Si Bridges Research Articles

Novel nanostructure architectures

We combine self-assembled island growth with in situ and ex situ selective etching techniques to create advanced semiconductor nanostructure architectures. Such architectures include lateral InAs/GaAs quantum dot molecules and unstrained inverted GaAs/AlGaAs quantum dots (QDs) with photoluminescence (PL) peak linewidths as narrow as 8.9meV. Micro-PL of single GaAs/AlGaAs QDs reveals well-behaved and sharp exciton emission lines in the red spectral range, which renders these novel nanostructures interesting candidates for future coherent optical investigations. Furthermore, we overgrow self-assembled Ge islands with a thin Si cap layer and use standard e-beam lithography and reactive ion etching to define mesa structures on the surface. The SiGe island core is then selectively etched away, which leaves ultra-thin free-standing Si bridges as remainders on the surface. Such thin Si bridges present an alternative route to produce SiGe-free Si-on-nothing (SON) for advanced complementary metal oxide semiconductor (CMOS) technology.

Variations in the physico-chemical properties of near-stoichiometric silica deposited from SiH 4–N 2O and SiH 4–N 2O–He radiofrequency discharges

Silicon oxide thin films were deposited at low temperatures by Plasma-Enhanced Chemical Vapour Deposition (PECVD) from silane–nitrousoxide (SiH 4–N 2O) and silane–nitrous oxide–helium (SiH 4–N 2O–He) mixtures. The film structure is shown to vary with the position in the reactor by means of several physico-chemical analyses (infrared, Raman, X photon spectroscopy). The main features are an increase of both the constrain of the Si–O–Si bridges and film compactness, whereas the amount of neighboring-OH groups decreases. The appearance of those specific OH groups is favored by a progressive post-venting hydrolysis. By comparing the experimental results with modeling results, the film property modifications are put in relation with the film precursors and the deposition rate. In some conditions and especially in helium-diluted mixtures, stoichiometric and dense films but different from thermal silica are obtained. A low deposition rate seems to be a determining factor in order to obtain such films, but the helium is also shown to play a special role.

Haüyne: phase transition and high-temperature structures obtained from synchrotron radiation and Rietveld refinements

AbstractThe structural behaviour of a haüyne with a chemical composition of Na4.35Ca2.28K0.95[Al6Si6O24]- (SO4)2.03, at room pressure and from 33 to 1035°C on heating, was determined by using in situ synchrotron X-ray powder diffraction data (λ = 0.92249(5) Å). The satellite reflections in haüyne are lost at ∼400°C and a true substructure results because of this phase transition. There is a discontinuity in the a unit-cell parameter at ∼585°C. The α parameter increases rapidly and non-linearly to 585°C, but above 585°C, the expansion rate decreases. The percent volume change between 33 and 576°C is 2.0(3)%, and 0.6(3)% between 593 and 1035°C. Between 33 and 1035°C, the Al–O, Si–O and S–O distances are constant. Between 33 and 576°C, the angle of rotation of the AlO4 tetrahedron, jAl, changesfrom 11.5 to 5.8°, while the angle of rotation of the SiO4 tetrahedron, φSi, changesfrom 12.4 to 6.3°. The Al–O–Si bridging angle changesfrom 150.05(2) to 153.08(1)° from 33 to 576°C. Beyond 585°C, φAl and φSi angles remain nearly constant even though the maximum rotation of the tetrahedra is not achieved. Moreover, the Al–O–Si angle continues to increase at a slower rate from 585 to 1035°C by 1.05(2)°. From 33 to ∼585°C, the K atom position migrates at a slower rate than the Na and Ca atoms, and the structure expands at a high rate. Beyond 585°C, all the atomic positions of the interstitial cations (Na+, K+, Ca2+) remain nearly constant and the expansion of the structure is retarded.

Structural Characterization of Silver Doped Silica Prepared by Two Different Wet Chemical Methods

Two sets of silver doped silica samples were prepared, one using the traditional sol-gel method and the other from colloidal silica. In samples prepared by the first method, the addition of Ag promotes crystallization of the SiO2 matrix when annealed at temperatures below those marked by the phase diagram. Before crystallization of the silica glass into the α-cristobalite phase occurs, the silver diffuses throughout the amorphous network to form silver colloidal particles at annealing temperatures that depend on the silver concentration. In samples obtained from the colloidal silica, larger Ag particles are formed at lower annealing temperatures. Further annealing at higher temperatures crystallizes the glass into the already mentioned phase. The reason of having larger Ag particles at lower temperatures in the latter set of samples is probably because they have a more open structure, produced by a wider distribution in the Si—O—Si bridging angle.

Crystal structure of tetrarubidium hexathiodisilicate(IV), Rb4Si2S6

Rb4S6Si2, monoclinic, CYUmX (no. 12), a = 13.23(2) A, b = 6.864(2) A , c = 9.53(1) A . / 3 = 125.15(5)°, V= 707.6 A 3 , Z = 2, Rgi(F) = 0.048, wflreffF) = 0.052, T = 296 K. Source of material Rb4Si2S6 was obtained by reacting a mixture of 4.4 mmol Rb2S with 4.4 mmol Si and 13 mmol S powder (99.999 % purity) in aluminum oxide crucibles which were sealed into evacuated silica ampoules at 973.15 K, followed by cooling at a constant rate of 3 K/h. The reaction product consisted of colorless prismatic crystals which were sensitive to air and humidity. Discussion Rb4Si2S6 is isostructural as confirmed by STRUCTURE TIDY [1] with Rb4Ge2Se6 [2] and Rb4Ge2S6 [3] both crystallizing with the Cs4Sn2See structure type [4]. The crystal structure is characterized by discrete centrosymmetric hexathiodisilicate(IV) anions [Si2S6] which are built up by two edge sharing SiS4tetrahedra. The two independent terminal bonds are virtually identical (d(Si—SI) = 2.063(4) A and d(Si—S2) = 2.063(6) A ) and are significantly shorter than the bridging bond (?(Si—S3) = 2.196(3) A ) . The bond angle Sl-Si-S2 calculates as 116.7(2)° while that to the bridging S3 atoms is almost rectangular (94.3(2)°). These values are in fair agreement with those found in 11(51256 [5] the only other compound where this anion has so far been reported. In the isoelectronic molecule Si2S2Cl4 [6] the bridging Si—S bond length is significantly shorter (?(Si—S) = 2.116 A ) . The crystal structure of the title compound contains two independent rubidium cations, both coordinated by seven sulfur atoms in distorted pentagonal bipyramidal configurations (d(Rb—S) = 3.326 A 3.814 A ) . Table 1. Data collection and handling. Crystal: Wavelength: /*• Diffractometer, scan mode: 20max: N(hkl)nKasimdy Wli/Junique: Criterion for /obs, N(hkl)gc. N(param)n fined: Programs: colorless prism, size 0.0S x 0.07 x 0.20 mm Mo Ka radiation (0.7107 Â) 147.40 cm Enraf-Nonius CAD4, o>IW 59.82° 1148,1105 /obs > 2 crf/obsj, 700 36 CrystalStmcture [7], SIR92 [8], CRYSTALS [9] Table 2. Atomic coordinates and displacement parameters (in Â). Atom Site Un UZ2 I/33 Un U13 Uz> Rb(l) Rb(2) S C I ) S(2) S(3) Si(l) 41 4 i 41 4/ 4g 4 i 0.5803(1) 0.8058(1) 0.1122(3) 0.2874(3) 0 0.1155(3) 0 0 0 0 0.2346(4) 0 0.3616(1) 0.1881(1) 0.3921(3) 0.2217(4) 0 0.1783(3) 0.0308(6) 0.0417(7) 0.029(2) 0.033(1) 0.037(2) 0.027(1) 0.0263(6) 0.0317(7) 0.035(2) 0.028(1) 0.011(1) 0.015(1) 0.0203(5) 0.0264(6) 0.024(1) 0.016(1) 0.018(1) 0.010(1) 0.0121(4) 0.0189(5) 0.017(1) 0.015(1) 0.008(1) 0.008(1)

Viscous Flow and Plastic Deformation of Glasses in the Model of Excited Atoms

The critical displacement of an atom (a group of atoms) Δrmax, which corresponds to the interatomic interaction force at the maximum, is treated as the atomic excitation in liquids and glasses. The formation and migration of excited atoms are governed by local fluctuations of the configurational entropy. In amorphous linear polymers, the role of an excited kinetic unit is played by a small-sized macromolecular segment (an atomic group in a monomer). The atomic excitation in silicate glasses corresponds to the critical displacement of a bridging oxygen atom in the Si–O–Si bridge upon switching of adjacent bridging bonds. The activation energy e h = Pmaxνh and the activation volume νh = πd2Δrmax of the atomic excitation are introduced. The activation energy e h is determined by the work done against the forces of the internal pressure Pmax. The formation of an excited kinetic unit in polymers and glasses is a small-scale low-energy process (e h = 10–20 kJ/mol, νh = 5–70 A3). The total activation volume of the system Vf = νhNh is termed the fluctuation volume, and the model under consideration is referred to as the fluctuation volume model (or the model of excited atoms). The viscosity equation and other relationships of the hole theory are interpreted in the framework of the proposed model. This model is also applied to analyze the plasticity of amorphous polymers and glasses. A relationship between the glass transition condition and the Lindemann melting criterion is established.

A molecular orbital study on the chemical interaction across the indomethacin/silica interparticle boundary due to mechanical stressing

A discrete variational-Xα (DV-Xα) method was applied to elucidate the formation of C–O–Si bridging bonds, produced when a silanol group of SiO 2 comes close enough to react with a carboxyl group of indomethacin (IM). A decrease in the coordination number (CN) of oxygen atoms per silicon atom at the SiO 2 surface increased the net charge (NC) of the silanolic hydrogen atom and decreased the bond overlap population (BOP) between the silanolic oxygen and hydrogen atoms. These changes favored the formation and stabilization of C–O–Si bridging bonds with simultaneous dehydration. The computational results agreed well with our previous experimental study of a ground indomethacin–SiO 2 mixture to obtain a better solid dispersion of the drug.

A combined density functional theory and interatomic potential-based simulation study of the hydration of nano-particulate silicate surfaces

Density functional theory (DFT) calculations as well as interatomic potential-based simulations have been employed to study the adsorption of water at two α-quartz (0 0 0 1) surfaces. The different methods are found to be in agreement, both as to modes and energies of adsorption. When under-coordinated surface silicon and oxygen atoms are present, water adsorbs dissociatively at the surface, thereby annihilating dangling bonds by the formation of surface hydroxy groups. However, when the surface species are linked by Si–O–Si bridges and fully coordinated, water adsorbs associatively, releasing approximately 40 kJ mol −1. The comparison study shows that the use of complementary computational techniques is efficient in identifying and investigating low-energy surface features and behaviour. The potential model for hydrated silica performs sufficiently well to be suitable for use in further simulations of the hydration of a silicate nano-tube. Results of these calculations show that the side of the nano-tube is relatively resistant against dissociative chemisorption and silicon dissolution, but that the end of the nano-tube is highly reactive towards water and amenable to dissolution.

SiO 2/Si(100) interface characterization using infrared spectroscopy: estimation of substoichiometry and strain

The transverse optical (TO) and longitudinal optical (LO) phonons of the asymmetric stretch of the O in SiOSi bridging bond in thermal SiO 2 show red shift with decreasing oxide thickness. These shifts are primarily due to interface effects like strain and substoichiometric silicon oxides (suboxides). A method to isolate the contributions of strain and suboxide concentration towards the observed shifts is proposed. The procedure, which utilizes simple optical model and effective medium approximation, allows estimation of the average strain and suboxide concentration in films of different thickness. Analysis of infrared spectra shows that suboxide-rich layers in low temperature dry and wet oxides are confined to a distance of ∼1.5 nm from the interface; wet oxidation may generate lower stress near the interface.

NOE and PGSE NMR spectroscopic studies of solution structure and aggregation in metallocenium ion-pairs.

The solution structures of the metallocenium homogeneous polymerization catalyst ion-pairs [Cp(2)ZrMe](+)[MeB(C(6)F(5))(3)](-) (1), [(1,2-Me(2)Cp)(2)ZrMe](+)[MeB(C(6)F(5))(3)](-) (2), [(Me(2)SiCp(2))ZrMe](+)[MeB(C(6)F(5))(3)](-) (3), [Me(2)C(Fluorenyl)(Cp)ZrMe](+)[FPBA](-) (FPBA = tris(2,2',2' '-nonafluorobiphenyl)fluoroaluminate) (4), [rac-Et(Indenyl)(2)ZrMe](+)[FPBA](-) (5), [(Me(5)Cp)(2)ThMe](+)[B(C(6)F(5))(4)](-) (6), [(Me(2)SiCp(2))Zr(Me)(THF)](+)[MeB(C(6)F(5))(3)](-) (7), [(Me(2)SiCp(2))Zr(Me)(PPh(3))](+)[MeB(C(6)F(5))(3)](-) (8), [(Me(2)SiCp(2))Zr(Me)(THF)](+)[B(C(6)F(5))(4)](-) (9), [(Me(2)Si(Me(4)Cp)(t-BuN)Zr(Me)(solvent)](+)[B(C(6)F(5))(4)](-) (solvent = benzene, toluene) (10), [(Cp(2)ZrMe)(2)(mu-Me)](+)[MePBB](-) (PBB = tris(2,2',2"-nonafluorobiphenyl)borane) (11), and [(Cp(2)Zr)(2)(mu-CH(2))(mu-Me)](+)[MePBB](-) (12), having the counteranion in the inner (1, 3, 4, 5, and 6) or outer (7, 8, 9, 10, 11, and 12) coordination sphere, have been investigated for the first time in solvents with low relative permittivity such as benzene or toluene by (1)H NOESY and (1)H,(19)F HOESY NMR spectroscopy. It is found that the average interionic solution structures of the inner sphere contact ion-pairs are similar to those in the solid state with the anion B-Me (1, 3) or Al-F (5) vectors oriented toward the free zirconium coordination site. The HOESY spectrum of complex 6 is in agreement with the reported solid-state structure. In contrast, in outer sphere contact ion-pairs 7, 8, 9, and 10, the anion is located far from the Zr-Me(+) moiety and much nearer to the Me(2)Si bridge than in 3. The interionic structure of 8 is concentration-dependent, and for concentrations greater than 2 mM, a loss of structural localization is observed. PGSE NMR measurements as a function of concentration (0.1-5.0 mM) indicate that the tendency to form aggregates of nuclearity higher than simple ion-pairs is dependent on whether the anion is in the inner or outer coordination sphere of the metallocenium cation. Complexes 2, 3, 4, 5, and 6 show no evidence of aggregation up to 5 mM (well above concentrations typically used in catalysis) or at the limit of saturated solutions (complexes 3 and 6), while concentration-dependent behavior is observed for complexes 7, 8, 10, and 11. These outer sphere ion-pairs begin to exhibit significant evidence for ion-quadruples in solutions having concentrations greater than 0.5 mM with the tendency to aggregate being a function of metal ligation and anion structure. Above 2 mM, compound 8 exists as higher aggregates that are probably responsible for the loss of interionic structural specificity.

Density fluctuation in silica–PVA hybrid gels determined by small-angle X-ray scattering

A series of silica–polyvinyl alcohol (PVA) hybrids were prepared by acid-catalyzed hydrolysis of tetraethoxysilane (TEOS) in the mixture of ethanol and water containing dissolved polyvinyl alcohol via a sol–gel process. A small-angle X-ray scattering (SAXS) study on those hybrid gels has been performed utilizing synchrotron radiation. Intensive positive deviation from Porod’s law indicated that there existed density fluctuation within the matrix of silica–PVA hybrid gel. Using the differential d[ q 3 I( q)]/d( q 2) as a variant slo, plotting ln(slo) versus ln( q) can produce the dimension n and the amplitude F l of density fluctuation. Density fluctuation resulted from both the micropores in gel and Si–O–PVA–O–Si bridge between SiO 2 particle and PVA chain. When PVA increased in gel, the decreased micropores reduced the fluctuation but PVA enhanced the fluctuation. With the conjunction of correlation function C( r), it was clear that the bridge of Si–O–PVA–O–Si enlarged the compositional heterogeneity within gel matrix and made n increase with the increase of PVA. In addition, the fluctuation dimension n is a fraction rather than an integer that was formerly predicted by Ruland, which may relate to the fractal structure of hybrid gel.

Signatures of a drying SiO 2 · (H 2O) x gel from Raman spectroscopy and quantum chemistry

The dehydration process, induced by thermal treatment, of a silica gel, obtained from colloidal nano-particles, has been investigated. At sufficiently low water contents in the structure; water molecules wet the hydrophilic interior surface of the pores rather than forming droplets of pore water. This is manifested by elongation of the OH-bonds of the acidic silica groups and a dramatic downshift in the OH-vibrational frequency is observed. Further dehydration results in a dry, partially hydroxylated, porous silica consisting of a three dimensional network SiO 2 nano-particles. Upon further thermal treatment the remaining hydroxyl groups condense to Si–O–Si bridges between the colloidal particles.

Difficulties of the microscopic theory of leakage current through ultra‐thin oxide barriers: point defects

AbstractWe use a combination of first‐principles density functional theory and non‐perturbative scattering theory to investigate the effect of point defects on the hole leakage current through ultra thin oxide films. In particular, we consider O vacancies and B interstitial in monoclinic HfO2; five different defects are considered: (1) O vacancy at a three‐ and (2) a four‐coordinated O site located in the HfO2 region, (3) O vacancy along a Hf–O–Si bond and (4) along a Si–O–Si bond at the Si/HfO2 interface, and (5) an interstitial Batom in the HfO2 region. We find that the neutral bulk vacancies and an interface vacancy along theSi–O–Si bond have little impact on the leakage current. On the contrary, an interface vacancy along the Hf–O–Si bridge and an interstitial B atom in the HfO2 region introduce states in the Si band gap and in the region just below the Si valence band edge thus strongly enhancing the leakage current at a low bias. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An organosilyl derivative of trivacant tungstophosphate. Synthesis, characterization and crystal structure determination of α-A-[NBu n4] 3[PW 9O 34(C 2H 5SiO) 3(C 2H 5Si)

In the presence of NBu 4 n Br acting as phase-transfer reagent, organosilicon trichloride C 2H 5SiCl 3 reacts in acetonitrile with the trivacant tungstophosphate sodium salt β-A-Na 8H[PW 9O 34]·24H 2O to give hybrid organosilyl polyoxotungstate derivative α-A-[NBu 4 n ] 3[PW 9O 34(C 2H 5SiO) 3(C 2H 5Si)]. X-ray single crystal structural analysis indicates that the title compound is monoclinic, space group Cc, with lattice constants a=26.828(5), b=22.459(5), c=17.517(4) Å, β=103.19(3)°, V=10,276(4) Å 3, Z=4, R=0.0462. According to the result of X-ray single crystal diffraction and chemical analysis, the hybrid polyanion consists of one α-A-[PW 9O 34] 9− framework on which are grafted simultaneously three RSiO groups through six Si–O–W bridge bonds, each of which is attached to the fourth RSi group through three Si–O–Si bridge bonds. The hybrid polyanion becomes a partial saturated, closed cage structure and also has an assembly of virtual C 3 V symmetry.

New Silica‐Immobilized Nickel Catalysts for Cyclotrimerizations of Acetylenes

AbstractNew dicarbonylnickel catalysts with a variety of mono‐ and bidentate phosphine ligands, such as Ph2P(CH2)xPPh(CH2)ySi(OEt)3 (x=2, 3; y=2, 3), have been synthesized and fully characterized, three of them by X‐ray analyses. All the catalysts have been immobilized on silica by reaction of the ethoxysilane or hydroxy groups of the phosphine linkers with the surface silanol groups. The clean immobilization was proved by 31P solid‐state NMR. It has been demonstrated that the COSi bridge, in contrast to the strong SiOSi bond, is easily cleaved by organic solvents and water. With respect to the cyclotrimerization of phenylacetylene the optimal reaction conditions for all molecular and immobilized catalysts have been determined. Cyclooctane was the best solvent, and the optimal reaction temperature was 100 °C for reactions in homogeneous phase, and 155 °C for surface‐bound catalysts. The bite angles and spacer lengths of the chelating ligands did not play a major role for the performance of the homogeneous or immobilized catalysts. The latter could be recycled for 12 times, with final substrate conversions still typically between 30 and 40%, and turnover numbers (TON) around 1500. With an excess of substrate in one run a TON of 4810 was obtained for an immobilized carbonylnickel complex with a dppp‐type chelate phosphine (x=3, y=2). Reduction of the surface coverage generally resulted in catalysts with longer lifetimes, for example, reduction to one fourth gave a record TON of 7616 for this catalyst. The selectivities of the catalysts all followed one trend. The main products were the cyclotrimers 1,2,4‐ and 1,3,5‐triphenylbenzene, besides dimers, linear trimers and tetramers as side‐products. The fraction of the latter decreased at higher temperatures with homogeneous catalysts, and vanished entirely after a few cycles with the immobilized catalysts. On recycling, the initial ratio of unsymmetrical to symmetrical cyclotrimers of typically 5 : 1 gradually changed to about 1 : 1 for all catalysts.

A quantum chemical mechanism for the water-initiated decomposition of silica

An ab initio quantum chemical investigation of the interaction of water with amorphous silica is carried out using model systems that contain the Si–O–Si bridging unit. Interaction of the silicon–oxygen bond with a water dimer is found to be most favorable, in contrast to the Michalske–Freiman model, which assumes that the interaction occurs with a single water molecule. Formation of a five-coordinated silicon atom is an essential intermediate in the bond fracture process, which involves proton transfer from the water dimer to the bridging oxygen, proton transfer within the water dimer, and the formation of a new Si–O bond. The activation barrier to rupture the Si–O bond in the Si–O–Si unit in the presence of water dimer is ∼30 kcal/mol.

Binding and surface diffusion of SiH3 radicals and the roughness of hydrogenated amorphous silicon

Local density formalism pseudopotential calculations find that the growth radical SiH3 binds to the hydrogen-terminated (111)Si surface. The bound site is not the three-center Si–H–Si bridging site previously assumed. It has a direct Si–Si bond between the SiH3 and the surface Si, and the terminal hydrogen is displaced to a bond center of a lateral surface Si–Si bond. This site is more stable as the unpaired electron can delocalize over more Si–Si bonds. A bound site validates the standard model of the growth of hydrogenated amorphous silicon (a-Si:H) and microcrystalline Si, in which a mobile growth species allows surface diffusion and creates smooth surfaces.

Surface diffusion of SiH 3 radicals and growth mechanism of a-Si:H and microcrystalline Si

Existing growth mechanisms of hydrogenated amorphous silicon (a-Si:H) and microcrystalline silicon (μc-Si) assume that the growth species SiH 3 can diffuse over the hydrogen-saturated Si surface. However, recent calculations suggest that this could not happen. We have carried out local density formalism pseudopotential calculations of the binding of SiH 3 to hydrogen-terminated (1 1 1)Si surfaces. The bound site is not the three-centre SiHSi bridging site previously assumed. It has a direct SiSi bond between the SiH 3 and the surface Si, and the surface hydrogen is displaced to a bond centre of a surface SiSi bond. A bound site validates conventional models of growth of a-Si:H and μc-Si, in which a mobile growth species creates smooth surfaces.

Heat conduction investigations of the Si bridge in infrared emitter using micro- Raman scattering

Micro-Raman scattaring has been used to study the characteristics of heat conduction on heavy boron-doped Si bridge in an infrared emitter. Based on the proper spectral modeling and the temperature dependence of the position of the Raman peak, the bridge temperature rise due to the heating of high power laser is obtained. Using this method and in the way of point by point, the direct imaging of heat conduction as a distribution map of temperature rise has been also obtained. Compared with the simulated temperature distribution obtained by the finite element software, the experimental and theoretical results are in agreement with each other. While experiments have revealed the local fluctuations of heat conduction in detail, reflecting the nonuniformity of the actual device, and providing experimental bases for the micro-device optimization of the structure design and its fabrication.

Isospecific bulk polymerization of propylene with the use of ansa-metallocenes as a mixture of rac and meso isomers

The effects of various pathways of the formation of catalytic systems based on the rac-Me2SiInd2ZrCl2 metallocene on the activity and properties of polypropylene prepared by the bulk polymerization of propylene were studied in detail. It was found that the conditions of formation of the catalytic system affect not only its activity and the character of kinetic curves but also the molecular weight of the synthesized polymer. Propylene polymerization was studied with the use of a number of bisindenyl derivatives of zirconium, which were mixtures of rac and meso forms that differ in the nature of substituents in the Si bridge or the indenyl ligand. The conclusion was drawn that, with the use of metallocenes as a mixture of rac and meso forms, high-molecular-weight isotactic polypropylene can be prepared with high stereoregularity at a very high rate; thereby, the stage of separation of a pure rac isomer can be excluded in the synthesis of the catalyst.