Engineering the semiconductor/oxide interaction for stacking twin suppression in single crystalline epitaxial silicon(111)/insulator/Si(111) heterostructures

The integration of alternative semiconductor layers on the Si material platform via oxide heterostructures is of interest to increase the performance and/or functionality of future Si-based integrated circuits. The single crystalline quality of epitaxial (epi) semiconductor–insulator–Si heterostructures is however limited by too high defect densities, mainly due to a lack of knowledge about the fundamental physics of the heteroepitaxy mechanisms at work. To shed light on the physics of stacking twin formation as one of the major defect mechanisms in (111)-oriented fcc-related heterostructures on Si(111), we report a detailed experimental and theoretical study on the structure and defect properties of epi-Si(111)/Y2O3/Pr2O3/Si(111) heterostructures. Synchrotron radiation-grazing incidence x-ray diffraction (SR-GIXRD) proves that the engineered Y2O3/Pr2O3 buffer dielectric heterostructure on Si(111) allows control of the stacking sequence of the overgrowing single crystalline epi-Si(111) layers. The epitaxy relationship of the epi-Si(111)/insulator/Si(111) heterostructure is characterized by a type A/B/A stacking configuration. Theoretical ab initio calculations show that this stacking sequence control of the heterostructure is mainly achieved by electrostatic interaction effects across the ionic oxide/covalent Si interface (IF). Transmission electron microscopy (TEM) studies detect only a small population of misaligned type B epi-Si(111) stacking twins whose location is limited to the oxide/epi-Si IF region. Engineering the oxide/semiconductor IF physics by using tailored oxide systems opens thus a promising approach to grow heterostructures with well-controlled properties.


Introduction
With further aggressive scaling of microelectronic devices, silicon (Si) is running more and more into fundamental physical limits. To increase the performance and/or functionality of future Si-based integrated circuits (ICs), global and local integration approaches of alternative semiconductors (IV-IV (e.g. SiGe, SiC), III-V (e.g. GaAs, AlN) and II-VI (e.g. ZnO, CdTe)) on the Si material platform are in consequence intensively studied [1]. Global integration approaches address the deposition of functional semiconductor layers over the whole wafer structure and are typically pursued by wafer supplier companies to further develop their substrate product portfolio [2]. In contrast, integrated device manufacturers (IDMs) focus on the local integration of high-quality semiconductor layers within the processed area of the future device structure [3]- [5]. An important innovation in the field with high commercial impact are layer transfer techniques which are nowadays well suited to tackle global (e.g. silicon-oninsulator (SOI) and germanium-on-insulator (GOI) substrates via combined layer transfer and wafer bonding techniques [6,7]) as well as local (e.g. flip-chip techniques [8], die-to-waferbonding [9] and microstructure printing [10]) integration tasks. The classical heteroepitaxy approach to deposit alternative semiconductor layers (e.g. GaAs [11,12], GaN [13,14], InP [15] etc) with high crystalline quality on Si substrates remains highly attractive due to its costeffectiveness. For example, a recent breakthrough in setting up a cost-effective GaN materials platform was reported by the heteroepitaxial deposition of crack-free, single crystalline GaN layers on Si(001) via AlN buffer layers [16].
Dielectric oxide heterostructures on Si are another promising class of buffer materials with a wide range of properties for the integration of functional semiconductors [17]. It must however be pointed out that, to the best of our knowledge, the quality of the up to nowadays prepared semiconductor (S)-insulator (I)-Silicon (Si) heterostructures grown by two simple, subsequent oxide and semiconductor epitaxy steps has not yet achieved the level of technological relevance.
3 This is mainly due to the fact that the fundamental physical mechanisms of the interaction between alternative functional semiconductors of interest (i.e. SiGe and III-V materials) and the most widely used buffer dielectric materials (i.e. transition and rare earth oxides) are only poorly understood at present. Typical unsolved solid state physics issues, limiting the structural and in consequence electrical properties of such S-I-Si systems, concern for example the control of the growth mode to achieve closed, atomically smooth semiconductor layer structures, the mechanisms at work in the creation of defects in the epitaxial (epi) semiconductor film, the possibility of preparing strained semiconductor layers by heteroepitaxial overgrowth of lattice mismatched oxide buffers etc.
Recently, we introduced single crystalline, (111)-oriented Pr 2 O 3 -Y 2 O 3 double oxide film structures on Si(111) as a flexible buffer layer system to achieve the lattice matched or mismatched integration of functional semiconductors [18]. The advantages of this mixed oxide buffer approach is given by its flexibility to engineer the lattice and interface (IF) properties, as discussed in the following. First, the (111)-oriented Pr 2 O 3 -Y 2 O 3 double oxide films can be grown in the form of truly single crystalline epi layers, characterized especially by a twinfree type B epitaxy relationship with respect to the Si(111) substrate [18,19]. It is noted that the type A/B heteroepitaxy nomenclature refers to the stacking sequence of fcc-related (111)oriented heterostructures on Si(111) substrates, namely whether the (111) layers of the epi film structure exhibit the same stacking vector as the Si(111) substrate (type A) or whether a stacking fault at the epilayer/Si(111) IF rotates the stacking vector in the film by 180 • around the Si(111) surface normal (type B) [20]- [22]. A unique stacking configuration of the oxide buffer is an important precondition to achieve the epi overgrowth of these buffer oxides by truly single crystalline, i.e. stacking twin-free (111)-oriented, fcc-related semiconductor layers (e.g. Si, Ge, GaAs etc). Stacking twin formation in (111)-oriented, fcc-related semiconductor epilayers, integrated on the Si(111) material platform via buffer layer systems, is one of the major defect mechanisms, severely suppressing the achievable crystalline and electrical quality of the functional semiconductor layer (e.g. epi-Si(111)/CaF 2 /Si(111) [23], epi-Si(111)/hex-Pr 2 O 3 /Si(111) [24,25], epi-Si(111)/CeO 2 /Si(111) [26,27] etc). The second advantage of our mixed Pr 2 O 3 -Y 2 O 3 buffer layer approach is given by the fact that both oxides crystallize in the cubic (cub)-bixbyite oxide structure (space group: Ia-3) so that the formation of solid solutions over the whole Pr 2−x Y x O 3 (x = 0 to 2) stoichiometry range is feasible [28,29]. In consequence, with Y 2 O 3 (a = 1.0604 nm) and Pr 2 O 3 (a = 1.1152 nm) lattice dimensions being 2.4% smaller and 2.4% bigger, respectively, than twice the Si lattice (2a = 1.0862 nm), it is possible for example to study the integration of lattice matched (Pr 2−x Y x O 3 (x = 1) buffer) as well as mismatched (Pr 2−x Y x O 3 (x = 1) buffer) epi Si(111) films. The third advantage of the Pr 2 O 3 -Y 2 O 3 double oxide buffer structure is given by the fact that Y 2 O 3 is thermodynamically more stable in contact with Si than Pr 2 O 3 and Y 2 O 3 addition allows therefore to tailor the IF reactivity to achieve the epi Si overgrowth [30]- [32].
In this paper, we report a detailed experimental and theoretical study on the structure and defects of compressively strained epi Si(111) layers grown on lattice mismatched Y 2 O 3 /Pr 2 O 3 /Si(111) support systems. The aim of the paper is (i) to prepare stacking-twin free high-quality epi Si(111)/insulators/Si(111) heterostructures, (ii) to shed light on the fundamental physics mechanisms at work in defining the transition of the stacking information from the ionic oxide buffer to the growing covalent semiconductor layer, and (iii) to evaluate the possibility of creating strained epi Si layers via lattice mismatched oxide heterostructures.

Experimental
Boron-doped Si(111) substrates were cleaned by Piranha and NH 4 F wet etching techniques according to a recipe recently described in detail [33]. The H-terminated Si(111) wafers were loaded into the ultrahigh vacuum (UHV) (base pressure 10 −10 mbar) molecular beam epitaxy (MBE) facility which consists of two separated oxide and SiGe chambers. Prior to oxide deposition in the oxide MBE chamber, the sample was annealed for 5 min at 700 • C to prepare the high quality (7 × 7)-Si(111) surface [34]. The preparation of the 10 nm Pr 2 O 3 /10 nm Y 2 O 3 thick double oxide heterostructure followed a procedure recently summarized in detail elsewhere [18,19,35]. In the following discussion, both metal (Me) oxides are referred to as Me 2 O 3 (Me = Pr, Y) when common insulator characteristics are discussed. After preparing the Y 2 O 3 /Pr 2 O 3 /Si(111) heterostructure in the oxide MBE chamber, the sample was transferred in situ to the separated MBE SiGe setup to avoid the presence of metal contaminations in the epi-Si layers. Epi-Si films with thicknesses of 20 and 130 nm were grown at 625 • C on the Y 2 O 3 /Pr 2 O 3 /Si(111) support, using typically a flux of 1.5 nm min −1 .
An EK 35 reflection high energy electron diffraction (RHEED) apparatus from Staib instruments (E = 15.8 keV) as well as a VSI low energy electron diffraction (LEED) system (E = 85 eV) were employed to control the quality of the epi-Si layer by monitoring the Si(111)-(7 × 7) surface reconstruction. A FEI Tecnai F20 Cs-corrected transmission electron microscope (TEM) was used at TU Dresden to measure high resolution direct lattice crosssection images along the bulk Si 1 10 -direction. These invasive and local TEM measurements were supplemented by ex situ non-destructive x-ray reflectivity and diffraction (XRR and XRD, respectively) studies which yield highly averaged, global information about the sample structure [36]. A laboratory-based Rigaku SmartLab diffractometer (Cu K α -radiation (λ = 0.154 nm)), was used for XRR measurements to characterize the layer structure morphology of the epi-Si/insulator/Si (111) heterostructure. Typically, the x-ray footprint averages over a sample surface of about 1 cm 2 . Quantitative XRR fits were performed to evaluate thickness as well as roughness root mean square (rms) values (given in nanometer (nm)) [37]. Synchrotron radiation (SR)-based XRD studies, having far superior sensitivity and resolution characteristics with respect to laboratory-based XRD equipment, were carried out at the insertion device beamline ID 32 of the European Synchrotron Radiation Facility (ESRF) to study the structure and defect characteristics of the nano-scaled epi-Si/insulator/Si (111) heterostructure [38]. Here, a Kappa-six circle diffractometer was used in the grazing incidence (GI) mode at an x-ray beam energy of 10.6 keV (0.117 nm). Total reflection of the incident 10.6 keV x-ray beam from Si, Y 2 O 3 and Pr 2 O 3 surfaces occurs below the critical angles α c of 0.17 • , 0.23 • and 0.27 • , respectively, allowing thus to carry out non-destructive depth profiling structure studies of the epi-Si/Y 2 O 3 /Pr 2 O 3 /Si(111) heterosystem by decreasing the incident angle α from 0.6 • (bulk sensitive mode) up to 0.1 • (surface sensitive mode). The XRD intensities shown hereafter are given in counts per second (cps) and are indexed in reciprocal hexagonal Si(111) surface (labelled Surf ) H K L coordinates but the Si, Pr 2 O 3 and Y 2 O 3 Bragg peaks are also labelled with respect to their reciprocal cubic bulk (denoted Bulk) lattices [25].
Ab initio calculations were done with the ab initio pseudopotential plane wave code fhi96md [39]. We applied the local density approximation (LDA) for the exchange and correlation energies [40,41] and nonlocal pseudopotentials in the Trouller-Martins scheme [42,43] with 40 Ryd cut-off for plane waves.

X-Ray structure studies
3.1.1. Heterostructure morphology. XRR, RHEED and LEED were applied to study the layer morphology and surface characteristics of the epi-Si/Y 2 O 3 /Pr 2 O 3 /Si(111) heterostructure.
According to the above given growth conditons, a typical XRR scan of about 20 nm thick epi-Si layer on a Me 2 O 3 /Si(111) heterostructure is shown in figure 1(a). For the sake of clarity, the fit (red line) is displaced on purpose from the experimental data (blue line) to demonstrate the excellent correspondence. The sketch on the right side of figure 1 shows the applied fit model which consists of an epi-Si/Y 2 O 3 /Pr 2 O 3 /IF/Si(111) multilayer system. It is noted that the IF layer between Si(111) and Pr 2 O 3 consists of amorphous Pr-silicate and is formed during the hex → cub-Pr 2 O 3 PT [19,44]. Assuming bulk electron densities in the model, the quantitative analysis proves that the various layer thicknesses (bold numbers) reproduce well the targeted growth parameters of the deposited layers and that the IF roughness rms values (italic numbers) are small. Interestingly, the highest IF roughness value is found in the data fitting for the Y 2 O 3 /Pr 2 O 3 IF. This experimental finding is probably an indirect result of the mixing of the two isomorphic oxides Y 2 O 3 and Pr 2 O 3 in consequence of an IF reaction at the oxide/oxide boundary, as recently detected by a detailed synchrotron radiation-grazing incidence x-ray diffraction (SR-GIXRD) [18]. Most importantly, the epi-Si layer surface roughness is very low even for an only 23 nm thick Si layer. The two-dimensional (2D) character of the epi-Si surface is demonstrated by the very streaky nature of the RHEED pattern in figure 1(b) which shows only a very small intensity modulation along the rods. The RHEED image figure 1(b) is recorded with the electron beam aligned along the Si Bulk 110 azimuth and the white arrows depict the reciprocal (1 × 1) unit cell. Using the Si(111) substrate wafer as reference, the spacing of the observed reciprocal (1 × 1) unit cell points to a (111)-oriented epi-Si surface orientation. This assignment is corroborated by the observation of a (7 × 7) Si(111) surface reconstruction in the RHEED (white dotted lines) as well as in the LEED study ( figure 1(c)). Certainly, a welldeveloped (7 × 7) surface reconstruction is an indication of the high epi-Si(111) film quality. It is noted for completeness that these results were achieved after optimization of the Si growth mode on the Y 2 O 3 /Pr 2 O 3 /Si(111) support system. Under the present growth conditions, the Si growth mode is initially characterized by Volmer-Weber behaviour but the Si multilayer growth front typically reduces towards a single layer growth mode at an epi Si layer thickness above 15 nm (data not shown). Choosing too low (<400 • ) or too high (>800 • ) deposition temperatures, epi-Si layers of poor quality result either due to the too low mobility of the Si deposit or the occurrence of an IF reaction towards amorphous Y-silicate, respectively. 10   figure 4(a). This result guarantees that the observed Si (044) Bragg peak at α = 0.1 • in figure 4(b) is entirely due to the epi-Si(111) layer. In consequence, the SR-GIXRD allows also to study the strain properties of the epi-Si(111) layer without any influence from the oxide   azimuth (data not shown) and resulted in similar values for the in-plane strain as well as the average domain size of the epi-Si(111) film.

Stacking sequence study.
A further important structure property of the epi-Si(111) layer on the Y 2 O 3 /Pr 2 O 3 /Si(111) heterostructure concerns its stacking sequence along the (111) growth direction, i.e. whether it grows in a bicrystalline twinned or in a single crystalline untwinned configuration. This phenomenon can be studied by stacking sensitive out-of plane SR-GIXRD rod scan measurements, as summarized in figure 5. The sketch shows the location of the KL lattice plane in the reciprocal hexagonal Si Surf coordinate system. Furthermore, the Bragg peak intensity distribution is given in the Si Surf KL lattice plane for an epi-Si rod scan study in figure 5. In contrast, a clear sixfold symmetry is detected in the off-plane scan at α = 0.15 • (solid line) which is characterized by a sampling depth of about 100 nm in the 130 nm thick epi-Si(111) Bragg peak layer structure. This is true because, besides the strong type A Si(131) Bragg peaks (>10 6 cps) at = −120 • , 0 • and 120 • , weak type B Si(131) Bragg peaks (<10 3 cps) are additionally detected at = −60 • and 60 • . Due to the fact that type A and type B epi-Si layer Bragg peaks in this study belong to the same Bragg peak family, a simple intensity comparison of type A and type B epi-Si layer Bragg peaks allows to give an estimate of the misaligned type B twin population in the preferentially type A-oriented epi-Si(111) layer structure. It is found that less than 0.1% of the epi-Si(111) layer structure is crystallized in the vicinity of the epi-Si/oxide IF in the misaligned type B stacking configuration.   In summary, the TEM study on the structure and defect characteristics of the epi-Si(111)/Y 2 O 3 /Pr 2 O 3 /Si(111) heterostructure locally corroborates the results of a recent, highly averaging XRD defect study [47].

Theory studies
Theoretical calculations were applied to gain a deeper understanding of the heteroepitaxy mechanisms at work in stabilizing the type B epitaxy relationship between the Si(111) structures and the Me 2 O 3 (111) oxide films. In the following, the discussion of figure 8 will be focused on the interaction of the cub-Pr 2 O 3 (111) film with Si(111) but can be applied in an analogous way to the cub-Y 2 O 3 (111)/Si(111) IF. Figure 8 structures differ by the stacking order of (111) layers, namely the essential difference between these configurations is the relative position of metal atoms in the first layer of the oxide and unoxidized Si atoms in the first and second (111) double layers. Figure 8(b) shows the registry of Pr and Si atoms in type A (left) and type B (right) IFs; top and side views are given in the upper and lower panels, respectively. Oxygen atoms are not shown for clarity. In type A IF, Pr atoms from the first oxide layer sit above Si atoms from the second (111) double-layer of Si. In type B IF, Pr atoms from the first oxide layer sit above Si atoms from the first (111) double-layer of Si. Figure 8(c) shows that the type A (left) and type B (right) geometries are associated with a different strength of the electrostatic interaction between the metal atoms and the electrons in Si-Si bonds at the IF (indicated by thick black lines) as well as with the Si core. In B-type configuration (right), the positively charged Pr ion is repelled by four Si cores to which it is equidistant, whereas in A-type configuration (left) the Pr ion is repelled by six Si cores. Three of the latter are the same distance from Pr as in the B-type configuration, and the other three are further away. By summing up the electrostatic energies one finds that the core-core electrostatic repulsion is stronger in the IF of type A. On the other hand, the A-type Pr ion is attracted electrostatically by electrons in six Si-Si bonds, while the B-type Pr ion is attracted by only three Si-Si bonds (although the centres of weight of these bonds are closer to the Pr ion in the IF B). By summing up these electrostatic contributions one estimates that the IF of type B has noticeably lower energy than the IF of type A. Assuming that the electrostatic charge of Pr is +3e, that the charge of the bond may be approximated by a bond-centre point charge of −0.5e, that the effective charge of the Si core is thus +e, and that screening of the This agreement also indicates that there is no strong enhancement of short-range electrostatic screening at the IF. Since electrons in the backbonds form IF resonances, one may expect that, being largely decoupled from the rest of the crystal, they are more easily polarizable than bulk electrons. One of these IF states is shown in the left panel of figure 8(d). However, the interatomic distances and angles between the atoms contributing to the IF states are largely independent of the type of the IF, and so is the charge localized on oxygen orbitals. This result is shown on the right of figure 8(

Conclusion and outlook
It was reported in the past that epi Si(111) layers can be grown on hex-Pr 2 O 3 (0001) films on Si(111) [24]. However, these layers suffer from the fact that the hex-Pr 2 O 3 (0001) buffer oxide films suppress the stacking information of the Si(111) substrate so that the epi Si(111) layers are characterized in consequence by poor long-range order due to stacking twin formation [25]. In order to transport the stacking information to the epi Si(111) layer, the buffer oxide system was engineered by inducing a hex → cub-Pr 2 O 3 phase transition [50], resulting under optimized growth conditions in the preparation of twin-free, single crystalline Pr 2 O 3 (111) layers with an exclusive type B stacking orientation on Si(111) [19]. In addition, the functionality of the buffer oxide heterostructure was increased by preparing single crystalline Pr 2−x Y x O 3 (x = 0 to 2) solid state solutions on Si(111) out of the isomorphic cub-Y 2 O 3 and cub-Pr 2 O 3 phases [18]. In consequence, the Y 2 O 3 -Pr 2 O 3 heterostructure approach allows a flexible variation of important buffer layer parameters, i.e. lattice constants can be varied to study lattice matched and mismatched semiconductors as well as the IF reactivity can be tailored to improve the wetting of the buffer oxide by the semiconductor and avoid parasitic IF reactions.
In this study, we focus on the structure of single crystalline epi Si(111) layers on lattice mismatched Y 2 O 3 -Pr 2 O 3 bilayer heterostructures on Si(111), i.e. on the transfer of the stacking information between the engineered ionic buffer heterostructure and covalent Si(111). The resulting epi Si(111)/Y 2 O 3 /Pr 2 O 3 /Si(111) heterostructure is atomically smooth, exhibits a (7 × 7) surface reconstruction and single crystalline nature, characterized by a type A/B/A stacking relationship. Theoretical ab initio calculations identified the electrostatic interaction across the ionic oxide/covalent Si IF as the main driving force for the stabilization of this A/B/A stacking configuration in the epi-Si(111)/insulator/Si(111) heterostructure. Interestingly, as the type A and B stacking at the oxide/Si boundary can be viewed as a local cubic ABC. . . and hexagonal ABA. . . stacking structure, respectively, this result can be compared on the basis of the simple Born-Mayer equation with ionic crystals. For the same charge and atomic distance values, the Born-Mayer equation predicts a preference of the wurtzite (hexagonal ABA. . . over the zinc-blende (cubic ABC. . . ) structure due to the higher Madelung constant A (wurtzite: A = 1.641; zinc-blende: A = 1.638) [51]. Indeed, it is a well-established result of theoretical structure calculations on III-V materials that the preference of the wurtzite over the zinc-blende structure correlates with the ionic character of the compound semiconductor [52,53].
In addition, compressive strain creation in the epi-Si layer structure by the lattice mismatched Y 2 O 3 /Pr 2 O 3 /Si(111) heterostructure was studied with high resolution by nondestructive depth profiling GI-XRD studies. Theoretically, Y 2 O 3 is by about 2.4% smaller than twice the Si bulk lattice parameter but the non-destructive depth profiling GI-XRD detected an extension of the Y 2 O 3 lattice by about 1.7% due to the interaction with the bigger Pr 2 O 3 and Si lattices. In consequence, a compressive strain of about 0.7% could be expected at maximum in the growing epi-Si layer but GI-XRD detected only a deviation of 0.1%. It is thus obvious that the creation of strain in the epi-Si layer with the help of lattice mismatched oxide heterostructures cannot be directly derived from bulk lattice parameters but compliant effects in the buffer oxide require to strictly control the interplay of the semiconductor and oxide buffer stiffnesses. An epi-Si film thickness-dependent combined Raman and GI-XRD study is currently under way to study this point in more detail.
Furthermore, two kinds of defect structures, namely stacking twins and stacking faults, were detected in the epi-Si(111) layer structure. Misaligned type B-oriented Si twin domains account for less than 0.1% of the total quantity of the deposited epi-Si(111) layer structure and the location of these stacking twin defects is restricted to the vicinity of the oxide/Si boundary. This observed location is in line with the fact that the defect energy of stacking twins is far higher than in the case of stacking faults so that, as for example nicely demonstrated by Ernst et al in case of GaP heteroepitaxy on Si [45], stacking twins tend to nucleate at the IF but do not grow with the thickening film structure. In contrast, stacking faults do and the threading behaviour of stacking faults from the oxide buffer through the epi-Si(111) layer up to the surface region is also observed in the present case. Indeed, a recent XRD study was applied to investigate the stacking fault structure of the epi-Si(111) layer and a clear linear correlation of the intensity of stacking fault derived XRD signals with film thickness was detected [47]. Future work will concentrate on defect engineering approaches to improve the long-range order of the epi-Si(111) layer structure on the lattice mismatched Y 2 O 3 /Pr 2 O 3 /Si(111) support system. Special emphasize will be given to approaches to tailor the surface structure of the oxide buffer in order to suppress the identified stacking fault formation mechanisms in the epi-Si(111) layer, namely the nucleation of stacking faults by the oxide roughness and by the initially formed Si island structures. In this respect, surface modification epitaxy is currently employed to (i) reduce the oxide surface roughness and (ii) to improve the Si wetting behaviour.
Certainly, progress in the preparation of high quality semiconductor/insulator/Si heterostructures by engineered oxide heterostructures is expected to also push ahead the controlled study of new revolutionary device physics concepts based on the tremendous diversity of solid state phenomena encountered in complex oxide systems (electric field effects in correlated oxide systems [54], correlated electron physics in transition metal oxides [55], all-oxide electronics [56,57] etc).