momentum (q)-dependent EELS measurements showed that the SEP features at about 7 and 10.2 eV energy loss appeared to be a function of q and revealed the nondispersive behavior for both VP at 14.5 eV and SEP at about 36 eV energy loss. Indeed, variations in the critical wavevector q c were observed in different q directions, indicating the anisotropy of the electronic structure of monoclinic Gd 2 O 3 .

Conflicts of interest
There are no conicts of interest to declare.