Strain-Driven Mound Formation of Substrate under Epitaxial

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Strain-driven mound formation of substrate under epitaxial nanoparticles Tanya Gupta, James B. Hannon, Jerry Tersoff, Rudolf M. Tromp, John A Ott, John Bruley, and Daniel A Steingart Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl502516y • Publication Date (Web): 15 Dec 2014 Downloaded from http://pubs.acs.org on December 21, 2014

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Strain-Driven Mound Formation of Substrate under Epitaxial Nanoparticles Tanya Gupta,1 James B Hannon,2, ∗ J. Tersoff,2 Rudolf M Tromp,2 John A Ott,2 John Bruley,2 and Daniel A Steingart1, † Department of Mechanical and Aerospace Engineering and the

1

Andlinger Center for Energy and The Environment IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598

2

(Dated: December 7, 2014)

ACS Paragon Plus Environment

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We observe the growth of crystalline SiC nanoparticles on Si(001) at 900°C using in situ electron microscopy. Following nucleation and growth of the SiC, there is a massive migration of Si, forming a crystalline Si mound underneath each nanoparticle that lifts it 4-5 nm above the initial growth surface. The volume of the Si mounds is roughly five to seven times the volume of the SiC nanoparticles. We propose that relaxation of strain drives the mound formation. This new mechanism for relieving interfacial strain, which involves a dramatic restructuring of the substrate, is in striking contrast to the familiar scenario in which only the deposited material restructures to relieve strain. Keywords: Si (100), SiC, Interfacial strain, LEEM, AFM, TEM

Strain is present in essentially every heteroepitaxial growth system. The difference

in

lattice constant between a film and a substrate necessarily leads to the distortion of both lattices near the interface. Strain has important consequences for both the mechanical and electrical properties of film and tailoring the strain at interfaces is an integral part of many advanced technologies. For example, strain is used to enhance the carrier mobility in Si field effect transistors1. Strain can also drive the spontaneous formation of ‘self organized’ periodic patterns with nanoscale dimensions2–4. Strain-driven assembly can be exploited to create arrays of nanoscale objects with unique electronic and optical properties, such as ‘quantum dots,’ that are difficult to produce using conventional patterning techniques5–8. Understanding the role of strain in surface morphology is an active area of research, particularly for semiconductor systems5–8. The growth of Ge on Si(001) is a well-known example. Epitaxial Ge assembles into quantum dots to relieve strain6,7. The energy cost of increased surface area is more than compensated by the reduction in strain energy. Theoretical treatments often consider the substrate as a passive platform that can only deform elastically9,10. This is a good approximation for the most-studied systems, Ge on Si and InAs on GaAs, because there the substrate material is much less mobile than the epilayer at the growth temperature.


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Here we describe a response to interfacial strain which, to our knowledge, has not been previously observed: a massive restructuring of the substrate rather than of the epitaxial material. The surface evolution is shown schematically in Fig. 1.

FIG. 1. Strain-driven mound formation. (a) A carbon flux leads to the nucleation and growth of SiC nanoparticles. (b) Once the nanoparticles form, Si diffuses to the particles, forming mounds underneath each particle that lifts them off the surface. (c) Even after the carbon flux is terminated, the mounds continue to grow.

Exposing Si(001) to a carbon flux at 900°C leads to the nucleation and growth of polycrystalline SiC nanoparticles. After the nanoparticles form, a large-scale migration of Si to the nanoparticles is observed. The migrating Si forms crystalline mounds, 4-5 nm in height and 250 nm wide underneath each nanoparticle, lifting them off the surface. We argue that interfacial strain drives the migration of Si and the formation of mounds. We use a simple model to estimate the elastic energy gain associated with mound formation, and to understand the shape and height of the Si mounds. Unlike Ge, SiC is refractory with a fixed stoichiometry. At the growth temperature of 900°C, Si is very mobile and we see long-range Si mass transport while the SiC nanoparticles remain intact. Thus, the system responds to strain primarily by rearrangement of the Si substrate. This is in striking contrast to Ge grown on Si(001) at lower temperatures, where the SiGe islands can easily change shape and stoichiometry. The substrate is unchanged aside from the formation of trenches where stress is concentrated at the island edge11. Our experiments were performed on extremely flat Si(001) surfaces prepared using lithographic patterning12. The samples were cleaned in vacuum by flashing to 1250°C for several seconds. SiC nanoparticles were grown during LEEM imaging via chemical vapor deposition (CVD) using either ethylene (∼ 10−6 Torr) or ethylene carbonate


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vapor (∼ 10−7 Torr) with the substrate at 900°C. Once nucleation was observed, the carbon exposure was terminated. A sequence of dark-field LEEM images recorded during ethylene carbonate exposure is shown in Fig. 2.

FIG. 2. Sequence of dark-field LEEM images recorded during the nucleation and growth of SiC islands at 900°C. The images are labeled by the time after the first nucleation event. At 25 s, monolayer deep holes appear in the surface, indicating the removal Si. At 32 s, 2 ML deep regions. The final image is labeled by with the height, in monolayers, relative to the starting surface.

In this imaging mode, the contrast changes from light to dark at an atomic step. In the final panel (t = 0) the large bright area at the center of the image indicates an atomicallyflat region approximately 3 by 3 µm in size. In panel (b), several nuclei are visible, indicated by red arrows. Ex-situ chemical imaging using transmission electron microscopy (TEM) indicates that each nucleus consists of a polycrystalline SiC nanoparticle. In panel (c) additional nuclei are observed, and several regions of dark contrast have appeared. At this point the valve to the ethylene carbonate source was closed. Ex-situ Atomic Force Microscopy (AFM) imaging, described below, shows that these dark regions are one monolayer (ML) lower than the surrounding terrace. That is, in these regions, one atomic layer of Si has been removed from the surface. As we


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discuss below, the Si removed from the terrace forms mounds underneath each nucleus. In panel (d) the nanoparticles have grown, the areas of dark contrast have expanded, and new regions of bright contrast have appeared inside the dark regions. These new regions are 2 ML below the starting surface. Note that significant Si migration is taking place even though the ethylene carbonate flow was terminated and no further nucleation is observed (chamber pressure < 5 × 10−9 Torr). In the final panel, still more Si has been removed, with both the 1 ML and 2 ML deep regions expanding. The LEEM imaging shows that the migration of the Si is triggered by the nucleation of the SiC nanoparticles. The Si continues to diffuse even after the carbon source gas has been removed. A movie of this sequence can be found in the supplemental material. Growth using ethylene rather than ethylene carbonate vapor gives indistinguishable results. After growth, the sample was cooled to room temperature. Ex-situ AFM measurements were performed immediately after removing the sample from vacuum. An AFM image from the same region of the surface imaged in LEEM is shown in Fig. 3(a). Note the correspondence to the LEEM image in Fig. 2(d). Horizontal AFM line scans over selected features are shown in Fig. 3(b). The jagged ‘summit’ of each feature corresponds to the individual SiC nanoparticles. The most striking feature is the height of the ‘mounds.’ Despite the fact that only about 0.3 nm of Si has been removed from the surrounding area, the heights of the mounds are in the range 6-10 nm. TEM imaging was used to determine the internal structure of the mounds. As described in detail in the supplemental material, each mound consists of a crystalline Si base with crystalline SiC nanoparticles decorating the apex. Critically, the SiC particles do not extend down to the initial growth surface. A representative cross-sectional TEM image is shown in Fig. 3(d), which was obtained from the region marked in red and labeled island ‘B’ in Fig. 3(a). The white dotted line indicates the initial growth surface. The height of the mound is about 8 nm, which agrees well with the AFM line scan shown in Fig. 3(b). SiC nanoparticles are visible at the center of the image. A clear boundary between the Si base and the SiC is also observed. Additional TEM images, including chemical maps, are found in the supplemental material.


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FIG. 3. (a) Ex situ AFM image of the region shown in Fig. 2. (b) AFM line scans across selected islands. The dashed line indicates the height of the surface at the start of growth. (c) TEM image of island B with the horizontal scale compressed. The dashed line indicates the starting surface. The SiC nanoparticles at the apex of the mound does not extend down to the starting surface. Inset: a 3D AFM rendering of the island. (d) TEM image of a second island showing that both the SiC nanoparticle and Si mound are crystalline.

Our observations point to a remarkable growth mode. First, the nucleation of the SiC nanoparticles is accompanied by a massive migration of Si towards the nucleation sites. Surprisingly, the diffusion of Si continues long after the carbon flux is terminated, suggesting that the Si migration is not directly linked to the growth of the nanoparticles, but rather, is driven by their mere presence. Most striking, the mound formation raises the nanoparticles 4-5 nm above the starting growth surface. The


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volume of the Si base is roughly 5-7 times larger than the volume of the SiC nanoparticles at the apex. Moreover, the mounds appear to be quite stable. In order to assess the stability we annealed the surface for one hour at 900°C in vacuum immediately after growth. The ‘footprints’ of the mounds did not change, and very little Si migration to or from surface steps was observed. We conclude that the amount of Si in each mound does not change significantly during annealing. Movies of mounds recorded during post-growth annealing are given in the supplemental material. The key question is: what drives the Si migration and mound formation? We propose that strain relaxation is the likely reason. Lattice mismatch between SiC and Si means that SiC growing on Si is inevitably under stress, which also strains the nearby Si. Under certain growth conditions, large strains have been reported for SiC nanoparticles and Si-C alloys grown on Si(001). For example, SiC strains on the order of 1% have been reported for nanoscale SiC particles embedded in Si13. Biaxial stresses in excess of 2 GPa have been reported for dilute Si-C alloy films grown on Si(001)14. In the present case, the formation of a mound lowers the strain energy by moving the highly-strained SiC/Si interface away from the substrate. The height and shape of the mound will be determined by a balance between the elastic energy gain associated mound formation and the cost of increasing the surface area. If the decrease in the strain energy is sufficiently large, formation of a mound will be energetically favorable. We first perform a simple calculation to determine if the observed height and shape of the Si mounds are consistent with a strain relaxation mechanism. We model the Si as an isotropic elastic material with Young’s modulus 130 GPa and Poisson ratio 0.28. We approximate the assembly of SiC nanoparticles at the apex of the mound by a disk of radius r0 = 60 nm and height 4 nm. The dimensions of this nanocluster were chosen based on the TEM results. We assume a uniform biaxial stress of 2 GPa in the SiC, corresponding to a strain of about 1%. For this simple, symmetric geometry, the SiC nanoparticles exert a force on the Si surface of 8 N/m on a circle of radius r0.


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FIG. 4. (a) The strain energy density, u(r), (red) and step relaxation energy, U (r), (blue) computed for a 60 nm disk with F = 8 N/m at the boundary, corresponding to a SiC strain of about 1%. The inset illustrates the mound geometry. The force loop at the top of the mound is indicated by the red arrows. (b) Formation energy of a mound as a function of the height. Points are labeled by the number of step loops in the mound. (c) AFM line scans for selected mounds in Fig. 3(a). The computed minimum energy mound shape is shown in red. (d) 3D rendering of the optimized mound shape

The mound is composed of circular, atomic-height steps (h = 0.136 nm) with radii ri centered on the disk, as shown in the inset to Fig. 4(a). To understand the elastic relaxation, it is convenient to consider creating the mound by starting with the SiC disk on a flat surface and then removing Si from the surrounding region. The reduction in strain energy associated with creating a single step loop can be computed in the following manner: consider a step with radius rb that surrounds the SiC disk. The radius of the step loop is then decreased from rb to ra < rb. This process reduces the elastic energy because strained silicon in range ra to rb is removed. The energy gain can be computed by integrating the strain energy density, u(r), over the volume of the removed silicon:

𝑟

∆𝐸(𝑟𝑎 , 𝑟𝑏 ) = − ∫𝑟 𝑏 2𝜋𝑟ℎ 𝑢(𝑟)𝑑𝑟 …(1) 𝑎

where h is the step height. The reduction in strain energy associated with forming a mound with N steps is the sum of the energies gained by introducing each step with a


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very large radius (rb = ∞) and then reducing the radius to ra = ri:

𝑁 𝐸𝑒 = ∑𝑁 𝑖=1 ∆𝐸(𝑟𝑖 , ∞) = − ∑𝑖=1 𝑈(𝑟𝑖 ) …(2)

where U (r), the step relaxation energy, is defined as

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𝑈(𝑟) = ℎ ∫𝑟 2𝜋𝑥 𝑢(𝑥)𝑑𝑥 …(3)

The elastic energy density, u(r), is computed from the strain tensor15. For a general mound shape, implementing the boundary condition, that the force normal to the surface vanish, makes direct calculation of the strain tensor difficult. However, in the present case the mounds are shallow and the small-slope approximation is valid. That is, we can assume that the displacement field in the mound is equal to that of a flat surface. It is implicit in the assumption that to first order there is no change in the strain distribution in silicon before and after mound formation. The lowering of the overall energy is brought about by redistribution of atoms to relatively less strained regions. For this simplified geometry, the strain tensor can be easily computed. At the center of the disc, a maximum strain of 0.04% was calculated at a depth roughly equal to the radius of the monopole disk. As shown in Fig. 4(a), both the strain energy density, u(r), and relaxation energy, U(r), fall off very rapidly with distance from the disk (as r-6 and r-4, respectively). Thus only steps relatively close to the disk will generate a significant reduction in the elastic energy: more than 90% of the total elastic relaxation energy comes from the 10 shortest step loops. The total reduction in strain energy can be estimated by evaluating Ee for a step profile that approximates the mound shape measured in experiment. For example, the reduction in strain energy for the profile shown in Fig. 4(c) is 218 eV. For this mound to be favorable, the energy associated with creating the steps must be less than this value. The total step length is 13.2 µm, implying that the step formation energy must be somewhat less than 17 meV/nm. This simple estimate is consistent with step energies


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inferred from the measurements of Bartelt et al.16. The relatively small step formation energy of Si(001) is crucial to the formation of the mounds. Experiments of SiC growth on Si(111) under similar conditions support this conclusion. On Si(111) the step energy is 40-50 times larger than on Si(001)17. While the SiC nanoparticles that form on Si(111) are of similar size and shape to those we observe on Si(001), no large-scale step motion is observed, and Si mounds do not form, as the large step energy makes mound formation unfavorable. The mound formation we observe for SiC/Si(001) is quite different from the trench formation observed when Ge quantum dots are grown on Si(001)11,18. Trenches form when strained Si near the Ge dot diffuses away from the dot to a region of lower strain. In the present case Si diffuses towards the SiC nanoparticle, forming a mound underneath. Mound formation is always energetically superior to trench formation, requiring less increase in surface area (or step length) for the same amount of elastic relaxation. However, trench formation is much easier kinetically. Thus trench formation occurs in systems where the substrate has very limited mobility. Here we have the same substrate – Si(001) – but the temperature is much higher (900°C) than for Ge growth (600°C), so the Si is quite mobile. The above analysis shows that Si mound formation is energetically favorable for highly-strained SiC nanoparticles. We now calculate the mound shape and height within a simple equilibrium model. In general, there is a repulsion between steps, due to both entropy19 and elastic interactions20,21. Steep sidewalls provide maximum strain relaxation with minimum step length. Thus the shallow the slope observed in experiment gives direct evidence that step repulsion is the dominant term in the step energy, consistent with model calculations22. We express the formation energy of the mound as E = Es +Ee, where the step energy, Es, includes a simple 1/r4 repulsion between neighboring steps (in addition to a noninteracting step formation energy, proportional to the total step length):


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𝑁−1 4 𝐸𝑠 = ∑𝑁 𝑖=1 2𝜋𝜆 𝑟𝑖 + ∑𝑖=1 𝜋𝛼 (𝑟𝑖+1 + 𝑟𝑖 )⁄(𝑟𝑖+1 − 𝑟𝑖 ) …(4)

where λ is the step formation energy and α is the strength of the step-step repulsion. The exact form of the potential is not critical, but this choice conveniently captures the features of both a hard-wall and a long-range repulsion between steps. To compute the equilibrium mound shape for a particular choice of λ and α, the number of steps (N ) is fixed and the step radii (ri) are optimized. That is, the volume of the mound is optimized for each height. The process is repeated for different values of N until a minimum energy is found. The result of this optimization for α = 6.4 meV nm3 and λ = 0.13 meV/nm gives good agreement with the measured mound shapes, as shown in Fig. 4 c,d. In this model, the monopole strength and mound radius can be traded off. Keeping the monopole strength fixed the height of the mound increases as the radius is increased. We want to re-emphasize that this model is significantly simplified and does not factor in the detailed structure of the polycrystalline SiC nanoparticle. The model only establishes the plausibility of strain relaxation to be the cause of these mound formation. The value of λ is smaller than that reported in an earlier study16. However, we note that these values are not unique; different choices for the form of the repulsion give very different values of λ, yet similar mound shape and similar total step energy Es. In addition, it is possible that the step energy is actually reduced here by the incorporation of carbon into the step structure. Chemisorption energies can be on the order of an eV/atom, and preferential adsorption at steps (e.g. H/Si(001)23) can significantly lower the step formation energy, even if the density of adsorbates is small. For example, B segregation to steps on Si(001) at 900°C dramatically reduces the step energy24. In summary, we have used a combination of in situ and ex situ surface microscopy to study the formation of SiC nanoparticles on Si(001) at 900°C. After nucleation of the nanoparticles, Si from the terraces diffuses to the SiC, forming crystalline Si mounds that lift each nanoparticle 4-5 nm above the surface. The volume of the Si mound is roughly 5-7 times larger than the SiC nanoparticle volume. Elastic relaxation drives the migration of Si and the formation of the mound. The low formation energy of steps on


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Si(001) is critical in enabling mound formation. On Si(111), where the step formation energy is much higher, SiC nanoparticles nucleate but mound formation is not observed. Mound formation represents a new type of morphological response to interfacial strain, where the substrate is not a passive bystander, but rearranges its morphology in response to, and to minimize, the strain energy. This new mechanism is expected to be important for growth systems where the substrate material is highly mobile.

ACKNOWLEDGEMENTS

This work was funded by the Andlinger Center for Energy and The Environment Innovation Fund, NSF CMMI 1031208, and the IBM Research Division. This data has not been previously published. There are no known conflicts of interests between the authors and any institutions and/or companies involved in this work.

Supporting Information Available: LEEM video showing growth of SiC nanoparticles on

Si(001) at 900°C on exposure to Ethylene Carbonate (s1.mp4). STEM image (Fig. 1) and EELS analysis (Fig. 2) of SiC on top of Si mound. The stability of these mounds on anneal is shown in LEEM videos (s2a.mp4 and s2b.mp4) and Fig.3. LEEM video and AFM of mound formation on exposure to Ethylene (s3.mp4, Fig.4). SiC mound analysis on Si(111) (Fig. 5) using LEEM, AFM and TEM. This material is available for free via the Internet at http://pubs.acs.org.

∗

Electronic address: [email protected]

†

Electronic address: [email protected]

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