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Shape transition of endotaxial islands growth from kinetically constrained to equilibrium regimes
Materials Research Bulletin 48 (2013) 2998–3008
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Shape transition of endotaxial islands growth from kinetically constrained to equilibrium regimes Zhi-Peng Li a,b,*, Engsoon Tok a, Yonglim Foo c a
Department of Physics, National University of Singapore, 2 Science Drive 3, S117542 Singapore, Singapore Global Research Center for Environment and Energy based on Nanomaterials Science, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan c Institute of Materials Research and Engineering, 3 Research Link, S117602 Singapore, Singapore b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 10 May 2012 Received in revised form 9 April 2013 Accepted 16 April 2013 Available online 26 April 2013
A comprehensive study of Fe grown on Ge(0 0 1) substrates has been conducted at elevated temperatures, ranging from 350 to 675 8C. All iron germinide islands, with the same Fe13Ge8 phase, grow into the Ge substrate with the same epitaxial relationship. Shape transition occurs from small square islands (low temperatures), to elongated orthogonal islands or orthogonal nanowires (intermediate temperatures), and then finally to large square orthogonal islands (high temperatures). According to both transmission electron microscopy (TEM) and atomic force microscopy (AFM) investigations, all islands can be defined as either type-I or type-II. Type-I islands usually form at kinetically constrained growth regimes, like truncated pyramids. Type-II islands usually appear at equilibrium growth regimes forming a dome-like shape. Based on a simple semi-quantitative model, type-II islands have a lower total energy per volume than type-I, which is considered as the dominant mechanism for this type of shape transition. Moreover, this study not only elucidates details of endotaxial growth in the Fe–Ge system, but also suggests the possibility of controlled fabrication of temperature-dependent nanostructures, especially in materials with dissimilar crystal structures. ß 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructure A. Interfaces B. Epitaxial growth C. Electron microscopy D. Microstructure
1. Introduction Low-dimensional nanostructures, such as quantum dots, nanorods, nanotubes, and nanowires (NWs), are essential building blocks for bottom-up approaches in nanotechnology device fabrications [1,2]. Self-assembly growth of these materials provides an attractive approach since many similar nanostructures can be formed simultaneously. A fundamental issue for selfassembly growth is the understanding of the physical mechanisms dominating the morphology and size distribution of nanostructures [3,4]. Therefore, in order to fabricate well-controlled nanostructural materials, e.g., with uniform morphology and/or narrow size distribution, it is desirable to obtain detailed knowledge of the fundamental growth processes, especially at the atomic scale. It is well established that, for the case of metal silicide nanostructure growth, the driving force for nanowire formation is anisotropic strain arising from lattice mismatch in the
* Corresponding author at: Global Research Center for Environment and Energy based on Nanomaterials Science, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan. Tel.: +81 29 8513354; fax: +81 29 8604712. E-mail addresses: [email protected], [email protected] (Z.-P. Li). 0025-5408/$ – see front matter ß 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.materresbull.2013.04.037
epitaxial growth process [5–8]. Compared to metal silicide heterostructures, few studies have focused on metal germanide systems [9,10]. Metal germanide nanostructures have been considered potential candidates for spin-polarized contacts, opto-electronic components, and in applications that can be integrated with conventional and other Si-based technology [11– 13]. This is because Ge has a higher carrier mobility and larger exciton Bohr radius compared to Si [10]. In this study, we investigate Fe–Ge nanostructure formation over a temperature range from 350 8C to 675 8C. Systematic observations of the nanostructure morphology transition as a function of deposition temperature are performed accordingly. In situ ultra-high vacuum transmission electron microscopy (UHVTEM) can provide a unique view into nanostructure formation, and was utilized to explore the kinetics of the reaction and growth mechanism of Fe–Ge nanostructures during epitaxial growth. Previous studies have reported that most theoretical and experimental reports of NW formation in other systems were performed at high temperatures (i.e., 800 8C) and assumed that growth occurred due to equilibrium conditions driven by thermodynamics considerations [6,14–17]. Therefore, it is also necessary to explore whether NWs form at high deposition temperatures in the Fe–Ge materials system, as well as, whether the NWs in this system are in the equilibrium state.
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2. Experimental The Fe–Ge system has been investigated by examining the shape evolution of Fe–Ge islands during each individual deposition process, using the same deposition flux at different deposition temperatures on different samples. Experiments were performed in an in situ JEOL2100 UHV-TEM operated at 200 kV using a JEOL double-tilt heating specimen holder. The cleaning process and experimental set up have been discussed in a previous report [18]. After the specimen is thermally cleaned in the TEM chamber by out-gassing and flashing to obtain atomic cleaned surface, it is ready for the reactive deposition at ultra high vacuum (109 Torr) condition. The electron beam evaporator control mains are then turned on and the high voltage (HV) is slowly brought up to the deposition voltage (800 V in our experiments). The electron emission will be continuously increased (10 mA) until the desired deposition flux is observed (1 nA in the reactive deposition epitaxy process). During reactive deposition, constant deposition flux is maintained through the adjustment of the electron emission
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current. The deposition temperature varies from different samples (from 350 to 675 8C), resulting in different growth rates (varying from 8.1 to 61.3 nm S1) obtained. After deposition, we can also take DP or images of other areas of this specimen to get a globe view of the growing islands morphology on the whole substrate surface. Ex situ cross-sectional TEM observations were carried out using a 300 keV Philips CM300 field emission TEM to obtain high resolution TEM (HR-TEM) images. For cross-sectional TEM sample preparation, iron was ex situ deposited on different clean Ge(0 0 1) substrates at different temperatures with the same deposition flux and growth time, with no anneal. Next, two identical samples were glued film-to-film and the glued sample cut vertically to obtain cross section segments. Mechanical grinding was used to thin the glued sample to 20 mm thick, which was followed by polishing with diamond paste. Final thinning to electron transparency was accomplished by Ar ion milling in a Gatan Precision Ion Polishing System, with the angle of incident beam and energy progressively reduced from 88 to 58 and 5–1.5 kV in order to ensure ion-milled samples were of relatively even thickness.
Fig. 1. Bright-field plan-view TEM images and corresponding SAED patterns (insets) of Fe13Ge8 islands grown at (a) 350, (b) 430, (c) 480, (d) 510, (e) 570 and (f) 675 8C, respectively.
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Fig. 2. Plots of Fe13Ge8 islands (a) length and width evolution as a function of deposition temperatures and (b) aspect ratio of length versus width as a function of deposition temperature.
Atomic force microscope (AFM) using a Digital Instruments Nanoscope IIIa was conducted to probe island height and to obtain three-dimensional (3D) information of islands grown at different temperatures. The series of AFM samples were prepared by depositing Fe directly onto Ge(0 0 1) substrates during reactive
deposition epitaxy (RDE) processes with the same deposition flux and time as in the TEM, but this occurred with different temperatures. All samples were examined immediately after they were transferred from the growth chamber (typically within 30 min) by AFM, in order to minimize the effect of exposure to atmosphere.
Fig. 3. Time series of BF TEM images of Ge(0 0 1) substrate surface during reactive deposition of Fe at 570 8C. (a) Cleaned pure Ge(0 0 1) substrate prior to deposition. (b)–(i) Real time observation images about shape evolution of growing islands on Ge(0 0 1) substrate as a function of deposition time. Insets in (a) and (i) are corresponding SAED patterns.
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3. Results 3.1. Plan-view island morphology by TEM Fig. 1 demonstrates typical bright-field (BF) plan-view TEM micrographs of iron germinide islands grown at different temperatures ranging from 350 to 675 8C. Depositions were conducted using the same constant Fe flux for the same deposition time (50 min) at different temperatures in the pre-coalescence regime. Fig. 1(a) is a TEM image of islands grown at 350 8C, which clearly shows that all grown islands are predominately small and square in shape at orthogonal directions to the substrate. At a higher deposition temperature on a different sample (430 8C), two types of islands begin to appear, namely square and elongated, as shown in Fig. 1(b). At a deposition temperature of 480 8C, only elongated rectangular islands are formed along two orthogonal Ge h1 1 0i azimuths (Fig. 1(c)). At 510 8C, long NWs are formed (Fig. 1(d)). More details about Fe13Ge8 islands grown at deposition temperatures ranging from 350 to 510 8C have been discussed in the previous report [18]. Interestingly, as the deposition temperature was further increased to 570 8C, NWs could be seldom observed, which was unexpected from the trend of island shape evolution that occurred between deposition temperatures from 350 to 510 8C. At 570 8C, all islands have larger sizes with rectangular shapes having larger length versus width aspect ratios while still maintaining an orthogonal relationship with the substrate (Fig. 1(e)). Moreover, the islands aspect ratios decreases as the deposition temperature increased to 675 8C (Fig. 1(f)), only square shape islands were observed. Nevertheless, these square islands have a much larger size than those formed at lower temperatures (i.e. 350 8C). The number of islands decreases rapidly, as expected, when deposition temperatures increase from 350 to 675 8C.
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The inset in each frame in Fig. 1 is the corresponding selected area electron diffraction (SAED) of all grown islands on the Ge(0 0 1) substrate. By indexing these SAED pattern, the phase of grown islands (Fe13Ge8) as well as the epitaxial relationship to the underlying Ge(0 0 1) substrate was determined as Fe13 Ge8 ½1¯ 1 0 2==Ge ½0 0 1 and Fe13 Ge8 ð1 1 2¯ 0Þ==Geð1 1 0Þ, which is in accordance with previous results [18,19]. Note that all SAED patterns appear similar to each other, clearly indicating that all islands have the same phase as well as the same epitaxial orientation with respect to the underlying Ge(0 0 1) substrate. In order to clarify island shape evolution, the average islands’ length and width versus deposition temperatures has been plotted in Fig. 2(a). Moreover, the island aspect ratio as the function of deposition temperature has been presented in Fig. 2(b). Note that there are two different trends for island morphology evolution. One trend is that the aspect ratio keeps increasing with increasing temperature from 350 to 510 8C, which is where island shape transition from small square to long wires occurred. The other trend has the aspect ratio decreasing as the temperature increases over 510 8C, with the shape evolution from long wires to large square islands. The two types of island shape evolution appeared at different temperature regimes, one below and the other above 510 8C, implying that there may be two different growth mechanisms that dominate island formation. This is especially intriguing since all grown islands have the same phase and epitaxial relationship. 3.2. In situ TEM observation of island growth during RDE process To further explore the temperature dependent island growth transition at two different temperature regimes (below and above 510 8C), in situ UHV-TEM was employed to follow the dynamics of the island growth processes by directly observing island shape
Fig. 4. Plots of length and width of the growing Fe13Ge8 island as a function of deposition time at (a) 570 8C and (c) 675 8C, respectively. Plots of the corresponding growing island aspect ratio of length versus width as a function of deposition time at (b) 570 8C and (d) 675 8C, respectively.
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Fig. 5. HRTEM images of Fe13Ge8 islands endotaxially grown at (a) 400, (b) 450, (c) 500 and (d) 650 8C, respectively. Insets in (b) and (d) are corresponding diffractograms.
evolution during RDE processes at these different temperatures. The length and width evolution of growing islands as a function of deposition time at different deposition temperatures below 510 8C have been demonstrated previously [19]. In this study, in situ observations were focused on island growth at deposition temperatures above 510 8C. Fig. 3 displays a series of typical BF plan-view TEM images of Fe13Ge8 island growth during the RDE process at 570 8C. The BF image of the Ge(0 0 1) substrate surface is clean prior to deposition (Fig. 3(a)), as seen from the inset SAED pattern oriented along the Ge[0 0 1] zone axis (ZA). When the electron beam evaporator shutter is opened, Fe is directly deposited onto the Ge(0 0 1) substrate in the TEM. Random islands nucleating on the Ge(0 0 1) substrate are observed in less than 1 min, with a low island density, which is as expected, since high temperatures result in fast nucleation rates and low island density. All randomly nucleated islands initially have an approximately square shape (Fig. 3(b)). As deposition continues, the growing islands increase their size rapidly, while retaining their near-square shape during the entire deposition process (Fig. 3(b)–(i)). The inset in Fig. 3(i) is the corresponding SAED pattern with the same epitaxial orientation and Fe13Ge8 phase as obtained below 510 8C. Similar observations are also obtained when the RDE process occurred at 675 8C. Fig. 4(a) shows the length and width evolution of growing islands (Fig. 3) during the RDE process at 570 8C. Fig. 4(b) is the corresponding aspect ratio of island length versus width as a function of deposition time, which shows that the growing islands maintain a near square shape with a mean aspect ratio of 1.2:1. Similar results were also obtained for islands grown at 675 8C (Fig. 4(c) and (d)). This phenomenon is completely different from that observed below 510 8C, where significant morphology evolution and growth dynamics occurred as a function of deposition temperatures [19]. Moreover, during deposition at
temperatures of 570 and 675 8C, the length and width of the growing islands are non-linear over time, differing from the linear growth observed at temperatures below 510 8C [18]. 3.3. Cross-sectional TEM and AFM studies of island shape transition According to plan-view TEM observations, it is clear that island shape evolution at different temperatures can be divided into two regimes: one is the shape transition from small squares to wires, at a temperature range between 350 and 510 8C; the other is the
Fig. 6. Stereographic projection plot of Fe13Ge8–Ge system with defined epitaxial relationship, projected from ZA of both Fe13Ge8 ½1¯ 1 0 2 and Ge [0 0 1]. Red and green colored dots stand for the poles of Ge and Fe13Ge8, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Fig. 7. AFM images of Fe13Ge8 islands grown at (a) 350, (c) 450, (e) 510, and (g) 600 8C separately. (b), (d), (f) and (h) are profiles of AFM line scans denoted by blue lines in (a), (c), (e) and (g), respectively.
shape transition from wires to large square islands, which occurred above 510 8C. Even though island shape transition has been studied by measuring length and width evolution, as well as length versus width aspect ratio as a function of deposition temperatures, all these studies were based only on plan-view TEM observations. Therefore, in order to comprehensively investigate island shape transitions, it is necessary to observe island morphology from the cross-sectional view, which can provide information of island facets, as well as the interfaces between the grown islands and the underlying substrate. Fig. 5 shows HR-TEM images of Fe13Ge8 islands grown at 400, 450, 500 and 600 8C, respectively. All islands are not just growing flush on the flat Ge(0 0 1) substrate, instead, all islands diffuse along inclined Ge planes and grow into the Ge(0 0 1) substrate, which is the so-called ‘endotaxial’ growth. Interestingly, all Fe13Ge8 islands, grown at temperatures below 510 8C, have similar cross-sectional configurations (Fig. 5(a)–(c)). All these (low temperature) islands are bound by similar facets and interfacial planes. In contrast, islands grown above 510 8C have significantly different cross-sectional configurations (Fig. 5(d)). At these higher temperatures, new facets begin to appear around the islands. Stereographic projection was used to precisely define the facets and interfacial planes bound around the islands. Fig. 6 is a combination stereographic projection plot showing the epitaxial relationship between Fe13Ge8 and Ge, projected along
the ZA of Fe13 Ge8 ½1¯ 1 0 2 and Ge[0 0 1]. Red and green colored dots indicate poles of Ge and Fe13Ge8, respectively. Since each pole corresponds to each plane belonging to either Fe13Ge8 or Ge, then each crystal plane, as well as the angular relation between the crystal planes, can be directly interpreted from this stereographic projection. By measuring the angular relationship between the facets or interfacial planes bound around the Fe13Ge8 islands, we can identify interfacial planes between islands and the substrate, as well as island facets. For example, for Fe13Ge8 islands grown ¯ f4 4¯ 0 1g ¯ and below 510 8C, there are three types of facets (f1 1¯ 0 2g, ¯ that are bound above the Ge(0 0 1) substrate. The flat top ð2 2¯ 0 1Þ) ¯ which is of each island is formed by the facet of Fe13 Ge8 ð2 2¯ 0 1Þ parallel to Ge(0 0 1) surface, while the other two inclined sides are ¯ and f4 4¯ 0 1g. ¯ The three types of facets bound by the facets f1 1¯ 0 2g above the substrate surface thus form a trapezoidal shape, as viewed in cross-section, which can be observed along both projections of island length and width azimuths. For islands grown above 510 8C, some other steeper facets are introduced, as ¯ shown in Fig. 5(d). The two types of shallow facets of the f1 1¯ 0 2g ¯ interfaces with side-facet angles to the substrate and f4 4¯ 0 1g surface of 358 and 558, respectively, are substituted by discontinuous introduction of considerably steeper facets ð2 2¯ 0 1Þ and ¯ which both have the side-facet angle 708 to the substrate. ð1¯ 1 0 2Þ ¯ formed below 510 8C is also Meanwhile, the flat top ð2 2¯ 0 1Þ gradually substituted by other newly formed facets ð4 4¯ 0 1Þ,
Table 1 AFM results of average height of Fe13Ge8 islands grown at different deposition temperatures. Deposition temperature
Number of islands investigated per mm2 Average height (nm) Deposition temperatures Number of islands investigated per mm2 Average height (nm)
350 8C (wire-like)
430 8C (wire-like)
480 8C (wire-like)
510 8C (wire-like)
311 8.5 1.5 550 8C (wire and dome-like) 90 25.2 3.0
255 20.1 3.0 600 8C (dome-like) 81 49.4 4.0
183 20.8 3.0 650 8C (dome-like) 64 52.9 4.0
107 18.2 4.5
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Fig. 8. Three-dimensional AFM images of Fe13Ge8 islands grown at (a) 450 8C and (b) 600 8C, respectively. Corresponding schematic view of Fe13Ge8 islands are shown in (c) grown below 510 8C and (d) grown above 510 8C separately.
¯ ð1 1¯ 0 1Þ ¯ and ð1 1¯ 0 3Þ, ¯ with side-facet angles 558, 158, 188, ð4 4¯ 0 1Þ, and 408, respectively, to the horizontal azimuth of substrate, and finally evolve to form a vertex at the top. Fig. 5 not only demonstrates the difference between facets and interface planes bound around islands, but also shows the height evolution of islands at the two different temperature regimes. Systematical investigations reveal that islands grown below 510 8C have similar heights 20 nm. However, the heights of islands grown above 510 8C increase significantly and reach 60 nm, with some as high as 80 nm. Due to the limitation of both plan-view and cross-sectional view within a TEM, only relatively small thin regions can be observed. To fully investigate islands morphology, especially island height evolution, it is necessary to employ AFM, which can probe the morphology over a larger sample surface, providing a comprehensive global view of islands grown on Ge substrates. Fig. 7 shows AFM images of Fe13Ge8 islands grown at 350, 450, 510, and 600 8C. These AFM results illustrate that, at low
temperatures (350 8C), islands have a square trapezoidal shape with a small size. With an increase in the deposition temperature, the islands begin to evolve into elongated shapes (450 8C). Wires appear at higher temperatures around 510 8C. However, at 600 8C, the islands revert to their square shape but with increased size. Moreover, islands grown at 600 8C are much higher above the substrate than those grown below 510 8C, according to island height measurement shown in Fig. 7. Fig. 7(g) and (h) also demonstrates that square islands are much higher above the substrate than those elongated islands formed at the same temperature. Together with the results shown in Fig. 7, the heights of Fe13Ge8 islands grown at different temperatures (i.e., 430, 480, 550, and 650 8C) were also detected by AFM (Table 1). Also, these AFM results are in accord with our current crosssectional TEM observations. On the basis of both AFM and TEM investigations, islands grown below and above 510 8C can be divided into two types as shown in Fig. 8. Fig. 8(a) is typical three-dimensional AFM image of islands
Table 2 HRTEM results of average height and aspect ratio of Fe13Ge8 islands grown at different deposition temperatures. Deposition temperature
Number of islands investigated Average height(above substrate) (nm) Average height(below substrate) (nm) Height(above substrate) versus height(below substrate)
350 8C (wire-like)
400 8C (wire-like)
450 8C (wire-like)
500 8C (wire-like)
600 8C (dome-like)
650 8C (dome-like)
31 9.1 1.5 19.1 3.0 0.49
20 20.1 3.0 35.9 3.0 0.56
19 21.1 3.0 37.1 3.0 0.57
13 22.9 3.0 46.1 4.0 0.52
15 45.2 4.0 23.5 3.0 1.92
23 63.9 5.0 30.9 3.0 2.07
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Fig. 9. Plots of (a) AFM and cross-sectional TEM results of Fe13Ge8 island average height as a function of deposition temperatures. (b) TEM results of aspect ratio (height above substrate versus height below substrate) as a function of deposition temperatures. Insets are typical HRTEM images of Fe13Ge8 islands with different configurations.
grown at 450 8C. All islands have distinct shallow facets bound at each side and have a truncated pyramid-like shape. For islands formed at 600 8C, all the surrounding shallow facets disappear and are substituted by steeper facets, leading to multifaceted domelike islands (Fig. 8(b)). The corresponding schematic diagrams of these two types of islands are shown in Figs. 8(c) and (d) respectively. As a consequence, islands grown below 510 8C have a truncated pyramid-like shapes with either a square or elongated base, and are assigned as type-I. While islands grown above 510 8C, have dome-like shapes with either a square or small aspect ratio rectangular base, denoted as type-II. It is emphasized that island height evolution at different temperatures can be explained not only by the height above the Ge(0 0 1) substrate, but also by the height below the Ge(0 0 1) substrate. Therefore, it is essential to characterize height evolution by comparing island height both above and below the Ge(0 0 1) substrate with the aid of cross-sectional TEM observations. TEM results of average height (both above and below the Ge(0 0 1) substrate) and the corresponding epitaxial/endotaxial ratio (height above substrate versus height below substrate) of Fe13Ge8 islands grown at different temperatures are listed in Table 2. It clearly illustrates that island heights (both above and below substrate) as
well as the aspect ratios change significantly at temperatures below and above 510 8C. Plots in Fig. 9 intuitively display island height evolution (above substrate, Fig. 9(a)) as well as the aspect ratio of island height above substrate versus the height below substrate as a function of deposition temperatures (Fig. 9(b)). From Fig. 9(a), all type-I islands have an average height 20 nm, which is independent of the island’s basal shape (e.g., square, rectangle or wire). However, the average height of type-II islands greatly increases to 55 nm around 600 8C. On one hand, the average height (above substrate) of Fe13Ge8 islands has a transition from 20 nm to 55 nm between type-I and type-II islands. On the other hand, the change of island height (above substrate) results in the aspect ratio (height(above substrate) versus height(below substrate)) transition from 0.5 to 2 below and above 510 8C as shown in Fig. 9(b). 4. Discussion Since all observed islands have the same phase (Fe13Ge8) as well as the same epitaxial orientation relationship to the underlying Ge(0 0 1) substrate at all deposition temperatures, therefore, it is unlikely that island shape transition, from small square shapes to
Fig. 10. Schematic cross-sectional view of an interface between Fe13Ge8 and Ge(0 0 1) substrate. Both views are projected from Ge[1 1 0] ZA. The colored unit cells are used to indicate the orientation directions. Fe atoms in Fe13Ge8 crystal structure are omitted for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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long wires and then to large square islands, is due to either phase transformation or different island orientations to the Ge(0 0 1) substrate. Previous work demonstrated that at temperatures below 510 8C, island shape transition from squares to long wires is due to the kinetic growth constraint in terms of anisotropic ledge diffusion and corner barriers [18]. In order to further understand the shape transition from wires to large squares above 510 8C, it is necessary to analyze the atomic scale relation between islands and substrate in more detail. Similar phenomena, that different types of islands form having the same phase and diffraction pattern, have been widely observed in XSi2 (X = Ni, Co) systems [20–22]. The Gibson model elucidated that in such systems, the so-called type-A (square shape) and typeB (elongated shape) island formation is due to interface structure differences [23,24]. In type-A structures, grown islands have a continuous extended structure similar to that of substrate. While in type-B structures, the epitaxial structure has a 1808 rotation along the ZA retaining the same orientation relationship with the substrate, resulting in the formation of a single stacking fault in the interface plane. In this study, since all islands endotaxially grew into the substrate, it is necessary to investigate the interface structure. Fig. 10(a) demonstrates a schematic diagram of the crosssectional view of an interface structure between an Fe13Ge8 island and the Ge(0 0 1) substrate, projected along the Ge [1 1 0] with the defined epitaxial relationship. All Fe atoms in Fe13Ge8 crystal structure are omitted for clarity. Fig. 10(b) is a similar to Fig. 10(a) except that the Fe13Ge8 crystal structure has been rotated by1808 along the Ge [0 0 1] ZA while the Ge(0 0 1) substrate maintains the same orientation. Comparing Fig. 10(a) and Fig. 10(b), all the Ge atoms in Fe13Ge8 lay along the same Ge lattice planes as that in the underlying Ge(0 0 1) substrate. Therefore no single stacking faults are formed in the plane because of the Fe13Ge8 rotation. And only one type of interface exists between the Fe13Ge8 island and the Ge substrate. It can be concluded that different types of island morphology formed in this study are not due to type-A or type-B interface formation as predicted by the Gibson model [23,24]. As a consequence, we need to probe the mechanism that causes island shape transition. At high temperatures (above 510 8C) this mechanism is different from the kinetically constrained Fe13Ge8 island shape evolution below 510 8C [18], it seems that thermodynamics may be the driving force for the formation of small square islands. There is a well-developed understanding of island shape transition from shallow faceted pyramid to multifaceted dome for the Ge nanocrystal grown on a Si surface, as well as the InAs/ GaAs(0 0 1) quantum dots faceting process [25–29]. Using thermodynamic considerations, these transitions are controlled by the complex interplay between the surface energy and the builtup strain energy (due to the lattice mismatch between the epilayer and substrate). Nevertheless, in the Fe13Ge8/Ge(0 0 1) system, islands grow along the co-planar inclined Geð1 1¯ 1Þ plane and form the coherent interface, that leads to endotaxial growth [30,31]. The interfacial energy between growing islands and the substrate thereby begins to play a more important role than that of strain energy in the endotaxial growth process. Compared with the pyramid-to-dome shape transition, which depends on surface and strain energies, our considerations mainly focuses on the complex interplay between surface and interface energies.
¯ plane with neighboring atoms of (a) Fig. 11. Computer simulated Fe13 Ge8 ð1 1¯ 0 2Þ side-view and (b) plan-view. Green and red dots stand for germanium and iron atoms in Fe13Ge8 respectively, while white and red colored dots denote iron atoms ¯ plane. (For interpretation of the references to color in this figure in the ð1 1¯ 0 2Þ legend, the reader is referred to the web version of the article.)
For island surface and interface energies calculations, our analysis is based on the dangling bound energy, which is the main contribution to surface free energy in the absence of strain. The nearest-neighbor (NN) atom–atom interaction method is applied to calculate surface energy for each facet and/or plane. Consider ¯ plane for example, where Fig. 11 shows the the Fe13 Ge8 ð1 1¯ 0 2Þ ¯ plane with neighboring atoms with (a) side-view Fe13 Ge8 ð1 1¯ 0 2Þ and (b) plan-view. Green and red dots denote Ge and Fe atoms respectively in Fe13Ge8, while white and red-striped dots represent ¯ plane. By measuring the atom–atom Fe atoms in the ð1 1¯ 0 2Þ distance, it was found that the NN distance between Ge and Fe in ¯ plane was 2.49 A˚, while the Fe to Fe NN distance is the ð1 1¯ 0 2Þ 2.50 A˚. We can simply count the NN atom–atom interactions and use this as a substitute for the dangling bond energy, where the notation bFe/Ge and bFe/Fe, denotes the dangling bond energy between Fe–Ge atoms and Fe–Fe atoms, respectively. After determining all possible dangling bonds between the target plane and its NN atoms, we can divide this value by the unit cell of the corresponding plane, such as the 3.99 7.35 A˚2 rectangle which is ¯ plane, as shown in Fig. 11(b). The the unit cell of Fe13 Ge8 ð1 1¯ 0 2Þ dangling bond density of each crystal plane can be obtained using this method. Table 3 shows the dangling bond density of all crystal planes bound around islands grown at different temperatures, notated as the number of dangling bond per A˚2. Fig. 12(a) and (b) represents the schematic cross-sectional view of type-I and type-II island shapes, projected along the island length azimuth, while maintaining the same cross-sectional area. We treat this problem in 2D for simplicity, nevertheless all the key results developed here are also applicable in 3D, as discussed later. After defining the surface energy of each facet/plane in terms of dangling bond density, we calculated the free surface energies per
Table 3 Dangling bond density of each crystal plane in Fe13Ge8. Fe13Ge8 planes
¯ ð2 2¯ 0 1Þ
¯ ð1 1¯ 0 2Þ
ð4 4¯ 0 1Þ
¯ ð0 0 0 1Þ
¯ ð1 1¯ 0 1Þ
¯ ð1 1¯ 0 3Þ
¯ ð4 4¯ 0 1Þ
No. of dangling bond per A˚2
0.0413bFe/Fe + 0.0826bFe/Ge
0.0341bFe/Fe + 0.0682bFe/Ge
0.0237bFe/Fe + 0.0712bFe/Ge
0.0725bFe/Fe + 0.1450bFe/Ge
0.0588bFe/Fe + 0.0881bFe/Ge
0.0235bFe/Fe + 0.0353bFe/Ge
0.0237bFe/Fe + 0.0712bFe/Ge
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Fig. 12. Schematic diagrams of cross-section configurations of (a) type-I and (b) type-II islands.
unit length for the top, shallow, and steep side facets, as well as the interface planes below the substrate. The total energy of the island can be described in the form of E = Es + Ei, where Es is the facet surface energy and Ei is the island–substrate interface energy. We assume type-I and type-II islands have the same volume to simplify this into a 2D problem by setting the two types of islands with the same unit length, which means the total cross-sectional area (S) of the 2D islands shown in Fig. 12(a) and (b) are the same. Then the total energy of the island can be written in the following P P way: E = Es + Ei = sgsLs + igiLi, where gs is surface energy (per unit length) of each island facet, Ls is each facet’s length of the 2D island cross-sectional diagram as shown in Fig. 12(a) and (b), the gi is the island–substrate interface energy (per unit length) and Li is the corresponding length of each interface side. Since the total cross-sectional area of the two types of islands is the same, we can obtain the individual side length Ls and Li for the 2D island from direct HR-TEM measurements. Comparing the results calculated from Table 3, the energy per unit area (E/S) for the two types of islands is as follows. It was found that the E/S for type-I islands (Fig. 12(a), 2.41 104bFe/Fe + 5.47 104bFe/Ge per A˚2) is less than that of type-II islands (Fig. 12(b), 3.21 104bFe/ 4 bFe/Ge per A˚2), which illustrates that type-I islands Fe + 7.11 10 have a lower total surface and interface energy per unit volume than type-II islands. Therefore, for a given volume, this indicates that the island prefers to adopt the optimal shape of type-II to minimize its total surface and interface energies at high temperatures. From our semi-quantitative model as shown in Fig. 12 and Table 3, the appearance of different facets/planes bounded the island is temperature dependent. Note that highly inclined steeper ¯ together facets induced at the base of islands (i.e. ð2 2¯ 0 1Þ, ð1¯ 1 0 2Þ) ¯ with the newly formed inclined facets/interfaces (i.e. ð4 1¯ 0 1Þ, ¯ ð1 1¯ 0 3Þ) ¯ become slightly more favorable because of their ð1 1¯ 0 1Þ, lower surface/interface energies, compared to those facets formed below 510 8C. The island shape transition from wire-like to the optimal shape of dome-like square base island is dominated by the driving force associated with minimization of its total surface and interface energies as discussed in our model. Therefore, the faceting process provides the possibility to stabilize the island configuration and reach its equilibrium state [32–34]. At high temperatures, deposited Fe adatoms can obtain sufficient energy to overcome surface and interface diffusion barriers, or corner barriers, and can rapidly diffuse on the substrate as well as the
facets to find the most stable sites, subsequently forming low surface/interface energy facets/planes. The rapid accumulation of adatoms to existing islands and fast adatoms diffusion on the island surface/interface will drive islands to adopt a larger size, rapidly increasing the growth rate of higher energy planes and dramatically increasing island height, by leaving behind the slowly growing planes. The faster growth of the high energy facets will replace the flat top with additional higher Miller indices facets to form a vertex at the top. Therefore, island growth terminates at lower surface/interface energy planes [35–37]. In addition, in order to be epitaxially registered on the isotropic Ge(0 0 1) surface, islands prefer to adopt a square shape which can reflect the symmetry of the underlying substrate and thus to reduce the length/width aspect ratio to reach the equilibrium state. Consequently, this leads to the formation of type-II islands. All islands grown above 510 8C maintain their square shape during the whole annealing process, which indicates that type-II islands exist in their equilibrium state. This island shape transition at different deposition temperatures provides a dramatic illustration of the importance of surface and interface energies in controlling the island growth habit and formation, especially for the endotaxial growth process. 5. Conclusions In summary, Fe13Ge8 islands formation on single crystal Ge(0 0 1) substrates at 350, 430, 480, 510, 570 and 675 8C have been comprehensively studied by using various of techniques: in situ UHV-TEM, HR-TEM, SAED, and AFM. Distinct island shapes form at different temperatures. At low temperatures (350 8C) small square islands form. As the deposition temperature increased, islands grew with elongated shapes (430 8C) and the length versus width aspect ratio increased as a function of the deposition temperature, which finally grew into long NWs at high temperatures (510 8C). Nevertheless, larger square islands formed at higher temperatures (above 510 8C) in preference to the long NWs. All the islands, grown at different temperatures, have the same phase and share the same epitaxial relationship to the underlying Ge(0 0 1) substrate. It suggests that this type of temperature dependent island shape transition is not due to a phase transformation, nor the type-A and type-B interface structures formation as predicted in Gibson model. We propose that island morphology evolution below 510 8C is due to kinetic
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constraints in terms of anisotropic ledge diffusion and corner barriers. Whereas at temperatures above 510 8C, facets/interfaces bounded around islands begin to change. Below 510 8C, all the islands have a similar cross-sectional shape and is defined as typeI. They appear as truncated pyramids with shallow facets at each side and a flat facet at the top. The aspect ratio of the epitaxial versus the endotaxial height of type-I island is 0.5. Type-II islands appear above 510 8C, and have much steeper facets at the bottom with larger heights above the substrate, forming dome-like shape with a square base. The aspect ratio of height above substrate versus height below substrate of type-II islands is 2. According to the surface/interface energy calculation per unit volume of the two types of islands, this illustrates that type-II islands have a lower total energy per unit volume than that of type-I. It can be concluded that minimizing the total surface and interface energies to reach their equilibrium state may be the driving force that leads to the shape transition from type-I to type-II. Moreover, this study demonstrates that the NWs formed in the hex-Fe13Ge8/Ge system are not structures in thermodynamic equilibrium. This study provides a comprehensive understanding of low dimensional structure formation and shape transition from kinetically constrained to equilibrium regimes. Acknowledgment Z.P. Li would like to thank G.J. Auchterlonie (The University of Queensland, Australia) for helpful discussions and proof reading. References [1] Y. Cui, C.M. Lieber, Science 291 (2001) 851. [2] J.B. Hannon, J. Tersoff, R.M. Tromp, Science 295 (2002) 299. [3] K. Bromann, C. Felix, H. Brune, W. Harbinch, R. Monot, J. Buttet, K. Kern, Science 274 (1996) 956. [4] V.G. Dubrovskii, T. Xu, Y. Lambert, J.P. Nys, B. Grandidier, D. Stievenard, W. Chen, P. Pareige, Phys. Rev. Lett. 108 (2012) 105501. [5] L.J. Chen, K.N. Tu, Mater. Sci. Rep. 6 (1991) 53.
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Materials Research Bulletin journal homepage: www.elsevier.com/locate/matresbu
Shape transition of endotaxial islands growth from kinetically constrained to equilibrium regimes Zhi-Peng Li a,b,*, Engsoon Tok a, Yonglim Foo c a
Department of Physics, National University of Singapore, 2 Science Drive 3, S117542 Singapore, Singapore Global Research Center for Environment and Energy based on Nanomaterials Science, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan c Institute of Materials Research and Engineering, 3 Research Link, S117602 Singapore, Singapore b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 10 May 2012 Received in revised form 9 April 2013 Accepted 16 April 2013 Available online 26 April 2013
A comprehensive study of Fe grown on Ge(0 0 1) substrates has been conducted at elevated temperatures, ranging from 350 to 675 8C. All iron germinide islands, with the same Fe13Ge8 phase, grow into the Ge substrate with the same epitaxial relationship. Shape transition occurs from small square islands (low temperatures), to elongated orthogonal islands or orthogonal nanowires (intermediate temperatures), and then finally to large square orthogonal islands (high temperatures). According to both transmission electron microscopy (TEM) and atomic force microscopy (AFM) investigations, all islands can be defined as either type-I or type-II. Type-I islands usually form at kinetically constrained growth regimes, like truncated pyramids. Type-II islands usually appear at equilibrium growth regimes forming a dome-like shape. Based on a simple semi-quantitative model, type-II islands have a lower total energy per volume than type-I, which is considered as the dominant mechanism for this type of shape transition. Moreover, this study not only elucidates details of endotaxial growth in the Fe–Ge system, but also suggests the possibility of controlled fabrication of temperature-dependent nanostructures, especially in materials with dissimilar crystal structures. ß 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Nanostructure A. Interfaces B. Epitaxial growth C. Electron microscopy D. Microstructure
1. Introduction Low-dimensional nanostructures, such as quantum dots, nanorods, nanotubes, and nanowires (NWs), are essential building blocks for bottom-up approaches in nanotechnology device fabrications [1,2]. Self-assembly growth of these materials provides an attractive approach since many similar nanostructures can be formed simultaneously. A fundamental issue for selfassembly growth is the understanding of the physical mechanisms dominating the morphology and size distribution of nanostructures [3,4]. Therefore, in order to fabricate well-controlled nanostructural materials, e.g., with uniform morphology and/or narrow size distribution, it is desirable to obtain detailed knowledge of the fundamental growth processes, especially at the atomic scale. It is well established that, for the case of metal silicide nanostructure growth, the driving force for nanowire formation is anisotropic strain arising from lattice mismatch in the
* Corresponding author at: Global Research Center for Environment and Energy based on Nanomaterials Science, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan. Tel.: +81 29 8513354; fax: +81 29 8604712. E-mail addresses: [email protected], [email protected] (Z.-P. Li). 0025-5408/$ – see front matter ß 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.materresbull.2013.04.037
epitaxial growth process [5–8]. Compared to metal silicide heterostructures, few studies have focused on metal germanide systems [9,10]. Metal germanide nanostructures have been considered potential candidates for spin-polarized contacts, opto-electronic components, and in applications that can be integrated with conventional and other Si-based technology [11– 13]. This is because Ge has a higher carrier mobility and larger exciton Bohr radius compared to Si [10]. In this study, we investigate Fe–Ge nanostructure formation over a temperature range from 350 8C to 675 8C. Systematic observations of the nanostructure morphology transition as a function of deposition temperature are performed accordingly. In situ ultra-high vacuum transmission electron microscopy (UHVTEM) can provide a unique view into nanostructure formation, and was utilized to explore the kinetics of the reaction and growth mechanism of Fe–Ge nanostructures during epitaxial growth. Previous studies have reported that most theoretical and experimental reports of NW formation in other systems were performed at high temperatures (i.e., 800 8C) and assumed that growth occurred due to equilibrium conditions driven by thermodynamics considerations [6,14–17]. Therefore, it is also necessary to explore whether NWs form at high deposition temperatures in the Fe–Ge materials system, as well as, whether the NWs in this system are in the equilibrium state.
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2. Experimental The Fe–Ge system has been investigated by examining the shape evolution of Fe–Ge islands during each individual deposition process, using the same deposition flux at different deposition temperatures on different samples. Experiments were performed in an in situ JEOL2100 UHV-TEM operated at 200 kV using a JEOL double-tilt heating specimen holder. The cleaning process and experimental set up have been discussed in a previous report [18]. After the specimen is thermally cleaned in the TEM chamber by out-gassing and flashing to obtain atomic cleaned surface, it is ready for the reactive deposition at ultra high vacuum (109 Torr) condition. The electron beam evaporator control mains are then turned on and the high voltage (HV) is slowly brought up to the deposition voltage (800 V in our experiments). The electron emission will be continuously increased (10 mA) until the desired deposition flux is observed (1 nA in the reactive deposition epitaxy process). During reactive deposition, constant deposition flux is maintained through the adjustment of the electron emission
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current. The deposition temperature varies from different samples (from 350 to 675 8C), resulting in different growth rates (varying from 8.1 to 61.3 nm S1) obtained. After deposition, we can also take DP or images of other areas of this specimen to get a globe view of the growing islands morphology on the whole substrate surface. Ex situ cross-sectional TEM observations were carried out using a 300 keV Philips CM300 field emission TEM to obtain high resolution TEM (HR-TEM) images. For cross-sectional TEM sample preparation, iron was ex situ deposited on different clean Ge(0 0 1) substrates at different temperatures with the same deposition flux and growth time, with no anneal. Next, two identical samples were glued film-to-film and the glued sample cut vertically to obtain cross section segments. Mechanical grinding was used to thin the glued sample to 20 mm thick, which was followed by polishing with diamond paste. Final thinning to electron transparency was accomplished by Ar ion milling in a Gatan Precision Ion Polishing System, with the angle of incident beam and energy progressively reduced from 88 to 58 and 5–1.5 kV in order to ensure ion-milled samples were of relatively even thickness.
Fig. 1. Bright-field plan-view TEM images and corresponding SAED patterns (insets) of Fe13Ge8 islands grown at (a) 350, (b) 430, (c) 480, (d) 510, (e) 570 and (f) 675 8C, respectively.
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Fig. 2. Plots of Fe13Ge8 islands (a) length and width evolution as a function of deposition temperatures and (b) aspect ratio of length versus width as a function of deposition temperature.
Atomic force microscope (AFM) using a Digital Instruments Nanoscope IIIa was conducted to probe island height and to obtain three-dimensional (3D) information of islands grown at different temperatures. The series of AFM samples were prepared by depositing Fe directly onto Ge(0 0 1) substrates during reactive
deposition epitaxy (RDE) processes with the same deposition flux and time as in the TEM, but this occurred with different temperatures. All samples were examined immediately after they were transferred from the growth chamber (typically within 30 min) by AFM, in order to minimize the effect of exposure to atmosphere.
Fig. 3. Time series of BF TEM images of Ge(0 0 1) substrate surface during reactive deposition of Fe at 570 8C. (a) Cleaned pure Ge(0 0 1) substrate prior to deposition. (b)–(i) Real time observation images about shape evolution of growing islands on Ge(0 0 1) substrate as a function of deposition time. Insets in (a) and (i) are corresponding SAED patterns.
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3. Results 3.1. Plan-view island morphology by TEM Fig. 1 demonstrates typical bright-field (BF) plan-view TEM micrographs of iron germinide islands grown at different temperatures ranging from 350 to 675 8C. Depositions were conducted using the same constant Fe flux for the same deposition time (50 min) at different temperatures in the pre-coalescence regime. Fig. 1(a) is a TEM image of islands grown at 350 8C, which clearly shows that all grown islands are predominately small and square in shape at orthogonal directions to the substrate. At a higher deposition temperature on a different sample (430 8C), two types of islands begin to appear, namely square and elongated, as shown in Fig. 1(b). At a deposition temperature of 480 8C, only elongated rectangular islands are formed along two orthogonal Ge h1 1 0i azimuths (Fig. 1(c)). At 510 8C, long NWs are formed (Fig. 1(d)). More details about Fe13Ge8 islands grown at deposition temperatures ranging from 350 to 510 8C have been discussed in the previous report [18]. Interestingly, as the deposition temperature was further increased to 570 8C, NWs could be seldom observed, which was unexpected from the trend of island shape evolution that occurred between deposition temperatures from 350 to 510 8C. At 570 8C, all islands have larger sizes with rectangular shapes having larger length versus width aspect ratios while still maintaining an orthogonal relationship with the substrate (Fig. 1(e)). Moreover, the islands aspect ratios decreases as the deposition temperature increased to 675 8C (Fig. 1(f)), only square shape islands were observed. Nevertheless, these square islands have a much larger size than those formed at lower temperatures (i.e. 350 8C). The number of islands decreases rapidly, as expected, when deposition temperatures increase from 350 to 675 8C.
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The inset in each frame in Fig. 1 is the corresponding selected area electron diffraction (SAED) of all grown islands on the Ge(0 0 1) substrate. By indexing these SAED pattern, the phase of grown islands (Fe13Ge8) as well as the epitaxial relationship to the underlying Ge(0 0 1) substrate was determined as Fe13 Ge8 ½1¯ 1 0 2==Ge ½0 0 1 and Fe13 Ge8 ð1 1 2¯ 0Þ==Geð1 1 0Þ, which is in accordance with previous results [18,19]. Note that all SAED patterns appear similar to each other, clearly indicating that all islands have the same phase as well as the same epitaxial orientation with respect to the underlying Ge(0 0 1) substrate. In order to clarify island shape evolution, the average islands’ length and width versus deposition temperatures has been plotted in Fig. 2(a). Moreover, the island aspect ratio as the function of deposition temperature has been presented in Fig. 2(b). Note that there are two different trends for island morphology evolution. One trend is that the aspect ratio keeps increasing with increasing temperature from 350 to 510 8C, which is where island shape transition from small square to long wires occurred. The other trend has the aspect ratio decreasing as the temperature increases over 510 8C, with the shape evolution from long wires to large square islands. The two types of island shape evolution appeared at different temperature regimes, one below and the other above 510 8C, implying that there may be two different growth mechanisms that dominate island formation. This is especially intriguing since all grown islands have the same phase and epitaxial relationship. 3.2. In situ TEM observation of island growth during RDE process To further explore the temperature dependent island growth transition at two different temperature regimes (below and above 510 8C), in situ UHV-TEM was employed to follow the dynamics of the island growth processes by directly observing island shape
Fig. 4. Plots of length and width of the growing Fe13Ge8 island as a function of deposition time at (a) 570 8C and (c) 675 8C, respectively. Plots of the corresponding growing island aspect ratio of length versus width as a function of deposition time at (b) 570 8C and (d) 675 8C, respectively.
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Fig. 5. HRTEM images of Fe13Ge8 islands endotaxially grown at (a) 400, (b) 450, (c) 500 and (d) 650 8C, respectively. Insets in (b) and (d) are corresponding diffractograms.
evolution during RDE processes at these different temperatures. The length and width evolution of growing islands as a function of deposition time at different deposition temperatures below 510 8C have been demonstrated previously [19]. In this study, in situ observations were focused on island growth at deposition temperatures above 510 8C. Fig. 3 displays a series of typical BF plan-view TEM images of Fe13Ge8 island growth during the RDE process at 570 8C. The BF image of the Ge(0 0 1) substrate surface is clean prior to deposition (Fig. 3(a)), as seen from the inset SAED pattern oriented along the Ge[0 0 1] zone axis (ZA). When the electron beam evaporator shutter is opened, Fe is directly deposited onto the Ge(0 0 1) substrate in the TEM. Random islands nucleating on the Ge(0 0 1) substrate are observed in less than 1 min, with a low island density, which is as expected, since high temperatures result in fast nucleation rates and low island density. All randomly nucleated islands initially have an approximately square shape (Fig. 3(b)). As deposition continues, the growing islands increase their size rapidly, while retaining their near-square shape during the entire deposition process (Fig. 3(b)–(i)). The inset in Fig. 3(i) is the corresponding SAED pattern with the same epitaxial orientation and Fe13Ge8 phase as obtained below 510 8C. Similar observations are also obtained when the RDE process occurred at 675 8C. Fig. 4(a) shows the length and width evolution of growing islands (Fig. 3) during the RDE process at 570 8C. Fig. 4(b) is the corresponding aspect ratio of island length versus width as a function of deposition time, which shows that the growing islands maintain a near square shape with a mean aspect ratio of 1.2:1. Similar results were also obtained for islands grown at 675 8C (Fig. 4(c) and (d)). This phenomenon is completely different from that observed below 510 8C, where significant morphology evolution and growth dynamics occurred as a function of deposition temperatures [19]. Moreover, during deposition at
temperatures of 570 and 675 8C, the length and width of the growing islands are non-linear over time, differing from the linear growth observed at temperatures below 510 8C [18]. 3.3. Cross-sectional TEM and AFM studies of island shape transition According to plan-view TEM observations, it is clear that island shape evolution at different temperatures can be divided into two regimes: one is the shape transition from small squares to wires, at a temperature range between 350 and 510 8C; the other is the
Fig. 6. Stereographic projection plot of Fe13Ge8–Ge system with defined epitaxial relationship, projected from ZA of both Fe13Ge8 ½1¯ 1 0 2 and Ge [0 0 1]. Red and green colored dots stand for the poles of Ge and Fe13Ge8, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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Fig. 7. AFM images of Fe13Ge8 islands grown at (a) 350, (c) 450, (e) 510, and (g) 600 8C separately. (b), (d), (f) and (h) are profiles of AFM line scans denoted by blue lines in (a), (c), (e) and (g), respectively.
shape transition from wires to large square islands, which occurred above 510 8C. Even though island shape transition has been studied by measuring length and width evolution, as well as length versus width aspect ratio as a function of deposition temperatures, all these studies were based only on plan-view TEM observations. Therefore, in order to comprehensively investigate island shape transitions, it is necessary to observe island morphology from the cross-sectional view, which can provide information of island facets, as well as the interfaces between the grown islands and the underlying substrate. Fig. 5 shows HR-TEM images of Fe13Ge8 islands grown at 400, 450, 500 and 600 8C, respectively. All islands are not just growing flush on the flat Ge(0 0 1) substrate, instead, all islands diffuse along inclined Ge planes and grow into the Ge(0 0 1) substrate, which is the so-called ‘endotaxial’ growth. Interestingly, all Fe13Ge8 islands, grown at temperatures below 510 8C, have similar cross-sectional configurations (Fig. 5(a)–(c)). All these (low temperature) islands are bound by similar facets and interfacial planes. In contrast, islands grown above 510 8C have significantly different cross-sectional configurations (Fig. 5(d)). At these higher temperatures, new facets begin to appear around the islands. Stereographic projection was used to precisely define the facets and interfacial planes bound around the islands. Fig. 6 is a combination stereographic projection plot showing the epitaxial relationship between Fe13Ge8 and Ge, projected along
the ZA of Fe13 Ge8 ½1¯ 1 0 2 and Ge[0 0 1]. Red and green colored dots indicate poles of Ge and Fe13Ge8, respectively. Since each pole corresponds to each plane belonging to either Fe13Ge8 or Ge, then each crystal plane, as well as the angular relation between the crystal planes, can be directly interpreted from this stereographic projection. By measuring the angular relationship between the facets or interfacial planes bound around the Fe13Ge8 islands, we can identify interfacial planes between islands and the substrate, as well as island facets. For example, for Fe13Ge8 islands grown ¯ f4 4¯ 0 1g ¯ and below 510 8C, there are three types of facets (f1 1¯ 0 2g, ¯ that are bound above the Ge(0 0 1) substrate. The flat top ð2 2¯ 0 1Þ) ¯ which is of each island is formed by the facet of Fe13 Ge8 ð2 2¯ 0 1Þ parallel to Ge(0 0 1) surface, while the other two inclined sides are ¯ and f4 4¯ 0 1g. ¯ The three types of facets bound by the facets f1 1¯ 0 2g above the substrate surface thus form a trapezoidal shape, as viewed in cross-section, which can be observed along both projections of island length and width azimuths. For islands grown above 510 8C, some other steeper facets are introduced, as ¯ shown in Fig. 5(d). The two types of shallow facets of the f1 1¯ 0 2g ¯ interfaces with side-facet angles to the substrate and f4 4¯ 0 1g surface of 358 and 558, respectively, are substituted by discontinuous introduction of considerably steeper facets ð2 2¯ 0 1Þ and ¯ which both have the side-facet angle 708 to the substrate. ð1¯ 1 0 2Þ ¯ formed below 510 8C is also Meanwhile, the flat top ð2 2¯ 0 1Þ gradually substituted by other newly formed facets ð4 4¯ 0 1Þ,
Table 1 AFM results of average height of Fe13Ge8 islands grown at different deposition temperatures. Deposition temperature
Number of islands investigated per mm2 Average height (nm) Deposition temperatures Number of islands investigated per mm2 Average height (nm)
350 8C (wire-like)
430 8C (wire-like)
480 8C (wire-like)
510 8C (wire-like)
311 8.5 1.5 550 8C (wire and dome-like) 90 25.2 3.0
255 20.1 3.0 600 8C (dome-like) 81 49.4 4.0
183 20.8 3.0 650 8C (dome-like) 64 52.9 4.0
107 18.2 4.5
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Fig. 8. Three-dimensional AFM images of Fe13Ge8 islands grown at (a) 450 8C and (b) 600 8C, respectively. Corresponding schematic view of Fe13Ge8 islands are shown in (c) grown below 510 8C and (d) grown above 510 8C separately.
¯ ð1 1¯ 0 1Þ ¯ and ð1 1¯ 0 3Þ, ¯ with side-facet angles 558, 158, 188, ð4 4¯ 0 1Þ, and 408, respectively, to the horizontal azimuth of substrate, and finally evolve to form a vertex at the top. Fig. 5 not only demonstrates the difference between facets and interface planes bound around islands, but also shows the height evolution of islands at the two different temperature regimes. Systematical investigations reveal that islands grown below 510 8C have similar heights 20 nm. However, the heights of islands grown above 510 8C increase significantly and reach 60 nm, with some as high as 80 nm. Due to the limitation of both plan-view and cross-sectional view within a TEM, only relatively small thin regions can be observed. To fully investigate islands morphology, especially island height evolution, it is necessary to employ AFM, which can probe the morphology over a larger sample surface, providing a comprehensive global view of islands grown on Ge substrates. Fig. 7 shows AFM images of Fe13Ge8 islands grown at 350, 450, 510, and 600 8C. These AFM results illustrate that, at low
temperatures (350 8C), islands have a square trapezoidal shape with a small size. With an increase in the deposition temperature, the islands begin to evolve into elongated shapes (450 8C). Wires appear at higher temperatures around 510 8C. However, at 600 8C, the islands revert to their square shape but with increased size. Moreover, islands grown at 600 8C are much higher above the substrate than those grown below 510 8C, according to island height measurement shown in Fig. 7. Fig. 7(g) and (h) also demonstrates that square islands are much higher above the substrate than those elongated islands formed at the same temperature. Together with the results shown in Fig. 7, the heights of Fe13Ge8 islands grown at different temperatures (i.e., 430, 480, 550, and 650 8C) were also detected by AFM (Table 1). Also, these AFM results are in accord with our current crosssectional TEM observations. On the basis of both AFM and TEM investigations, islands grown below and above 510 8C can be divided into two types as shown in Fig. 8. Fig. 8(a) is typical three-dimensional AFM image of islands
Table 2 HRTEM results of average height and aspect ratio of Fe13Ge8 islands grown at different deposition temperatures. Deposition temperature
Number of islands investigated Average height(above substrate) (nm) Average height(below substrate) (nm) Height(above substrate) versus height(below substrate)
350 8C (wire-like)
400 8C (wire-like)
450 8C (wire-like)
500 8C (wire-like)
600 8C (dome-like)
650 8C (dome-like)
31 9.1 1.5 19.1 3.0 0.49
20 20.1 3.0 35.9 3.0 0.56
19 21.1 3.0 37.1 3.0 0.57
13 22.9 3.0 46.1 4.0 0.52
15 45.2 4.0 23.5 3.0 1.92
23 63.9 5.0 30.9 3.0 2.07
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Fig. 9. Plots of (a) AFM and cross-sectional TEM results of Fe13Ge8 island average height as a function of deposition temperatures. (b) TEM results of aspect ratio (height above substrate versus height below substrate) as a function of deposition temperatures. Insets are typical HRTEM images of Fe13Ge8 islands with different configurations.
grown at 450 8C. All islands have distinct shallow facets bound at each side and have a truncated pyramid-like shape. For islands formed at 600 8C, all the surrounding shallow facets disappear and are substituted by steeper facets, leading to multifaceted domelike islands (Fig. 8(b)). The corresponding schematic diagrams of these two types of islands are shown in Figs. 8(c) and (d) respectively. As a consequence, islands grown below 510 8C have a truncated pyramid-like shapes with either a square or elongated base, and are assigned as type-I. While islands grown above 510 8C, have dome-like shapes with either a square or small aspect ratio rectangular base, denoted as type-II. It is emphasized that island height evolution at different temperatures can be explained not only by the height above the Ge(0 0 1) substrate, but also by the height below the Ge(0 0 1) substrate. Therefore, it is essential to characterize height evolution by comparing island height both above and below the Ge(0 0 1) substrate with the aid of cross-sectional TEM observations. TEM results of average height (both above and below the Ge(0 0 1) substrate) and the corresponding epitaxial/endotaxial ratio (height above substrate versus height below substrate) of Fe13Ge8 islands grown at different temperatures are listed in Table 2. It clearly illustrates that island heights (both above and below substrate) as
well as the aspect ratios change significantly at temperatures below and above 510 8C. Plots in Fig. 9 intuitively display island height evolution (above substrate, Fig. 9(a)) as well as the aspect ratio of island height above substrate versus the height below substrate as a function of deposition temperatures (Fig. 9(b)). From Fig. 9(a), all type-I islands have an average height 20 nm, which is independent of the island’s basal shape (e.g., square, rectangle or wire). However, the average height of type-II islands greatly increases to 55 nm around 600 8C. On one hand, the average height (above substrate) of Fe13Ge8 islands has a transition from 20 nm to 55 nm between type-I and type-II islands. On the other hand, the change of island height (above substrate) results in the aspect ratio (height(above substrate) versus height(below substrate)) transition from 0.5 to 2 below and above 510 8C as shown in Fig. 9(b). 4. Discussion Since all observed islands have the same phase (Fe13Ge8) as well as the same epitaxial orientation relationship to the underlying Ge(0 0 1) substrate at all deposition temperatures, therefore, it is unlikely that island shape transition, from small square shapes to
Fig. 10. Schematic cross-sectional view of an interface between Fe13Ge8 and Ge(0 0 1) substrate. Both views are projected from Ge[1 1 0] ZA. The colored unit cells are used to indicate the orientation directions. Fe atoms in Fe13Ge8 crystal structure are omitted for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
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long wires and then to large square islands, is due to either phase transformation or different island orientations to the Ge(0 0 1) substrate. Previous work demonstrated that at temperatures below 510 8C, island shape transition from squares to long wires is due to the kinetic growth constraint in terms of anisotropic ledge diffusion and corner barriers [18]. In order to further understand the shape transition from wires to large squares above 510 8C, it is necessary to analyze the atomic scale relation between islands and substrate in more detail. Similar phenomena, that different types of islands form having the same phase and diffraction pattern, have been widely observed in XSi2 (X = Ni, Co) systems [20–22]. The Gibson model elucidated that in such systems, the so-called type-A (square shape) and typeB (elongated shape) island formation is due to interface structure differences [23,24]. In type-A structures, grown islands have a continuous extended structure similar to that of substrate. While in type-B structures, the epitaxial structure has a 1808 rotation along the ZA retaining the same orientation relationship with the substrate, resulting in the formation of a single stacking fault in the interface plane. In this study, since all islands endotaxially grew into the substrate, it is necessary to investigate the interface structure. Fig. 10(a) demonstrates a schematic diagram of the crosssectional view of an interface structure between an Fe13Ge8 island and the Ge(0 0 1) substrate, projected along the Ge [1 1 0] with the defined epitaxial relationship. All Fe atoms in Fe13Ge8 crystal structure are omitted for clarity. Fig. 10(b) is a similar to Fig. 10(a) except that the Fe13Ge8 crystal structure has been rotated by1808 along the Ge [0 0 1] ZA while the Ge(0 0 1) substrate maintains the same orientation. Comparing Fig. 10(a) and Fig. 10(b), all the Ge atoms in Fe13Ge8 lay along the same Ge lattice planes as that in the underlying Ge(0 0 1) substrate. Therefore no single stacking faults are formed in the plane because of the Fe13Ge8 rotation. And only one type of interface exists between the Fe13Ge8 island and the Ge substrate. It can be concluded that different types of island morphology formed in this study are not due to type-A or type-B interface formation as predicted by the Gibson model [23,24]. As a consequence, we need to probe the mechanism that causes island shape transition. At high temperatures (above 510 8C) this mechanism is different from the kinetically constrained Fe13Ge8 island shape evolution below 510 8C [18], it seems that thermodynamics may be the driving force for the formation of small square islands. There is a well-developed understanding of island shape transition from shallow faceted pyramid to multifaceted dome for the Ge nanocrystal grown on a Si surface, as well as the InAs/ GaAs(0 0 1) quantum dots faceting process [25–29]. Using thermodynamic considerations, these transitions are controlled by the complex interplay between the surface energy and the builtup strain energy (due to the lattice mismatch between the epilayer and substrate). Nevertheless, in the Fe13Ge8/Ge(0 0 1) system, islands grow along the co-planar inclined Geð1 1¯ 1Þ plane and form the coherent interface, that leads to endotaxial growth [30,31]. The interfacial energy between growing islands and the substrate thereby begins to play a more important role than that of strain energy in the endotaxial growth process. Compared with the pyramid-to-dome shape transition, which depends on surface and strain energies, our considerations mainly focuses on the complex interplay between surface and interface energies.
¯ plane with neighboring atoms of (a) Fig. 11. Computer simulated Fe13 Ge8 ð1 1¯ 0 2Þ side-view and (b) plan-view. Green and red dots stand for germanium and iron atoms in Fe13Ge8 respectively, while white and red colored dots denote iron atoms ¯ plane. (For interpretation of the references to color in this figure in the ð1 1¯ 0 2Þ legend, the reader is referred to the web version of the article.)
For island surface and interface energies calculations, our analysis is based on the dangling bound energy, which is the main contribution to surface free energy in the absence of strain. The nearest-neighbor (NN) atom–atom interaction method is applied to calculate surface energy for each facet and/or plane. Consider ¯ plane for example, where Fig. 11 shows the the Fe13 Ge8 ð1 1¯ 0 2Þ ¯ plane with neighboring atoms with (a) side-view Fe13 Ge8 ð1 1¯ 0 2Þ and (b) plan-view. Green and red dots denote Ge and Fe atoms respectively in Fe13Ge8, while white and red-striped dots represent ¯ plane. By measuring the atom–atom Fe atoms in the ð1 1¯ 0 2Þ distance, it was found that the NN distance between Ge and Fe in ¯ plane was 2.49 A˚, while the Fe to Fe NN distance is the ð1 1¯ 0 2Þ 2.50 A˚. We can simply count the NN atom–atom interactions and use this as a substitute for the dangling bond energy, where the notation bFe/Ge and bFe/Fe, denotes the dangling bond energy between Fe–Ge atoms and Fe–Fe atoms, respectively. After determining all possible dangling bonds between the target plane and its NN atoms, we can divide this value by the unit cell of the corresponding plane, such as the 3.99 7.35 A˚2 rectangle which is ¯ plane, as shown in Fig. 11(b). The the unit cell of Fe13 Ge8 ð1 1¯ 0 2Þ dangling bond density of each crystal plane can be obtained using this method. Table 3 shows the dangling bond density of all crystal planes bound around islands grown at different temperatures, notated as the number of dangling bond per A˚2. Fig. 12(a) and (b) represents the schematic cross-sectional view of type-I and type-II island shapes, projected along the island length azimuth, while maintaining the same cross-sectional area. We treat this problem in 2D for simplicity, nevertheless all the key results developed here are also applicable in 3D, as discussed later. After defining the surface energy of each facet/plane in terms of dangling bond density, we calculated the free surface energies per
Table 3 Dangling bond density of each crystal plane in Fe13Ge8. Fe13Ge8 planes
¯ ð2 2¯ 0 1Þ
¯ ð1 1¯ 0 2Þ
ð4 4¯ 0 1Þ
¯ ð0 0 0 1Þ
¯ ð1 1¯ 0 1Þ
¯ ð1 1¯ 0 3Þ
¯ ð4 4¯ 0 1Þ
No. of dangling bond per A˚2
0.0413bFe/Fe + 0.0826bFe/Ge
0.0341bFe/Fe + 0.0682bFe/Ge
0.0237bFe/Fe + 0.0712bFe/Ge
0.0725bFe/Fe + 0.1450bFe/Ge
0.0588bFe/Fe + 0.0881bFe/Ge
0.0235bFe/Fe + 0.0353bFe/Ge
0.0237bFe/Fe + 0.0712bFe/Ge
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Fig. 12. Schematic diagrams of cross-section configurations of (a) type-I and (b) type-II islands.
unit length for the top, shallow, and steep side facets, as well as the interface planes below the substrate. The total energy of the island can be described in the form of E = Es + Ei, where Es is the facet surface energy and Ei is the island–substrate interface energy. We assume type-I and type-II islands have the same volume to simplify this into a 2D problem by setting the two types of islands with the same unit length, which means the total cross-sectional area (S) of the 2D islands shown in Fig. 12(a) and (b) are the same. Then the total energy of the island can be written in the following P P way: E = Es + Ei = sgsLs + igiLi, where gs is surface energy (per unit length) of each island facet, Ls is each facet’s length of the 2D island cross-sectional diagram as shown in Fig. 12(a) and (b), the gi is the island–substrate interface energy (per unit length) and Li is the corresponding length of each interface side. Since the total cross-sectional area of the two types of islands is the same, we can obtain the individual side length Ls and Li for the 2D island from direct HR-TEM measurements. Comparing the results calculated from Table 3, the energy per unit area (E/S) for the two types of islands is as follows. It was found that the E/S for type-I islands (Fig. 12(a), 2.41 104bFe/Fe + 5.47 104bFe/Ge per A˚2) is less than that of type-II islands (Fig. 12(b), 3.21 104bFe/ 4 bFe/Ge per A˚2), which illustrates that type-I islands Fe + 7.11 10 have a lower total surface and interface energy per unit volume than type-II islands. Therefore, for a given volume, this indicates that the island prefers to adopt the optimal shape of type-II to minimize its total surface and interface energies at high temperatures. From our semi-quantitative model as shown in Fig. 12 and Table 3, the appearance of different facets/planes bounded the island is temperature dependent. Note that highly inclined steeper ¯ together facets induced at the base of islands (i.e. ð2 2¯ 0 1Þ, ð1¯ 1 0 2Þ) ¯ with the newly formed inclined facets/interfaces (i.e. ð4 1¯ 0 1Þ, ¯ ð1 1¯ 0 3Þ) ¯ become slightly more favorable because of their ð1 1¯ 0 1Þ, lower surface/interface energies, compared to those facets formed below 510 8C. The island shape transition from wire-like to the optimal shape of dome-like square base island is dominated by the driving force associated with minimization of its total surface and interface energies as discussed in our model. Therefore, the faceting process provides the possibility to stabilize the island configuration and reach its equilibrium state [32–34]. At high temperatures, deposited Fe adatoms can obtain sufficient energy to overcome surface and interface diffusion barriers, or corner barriers, and can rapidly diffuse on the substrate as well as the
facets to find the most stable sites, subsequently forming low surface/interface energy facets/planes. The rapid accumulation of adatoms to existing islands and fast adatoms diffusion on the island surface/interface will drive islands to adopt a larger size, rapidly increasing the growth rate of higher energy planes and dramatically increasing island height, by leaving behind the slowly growing planes. The faster growth of the high energy facets will replace the flat top with additional higher Miller indices facets to form a vertex at the top. Therefore, island growth terminates at lower surface/interface energy planes [35–37]. In addition, in order to be epitaxially registered on the isotropic Ge(0 0 1) surface, islands prefer to adopt a square shape which can reflect the symmetry of the underlying substrate and thus to reduce the length/width aspect ratio to reach the equilibrium state. Consequently, this leads to the formation of type-II islands. All islands grown above 510 8C maintain their square shape during the whole annealing process, which indicates that type-II islands exist in their equilibrium state. This island shape transition at different deposition temperatures provides a dramatic illustration of the importance of surface and interface energies in controlling the island growth habit and formation, especially for the endotaxial growth process. 5. Conclusions In summary, Fe13Ge8 islands formation on single crystal Ge(0 0 1) substrates at 350, 430, 480, 510, 570 and 675 8C have been comprehensively studied by using various of techniques: in situ UHV-TEM, HR-TEM, SAED, and AFM. Distinct island shapes form at different temperatures. At low temperatures (350 8C) small square islands form. As the deposition temperature increased, islands grew with elongated shapes (430 8C) and the length versus width aspect ratio increased as a function of the deposition temperature, which finally grew into long NWs at high temperatures (510 8C). Nevertheless, larger square islands formed at higher temperatures (above 510 8C) in preference to the long NWs. All the islands, grown at different temperatures, have the same phase and share the same epitaxial relationship to the underlying Ge(0 0 1) substrate. It suggests that this type of temperature dependent island shape transition is not due to a phase transformation, nor the type-A and type-B interface structures formation as predicted in Gibson model. We propose that island morphology evolution below 510 8C is due to kinetic
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constraints in terms of anisotropic ledge diffusion and corner barriers. Whereas at temperatures above 510 8C, facets/interfaces bounded around islands begin to change. Below 510 8C, all the islands have a similar cross-sectional shape and is defined as typeI. They appear as truncated pyramids with shallow facets at each side and a flat facet at the top. The aspect ratio of the epitaxial versus the endotaxial height of type-I island is 0.5. Type-II islands appear above 510 8C, and have much steeper facets at the bottom with larger heights above the substrate, forming dome-like shape with a square base. The aspect ratio of height above substrate versus height below substrate of type-II islands is 2. According to the surface/interface energy calculation per unit volume of the two types of islands, this illustrates that type-II islands have a lower total energy per unit volume than that of type-I. It can be concluded that minimizing the total surface and interface energies to reach their equilibrium state may be the driving force that leads to the shape transition from type-I to type-II. Moreover, this study demonstrates that the NWs formed in the hex-Fe13Ge8/Ge system are not structures in thermodynamic equilibrium. This study provides a comprehensive understanding of low dimensional structure formation and shape transition from kinetically constrained to equilibrium regimes. Acknowledgment Z.P. Li would like to thank G.J. Auchterlonie (The University of Queensland, Australia) for helpful discussions and proof reading. References [1] Y. Cui, C.M. Lieber, Science 291 (2001) 851. [2] J.B. Hannon, J. Tersoff, R.M. Tromp, Science 295 (2002) 299. [3] K. Bromann, C. Felix, H. Brune, W. Harbinch, R. Monot, J. Buttet, K. Kern, Science 274 (1996) 956. [4] V.G. Dubrovskii, T. Xu, Y. Lambert, J.P. Nys, B. Grandidier, D. Stievenard, W. Chen, P. Pareige, Phys. Rev. Lett. 108 (2012) 105501. [5] L.J. Chen, K.N. Tu, Mater. Sci. Rep. 6 (1991) 53.
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