A novel engineered oxide buffer approach for fully lattice-matched SOI heterostructures

Epitaxial (epi) oxides on silicon can be used to integrate novel device concepts on the canonical Si platform, including functional oxides, e.g. multiferroics, as well as alternative semiconductor approaches. For all these applications, the quality of the oxide heterostructure is a key figure of merit. In this paper, it is shown that, by co-evaporating Y2O3 and Pr2O3 powder materials, perfectly lattice-matched PrYO3(111) epilayers with bixbyite structure can be grown on Si(111) substrates. A high-resolution x-ray diffraction analysis demonstrates that the mixed oxide epi-films are single crystalline and type B oriented. Si epitaxial overgrowth of the PrYO3(111)/Si(111) support system results in flat, continuous and fully lattice-matched epi-Si(111)/PrYO3(111)/Si(111) silicon-on-insulator heterostructures. Raman spectroscopy proves the strain-free nature of the epi-Si films. A Williamson–Hall analysis of the mixed oxide layer highlights the existence of structural defects in the buffer, which can be explained by the thermal expansion coefficients of Si and PrYO3.

Major issues in heteroepitaxy are (i) lattice and thermal mismatch between the film and the substrate, often resulting in unacceptable defect densities and/or cracking; (ii) difference in energetics between the epilayer and the substrate, determining the wetting or non-wetting behavior of the former; and (iii) thermodynamical instability of the epi-film in contact with the substrate. An interesting example, which illustrates challenges (a) and (c), is provided by the above-mentioned epi-Si/(La x Y 1−x ) 2 O 3 /Si(111) heterostructure. The ternary oxide was deposited by MBE, using molecular oxygen and thermally evaporated La and Y with the target to achieve a layer lattice matched to the Si substrate. It was demonstrated that, by incorporating a small amount of La (larger atomic radius) into the growing bixbyite Y 2 O 3 film, the lattice mismatch of −2.4% between Y 2 O 3 and Si could be changed to +0.18% for x = 0.29. However, one disadvantage of the (La x Y 1−x ) 2 O 3 system is that the lattice window accessible is limited to x ∼ 0.35. For higher La concentrations, phase separation occurs, with formation of hexagonal La 2 O 3 domains in the main cubic Y 2 O 3 matrix [22].
In the present paper, it is proven that an epitaxial insulator perfectly lattice matched to Si(111) can be obtained by MBE by suitably mixing isomorphic oxides, Y 2 O 3 and Pr 2 O 3 , in their cubic phase. Both these oxides indeed crystallize in the bixbyite structure, which can be thought of as an oxygen-deficient fluorite, where the lattice parameter is doubled and an ordered oxygen vacancy superstructure exists by removing a quarter of the oxygen atoms [23,24]. The Y 2 O 3 and cub-Pr 2 O 3 lattice constants are 2.4% smaller (a y 2 o 3 = 1.604 nm) and 2.7% bigger (a cub-Pr 2 O 3 = 1.1152 nm) than twice the Si lattice parameter (a Si = 0.5430 nm), respectively. By controlling the co-evaporation of the Y 2 O 3 and Pr 2 O 3 sources and the deposition temperature, the (Pr x Y 1−x ) 2 O 3 ternary system can span the complete lattice window 0 < x < 1 without running into phase separation, matching the room temperature (RT) Si lattice constant for x = 0.47 (hereafter, the Si-lattice-matched mixed oxide is denoted as PrYO 3 for the sake of simplicity). In addition, it is shown that an epi-Si/PrYO 3 /Si(111) SOI heterostructure characterized as fully lattice matched at RT is not necessarily free from structural defects. Hightemperature measurements demonstrate that a more complex treatment, taking the different thermal expansion coefficients of oxide and the Si substrate into account, is required to obtain optimized buffer layers.

Experimental
Four-inch B-doped Si(111) wafers (ρ = 5-15 cm) were wet-cleaned according to a standard recipe, recently reported in detail [25]. Loaded onto the DCA 600 MBE machine, samples were first annealed at 700 • C for 5 min in ultra high vacuum (UHV) (base pressure 10 −10 mbar) to prepare high-quality (7 × 7) Si(111) reconstructed surfaces. Then epi-oxide thin films were deposited by simultaneous electron beam evaporation of Y 2 O 3 and Pr 2 O 3 powder materials from pyrolytic graphite crucibles at a substrate temperature of 780 • C and a growth rate of 0.1 nm s −1 . Tuning the Y 2 O 3 /Pr 2 O 3 ratio resulted in (Pr x Y 1−x ) 2 O 3 films with about x = 0.5, as estimated by XPS measurements [26]. The PrYO 3 oxide was then overgrown with epitaxial Si at a substrate temperature of 625 • C and a growth rate of 0.02 nm s −1 . The thickness and roughness of the epilayers composing the heterostructures were measured by x-ray reflectivity (XRR) (not shown). Samples were extensively investigated by x-ray diffraction (XRD) techniques. A Rigaku DMAX 1500 instrument equipped with Cu K α radiation was employed for specular θ-2θ scans, whereas a Kappa-Six circle diffractometer was used at the ID 32 beamline of the European Synchrotron Radiation Facility (ESRF) in Grenoble for synchrotron radiation grazing incident x-ray diffraction (SR-GIXRD) measurements. Here, a beam energy of 10.6 keV was selected, resulting in critical angles α c of 0.17 • , 0.22 • , and 0.26 • for total reflection at the Si, Y 2 O 3 and Pr 2 O 3 surfaces, respectively. SR-GIXRD in-plane scans are recorded in the following with respect to the Si(111) surface unit cell of hexagonal symmetry (indicated by the apex S) [27]. However, for the sake of simplicity, Bragg peaks are also labeled with respect to the bulk cubic unit cells of Si, Pr 2 O 3 and Y 2 O 3 . High-resolution φ-scans and high-temperature specular θ -2θ scans were performed by means of a Rigaku SmartLab diffractometer with a Cu K α source. Finally, Raman spectroscopy was applied to characterize the top epi-Si layers. It is a powerful tool to assess the extent of strain in semiconducting materials, since it is nondestructive, does not require sample preparation, provides a quick response and allows us to vary the analysis depth by tuning the laser wavelength [28]. An Invia Renishaw equipment with a wavelength of 364 nm was utilized to confine the excitation within the Si epilayers (the probing depth is about 12 nm).
The structural characterization of the epi-Si/PrYO 3 /Si(111) system is presented in the following section. For reference, the corresponding data of epi-Si/Y 2 O 3 /cub-Pr 2 O 3 /Si(111) heterostacks, widely described in [26], are included in the figures.  and in-plane strain variation of about 1% were estimated. Hence, the W-H study reveals that, although the oxide buffer is perfectly lattice matched to the Si substrate, it is not free from structural defects causing lattice micro-strain and tilt and limiting the long-range order. A point will be made on that at the end of the section.

Results and discussion
The anti-parallel indexing of the in-plane Si and oxide Bragg peaks is applied, due to the so-called type-B stacking configuration of ionic insulator heterostructures on Si(111) [17]. Here, it is recalled that a type-B (111)-oriented face centered cubic (fcc) epilayer has its stacking vector rotated by 180 • around [111] with respect to the type-A stacking vector of the Si(111) substrate [33]. Although it is well known that the Y 2 O 3 (111)/cub-Pr 2 O 3 (111) bilayer buffer grows on Si(111) in a type-B fashion [17], the stacking configuration of the  ( figure 5(a)). The former set of reflections mainly originates from the semi-infinite Si(111) substrate with type-A orientation, whereas the latter group of Bragg peaks clearly indicates the presence of some type-B orientation in the heterostructure. In contrast, the φ scan on the (200) Bragg peak, which is allowed only for the bixbyite structure, exhibits only three reflections at φ = 30 • , 150 • and 270 • ( figure 5(b)). It is concluded that the Si lattice-matched PrYO 3 oxide layer has its (111) netplanes oriented according to a type-B stacking configuration and it is free from rotational twins. Combining the data of figure 6 with the in-plane measurements of figure 2, the heterostructure azimuthal orientation can be assigned, resulting in Finally, the Si-Si Raman vibration line of about 20 nm-thick Si(111) epilayers grown on a 10 nm PrYO 3 /Si(111) support system and on a 10 nm Y 2 O 3 /10 nm cub-Pr 2 O 3 /Si(111) heterostructure, respectively, were compared, as illustrated in figure 6. As a reference, the Si-Si Raman line of a bare Si(111) wafer was also measured (solid curve (a)) and its position and width were found to be 520.5 and 3.3 cm −1 , respectively. It is seen that the Si-Si line for the  ) while keeping the Bragg-Brentano diffraction condition satisfied for either Si{200} or Si{400} (see [38] for details about φ scans).
Si(111) epilayer deposited on the mixed oxide (dashed curve (b)) is symmetric and has within the error limits the same position (520.6 cm −1 ) as the substrate feature, indicating that the epi-Si deposited on the Si-lattice-matched PrYO 3 buffer is not strained. However, curve (b) is wider (4.1 cm −1 ) than curve (a), pointing to the presence of structural defects in the epi-Si film, in agreement with the limited long-range order of the mixed oxide buffer. The Raman peak of the epi-Si film grown on the bilayer heterostructure (dashed dotted curve (c)) is asymmetric with a position of 522.1 cm −1 and is much broader (4.9 cm −1 ) than the Si(111) substrate line. The shift of the Raman line reveals in-plane compressive strain in the epi-Si film, whereas peak asymmetry and broadening are attributable to inhomogeneous strain distribution along the layer thickness and/or structural defects, as recently outlined for epi-Si layers on SiGe virtual substrates [28].
The fact that the PrYO 3 lattice is perfectly matched to the Si substrate while exhibiting structural imperfection, as unveiled by the W-H analysis, seems to be contradictory. However, it has to be kept in mind that the XRD analyses were performed at RT. To figure out what happens during the epitaxial process at 780 • C, high-resolution θ -2θ scans were performed around the Si(111) and Si(222) reflections at temperatures up to 725 • C under an N 2 atmosphere. The measured lattice constants in the direction normal to the wafer surface (a ⊥ ) are shown in figure 7 for the Si substrate and the 10 nm-thick PrYO 3 layer (any signal from the epi-Si layer is completely superimposed by the much stronger Si substrate reflection). At RT, the a ⊥ parameters of Si and PrYO 3 are nearly equal according to the matched lattice. However, with increasing temperature, the a ⊥ lattice constant of the mixed oxide increases much faster than that of Si. The main reason for this stronger increase is a significantly larger coefficient of thermal expansion of the oxide. As long as no plastic deformation occurs, the in-plane lattice constant of the oxide is fixed to that of the Si substrate and follows the expansion of Si with increasing temperature. Since the oxide expands more than the Si substrate, this leads to a tetragonal distortion of the oxide lattice, with the oxide a ⊥ lattice parameter expanding faster than expected for the bulk values as the temperature rises. The oxide point at 50 • C was measured after heating the sample to 725 • C and then cooling it down. The fact that this point is very close to lattice constant values measured during the ramp-up from RT to 725 • C indicates that no significant additional relaxation occurred during the high-temperature experiment. The trend of the lattice constants versus temperature is approximated in figure 7 by linear behavior, neglecting any temperature dependence of the expansion coefficients. It is evident that there exists a significant difference (0.0024 nm) between the a ⊥ lattice constants of the two materials at the oxide deposition temperature of 780 • C. The mixed oxide layer of the given stoichiometry is obviously strained at the growth temperature and it probably relaxes plastically by the generation of misfit dislocations, which are responsible for the measured mosaicity and micro-strain. In order to increase the long-range order of the mixed oxide, it is therefore important that lattice matching is achieved at the growth temperature (full circle in figure 7) rather than at RT. To do that, the stoichiometry of the (Pr x Y 1−x ) 2 O 3 has to be changed towards the Y 2 O 3 side (smaller x values). Cooling this structure down to RT would then result in an oxide a ⊥ lattice constant of about 0.5403 nm (the arrow and the empty circle in figure 7). This means that an oxide lattice with a well-defined mismatch at RT must be the goal for further improvement of the epilayer quality.

Conclusions and outlook
It was shown that, by electron gun co-evaporation of Pr 2 O 3 and Y 2 O 3 sources, it is feasible to grow (Pr x Y 1−x ) 2 O 3 epilayers on Si(111) that are perfectly lattice matched at RT. The PrYO 3 epi-films are (111) oriented and single crystalline and exhibit a type-B stacking configuration. At the deposition temperature of 780 • C, the cubic bixbyite structure is the thermodynamically stable phase of both Pr 2 O 3 and Y 2 O 3 . Therefore, no phase separation occurs within the mixed oxide. This means that the (Pr x Y 1−x ) 2 O 3 lattice constant can be tuned without any restriction, and especially in the range 0.47 < x < 1 it is possible to fit the lattice parameter of SiGe alloys up to Si 0.2 Ge 0.8 [34]. This is clearly an advantage compared to the (La x Y 1−x ) 2 O 3 system.
In this case, indeed, La-rich hexagonal domains start nucleating at 600 • C within the cubic matrix for La content x > 0.35, owing to the fact that, at high temperature, hex-La 2 O 3 and not cub-La 2 O 3 is the stable phase. Furthermore, on the PrYO 3 (111)/Si(111) support system, single crystalline, type-A-oriented epi-Si(111) films could be grown, achieving fully lattice-matched and unstrained epi-Si (111) However, the PrYO 3 domain size is rather limited (13 nm). An explanation for this phenomenon was provided by temperature-dependent XRD measurements. At the elevated growth temperature of 780 • C, PrYO 3 grows in a strained state, and misfit dislocations are probably generated at the PrYO 3 /Si(111) substrate interface, limiting in this way the longrange order of the oxide crystallinity. Experiments are ongoing to tune the (Pr x Y 1−x ) 2 O 3 epifilm stoichiometry so that lattice match of the mixed oxide to Si is achieved at the oxide growth temperature instead of at RT. It is then expected that the mixed oxide structural quality will be superior to that of the presented specimen. As a result of high-temperature XRD investigations, an optimization of the growth recipe is ongoing in parallel with further XRD/ TEM studies of the film defect structure to gain a deeper understanding of the factors limiting the lateral size of the mixed oxide domains. Finally, grazing incidence x-ray absorption finestructure (XAFS) experiments at the Y K-and Pr L 3 -absorption edges are planned in order to determine whether the mixed oxide exhibits random atomic-scale ordering or whether there is a preference for or against cation clustering [35]- [37]. Such studies could trigger the development of Eu : (Pr x Y 1−x ) 2 O 3 films as scintillator materials. To optimize the optical activity, it is indeed fundamental that the Eu 3+ activator cations reside solely on the non-centrosymmetric C 2 cation sites of the (Pr x Y 1−x ) 2 O 3 bixbyite crystal, which in principle offers two non-equivalent cation sites with different point group symmeties (C 2 and S 6 ) [23]. In general, the development of engineered oxide heterostructures with tailored properties (e.g. lattice constant) will pave the way for the integration of novel oxide and semiconductor device concepts in Si nanoeletronics.