Influences of the si(1 1 3) anisotropy on ge nanowire formation and related island shape transition

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 Sið1 1 3Þ anisotropy on Ge nanowire formation and related island shape transition

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

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

www.elsevier.com/locate/susc

* Corresponding author Tel.: 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 0 0 3 9 - 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
11 1 0 direction of less than 0:2° Ge

deposition at 1.4 ML/min, where 1 ML is defined

as 8:2 1014 atoms/cm2, 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 1010 Torr; and during substrate preparation

and Ge deposition the pressure typically remained

lower than 5 1010Torr 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

½3 3
2 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 ½3 3
2 and ½
33
33 2 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
11 1 0 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 ½3 3
2 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 the½
11 1 0 and ½1
11 0

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 the½3 3
2 direction

The compressive stress in a flat Ge film on Si(1 1 3) along ½3 3
2 is 9% larger than it is along

½
11 1 0 [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 rx and ry stand for the bulk stress

in the ½
11 1 0 and ½3 3
2 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 rxtan hx in the ½
11 1 0 direction and rytan hyin the½3 3
2 direction, where

hx and hy 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  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).

estimated to be ðrxtan hxÞ2=Ex andðrytan hyÞ2=Ey

in the½
11 1 0 and ½3 3
2 directions with Exand Eyof

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
11 1 0 is 9% lower than it is along ½3 3
2 [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 the½
11 1 0 direction is

actually much larger than it is along the½3 3
2

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 2 structure consisting

of dimers and rebounded adatoms make it more

energetically favorable to relax the 2D island along

the½
11 1 0 direction than along the ½3 3
2 direction

[4] From our STM observations of high

resolu-tion, this suggestion can be further strengthened

alternating rows of subsurface interstitials and rebounded adatoms along the½
11 1 0 direction [10]

So, from the beginning of 3D islanding the islands already relax more towards the½
11 1 0 than towards the ½3 3
2 As we mentioned above, the surface stiffness of the substrate along ½
11 1 0 is 5% smaller than it is along½3 3
2, while the compressive stress

in a flat Ge film on Si(1 1 3) along ½3 3
2 is 9% larger than it is along the½
11 1 0 It seems confusing why the islands always prefer to relax along the

½
11 1 0 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 the½
11 1 0 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
11 1 0 base edges of islands than their ½3 3
2 base edges The

Ge nucleation is therefore suppressed at the½
11 1 0 base edges but favored at the ½3 3
2 base edges, forming an elongated island shape perpendicular

to the softer direction of substrate stiffness Wire-like growth of the islands proceeds within

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 ½3 3
2 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
33 2 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, the½
33
33 2 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  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.

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 along½
11 1 0 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 is1.5 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
33 2 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
33 2 direction implies that relaxation of the islands is easier along the ½
33
33 2 direction than the ½3 3
2 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 isis-lands 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
1 1 1 0 of the wire-like islands (open

cir-cles) and the elongated islands (solid circir-cles) 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€ u uller, 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.