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Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học
Influences of the Sið113Þ anisotropy on Ge nanowire formation and related island shape transition Zhaohui Zhang 1 , Koji Sumitomo * , Hiroo Omi, Toshio Ogino NTT Basic Research Laboratories, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan Received 11 July 2001; accepted for publication 26 September 2001 Abstract Based on the scanning tunneling microscopy observations of Ge coherent growth on Si(1 1 3), we demonstrate that the anisotropy of substrate stiffness is responsible for the anisotropic relaxation of islands, which leads to island elongation perpendicular to the softer direction of the substrate surface. The transition from wire-like islands to dot-like islands indicates that relaxation of islands tends to become isotropic as the size of the islands increase. Island volume measurements reveal that the material grown on the substrate, including the wetting layer, is continuously rebuilt during island formation and transition. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Scanning tunneling microscopy; Surface structure, morphology, roughness, and topography; Surface stress; Epitaxy; Silicon; Germanium 1. Introduction Elongated growth of Ge hut-like islands on Si(1 0 0) was puzzling because the substrate is biaxially isotropic [1]. Theoretically, it was dem- onstrated that with an increase in its size, a co- herent island would take on a long thin shape for better elastic relaxation of its stress, and elongated hut-like islands have been regarded as an example of this [2]. Nevertheless, this type of shape transi- tion of Ge islands on Si(1 0 0) has not been ob- served. In fact, square-based pyramid-like islands do not grow in just one direction to adopt an elongated shape, they actually become larger and adopt a dome-like shape [3]. Thus, the sponta- neous formation of quantum wires on an isotro- pic substrate is questionable. For the formation of Ge or GeSi quantum wires, C 1v symmetry Si(1 1 3) seems to be a more attractive option be- cause of its structural and mechanical anisotropy. Despite its high-indices, Si(1 1 3) is stable during high temperature annealing, and is a good sub- strate for epitaxial growth [4]. In particular, Ge grown on Si(1 1 3) can form highly elongated islands called ‘‘nanowires’’ [5], which could be a possible candidate for self-assembled quan- tum wires. However, elongation of Ge islands on Si(1 1 3) actually occurs along the direction of maximum stress, which is contrary to a theoretical Surface Science 497 (2002) 93–99 www.elsevier.com/locate/susc * Corresponding author. Tel.: +81-462-40-3457; fax: +81- 462-40-4718. E-mail address: sumitomo@will.brl.ntt.co.jp (K. Sumi- tomo). 1 Permanent address: Department of Physics, Mesoscopic Physics National Laboratory, Peking University, Beijing 100871, China. 0039-6028/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 00 39 - 6 0 2 8 ( 0 1) 0 1 6 2 9- 6 expectation that when epitaxial stress is aniso- tropic, a coherent island should align itself per- pendicular to the direction of maximum stress [6]. So, it is interesting to investigate the mechanism of elongated growth of an island on an anisotropic substrate. Previous studies of Ge nanowire formation on Si(1 1 3) were based on atomic force microscopy (AFM) observations [5]. Because the observations were ex situ and the AFM resolution was not good enough, the growth morphology of the surface could not be unambiguously determined, and therefore the formation mechanism of the nano- wires could not be well understood. With help of scanning tunneling microscopy (STM), we have carefully observed the as-grown surfaces of Ge on Si(1 1 3) in situ on an atomic scale, and we have found new evidences for understanding the nano- wire formation and related island transition. Here we demonstrate that the anisotropy of the Si(1 1 3) substrate stiffness plays an important role in the formation of Ge nanowires and that the island transition from a wire-like to a dot-like one is ac- tually caused by a transition of island relaxation from anisotropy to isotropy. 2. Experimental Experiments were carried out in an ultrahigh vacuum STM system equipped with epitaxial growth facilities. Samples were cut from a Si(1 1 3) wafer (P doped, 1–10 X cm) with a misorientation towards the ½ 1110 direction of less than 0:2°.Ge deposition at 1.4 ML/min, where 1 ML is defined as 8: 2 Â 10 14 atoms/cm 2 , was conducted using a Knudsen cell, and the growth temperature was set at 430 °C in order to favor nanowire formation [5]. The base pressure of the system was lower than 1 Â 10 À10 Torr; and during substrate preparation and Ge deposition the pressure typically remained lower than 5 Â 10 À10 Torr. Ge deposition was moni- tored using reflection high-energy electron dif- fraction. The morphology of each grown surface was observed using STM, and a sample voltage of 2 V and tunneling current of 0.1 nA were typically used. 3. Results and discussion Our STM observations are consistent with previous reports [4,5] in that after $5 ML two- dimensional growth of a wetting layer, three- dimensional islanding began. As shown in Fig. 1a, the islands already appear elongated along the ½33 22 direction with widths of $20 nm at the initial nucleation stage. Increasing the Ge coverage by half a ML causes the elongated islands to become several hundreds of nm long while their widths did not increase, as shown in Fig. 1b. This growth morphology leads one to employ the term ‘‘nanowires’’. Further increasing the Ge coverage by another half a ML causes the wires to reach their maximum density, as can be seen in Fig 1c. STM images on an atomic scale indicate that the wires extend in ½33 22 and ½ 33 332 directions with (2 4 9)/(4 2 9) side facets near their ends and that they thicken with (1 5 9)/(5 1 9) side facets, but their ends are not faceted. The (2 4 9)/(4 2 9) facets are tilted at an angle of 8° with respect to the substrate surface, and the (1 5 9)/(5 1 9) facets are tilted at an angle of 16° . All the islands have a (1 1 3) top facet. Theoretical calculations indicated that there exists a strain energy concentration around a co- herent island at its base edges, which results from relaxation of the island and acts as an energy barrier to limit the lateral growth of the island [7,8]. Through experiments it was shown that this strain energy concentration could be relieved by the formation of trenches around the island [9]. As demonstrated above, the growth of wires is strongly limited laterally in the ½ 1110 direction. Checking the surface around the wires, we were unable to find any depression at their two ends; however we did observe depressions beside their base edges along the ½33 22 direction. Such as the wire-like island that is pointed out by an arrow in Fig. 1b, from its end on, the surface on the both sides first becomes 1 ML lower and then 2–3 ML lower, which can be determined by checking the sectional profiles such as along A–B and C–D as shown in Fig. 2. Despite the depressions, there is indication of a significant strain field beside the wires because the wires never contact each other laterally, but do interfere with one another, which causes the interruption of some wires, as can be 94 Z. Zhang et al. / Surface Science 497 (2002) 93–99 seen in Fig. 1c. All of these observations lead to the conclusion that relaxation of the islands at this growth stage is dominant, in the ½ 1110 and ½1 110 directions. Island growth in these two directions is therefore self-limited because energy barriers at their base edges. Height growth of the islands seems to be kinetically limited at this growth stage, as has been generally expected [2]. Thus length growth of the islands is dominant in the formation of ‘‘nanowires’’ along the ½33 22 direction. The compressive stress in a flat Ge film on Si(1 1 3) along ½33 22 is 9% larger than it is along ½ 1110 [6]. The observed orientation of the nano- wires is therefore contrary to Tersoff and Tromp’s prediction that when epitaxial stress is anisotropic, a coherent island should align itself perpendicular to the direction of maximum stress [2]. To clarify this controversy, we follow Tersoff and Tromp to estimate the relaxation energy of the Ge wires on Si(1 1 3). Let r x and r y stand for the bulk stress in the ½ 1110 and ½33 22 directions, respectively, of a flat Ge film that is uniformly strained to the Si substrate. Epitaxial contact of an island to the substrate, which is assumed to be strained in the same way as the film, may be estimated by the distribution of a point force r x tan h x in the ½ 1110 direction and r y tan h y in the ½33 22 direction, where h x and h y are the facet angles with respect to the substrate surface. Within an elastic range of the material, the resulting displacements of the sub- strate surface can be estimated using Hooke’s law, and therefore the work done by the point force is Fig. 1. STM images of Ge island growth on Si(1 1 3) at 430 °C for a total coverage of (a) 5.2 ML, (b) 5.7 ML, and (c) 6.2 ML, re- spectively. The three images are all 250 Â 500 nm 2 in size. The directions marked in (a) are common to (a)–(c). Fig. 2. The sectional line profiles of nanowires as marked A–B and C–D in Fig. 1(b). Z. Zhang et al. / Surface Science 497 (2002) 93–99 95 estimated to be ðr x tan h x Þ 2 =E x and ðr y tan h y Þ 2 =E y in the ½ 1110 and ½33 22 directions with E x and E y of the Young’s modulus of the substrate concerned in these two directions, respectively. As the total re- laxation energy of the island is determined by an integral of the work of the point force over the epitaxial contact area, relaxation of the island is therefore not only dependent on the stress of the island, but also on the substrate stiffness and the island shape. Unfortunately, Tersoff and Tromp did not pay attention to the substrate anisotropy in stiffness but assumed the same angles of island facets with respect to the substrate surface for an anisotropic substrate. The Young’s modulus of the substrate along ½ 1110 is 9% lower than it is along ½33 22 [6]. Fur- thermore, the wires are faceted on both sides with the (2 4 9) or (1 5 9) at an angle of 8° or 16° with respect to the substrate surface, but their ends gradually decrease to wet the surface, forming contact angles smaller than 2° but no defined facets, according to our measurements. As a result, the work of the point force in the ½ 1110 direction is actually much larger than it is along the ½33 22 di- rection, and the observed elongation of the islands is therefore more favorable for island relaxation. Besides, surface energy of a well-defined defined facet is obviously lower than that of an unfaceted one. Thus, compared with their unfaceted end fa- ces the observed elongation of islands with a larger area of the (2 4 9) or (1 5 9) facets indicates a lower surface energy of the islands. So, the observed is- land elongation along the direction of maximum stress is actually energetically favorable. Never- theless, the wire-like shape of the islands is never an equilibrium configuration, which will be seen in their shape transition displayed below. So, the observed wire-like shape of the islands is just metastable. Formation of the 3D nanowires can be traced back to Ge growth of 2D islands. Knall and Pethica suggested that a 2 Â 2 structure consisting of dimers and rebounded adatoms make it more energetically favorable to relax the 2D island along the ½ 1110 direction than along the ½33 22 direction [4]. From our STM observations of high resolu- tion, this suggestion can be further strengthened with another 2 Â 2 model, which consists of alternating rows of subsurface interstitials and rebounded adatoms along the ½ 1110 direction [10]. So, from the beginning of 3D islanding the islands already relax more towards the ½ 1110 than towards the ½33 22. As we mentioned above, the surface stiffness of the substrate along ½ 1110 is 5% smaller than it is along ½33 22, while the compressive stress in a flat Ge film on Si(1 1 3) along ½33 22 is 9% larger than it is along the ½ 1110. It seems confusing why the islands always prefer to relax along the ½ 1110. In fact, as has been seen in the estimation of the point force work, the surface stiffness acts directly but the point force may be a function of the stress and an island shape. Relaxation of an island is therefore competitive along these two directions. Since a 2D island already relaxes pref- erably along the ½ 1110 direction, in the case of Ge growth on Si(1 1 3), Ge islands may naturally first relax towards the softer direction of the substrate, which induces more compression at ½ 1110 base edges of islands than their ½33 22 base edges. The Ge nucleation is therefore suppressed at the ½ 1110 base edges but favored at the ½33 22 base edges, forming an elongated island shape perpendicular to the softer direction of substrate stiffness. Wire-like growth of the islands proceeds within a Ge coverage of $6.2 ML. For further Ge de- position, the wire compact surface, as shown in Fig. 1c, acts as a new precursor. We have observed that new islands form on the wires and then the wires disappear. As shown in Fig. 3a, the thinner features indicate the remaining wires and the thicker features indicate the newly formed islands. These new islands are elongated in the same ori- entation as the wires, but are much shorter than the wires. For simplicity, we refer to this type of island as an elongated island. In contrast to wires, all of the side faces of elongated islands are faceted with (1 5 9)/(5 1 9) at an angle of 16° with respect to the substrate surface, their ½33 22 ends are faceted with (15 3 17), (1 1 1) and (3 15 17) at the angles of 24°,30° and 24°, respectively, and their ½ 33 332 ends are faceted with (5 1 7) and (1 5 7) at the angle of 20°, as shown in Fig. 4b. In successive growth, the elongated islands become regular in size and dis- tribution, as can be seen in Fig. 3b and c. Mean- while, the ½ 33 332 ends of the elongated islands split into ‘‘dot-like islands’’, as marked by arrows in 96 Z. Zhang et al. / Surface Science 497 (2002) 93–99 Fig. 3b and c. The dot-like islands adopt the facet structure of the elongated islands by simply re- placing the (1 5 9)/(5 1 9) facets with the (1 7 11)/ (7 1 11) at an angle of 19° with respect to the Fig. 3. STM images of Ge island growth on Si(1 1 3) at 430 °C for a total coverage of (a) 6.7 ML, (b) 7.2 ML, and (c) 8.2 ML, re- spectively. The three images are all 250 Â 500 nm 2 in size. The directions marked in (a) are common to (a)–(c). Fig. 4. STM images showing the facets of (a) the wire-like islands, (b) the elongated islands, and (c) the dot-like islands. Z. Zhang et al. / Surface Science 497 (2002) 93–99 97 substrate surface. They grow bigger and higher at a fixed lateral aspect ratio near 1, as can be seen in Fig. 4c. Some of dot-like islands grow larger and finally become dislocated islands, which we ob- served when the Ge coverage was larger than 9 ML. Fig. 5 shows the average width, height, length, and number density along ½ 1110 of the wires and elongated islands versus the Ge coverage. Growth of the wires is clearly characterized by an increase in the island length and the number density. The width of the island is $20 nm and the height of the island is $1.5 nm. In comparison, growth of elongated islands mainly proceeds via increases in island height. As they grow higher up to an aver- age value of $3.5 nm, their lengths average to $120 nm, but their widths are limited to $30 nm. Moreover, the deposited material is condensed on the ½ 33 332 ends of elongated islands to form dot- like islands. Obviously, islands tend to lose their elongation, become higher, and their edge facets become steeper during shape transition. This type of shape transition is a more favorable condition for strained islands to relax. In particular, the config- urations of the island ends indicate significant re- laxation of the islands along their elongation direction while the formation of dot-like islands at the elongated island end of the ½ 33 332 direction implies that relaxation of the islands is easier along the ½ 33 332 direction than the ½33 22 direction. As a result of the enhanced energy barriers at the base edges, elongated growth of the islands tends to become self-limited in the same way as their lateral growth does. The resulting strain field around the islands is obvious in that with continuous growth the islands become more regular in size and dis- tribution and their number density decreases, as shown in Figs. 3 and 5. In growth kinetics it is unfavorable for diffusing atoms to attach them- selves to the top of islands because as we have seen, there is a height limit to wire-like growth. However, as Ge coverage increases, the enhanced interaction between the islands and the substrate surface tends to drive atoms to diffuse onto the islands, forming a more energetically stable island shape with less elongation. Island shape formation of Ge on Si(1 0 0) has been explained as being the energy-minimization of strained islands [3]. Nevertheless, it has been demonstrated that minimum-energy configuration of the islands is unnecessary, and that shape transition occurs due to coarsening during growth [11]. In the case of Ge growth on Si(1 1 3), the is- lands are energetically favorable within some ki- netic limits and may be metastable. Stability of the islands increases as island elongation decreases. However, in the end, no island is absolutely stable against shape transition to a dislocated island. Complete transition of the wires to the elongated islands took less than 40 s during the deposition for less than 1 ML, as can be seen in Figs. 1c to 3b. In comparison, the transition from elongated is- lands to dot-like islands was much slower. Within the limited time available for 10 ML Ge to be deposited, we observed the coexistence of elon- gated, dot-like, and dislocated islands. We also conducted coarsening experiments at a Ge cover- age of 6.2 ML by stopping the Ge deposition but maintaining the substrate temperature. As a result, the wire-like islands, as shown in Fig. 1c, almost completely changed into elongated islands within 25 s. However, afterwards the shape transition to Fig. 5. Changes in the average width, height, length, and number density along ½ 1110 of the wire-like islands (open cir- cles) and the elongated islands (solid circles) with increasing Ge coverage, as measured from STM images on a large scale of $1 lm. 98 Z. Zhang et al. / Surface Science 497 (2002) 93–99 dot-like and dislocated islands took more time than it did during the growth period. Moreover, after annealing the sample at 500 °C or higher temperatures, most of the islands became either dot-like islands or a combination of dot-like and dislocated islands. Volume measurements of each type of island demonstrate that the shape transition of the is- lands proceeds via mass transport. Interestingly, we also found that during growth of up to 7 ML the total island volume increased at a rate ap- proximately three times that of the deposition rate, followed by increases in the deposition rate. This indicates that after 3D growth begins there is also a mass transport from the wetting layer to the is- lands. Fig. 6 shows fractional coverage of the wetting layer and each type of island. The thick- ness of the wetting layer was determined by sub- tracting the total island volume from the amount of Ge deposited. Like the islands, the volume of the wetting layer increases up to a maximum value and then decreases. Mass transport from the wet- ting layer to the islands may be driven by the difference in the chemical potential between the wetting layer and the islands, as previously pre- dicted [12]. On the other hand, the surface mor- phology changes like depressions, as shown in Fig. 1b, beside the wire-like islands indicate that the mass transport process is enhanced by interaction between the islands and the wetting layer. 4. Summary In summary, depending on island relaxation, the interaction between the islands and the wetting layer influences growth kinetics so that islands tend to form lower strain energy configurations as the amount of deposited material increases. Dominant island relaxation along the softer di- rection of the Ge/Si(1 1 3) surface leads to elongated growth of the islands along the perpendicu- lar direction, which in turn forms ‘‘nanowires’’. This only occurs, however, when the height growth is kinetically limited. Higher island growth induces island relaxation along the direction of island elongation, which in turn causes the formation of ‘‘elongated islands’’ and ‘‘dot-like islands’’. Dur- ing island shape transition, the material grown on the substrate is continuously rebuilt to more effectively release the accumulated strain energy. Acknowledgements The authors would like to thank D. J. Bottom- ley and T. Fukuda for their fruitful discussion. References [1] Y W. Mo, D.E. Savage, B.S. Swartzentruber, M.G. Lagally, Phys. Rev. Lett. 65 (1990) 1020. [2] J. Tersoff, R.M. Tromp, Phys. Rev. Lett. 70 (1993) 2782. [3] G. Medeiros-Ribeiro et al., Science 279 (1998) 353. [4] J. Knall, J.B. Pethica, Surf. Sci. 265 (1992) 156. [5] H. Omi, T. Ogino, Appl. Phys. Lett. 71 (1997) 2163; H. Omi, T. Ogino, Phys. Rev. B 59 (1999) 7521. [6] D.J. Bottomley, H. Omi, T. Ogino, J. Cryst. Growth 225 (2001) 16. [7] Y. Chen, J. Washburn, Phys. Rev. Lett. 77 (1996) 4046. [8] S.A. Chaparro et al., Phys. Rev. Lett. 83 (1999) 1199. [9] S.A. Chaparro, Y. Zhang, J. Drucker, Appl. Phys. Lett. 76 (2000) 3534. [10] P. M € uuller, R. Kern, Surf. Sci. 457 (2000) 229. [11] F.M. Ross, J. Tersoff, R.M. Tromp, Phys. Rev. Lett. 80 (1998) 984. [12] J. Tersoff, Phys. Rev. B 43 (1991) 9377. Fig. 6. Measured fractional Ge coverage of the wetting layer (A), the wires (B), the elongated islands (C), and the dot-like islands (D) versus the amount of Ge deposited. Z. Zhang et al. / Surface Science 497 (2002) 93–99 99 . pref- erably along the ½ 11 10 direction, in the case of Ge growth on Si (1 1 3), Ge islands may naturally first relax towards the softer direction of the substrate, which. observations lead to the conclusion that relaxation of the islands at this growth stage is dominant, in the ½ 11 10 and 1 11 0 directions. Island growth