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Nucleation and growth of epitaxial ZrB2(0 0 0 1) on Si(1 1 1)
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Journal of Crystal Growth 267 (2004) 554–563
Nucleation and growth of epitaxial ZrB2(0 0 0 1) on Si(1 1 1) C.-W. Hua, A.V.G. Chizmeshyab, J. Tollec, J. Kouvetakisc, I.S.T. Tsonga,* a
Department of Physics and Astronomy, Arizona State University, P.O. Box 871504, Tempe, AZ 85287-1504, USA b Center for Solid State Science, Arizona State University, Tempe, AZ 85287-1704, USA c Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA Received 5 December 2003; accepted 7 April 2004
Communicated by D.W. Shaw
Abstract The growth behavior of epitaxial ZrB2(0 0 0 1) films on Si(1 1 1) via the thermal decomposition of the unimolecular precursor Zr(BH4)4 was studied in situ using low-energy electron diffraction and low-energy electron microscopy, and ex situ using cross-sectional transmission electron microscopy and atomic force microscopy. Under appropriate kinetic conditions, epitaxy was achieved in spite of the very large lattice mismatch between ZrB2(0 0 0 1) and Si(1 1 1). Our study followed the growth from the initial nucleation stage to the final epitaxial film at various growth temperatures. At 900 C, the growth of ZrB2(0 0 0 1) proceeded by the nucleation of two-dimensional islands. These islands eventually coalesced to form a smooth film with an RMS roughness of 0.9 nm. The interface between ZrB2(0 0 0 1) and Si(1 1 1) was modeled theoretically and the most favorable interface consisted of the ZrB2(0 0 0 1) growing on a Si(1 1 1)–(O3 O3)B surface with the Zr-layer nearest to the interface and the B-layer on the top surface. r 2004 Elsevier B.V. All rights reserved. PACS: 81.15.Hi; 68.55.a; 68.35.p Keywords: A1. Interfaces; A1. Substrates; A1. Surfaces; A3. Molecular beam epitaxy
1. Introduction Group III nitride semiconductors with direct band gaps are becoming increasingly important in optoelectronic and microelectronic applications in recent years. However, the practical integration of GaN-based wide band gap devices with Si-based *Corresponding author. Tel.: +1-480-965-3563; fax: 1-480965-7954. E-mail address: [email protected] (I.S.T. Tsong).
electronics remains problematic, e.g. the monolithic integration of nitride-based high-power integrated circuit architectures with conventional silicon-based low-power control circuits and components on a common Si substrate. Two of the most pressing problems are: (a) metallized contacts between the nitride and silicon devices, and (b) in the case of optical devices, the almost total absorption of the ultraviolet (UV) or near-UV light by Si [1]. In a recent report [2], we have shown that the solution of these problems lies in
0022-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2004.04.020
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the use of a buffer layer of ZrB2(0 0 0 1) on Si(1 1 1). The in-plane lattice constant of ( has a very small 0.6% ZrB2(0 0 0 1), a ¼ 3:169 A, mismatch with that of GaN(0 0 0 1) where ( The thermal expansion coefficients a ¼ 3:189 A. along the ½1 0 1 0 on the basal plane are also reasonably well% matched between ZrB2 and GaN, being 6.7 106 and 5.6 106 K1, respectively [3]. The similarities in structural and thermal properties between ZrB2 and GaN strongly suggest that the use of a Si(1 1 1) substrate with a ZrB2(0 0 0 1) buffer layer would allow the growth of GaN films with a favorable reduction of dislocation density and biaxial strain. Moreover, the ZrB2 buffer layer is metallic and fully reflective, thus serving the dual role of providing electrical contact and eliminating any loss of emission intensity from the light-emitting nitride layers. We have successfully demonstrated epitaxial GaN(0 0 0 1) growth on Si(1 1 1) substrates via ZrB2 buffer layers in a previous report [2]. This was accomplished by the remarkable nearperfect epitaxial growth of ZrB2(0 0 0 1) in spite ( of the large mismatch between dSi2Si ¼ 3:84 A, the in-plane distance between atoms on Si(1 1 1), ( the in-plane lattice parameter for and a ¼ 3:17 A, ZrB2(0 0 0 1). The growth axis is along the [0 0 0 1] or [1 1 1] direction with ½1 1 2 0ZrB2 J½1 1 0Si : With% 25 nm,%no threading in the buffer layer thickness of dislocations propagating in a direction normal to the substrate are observed by cross-sectional transmission electron microscopy (XTEM). The misfit at the interface is taken up by a pure edgetype dislocation parallel to the substrate surface by the insertion of extra f1 1 0 0g lattice planes along % this manner, epitaxy the ½1 1 2 0 direction. In % occurs via the so-called ‘‘magic mismatch’’ in which six ZrB2 lattice planes coincide with five Si lattice planes. In this report, we will follow the entire growth process of ZrB2(0 0 0 1) on Si(1 1 1) from initial nucleation to final film formation in order to elucidate in detail the epitaxial behavior of this highly mismatched system. First-principles calculations are conducted to study the stability of the interface with different bonding configurations and also the polarity of the ZrB2 epilayer.
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2. Experimental procedure The growth of ZrB2(0 0 0 1) on Si(1 1 1) was conducted inside a low-energy electron microscope (LEEM) [4,5] where low-energy electron diffraction (LEED) and LEEM operations were carried out interchangeably in situ and in real time. The base pressure in the LEEM was 2 1010 Torr. The Si(1 1 1) substrate surface was cleaned by flashing briefly to 1200 C until a (7 7) LEED pattern appeared when the sample was cooled to temperatures below the (1 1)–(7 7) transition temperature of B860 C. The substrate temperature was monitored by an infrared pyrometer and a calibrated thermocouple. Growth of ZrB2 films on Si(1 1 1) at temperatures between 820 C and 950 C was accomplished by the following chemical reaction: ZrðBH4 Þ4 ðgasÞ- ZrB2 ðfilmÞ þ B2 H6 ðgasÞ þ5H2 ðgasÞ: The unimolecular precursor Zr(BH4)4 has a vapor pressure of B8 Torr at room temperature, making it particularly suitable for gas-source molecular beam epitaxy (GSMBE) or ultrahigh vacuum chemical vapor deposition (UHV-CVD) applications [6,7]. The flow of the Zr(BH4)4 vapor was adjusted by a leak valve and delivered via a glass inlet tube which passed through the apertures in the objective lens of the LEEM. The glass inlet tube was positioned at 2.5 cm away from the substrate at an angle of 16 to the substrate surface. With this deposition geometry, the pressure in the LEEM sample chamber was maintained at B5 107 Torr to sustain a slow growth rate, in this case 10–12 nm/h, to produce epitaxial ZrB2(0 0 0 1) films. In order to monitor closely the evolution of growth in real time, the ZrB2 growth rate in the LEEM was deliberately set to less than half of the growth rate in a GSMBE chamber reported earlier [2]. In previous studies, it was found that high growth rates would invariably lead to growth of amorphous ZrB2 films [8,9]. The growth process was followed by the LEED patterns and LEEM images taken in real time. The surface morphology of the ZrB2 films was examined using atomic force microscopy (AFM)
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and the interface between ZrB2 and Si(1 1 1) studied by high-resolution XTEM.
3. Results and discussion 3.1. Low-energy electron diffraction Fig. 1 shows the evolution of the LEED pattern during growth at a substrate temperature of 900 C. Because the growth temperature was above the (1 1)–(7 7) phase transition temperature of Si(1 1 1), the growth commenced from a clean (1 1) surface. Immediately after the introduction of the Zr(BH4)4 precursor, the (1 1) LEED pattern changed to a sharp (O3 O3)R30 pattern, as shown in Fig. 1(a). The (O3 O3) reconstruction is due to the adsorption of the diborane gas, B2H6, onto the Si(1 1 1)–(1 1) surface when the Zr(BH4)4 decomposes on the heated substrate surface. The diborane B2H6 in
Fig. 1. Evolution of the LEED pattern during ZrB2(0 0 0 1) growth on Si(1 1 1) at 900 C. (a) Boron-induced (O3 O3)R30o after 30 s of growth. (b) (O3 O3) plus p(2 2) ZrB2(0 0 0 1) surface after 3 min of growth. Note the splitting of the (2 2) fractional-order spots. (c) ZrB2 p(2 2) surface without spots splitting after 25 min of growth. Note the fading of the (O3 O3) pattern. (d) Sharp (1 1) pattern of completed ZrB2(0 0 0 1) layer after 50 min of growth. All LEED patterns were recorded at 23.5 eV electron energy.
turn decomposes into B atoms and H2 gas, and the B atoms occupy the substitutional S5 sites in the second layer directly below the T4 positions of Si [10–14], giving rise to the (O3 O3)R30 LEED pattern. As growth proceeded, another (1 1) LEED pattern with a smaller primitive unit cell compared with that of Si(1 1 1) appeared along with the Si(1 1 1)–(1 1) spots, as shown in Fig. 1(b), taken after 3 min of growth. This new (1 1) pattern ( in gives an in-plane lattice constant of B3.2 A, ( of agreement with the lattice spacing a ¼ 3:17 A the ZrB2(0 0 0 1) surface. A p(2 2) pattern based on the ZrB2(1 1) unit cell is also observed in Fig. 1(b). The fractional-order p(2 2) spots are split while the integral spots are not. After 25 min of growth, the Si(1 1 1)–(O3 O3) LEED pattern gradually faded and the p(2 2) pattern dominated, as shown in Fig. 1(c), and the fractional spots were no longer split. As growth continued past 30 min, the p(2 2) pattern faded, leaving only the ZrB2(0 0 0 1)–(1 1) pattern. A distinct ZrB2(0 0 0 1)–(1 1) LEED pattern is shown in Fig. 1(d), taken after 50 min of growth. This (1 1) pattern was preserved as the grown film was cooled down to room temperature. We attribute the p(2 2) LEED pattern to an ordered structure on the ZrB2(0 0 0 1) surface due to the diffusion of Si atoms from the substrate to the film surface. We confirmed the Si-induced p(2 2) reconstruction by exposing a ZrB2(0 0 0 1)–(1 1) film surface such as that shown in Fig. 1(d) to a flux of Si atoms at temperatures from 600 C to 900 C. Adsorption of Si atoms caused the LEED pattern to change from (1 1) to p(2 2). In the early stages of growth in Figs. 1(b) and (c), the Si(1 1 1) substrate surface was not completely covered by the ZrB2(0 0 0 1) film and Si atoms could easily diffuse to the growing film surface at 900 C to produce the p(2 2) reconstruction. The p(2 2) pattern finally disappeared with the coalescence of the ZrB2(0 0 0 1) film, covering the substrate surface entirely and blocking further Si diffusion to the film surface, leaving only the ZrB2(0 0 0 1)–(1 1) bulk-like surface, as shown in Fig. 1(d). The splitting of the fractional-order spots of the p(2 2) pattern observed in Fig. 1(b) can be
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attributed to the formation of antiphase domains of the Si-induced reconstruction on the surface [15]. However, the splitting disappeared as growth continued, as shown in Fig. 1(c), suggesting that the p(2 2) antiphase domains had either greatly increased in size or had become largely single domain. Perkins et al. [16] have reported the observation of a p(2 2) LEED pattern in HfB2(0 0 0 1) annealed at temperatures below 1900 C versus a (1 1) pattern annealed above 1900 C. They proposed a missing row model to account for the p(2 2) metastable structure. However, in our case of ZrB2(0 0 0 1) grown on Si(1 1 1), we found that annealing the film at 1000 C changed the (1 1) LEED pattern to a p(2 2). Growing the ZrB2(0 0 0 1) film at a higher temperature, e.g. 950 C, also produced a p(2 2) LEED pattern which persisted. Both observations suggest that the p(2 2) pattern is caused by Si incorporation on the surface of ZrB2(0 0 0 1) because at these higher annealing or growth temperatures, the diffusion of Si atoms is enhanced to the extent that the atoms from the substrate diffuse through the ZrB2 epilayer to the surface. We note that throughout the growth sequence, the p(2 2) and later (1 1) LEED patterns of ZrB2 were in perfect registration with the (1 1) and (O3 O3) LEED patterns of the Si(1 1 1) substrate, as shown in Fig. 1. The registration remained unchanged even when we moved to different locations of the sample surface under the electron beam, thus confirming the epitaxial character of the growth process.
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grown for different periods of time were removed from the LEEM growth chamber and examined ex situ using AFM. At the very early growth stage of 30 s, the surface consisted of small two-dimensional (2D) islands nucleated on the Si(1 1 1)– (O3 O3)B surface, as shown in Fig. 2(a). The sizes of these islands vary from 20 to 40 nm in width and 0.4–0.7 nm in height. The RMS surface roughness over a scan area of 4 mm 4 mm is B0.4 nm, close to the 0.353 nm for the c-spacing of the ZrB2(0 0 0 1) lattice. After 3 min of growth, the islands became larger and began to merge together to form flat-top mesas of ZrB2(0 0 0 1), as shown in Fig. 2(b). The surface of these ZrB2(0 0 0 1) islands produced the p(2 2) LEED pattern while the gaps between these islands maintained the (O3 O3) pattern in Fig. 1(b). The RMS surface roughness of the surface after 3 min is similar to that of the surface during initial nucleation, i.e. B0.4 nm. After 30 min of growth, the islands became more tightly merged, as shown in Fig. 2(c), resulting in the fading away of the Si(1 1 1)– (O3 O3)B surface in Fig. 1(c). The RMS
3.2. Surface morphology The LEEM images of the growth of ZrB2(0 0 0 1) on Si(1 1 1)–(1 1) at 900 C showed very little change in contrast except at the very beginning when the (1 1) high-temperature phase changed to the (O3 O3)R30 boron phase. Thereafter, the LEEM images showed small grainy features which did not appear to change as growth proceeded. To overcome the unforeseen lack of information provided by the LEEM on the surface morphology during film growth, we conducted an interrupted growth experiment in which ZrB2 films
Fig. 2. AFM images showing the evolution of surface morphology during ZrB2(0 0 0 1) growth on Si(1 1 1) at 900 C. The images were taken ex situ after (a) 30 s, (b) 3 min, (c) 30 min, and (d) 50 min of growth. The scan areas are 0.5 0.5 mm2 in images (a)–(c) and 1 1 mm2 in image (d).
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Fig. 3. A large area, 10 10 mm2, image of the completed ZrB2(0 0 0 1) layer grown at 900 C for 60 min taken by AFM. The RMS roughness over this large area of the film is 0.9 nm.
roughness of this surface is 0.61 nm over a scan area of 5 mm 5 mm indicating the film is growing thicker. Finally, after 50 min of growth, the film became virtually continuous with an atomically flat surface as shown in the AFM image of Fig. 2(d). A large-area scan, 10 mm 10 mm, AFM image is shown in Fig. 3 for the ZrB2(0 0 0 1) layer completed after 60 min of growth, and the RMS roughness of this large area is B0.9 nm. 3.3. Temperature dependence The growth temperature plays a critical role in controlling the surface morphology of the completed ZrB2(0 0 0 1) film. Figs. 4(a)–(c) show AFM images of ZrB2(0 0 0 1) films grown at temperatures of 850 C, 900 C, and 950 C, respectively, with the same Zr(BH4)4 precursor flux. For the ZrB2 film grown at 900 C, Fig. 4(b) shows that the surface morphology is very flat, giving an RMS roughness of 0.4 nm in the 2 mm 2 mm scan area. However, growth at 850 C produces a bumpy surface, as shown in Fig. 4(a), with an RMS roughness of 2.3 nm. The LEED pattern of this surface is (1 1), but it is less sharp than the
Fig. 4. AFM images of the surface morphology of the ZrB2(0 0 0 1) film as a function of the growth temperature at (a) 850 C, (b) 900 C, and (c) 950 C. Scan area is 2 2 mm2 in all three cases. The RMS roughness is 2.3 nm in image (a), 0.4 nm in image (b), and 3.1 nm in image (c).
(1 1) pattern shown in Fig. 1(d) for the 900 C growth. Growth at the higher temperature of 950 C leads to the formation of large 3D islands including geometrically distinctive rod-shape islands distributed over a relatively flat surface, as shown in Fig. 4(c). The RMS roughness of this surface is 3.1 nm. As mentioned earlier in the LEED results section, the ZrB2 layers grown at 950 C exhibit a p(2 2) LEED pattern throughout the entire growth, indicative of enhanced diffusion of Si atoms through the ZrB2 epilayer at this higher temperature, resulting in the incorporation of Si atoms on the surface. The p(2 2) surface persists on cooling the sample to room temperature, implying that the Si remains on the ZrB2(0 0 0 1) surface. 3.4. Interface The microstructure of the ZrB2(0 0 0 1)/Si(1 1 1) sample grown at 900 C was studied using XTEM. The surface of the ZrB2 epilayer is atomically flat over 120 nm with a sharp transition at the
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Fig. 6. Schematic representation of the six-fold symmetric ZrB2(0 0 0 1) showing the crystallographic directions. Zr: blue circles; B: pink circles. Fig. 5. (a) An XTEM image of an 8-nm thick ZrB2(0 0 0 1) film grown on Si(1 1 1) at 900 C. The area outlined by the white rectangle is shown in the high-resolution image (b) where the transition of cubic Si(1 1 1) to hexagonal ZrB2(0 0 0 1) is clearly observed. Both images were taken along the ½1 1 0 projection of % Si (or the ½1 1 2 0 projection of ZrB2). %
interface, as shown in Fig. 5(a). It is interesting to note that in spite of growing over a bunched step of 3–4 nm in height on the Si(1 1 1) surface near the center of Fig. 5(a), the ZrB2 epilayer surface remains flat. The high-resolution XTEM image in Fig. 5(b) clearly shows the abrupt transition from the cubic Si(1 1 1) to the hexagonal ZrB2(0 0 0 1) at the interface. While Si(1 1 1) has three-fold symmetry, ZrB2(0 0 0 1) has six-fold symmetry, as shown in Figs. 6 and 7. The arrangement of the atom-columns perpendicular to the image in Fig. 5(b) suggests that the Si(1 1 1) is viewed along the ½1 1 0 direction and the ZrB2(0 0 0 1) is viewed % along the ½1 1 2 0 direction, i.e. the growth axis is along [0 0 0 1] %or [1 1 1] with ½1 1 2 0ZrB2 J½1 1 0Si : % % involThis leads to a heteroepitaxial relationship ving a coincidence mismatch of six ZrB2f1 1 0 0g % lattice planes with five Sif1 1 2g lattice planes as % proposed in an earlier report [1]. The 6:5 ‘‘magic mismatch’’ is due to the in-plane atom-pair ( on the Si(1 1 1) surface distance dSi2Si ¼ 3:84 A and the in-plane lattice parameter for ZrB2(0 0 0 1) ( However, the ratio of the paraof a ¼ 3:17 A. meters dSi2Si =a gives 1.21, not exactly 6:5. We
Fig. 7. Schematic drawings of the ZrB2 crystallographic unit cell and primitive unit cell. Views of the unit cell in the directions ½0 0 0 1; ½1 1 0 0; and ½1 1 2 0 are also shown. Zr: blue % % spheres; B: pink spheres.
believe that the initial nucleation stage of the (O3 O3)B reconstructed surface of the Si(1 1 1) substrate, which is known to cause a slight contraction of the dSi2Si distance due to the subsurface B in the S5 sites [10–14], brings the dSi2Si =a ratio closer to 1.20.
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To investigate what role the B-induced (O3 O3) reconstruction plays in the stability of the interface when Zr and B atoms begin to attach to the reconstructed surface, and also to answer the question of whether ZrB2(0 0 0 1) grows with the Zr-layer or the B-layer in contact with the Si(1 1 1) surface, we conduct first-principles density functional theory calculations using the Vienna Ab initio Simulation Package (VASP) [17–19]. This code employs projected augmented wave (PAW) pseudopotentials [20] and a plane-wave basis to treat the electronic structure within the PW 91 generalized gradient approximation (GGA) [21]. All atomic positions were allowed to relax fully in a supercell of fixed dimensions in the structural models considered. A 3 3 1 Monhorst-Pack grid was used to carry out k-space integrations in the first Brillouin zone, a 500 eV cutoff was used for the plane wave basis, and forces were ( converged to better than 0.01 eV/A. We consider four structural models of ZrB2(0 0 0 1)/Si(1 1 1) exhibiting distinctly different interface chemistry as shown schematically in
Fig. 8. Schematic representation of four interface models: Model 1: Zr-layer in contact with the Si(1 1 1)–(1 1) surface; Model 2: Zr-layer in contact with the Si(1 1 1)–(O3 O3)B surface; Model 3: B-layer in contact with the Si(1 1 1)–(1 1) surface; and Model 4: B-layer in contact with the Si(1 1 1)– (O3 O3)B surface.
Fig. 8. Model 1 is characterized by an interface in which a layer of Zr atoms is bonded to a Si(1 1 1)–(1 1) surface. Model 2 consists of an interface where a layer of Zr atoms is bonded to a Si(1 1 1)–(O3 O3)B surface. Models 3 and 4 follow Models 1 and 2, respectively, except the layer bonded to the Si substrate now consists of B atoms instead of Zr atoms. The interface configuration of Model 2 is illustrated in Fig. 9. Free-surface terminated slabs were employed to avoid the registry constraints and polarity issues associated with continuous slab models [22,23]. In particular, the absence of symmetry constraints along the interface normal direction, i.e. [0 0 0 1] of ZrB2 and [1 1 1] of Si, allows for the possibility of symmetry-lowering reconstructions along the basal directions, including registry shifts at the interface. In this representation, structural relaxation is understood in terms of two distinct contributions: (a) the surface relaxation of the free Si and ZrB2 edges of the slab, and (b) the relaxation of interface bonds, which is the focal point of our simulations. To decouple these mechanisms, and to ensure bulk-like behavior between the interface region and the free surface, we constructed slabs of five double-layers of Si and four ZrB2 layers with a vacuum spacing of about ( between slabs. This choice leads to bulk-like 20 A behavior only a few atomic layers away from the interface in both ZrB2 and Si. Since the commensurate length scale for ZrB2(0 0 0 1)/Si(1 1 1) derived from experiment ( which occurs at 5dSi2Si ¼ 6aðZrB2 Þ; or B19 A, would involve over 500 atoms in the computational cell, we need to truncate this length scale in order to make our simulations computationally feasible. We also took into account the initial nucleation phase of B-induced (O3 O3) reconstruction on the Si(1 1 1) surface and therefore fixed the hexagonal basal dimension to a= ( ( as shown in Fig. 10. While O3 3.84 A=6.65 A, this choice of unit cell length a introduces 4.5% strain in the ZrB2 layer, it is nevertheless far less than the strain required to simulate the colinearity ½1 1 2 0ZrB2 J½1 1 0Si in the (O3 O3) % setting as observed in% experiment. It should be noted that in the experimentally observed interface, this very large strain is relieved by edge
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Fig. 9. Model 2 of the interface between ZrB2(0 0 0 1) and Si(1 1 1)–(O3 O3)B. Si: gray spheres; Zr: blue spheres; B: pink spheres. The black vertical lines delineate the boundaries of the supercell in which first-principles DFT–GGA calculations were performed.
dislocations parallel to the interface. Accordingly, the models presented here have their in-plane unit ( to produce a plausible cell spacing fixed to 6.65 A lower strain orientation with ½1 10 0ZrB2 J½1 1 0Si % which allows the B atoms to occupy the S5 sites and the Zr atoms at T4 site (Fig. 10). This represents a 30 rotation from the experimentally observed ½1 1 2 0ZrB2 J½1 1 0Si ; which follows from % % full atomic force relaxation producing relaxed bonding configurations. The stoichiometry of all slabs is fixed to Si29Zr16B32 in all the four models considered so that a comparison of energies is possible. In all four models, the reconstructions at the free surfaces are isostructural, i.e. bond length differ-
( between models, with the interences of o0.01 A face energy being the dominant contribution to the total supercell energy. Using this procedure, we find that Model 2 (where the Zr-layer is bonded to a Si(1 1 1)–(O3 O3)B surface) possesses the lowest energy. Relative to Model 2, Models 1, 3, and 4 are higher in energy by 5, 18, and 25 meV/ atom, respectively. The resulting interface structure of Model 2 is shown in the ½1 1 0 projection of Si in Fig. 9. This optimum % model further ( between Zr predicts an interface spacing of 2.19 A ( and Si planes, bulk Si–Si bond lengths of 2.35 A along the Si [1 1 1] direction, and bulk Zr–Zr bond ( along the ZrB2 [0 0 0 1] direclengths of 3.47 A tion. The slightly contracted Zr–Zr bond length
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Epitaxy of ZrB2(0 0 0 1) proceeds via a coincidence ‘‘magic’’ mismatch of 5dSi2Si ¼ 6aðZrB2 Þ: First-principles calculations modeling the ZrB2 growth confirm that growth on a Si(1 1 1)– (O3 O3)B surface with the Zr-layer in contact with the (O3 O3) substrate surface has the lowest energy.
Acknowledgements
Fig. 10. Basal dimensions and relative positions of Zr, B, and Si atoms in the unit cell of the interface between ZrB2(0 0 0 1) and Si(1 1 1)–(O3 O3)B used in the calculations. Si: gray circles; Zr: blue circles; B: pink circles. The relative sizes of the circles indicate the different levels of depth in the cell.
This work was supported by the National Science foundation grant numbers DMR0221993, DMR-0303237, and ENG-0304362.
References ( compared to the known lattice parameter of 3.53 A along the c-axis of ZrB2(0 0 0 1) is consistent with our choice of 4.5% dilation in the ZrB2 basal dimensions.
4. Conclusions The epitaxial growth behavior of ZrB2(0 0 0 1) on Si(1 1 1) through thermal decomposition of the unimolecular precursor Zr(BH4)4 was studied in situ and in real time using LEED and LEEM, and ex situ using AFM and XTEM. The initial nucleation occurs with the accommodation of B atoms by the Si(1 1 1)–(1 1) surface to form the (O3 O3)R30 reconstruction. 2D ZrB2 islands form on the (O3 O3) surface initially show a p(2 2) reconstruction due to the diffusion of Si atoms onto the surface of the ZrB2 islands. As growth continues, the 2D ZrB2 islands coalesce to produce a continuous ZrB2 film which exhibits a sharp (1 1) LEED pattern confirming the formation of a clean and stoichiometric ZrB2(0 0 0 1) surface. The ideal growth temperature was determined to be 900 C. Growth at 850 C tends to produce a rough surface morphology, while growth at 950 C produces 3D islands as well as Si contamination on the film surface as a result of Si diffusion through the film.
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Nucleation and growth of epitaxial ZrB2(0 0 0 1) on Si(1 1 1) C.-W. Hua, A.V.G. Chizmeshyab, J. Tollec, J. Kouvetakisc, I.S.T. Tsonga,* a
Department of Physics and Astronomy, Arizona State University, P.O. Box 871504, Tempe, AZ 85287-1504, USA b Center for Solid State Science, Arizona State University, Tempe, AZ 85287-1704, USA c Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA Received 5 December 2003; accepted 7 April 2004
Communicated by D.W. Shaw
Abstract The growth behavior of epitaxial ZrB2(0 0 0 1) films on Si(1 1 1) via the thermal decomposition of the unimolecular precursor Zr(BH4)4 was studied in situ using low-energy electron diffraction and low-energy electron microscopy, and ex situ using cross-sectional transmission electron microscopy and atomic force microscopy. Under appropriate kinetic conditions, epitaxy was achieved in spite of the very large lattice mismatch between ZrB2(0 0 0 1) and Si(1 1 1). Our study followed the growth from the initial nucleation stage to the final epitaxial film at various growth temperatures. At 900 C, the growth of ZrB2(0 0 0 1) proceeded by the nucleation of two-dimensional islands. These islands eventually coalesced to form a smooth film with an RMS roughness of 0.9 nm. The interface between ZrB2(0 0 0 1) and Si(1 1 1) was modeled theoretically and the most favorable interface consisted of the ZrB2(0 0 0 1) growing on a Si(1 1 1)–(O3 O3)B surface with the Zr-layer nearest to the interface and the B-layer on the top surface. r 2004 Elsevier B.V. All rights reserved. PACS: 81.15.Hi; 68.55.a; 68.35.p Keywords: A1. Interfaces; A1. Substrates; A1. Surfaces; A3. Molecular beam epitaxy
1. Introduction Group III nitride semiconductors with direct band gaps are becoming increasingly important in optoelectronic and microelectronic applications in recent years. However, the practical integration of GaN-based wide band gap devices with Si-based *Corresponding author. Tel.: +1-480-965-3563; fax: 1-480965-7954. E-mail address: [email protected] (I.S.T. Tsong).
electronics remains problematic, e.g. the monolithic integration of nitride-based high-power integrated circuit architectures with conventional silicon-based low-power control circuits and components on a common Si substrate. Two of the most pressing problems are: (a) metallized contacts between the nitride and silicon devices, and (b) in the case of optical devices, the almost total absorption of the ultraviolet (UV) or near-UV light by Si [1]. In a recent report [2], we have shown that the solution of these problems lies in
0022-0248/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2004.04.020
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the use of a buffer layer of ZrB2(0 0 0 1) on Si(1 1 1). The in-plane lattice constant of ( has a very small 0.6% ZrB2(0 0 0 1), a ¼ 3:169 A, mismatch with that of GaN(0 0 0 1) where ( The thermal expansion coefficients a ¼ 3:189 A. along the ½1 0 1 0 on the basal plane are also reasonably well% matched between ZrB2 and GaN, being 6.7 106 and 5.6 106 K1, respectively [3]. The similarities in structural and thermal properties between ZrB2 and GaN strongly suggest that the use of a Si(1 1 1) substrate with a ZrB2(0 0 0 1) buffer layer would allow the growth of GaN films with a favorable reduction of dislocation density and biaxial strain. Moreover, the ZrB2 buffer layer is metallic and fully reflective, thus serving the dual role of providing electrical contact and eliminating any loss of emission intensity from the light-emitting nitride layers. We have successfully demonstrated epitaxial GaN(0 0 0 1) growth on Si(1 1 1) substrates via ZrB2 buffer layers in a previous report [2]. This was accomplished by the remarkable nearperfect epitaxial growth of ZrB2(0 0 0 1) in spite ( of the large mismatch between dSi2Si ¼ 3:84 A, the in-plane distance between atoms on Si(1 1 1), ( the in-plane lattice parameter for and a ¼ 3:17 A, ZrB2(0 0 0 1). The growth axis is along the [0 0 0 1] or [1 1 1] direction with ½1 1 2 0ZrB2 J½1 1 0Si : With% 25 nm,%no threading in the buffer layer thickness of dislocations propagating in a direction normal to the substrate are observed by cross-sectional transmission electron microscopy (XTEM). The misfit at the interface is taken up by a pure edgetype dislocation parallel to the substrate surface by the insertion of extra f1 1 0 0g lattice planes along % this manner, epitaxy the ½1 1 2 0 direction. In % occurs via the so-called ‘‘magic mismatch’’ in which six ZrB2 lattice planes coincide with five Si lattice planes. In this report, we will follow the entire growth process of ZrB2(0 0 0 1) on Si(1 1 1) from initial nucleation to final film formation in order to elucidate in detail the epitaxial behavior of this highly mismatched system. First-principles calculations are conducted to study the stability of the interface with different bonding configurations and also the polarity of the ZrB2 epilayer.
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2. Experimental procedure The growth of ZrB2(0 0 0 1) on Si(1 1 1) was conducted inside a low-energy electron microscope (LEEM) [4,5] where low-energy electron diffraction (LEED) and LEEM operations were carried out interchangeably in situ and in real time. The base pressure in the LEEM was 2 1010 Torr. The Si(1 1 1) substrate surface was cleaned by flashing briefly to 1200 C until a (7 7) LEED pattern appeared when the sample was cooled to temperatures below the (1 1)–(7 7) transition temperature of B860 C. The substrate temperature was monitored by an infrared pyrometer and a calibrated thermocouple. Growth of ZrB2 films on Si(1 1 1) at temperatures between 820 C and 950 C was accomplished by the following chemical reaction: ZrðBH4 Þ4 ðgasÞ- ZrB2 ðfilmÞ þ B2 H6 ðgasÞ þ5H2 ðgasÞ: The unimolecular precursor Zr(BH4)4 has a vapor pressure of B8 Torr at room temperature, making it particularly suitable for gas-source molecular beam epitaxy (GSMBE) or ultrahigh vacuum chemical vapor deposition (UHV-CVD) applications [6,7]. The flow of the Zr(BH4)4 vapor was adjusted by a leak valve and delivered via a glass inlet tube which passed through the apertures in the objective lens of the LEEM. The glass inlet tube was positioned at 2.5 cm away from the substrate at an angle of 16 to the substrate surface. With this deposition geometry, the pressure in the LEEM sample chamber was maintained at B5 107 Torr to sustain a slow growth rate, in this case 10–12 nm/h, to produce epitaxial ZrB2(0 0 0 1) films. In order to monitor closely the evolution of growth in real time, the ZrB2 growth rate in the LEEM was deliberately set to less than half of the growth rate in a GSMBE chamber reported earlier [2]. In previous studies, it was found that high growth rates would invariably lead to growth of amorphous ZrB2 films [8,9]. The growth process was followed by the LEED patterns and LEEM images taken in real time. The surface morphology of the ZrB2 films was examined using atomic force microscopy (AFM)
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and the interface between ZrB2 and Si(1 1 1) studied by high-resolution XTEM.
3. Results and discussion 3.1. Low-energy electron diffraction Fig. 1 shows the evolution of the LEED pattern during growth at a substrate temperature of 900 C. Because the growth temperature was above the (1 1)–(7 7) phase transition temperature of Si(1 1 1), the growth commenced from a clean (1 1) surface. Immediately after the introduction of the Zr(BH4)4 precursor, the (1 1) LEED pattern changed to a sharp (O3 O3)R30 pattern, as shown in Fig. 1(a). The (O3 O3) reconstruction is due to the adsorption of the diborane gas, B2H6, onto the Si(1 1 1)–(1 1) surface when the Zr(BH4)4 decomposes on the heated substrate surface. The diborane B2H6 in
Fig. 1. Evolution of the LEED pattern during ZrB2(0 0 0 1) growth on Si(1 1 1) at 900 C. (a) Boron-induced (O3 O3)R30o after 30 s of growth. (b) (O3 O3) plus p(2 2) ZrB2(0 0 0 1) surface after 3 min of growth. Note the splitting of the (2 2) fractional-order spots. (c) ZrB2 p(2 2) surface without spots splitting after 25 min of growth. Note the fading of the (O3 O3) pattern. (d) Sharp (1 1) pattern of completed ZrB2(0 0 0 1) layer after 50 min of growth. All LEED patterns were recorded at 23.5 eV electron energy.
turn decomposes into B atoms and H2 gas, and the B atoms occupy the substitutional S5 sites in the second layer directly below the T4 positions of Si [10–14], giving rise to the (O3 O3)R30 LEED pattern. As growth proceeded, another (1 1) LEED pattern with a smaller primitive unit cell compared with that of Si(1 1 1) appeared along with the Si(1 1 1)–(1 1) spots, as shown in Fig. 1(b), taken after 3 min of growth. This new (1 1) pattern ( in gives an in-plane lattice constant of B3.2 A, ( of agreement with the lattice spacing a ¼ 3:17 A the ZrB2(0 0 0 1) surface. A p(2 2) pattern based on the ZrB2(1 1) unit cell is also observed in Fig. 1(b). The fractional-order p(2 2) spots are split while the integral spots are not. After 25 min of growth, the Si(1 1 1)–(O3 O3) LEED pattern gradually faded and the p(2 2) pattern dominated, as shown in Fig. 1(c), and the fractional spots were no longer split. As growth continued past 30 min, the p(2 2) pattern faded, leaving only the ZrB2(0 0 0 1)–(1 1) pattern. A distinct ZrB2(0 0 0 1)–(1 1) LEED pattern is shown in Fig. 1(d), taken after 50 min of growth. This (1 1) pattern was preserved as the grown film was cooled down to room temperature. We attribute the p(2 2) LEED pattern to an ordered structure on the ZrB2(0 0 0 1) surface due to the diffusion of Si atoms from the substrate to the film surface. We confirmed the Si-induced p(2 2) reconstruction by exposing a ZrB2(0 0 0 1)–(1 1) film surface such as that shown in Fig. 1(d) to a flux of Si atoms at temperatures from 600 C to 900 C. Adsorption of Si atoms caused the LEED pattern to change from (1 1) to p(2 2). In the early stages of growth in Figs. 1(b) and (c), the Si(1 1 1) substrate surface was not completely covered by the ZrB2(0 0 0 1) film and Si atoms could easily diffuse to the growing film surface at 900 C to produce the p(2 2) reconstruction. The p(2 2) pattern finally disappeared with the coalescence of the ZrB2(0 0 0 1) film, covering the substrate surface entirely and blocking further Si diffusion to the film surface, leaving only the ZrB2(0 0 0 1)–(1 1) bulk-like surface, as shown in Fig. 1(d). The splitting of the fractional-order spots of the p(2 2) pattern observed in Fig. 1(b) can be
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attributed to the formation of antiphase domains of the Si-induced reconstruction on the surface [15]. However, the splitting disappeared as growth continued, as shown in Fig. 1(c), suggesting that the p(2 2) antiphase domains had either greatly increased in size or had become largely single domain. Perkins et al. [16] have reported the observation of a p(2 2) LEED pattern in HfB2(0 0 0 1) annealed at temperatures below 1900 C versus a (1 1) pattern annealed above 1900 C. They proposed a missing row model to account for the p(2 2) metastable structure. However, in our case of ZrB2(0 0 0 1) grown on Si(1 1 1), we found that annealing the film at 1000 C changed the (1 1) LEED pattern to a p(2 2). Growing the ZrB2(0 0 0 1) film at a higher temperature, e.g. 950 C, also produced a p(2 2) LEED pattern which persisted. Both observations suggest that the p(2 2) pattern is caused by Si incorporation on the surface of ZrB2(0 0 0 1) because at these higher annealing or growth temperatures, the diffusion of Si atoms is enhanced to the extent that the atoms from the substrate diffuse through the ZrB2 epilayer to the surface. We note that throughout the growth sequence, the p(2 2) and later (1 1) LEED patterns of ZrB2 were in perfect registration with the (1 1) and (O3 O3) LEED patterns of the Si(1 1 1) substrate, as shown in Fig. 1. The registration remained unchanged even when we moved to different locations of the sample surface under the electron beam, thus confirming the epitaxial character of the growth process.
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grown for different periods of time were removed from the LEEM growth chamber and examined ex situ using AFM. At the very early growth stage of 30 s, the surface consisted of small two-dimensional (2D) islands nucleated on the Si(1 1 1)– (O3 O3)B surface, as shown in Fig. 2(a). The sizes of these islands vary from 20 to 40 nm in width and 0.4–0.7 nm in height. The RMS surface roughness over a scan area of 4 mm 4 mm is B0.4 nm, close to the 0.353 nm for the c-spacing of the ZrB2(0 0 0 1) lattice. After 3 min of growth, the islands became larger and began to merge together to form flat-top mesas of ZrB2(0 0 0 1), as shown in Fig. 2(b). The surface of these ZrB2(0 0 0 1) islands produced the p(2 2) LEED pattern while the gaps between these islands maintained the (O3 O3) pattern in Fig. 1(b). The RMS surface roughness of the surface after 3 min is similar to that of the surface during initial nucleation, i.e. B0.4 nm. After 30 min of growth, the islands became more tightly merged, as shown in Fig. 2(c), resulting in the fading away of the Si(1 1 1)– (O3 O3)B surface in Fig. 1(c). The RMS
3.2. Surface morphology The LEEM images of the growth of ZrB2(0 0 0 1) on Si(1 1 1)–(1 1) at 900 C showed very little change in contrast except at the very beginning when the (1 1) high-temperature phase changed to the (O3 O3)R30 boron phase. Thereafter, the LEEM images showed small grainy features which did not appear to change as growth proceeded. To overcome the unforeseen lack of information provided by the LEEM on the surface morphology during film growth, we conducted an interrupted growth experiment in which ZrB2 films
Fig. 2. AFM images showing the evolution of surface morphology during ZrB2(0 0 0 1) growth on Si(1 1 1) at 900 C. The images were taken ex situ after (a) 30 s, (b) 3 min, (c) 30 min, and (d) 50 min of growth. The scan areas are 0.5 0.5 mm2 in images (a)–(c) and 1 1 mm2 in image (d).
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Fig. 3. A large area, 10 10 mm2, image of the completed ZrB2(0 0 0 1) layer grown at 900 C for 60 min taken by AFM. The RMS roughness over this large area of the film is 0.9 nm.
roughness of this surface is 0.61 nm over a scan area of 5 mm 5 mm indicating the film is growing thicker. Finally, after 50 min of growth, the film became virtually continuous with an atomically flat surface as shown in the AFM image of Fig. 2(d). A large-area scan, 10 mm 10 mm, AFM image is shown in Fig. 3 for the ZrB2(0 0 0 1) layer completed after 60 min of growth, and the RMS roughness of this large area is B0.9 nm. 3.3. Temperature dependence The growth temperature plays a critical role in controlling the surface morphology of the completed ZrB2(0 0 0 1) film. Figs. 4(a)–(c) show AFM images of ZrB2(0 0 0 1) films grown at temperatures of 850 C, 900 C, and 950 C, respectively, with the same Zr(BH4)4 precursor flux. For the ZrB2 film grown at 900 C, Fig. 4(b) shows that the surface morphology is very flat, giving an RMS roughness of 0.4 nm in the 2 mm 2 mm scan area. However, growth at 850 C produces a bumpy surface, as shown in Fig. 4(a), with an RMS roughness of 2.3 nm. The LEED pattern of this surface is (1 1), but it is less sharp than the
Fig. 4. AFM images of the surface morphology of the ZrB2(0 0 0 1) film as a function of the growth temperature at (a) 850 C, (b) 900 C, and (c) 950 C. Scan area is 2 2 mm2 in all three cases. The RMS roughness is 2.3 nm in image (a), 0.4 nm in image (b), and 3.1 nm in image (c).
(1 1) pattern shown in Fig. 1(d) for the 900 C growth. Growth at the higher temperature of 950 C leads to the formation of large 3D islands including geometrically distinctive rod-shape islands distributed over a relatively flat surface, as shown in Fig. 4(c). The RMS roughness of this surface is 3.1 nm. As mentioned earlier in the LEED results section, the ZrB2 layers grown at 950 C exhibit a p(2 2) LEED pattern throughout the entire growth, indicative of enhanced diffusion of Si atoms through the ZrB2 epilayer at this higher temperature, resulting in the incorporation of Si atoms on the surface. The p(2 2) surface persists on cooling the sample to room temperature, implying that the Si remains on the ZrB2(0 0 0 1) surface. 3.4. Interface The microstructure of the ZrB2(0 0 0 1)/Si(1 1 1) sample grown at 900 C was studied using XTEM. The surface of the ZrB2 epilayer is atomically flat over 120 nm with a sharp transition at the
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Fig. 6. Schematic representation of the six-fold symmetric ZrB2(0 0 0 1) showing the crystallographic directions. Zr: blue circles; B: pink circles. Fig. 5. (a) An XTEM image of an 8-nm thick ZrB2(0 0 0 1) film grown on Si(1 1 1) at 900 C. The area outlined by the white rectangle is shown in the high-resolution image (b) where the transition of cubic Si(1 1 1) to hexagonal ZrB2(0 0 0 1) is clearly observed. Both images were taken along the ½1 1 0 projection of % Si (or the ½1 1 2 0 projection of ZrB2). %
interface, as shown in Fig. 5(a). It is interesting to note that in spite of growing over a bunched step of 3–4 nm in height on the Si(1 1 1) surface near the center of Fig. 5(a), the ZrB2 epilayer surface remains flat. The high-resolution XTEM image in Fig. 5(b) clearly shows the abrupt transition from the cubic Si(1 1 1) to the hexagonal ZrB2(0 0 0 1) at the interface. While Si(1 1 1) has three-fold symmetry, ZrB2(0 0 0 1) has six-fold symmetry, as shown in Figs. 6 and 7. The arrangement of the atom-columns perpendicular to the image in Fig. 5(b) suggests that the Si(1 1 1) is viewed along the ½1 1 0 direction and the ZrB2(0 0 0 1) is viewed % along the ½1 1 2 0 direction, i.e. the growth axis is along [0 0 0 1] %or [1 1 1] with ½1 1 2 0ZrB2 J½1 1 0Si : % % involThis leads to a heteroepitaxial relationship ving a coincidence mismatch of six ZrB2f1 1 0 0g % lattice planes with five Sif1 1 2g lattice planes as % proposed in an earlier report [1]. The 6:5 ‘‘magic mismatch’’ is due to the in-plane atom-pair ( on the Si(1 1 1) surface distance dSi2Si ¼ 3:84 A and the in-plane lattice parameter for ZrB2(0 0 0 1) ( However, the ratio of the paraof a ¼ 3:17 A. meters dSi2Si =a gives 1.21, not exactly 6:5. We
Fig. 7. Schematic drawings of the ZrB2 crystallographic unit cell and primitive unit cell. Views of the unit cell in the directions ½0 0 0 1; ½1 1 0 0; and ½1 1 2 0 are also shown. Zr: blue % % spheres; B: pink spheres.
believe that the initial nucleation stage of the (O3 O3)B reconstructed surface of the Si(1 1 1) substrate, which is known to cause a slight contraction of the dSi2Si distance due to the subsurface B in the S5 sites [10–14], brings the dSi2Si =a ratio closer to 1.20.
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To investigate what role the B-induced (O3 O3) reconstruction plays in the stability of the interface when Zr and B atoms begin to attach to the reconstructed surface, and also to answer the question of whether ZrB2(0 0 0 1) grows with the Zr-layer or the B-layer in contact with the Si(1 1 1) surface, we conduct first-principles density functional theory calculations using the Vienna Ab initio Simulation Package (VASP) [17–19]. This code employs projected augmented wave (PAW) pseudopotentials [20] and a plane-wave basis to treat the electronic structure within the PW 91 generalized gradient approximation (GGA) [21]. All atomic positions were allowed to relax fully in a supercell of fixed dimensions in the structural models considered. A 3 3 1 Monhorst-Pack grid was used to carry out k-space integrations in the first Brillouin zone, a 500 eV cutoff was used for the plane wave basis, and forces were ( converged to better than 0.01 eV/A. We consider four structural models of ZrB2(0 0 0 1)/Si(1 1 1) exhibiting distinctly different interface chemistry as shown schematically in
Fig. 8. Schematic representation of four interface models: Model 1: Zr-layer in contact with the Si(1 1 1)–(1 1) surface; Model 2: Zr-layer in contact with the Si(1 1 1)–(O3 O3)B surface; Model 3: B-layer in contact with the Si(1 1 1)–(1 1) surface; and Model 4: B-layer in contact with the Si(1 1 1)– (O3 O3)B surface.
Fig. 8. Model 1 is characterized by an interface in which a layer of Zr atoms is bonded to a Si(1 1 1)–(1 1) surface. Model 2 consists of an interface where a layer of Zr atoms is bonded to a Si(1 1 1)–(O3 O3)B surface. Models 3 and 4 follow Models 1 and 2, respectively, except the layer bonded to the Si substrate now consists of B atoms instead of Zr atoms. The interface configuration of Model 2 is illustrated in Fig. 9. Free-surface terminated slabs were employed to avoid the registry constraints and polarity issues associated with continuous slab models [22,23]. In particular, the absence of symmetry constraints along the interface normal direction, i.e. [0 0 0 1] of ZrB2 and [1 1 1] of Si, allows for the possibility of symmetry-lowering reconstructions along the basal directions, including registry shifts at the interface. In this representation, structural relaxation is understood in terms of two distinct contributions: (a) the surface relaxation of the free Si and ZrB2 edges of the slab, and (b) the relaxation of interface bonds, which is the focal point of our simulations. To decouple these mechanisms, and to ensure bulk-like behavior between the interface region and the free surface, we constructed slabs of five double-layers of Si and four ZrB2 layers with a vacuum spacing of about ( between slabs. This choice leads to bulk-like 20 A behavior only a few atomic layers away from the interface in both ZrB2 and Si. Since the commensurate length scale for ZrB2(0 0 0 1)/Si(1 1 1) derived from experiment ( which occurs at 5dSi2Si ¼ 6aðZrB2 Þ; or B19 A, would involve over 500 atoms in the computational cell, we need to truncate this length scale in order to make our simulations computationally feasible. We also took into account the initial nucleation phase of B-induced (O3 O3) reconstruction on the Si(1 1 1) surface and therefore fixed the hexagonal basal dimension to a= ( ( as shown in Fig. 10. While O3 3.84 A=6.65 A, this choice of unit cell length a introduces 4.5% strain in the ZrB2 layer, it is nevertheless far less than the strain required to simulate the colinearity ½1 1 2 0ZrB2 J½1 1 0Si in the (O3 O3) % setting as observed in% experiment. It should be noted that in the experimentally observed interface, this very large strain is relieved by edge
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Fig. 9. Model 2 of the interface between ZrB2(0 0 0 1) and Si(1 1 1)–(O3 O3)B. Si: gray spheres; Zr: blue spheres; B: pink spheres. The black vertical lines delineate the boundaries of the supercell in which first-principles DFT–GGA calculations were performed.
dislocations parallel to the interface. Accordingly, the models presented here have their in-plane unit ( to produce a plausible cell spacing fixed to 6.65 A lower strain orientation with ½1 10 0ZrB2 J½1 1 0Si % which allows the B atoms to occupy the S5 sites and the Zr atoms at T4 site (Fig. 10). This represents a 30 rotation from the experimentally observed ½1 1 2 0ZrB2 J½1 1 0Si ; which follows from % % full atomic force relaxation producing relaxed bonding configurations. The stoichiometry of all slabs is fixed to Si29Zr16B32 in all the four models considered so that a comparison of energies is possible. In all four models, the reconstructions at the free surfaces are isostructural, i.e. bond length differ-
( between models, with the interences of o0.01 A face energy being the dominant contribution to the total supercell energy. Using this procedure, we find that Model 2 (where the Zr-layer is bonded to a Si(1 1 1)–(O3 O3)B surface) possesses the lowest energy. Relative to Model 2, Models 1, 3, and 4 are higher in energy by 5, 18, and 25 meV/ atom, respectively. The resulting interface structure of Model 2 is shown in the ½1 1 0 projection of Si in Fig. 9. This optimum % model further ( between Zr predicts an interface spacing of 2.19 A ( and Si planes, bulk Si–Si bond lengths of 2.35 A along the Si [1 1 1] direction, and bulk Zr–Zr bond ( along the ZrB2 [0 0 0 1] direclengths of 3.47 A tion. The slightly contracted Zr–Zr bond length
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Epitaxy of ZrB2(0 0 0 1) proceeds via a coincidence ‘‘magic’’ mismatch of 5dSi2Si ¼ 6aðZrB2 Þ: First-principles calculations modeling the ZrB2 growth confirm that growth on a Si(1 1 1)– (O3 O3)B surface with the Zr-layer in contact with the (O3 O3) substrate surface has the lowest energy.
Acknowledgements
Fig. 10. Basal dimensions and relative positions of Zr, B, and Si atoms in the unit cell of the interface between ZrB2(0 0 0 1) and Si(1 1 1)–(O3 O3)B used in the calculations. Si: gray circles; Zr: blue circles; B: pink circles. The relative sizes of the circles indicate the different levels of depth in the cell.
This work was supported by the National Science foundation grant numbers DMR0221993, DMR-0303237, and ENG-0304362.
References ( compared to the known lattice parameter of 3.53 A along the c-axis of ZrB2(0 0 0 1) is consistent with our choice of 4.5% dilation in the ZrB2 basal dimensions.
4. Conclusions The epitaxial growth behavior of ZrB2(0 0 0 1) on Si(1 1 1) through thermal decomposition of the unimolecular precursor Zr(BH4)4 was studied in situ and in real time using LEED and LEEM, and ex situ using AFM and XTEM. The initial nucleation occurs with the accommodation of B atoms by the Si(1 1 1)–(1 1) surface to form the (O3 O3)R30 reconstruction. 2D ZrB2 islands form on the (O3 O3) surface initially show a p(2 2) reconstruction due to the diffusion of Si atoms onto the surface of the ZrB2 islands. As growth continues, the 2D ZrB2 islands coalesce to produce a continuous ZrB2 film which exhibits a sharp (1 1) LEED pattern confirming the formation of a clean and stoichiometric ZrB2(0 0 0 1) surface. The ideal growth temperature was determined to be 900 C. Growth at 850 C tends to produce a rough surface morphology, while growth at 950 C produces 3D islands as well as Si contamination on the film surface as a result of Si diffusion through the film.
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