Three-dimensional islands of Si and Ge formed on SiO ... · Three-dimensional islands of Si and Ge formed on SiO2 through crystallization and agglomeration from amorphous thin films

Three-dimensional islands of Si and Ge formed on SiO2 throughcrystallization and agglomeration from amorphous thin ®lms

Yutaka Wakayama*, Takashi Tagami1, Shun-ichiro Tanaka

Tanaka Solid Junction Project, ERATO, Japan Science and Technology Corporation, 1-1-1 Fukuura, Kanazawa-ku, Yokohama 236-0004, Japan

Received 1 March 1999; received in revised form 15 April 1999; accepted 15 April 1999

Abstract

The crystallization process was examined for amorphous thin ®lms of silicon (a-Si) and germanium (a-Ge) on quartz glass (SiO2)

substrate. Three-dimensional crystalline islands were formed through crystallization and agglomeration. These islands indicated a bimodal

size distribution. The mechanism of crystalline island (c-Si, c-Ge) formation was discussed on the basis of thermodynamics. In studying the

crystallization of the thin ®lms, the in¯uence of the ®lm-substrate interfacial energy should be taken into consideration. It was found that the

thickness of the as-deposited amorphous ®lms is an essential factor in determining the crystallization behavior and in controlling island size.

Above all, a high size uniformity of crystalline islands could be obtained under moderate thermal annealing conditions. q 1999 Elsevier

Science S.A. All rights reserved.

Keywords: Crystallization; Agglomeration; Interface energy; Silicon; Germanium

1. Introduction

In this study, we deal with amorphous ®lms ranging from

1 to 10 nm in thickness with a bare surface, deposited on

SiO2 substrates. Our main purpose is to investigate their

crystal growth process and to examine the possibility of

controlling of the size of crystalline islands on a nanometer

scale.

Amorphous semiconductor thin ®lms have been widely

used in such devices as a thin ®lm transistor and a solar cell.

Their crystallization processes have also been studied exten-

sively from a fundamental scienti®c viewpoint [1,2] On the

other hand, the discovery of visible light emission from

porous silicon [3], even though it has an indirect band

gap, has created a new aspect of semiconductor science. A

large number of techniques for Si nanoparticle formation

have been reported, e.g., chemical vapor deposition [4±7],

laser ablation [8,9] and ion implantation [10,11]. For these

cases, comprehension of crystal growth on a nanometer

scale is very important.

Regarding the fabrication of nanometer-scale materials,

recent research has focused on a self-assembly process. For

Ge deposition on the Si substrate, a high mismatch of lattice

constants induces three-dimensional island formation at the

initial stage of epitaxial growth, that is the Stranski±Kras-

tanov growth mode. Much effort has been made to under-

stand the growth kinetics of the Ge dots theoretically [12±

14] and experimentally [15±20]. Generally, molecular beam

epitaxy (MBE) or metalorganic chemical vapor deposition

(MOCVD) are employed for dot formation. One problem

which must be solved is the control of the size of the dots for

future device application. In these techniques, the dif®culty

in size control arises because gas-phase atoms are supplied

to form solid-state dots. Accordingly, some experimental

parameters, such as the substrate temperature or the deposi-

tion rate, should be varied to accurately control highly

mobile atoms.

Here, we demonstrate a solid-state process for growing

the crystalline islands of Si and Ge on SiO2 substrates.

Crystalline islands are formed through crystallization and

agglomeration from amorphous `thin' ®lms, the surface of

which is clean. The mechanism of crystal growth is quite

different from that of amorphous `thick' ®lms. Discussion

based on thermodynamics is also given to explain this

process.

Thin Solid Films 350 (1999) 300±307

0040-6090/99/$ - see front matter q 1999 Elsevier Science S.A. All rights reserved.

PII: S0040-6090(99)00294-1

* Corresponding author. Present address: Max-Planck Institute of Micro-

structure Physics, Weinberg 2, D-06120 Halle, Germany. Tel.: 149-345-

5582-50; fax: 181-345-5511-223.

E-mail address: [email protected] (Y. Wakayama)1 Present address: Tsukuba Research Center, Technical Research

Laboratory, Nippon Sheet Glass Co. Ltd., 5-4 Tokodai, Tsukuba, Ibaraki

300-26, Japan

2. Experimental conditions

Quartz glass (SiO2) substrates 1 cm2 in size were used for

Si and Ge deposition. A clean substrate surface is strictly

required for precise discussion of the crystallization process

of a-Si and a-Ge thin ®lms. Hence, the cleaning of the

substrate should be carried out carefully as follows. The

mirror-polished SiO2 substrates were chemically cleaned

by washing with isopropyl alcohol and acetone for 15 min

each. After dipping in diluted HF solution (2 wt.%) for 20 s,

they were rinsed in running ultrapure water for 10 min. The

substrates thus cleaned were introduced into a high-vacuum

chamber with a background pressure of 1 £ 1028 Torr.

Then, the substrates were baked at 6008C and maintained

at that temperature for 3 h to remove hydrocarbon contam-

ination and to obtain a clean surface.

Silicon and Ge were deposited on the SiO2 substrates at

room temperature by electron-beam evaporation. The typi-

cal deposition rates were 0.018 nm/s for Si and 0.023 nm/s

for Ge. The thickness of the as-deposited ®lms, denoted as

initial thickness di, was varied from 1 to 10 nm for Si and

was constant at 10 nm for Ge. The structure of the as-depos-

ited ®lms was con®rmed to be amorphous from transmission

electron microscope (TEM) images and electron diffraction

(ED) patterns.

Thermal annealing was performed immediately after the

®lm deposition in high vacuum for crystallization. The

temperature of the specimens was elevated at a rate of

158C/min to 550±6008C for Si and 275±3258C for Ge,

respectively. For both cases, the specimens were held at

each temperature for 30 min and cooled to room tempera-

ture.

The structure of specimens thus prepared was examined

by bright ®eld TEM (JEOL-2010) images those were taken

at an acceleration voltage of 200 kV. For plane-view TEM

observation, the SiO2 substrates were mechanically thinned

from the back surface to a thickness of less than 30 mm,

followed by Ar1 ion milling. A tapping-mode atomic force

microscope (AFM, Dimension 5000, Digital Instruments)

was used for morphological investigation after thermal

annealing.

3. Results and discussion

3.1. Formation of crystalline Si island with bimodal size

distribution

Fig. 1 show the plane-view TEM images of Si ®lms which

were annealed at 6008C. Their initial thicknesses, di, were

(a) 10, (b) 5 and (c) 1 nm. As can be seen here, round

crystallites were formed randomly on the substrate and

their mean size decreased with di. Meanwhile, the number

density of the Si crystallites grew with decreasing di. The

average radius, Ra, and number density of crystallites, D, are

plotted as a function of the initial thickness di in Fig. 2.

A cross-sectional TEM image of postannealed Si with di

of 10 nm is shown in Fig. 3. The image reveals that the Si

crystallites are hemispherical and disconnected from each

other. The height of the islands is about 30 nm and is greater

than di. Namely, three-dimensional (3D) crystalline Si

islands swelled up from two-dimensional (2D) amorphous

thin ®lms through crystallization by thermal annealing.

These results imply that the size of the islands is controlla-

ble by modifying the thickness of as-deposited amorphous

thin ®lms.

The histograms of Si island size are shown in Fig. 4, their

di being (a) 10, (b) 5 and (c) 1 nm. For all cases, the size of

more than 300 islands were measured to obtain these histo-

grams and to discuss the size distribution statistically. It is

clear that the size of the Si islands is widely distributed for

each case. For instance, the radius ranged from 12 nm to 36

Y. Wakayama et al. / Thin Solid Films 350 (1999) 300±307 301

Fig. 1. Plane-view TEM images of Si ®lms annealed at 6008C. The initial

thicknesses of the ®lms, di, are (a) 10, (b) 5 and (c) 1 nm.

nm and standard deviation was determined to be 38% of the

average radius of 24 nm for di � 10 nm.

It is worth emphasizing that the histograms indicate

bimodal size distribution. Dotted lines are drawn in these

®gures to clarify the size distribution. They consist of two

islands groups: small islands ranging from 12 to 28 nm in

radius and large islands ranging from 28 to 36 nm in radius,

at a rough estimate, for di � 10 nm.

To understand the origin of the bimodal size distribution,

the crystallization process of the a-Si ®lms should be exam-

ined in greater detail. For this purpose, a-Si ®lms were

thermally annealed at 550±6008C. Fig. 5 shows plane-

view TEM images. The histograms of Si islands annealed

at 575 and 6008C are shown in Fig. 6. The initial thickness

of these specimens was 10 nm. For comparison, the results

of the specimen annealed at 6008C are also shown in Figs.

5c and 6b, duplicated from Figs. 1a and 4a, respectively.

From the TEM images, it was found that round crystalline

islands, indicated by arrows in Fig. 5a, had started to form

on the substrate at an annealing temperature of 5508C. The

radius of the islands is about 30 nm, which coincides with

that of large islands mentioned above. The number of such

large islands increases on raising the annealing temperature

to 5758C. Thus, the crystallization of a-Si thin ®lms takes

place through the formation of disconnected crystalline Si

islands. Up to this stage of crystallization, the size of the

islands is relatively uniform, as shown in Fig. 6a. The aver-

age radius was determined to be 31 nm and the standard

deviation was found to be reduced to 13% of the average

radius.

Compared to this size uniformity of the islands, the speci-

men annealed at 6008C, which was completely crystallized,

indicates a wide size distribution of the islands. Here, it

should be noted that high annealing temperatures led to

the formation of relatively small islands but not large

ones. Some typical islands are indicated by arrows in Fig.

Y. Wakayama et al. / Thin Solid Films 350 (1999) 300±307302

Fig. 3. Cross-sectional TEM image of postannealed Si with di � 10 nm.

Hemispheric islands are observed. Their height of about 30 nm is greater

than di.

Fig. 2. Average radius, Ra, and number density of crystalline Si islands, D,

plotted as a function of initial thickness di.

Fig. 4. Size distribution of Si islands shown in Fig. 1, their di being (a) 10,

(b) 5 and (c) 1 nm. All histograms show bimodal size distribution: large

islands with narrow distribution and small islands with broad distribution

are represented by dotted lines.

5c. The upper limit of the island size, 36 nm, remained

constant for every thermal annealing condition for the speci-

men of di � 10 nm. No increase in the size of island was

observed, even if the annealing temperature was increased

to 7008C.

Here, we classify the Si islands into two groups: islands-

A whose size is large and has a narrow distribution and

islands-B whose size is small and has a broad distribution.

All of the histograms in Fig. 4 can be interpreted as an

overlap of the distribution of both islands-A and B.

Careful observation of Fig. 5a,b revealed that the Si

islands were surrounded by bright contrast, though such a

contrast was not observed in Fig. 5c. Fig. 7 exhibits a 3D

AFM image of a c-Si island. This image clearly demon-

strated that a ditch encircled the Si islands, which resulted

in the bright contrast in the TEM images. The depth of the

ditch roughly agreed with the initial thickness of the amor-

phous Si ®lm.

3.2. Thermodynamic considerations

On the basis of these experimental results, we consider

the crystallization process to be as follows. Change in the

free energy of the Si thin ®lm, DG1, can be described by

Eq. (1). To simplify the discussion, the shape of the crys-

tallites is assumed to be cylindrical with radius r and thick-

Y. Wakayama et al. / Thin Solid Films 350 (1999) 300±307 303

Fig. 5. Plane-view TEM images of postannealed Si ®lms of 10 nm initial

thickness: (a) 5508C, crystallization begins forming round islands as indi-

cated by arrows; (b) 5758C, the crystal growth proceeds, increasing the

number of islands and keeping their radius constant, relatively small islands

can be observed only near the large islands as indicated by the arrow, a

bright contrast is observed around the Si islands as shown in square; (c)

6008C, Crystallization is completed through the formation of relatively

small islands, as indicated by arrows.

Fig. 6. Size distribution of Si islands shown in Fig. 5b,c, annealed at (a) 575

and (b) 6008C. The average radius, Ra, is shown in the graphs. Lower

temperature produced larger islands with narrower size distribution. Higher

temperature gave rise to the formation of smaller islands in addition to

larger ones resulting in a wide size distribution. The two island groups

are denoted as islands-A and B, respectively.

ness d.

DG1 � pr2dDHac 1 2prdsac 1 pr2 sco 2 sao

ÿ �1 pr2 sa 2 sc

ÿ � �1�Here, DHac is the free energy of the amorphous-crystal

phase transition per unit volume, s ac, s co and s ao are the

interface energies of a-Si/c-Si, c-Si/SiO2 and a-Si/SiO2 per

unit area, and s a and s c represent the surface free energies

of a-Si and c-Si per unit area, respectively.

DG1 varies markedly depending on whether the value

of {DHac 1 �sco 2 sao�1 �da 2 sc�} is positive or nega-

tive. In other words, the crystallization behavior de-

pends strongly on ®lm thickness d. If

d . 2{�sco 2 sao�1 �sa 2 sc�}=DHac, DG1 increases

once at the beginning of the crystallization until a certain

radius is reached, which is expressed in Eq. (2) where

�DG=�r � 0. Continuous crystal growth occurs afterward,

decreasing the value of DG1.

r � 2dsac

dDHac 1 sco 2 sao

ÿ �1 sa 2 sc

ÿ � �2�

On the other hand, DG1 increases consistently with an

increase in the crystallite radius if

d , 2{�sco 2 sao�1 �sa 2 sc�}=DHac. Then, the Si/SiO2

system becomes unstable as crystal growth progresses.

For the Si/SiO2 system, a negative value of DHac (, 2103 J/cm3) [21] ®rst brings about an amorphous-crystal

phase transition. On the other hand, the interface energy

increases as the crystallization proceeds because both s ac

(,3 £ 1025 J/cm2) [22,23] and sco 2 sao (,1023 J/cm2)

[24] have positive values. Then, d ù 10 nm is the critical

thickness to determine the variation in DG1. We assumed

here that the change in the surface free energy through

crystallization, that is sa 2 sc, also has a positive value

and is of the same order of magnitude as s ac (,1025 J/

cm2). The initial thickness of a-Si, di, ranges from 1 to 10

nm in our experiments. Therefore, DG1 increases as the

crystallization proceeds, making the Si/SiO2 system

unstable.

Our experimental results can be interpreted as follows:

crystal growth halted to prevent a further increase in DG1,

and the cylindrical crystallites agglomerate to form hemi-

spheric islands, those are islands-A, in order to minimize the

total free energy of the Si/SiO2 system. The ditch observed

in the AFM image indicates clearly a trace of agglomeration

from the cylindrical crystallites to the hemispheric island.

This is the reason for the presence of the upper limit of

island size. The size uniformity of the islands at an early

stage of crystal growth can also be explained by the same

reasoning. Namely, the halt in the crystal growth occurred at

a certain radius rc. The critical radius rc can be observed as a

bright contrast around Si islands in the TEM images. The

value of rc was determined to be about 43 nm on average

from Fig. 5b, which is 35% larger than the radius of the Si

islands.

Crystallization was completed at a high annealing

temperature of 6008C. Then, the islands formed subse-

quently, those are islands-B, from residual a-Si among

islands-A. The growth of islands-B is not limited principally

within the area of the residual a-Si ®lm. As a result, their

size is smaller and their size distribution is broader than

those of islands-A. The average size of the whole island,

including island-A and B, was actually reduced from 31 to

24 nm. The islands-B, of course, can be formed even at

5758C if crystal nucleation starts near islands-A. One of

the typical example was indicated by arrow in Fig. 5b. Rela-

tively small island, that is islands-B, was formed just near

islands-A.

This also will be shown for the case of the Ge/SiO2

system later. Nevertheless, the size uniformity of the islands

can be maintained as long as the number density of the

islands is suf®ciently low. The crystallization process

described here is illustrated in Fig. 8a±c.

The free energy change DG1 shows a parabolic curve with

radius r. The value of DG1 tends to increase sharply with

decreasing di, as drawn in Fig. 9a. Therefore, the thinner di

resulted in the smaller rc. The critical radius rc can be

expressed as follows

rc ����������������������������������

DGc

p di´DHac 1 sco 2 sac

ÿ �� s�3�

Here, DGc is the critical free energy, at which the agglom-

eration of Si islands occurred. For instance, DGc was esti-

mated to be of the order of 10215 J for the case of di � 10

nm, and then rc � 43 nm. For Eq. (3), we neglected the

terms s ac and sa 2 sc because these values are two orders

of magnitude less than those of DHac and so 2 sao.

Fig. 9b shows the relation between di and the average

radius of islands-A, ra. Assuming that the value of DGc is

constant regardless of di, ra as well as rc will be proportional

top

(1/di), according to Eq. (3). Our results almost support

Y. Wakayama et al. / Thin Solid Films 350 (1999) 300±307304

Fig. 7. AFM image of c-Si islands formed by thermal annealing at 5758C. A

ditch is observed around the c-Si as a trace of the agglomeration.

this discussion, although the ®gure shows a slight curve as

indicated by the dotted line. The reason for the curvature

above di of 5 nm (belowp

(1/di) of 0.5 nm21/2) can be

explained as follows. It has been reported that a critical

size exist to induce the amorphous-crystal phase transition

for a-Si [2,25]. The critical diameter was estimated to be 2±

3 nm. Therefore, it is reasonable, for di below 3 nm, to

regard the crystallites as cylindrical from the beginning of

the crystallization. Then, change in free energy can be

described as Eq. (1), as mentioned above. For thick di

however, crystallites are spherical, to be exact, at the begin-

ning of the crystallization [24]. Then, the free energy change

accompanying the crystallization is described as

DG0 � �4=3�pr3DHac 1 4pr2sac �4�

The crystallite can not be regarded as cylindrical until the

crystallite contacts the substrate. As a result, the critical

radius, rc, becomes large for thick di. This two-step crystal-

lization process is the reason that ra tends to have large value

for thick di (smallp

(1/di)), as can be seen in Fig. 9b. This

crystallization process and the change in the free energies

are schematically illustrated in Fig. 10.

The critical radius is dependent only on the thickness of

the a-Si ®lms, di, as discussed here. It is independent of

other experimental parameters because the values of the

phase transition, surface and interface energies are peculiar

to a material system. These ®ndings suggest that the island

size can be controlled by modifying only the thickness of

the as-deposited ®lm.

For the case of the sandwiched structure of SiO2/a-Si/

SiO2 [22,24,26], crystallite growth has been reported to

halt after reaching a certain size mainly because the increase

in the Si/SiO2 interface energy, sco 2 sao, exceeds the

decrease in the a-Si/c-Si phase transition energy. Similarly,

a strong in¯uence of the interface energy on the crystalliza-

tion process has been reported for multilayered structures,

such as a-Ge/a-GeN [27] and a-Si/a-SiNx [28]. For these

multilayered structures, the ®lms remain 2D and continuous

even after crystallization. In contrast, the surface of a-Si thin

®lm is bare in the present experiments and there are no

capped layers on top of the ®lm. Accordingly, the free

surfaces permits the Si crystallites, which reach the critical

radius rc, to agglomerate by way of the reduction of the total

free energy, forming hemispheric islands.

Sakai et al. also reported the crystallization process of a-

Si ®lms with a clean surface [29]. In their study, they also

observed the ditch around Si crystal grains. They attributed

such a ditch formation to the surface diffusion of Si atoms

on the bare surface. However, the mechanism of the Si

island formation described here should be interpreted differ-

Y. Wakayama et al. / Thin Solid Films 350 (1999) 300±307 305

Fig. 8. Crystallization process of the a-Si thin ®lm on SiO2. (a) In the ®rst

stage, the cylindrical crystallites grow until they reach a critical radius rc.

(b) The crystallites with rc agglomerate, forming unconnected c-Si islands,

islands-A, in the second stage. (c) Finally, annealing at a higher tempera-

ture completes the entire crystallization process, forming small islands,

islands-B, among islands-A. Fig. 9. (a) Change in DG1 with various di are drawn as a function of the

radius of the cylindrical crystalline Si, r. The crystallites which reach rc and

DGc agglomerate to prevent a further increase in free energy. (b) Average

radius of islands-A, ra, is plotted as a function ofp

(1/di)

ently for the following reasons. First, the thickness of the a-

Si ®lms was 50 nm in their experiment, which was suf®-

ciently larger than the value of 2{�sco 2 sao�1 �sa 2sc�}=DHac ( ù 10 nm). Therefore, it was not necessary to

take the in¯uence of the Si/SiO2 interface on the crystal-

lization process into consideration. Additionally, if the

surface diffusion brings about the ditch formation, the island

size should depend on the annealing temperature. That is, a

high temperature leads to large diffusion length, which

should, in turn, lead to the formation of large islands.

However, an upper limit of the Si island size exists and is

independent of the annealing temperature in our experi-

ments. Furthermore, the surface diffusion mechanism can

not explain the size uniformity of islands-A. Consequently,

we concluded that the agglomeration mechanism holds for

the formation of Si islands.

3.3. Formation of crystalline Ge island on SiO2

Principally, for any ®lm/substrate system which has a

positive value of sco 2 sao and satis®es the relation

d , 2{�sco 2 sao�1 �sa 2 sc�}=DHac, 3D crystalline

islands can be formed from amorphous ®lms through crys-

tallization and agglomeration. We examined the crystalliza-

tion of a-Ge thin ®lms on SiO2 substrate in the same manner.

Fig. 11 shows plane-view TEM images of Ge ®lms with di

of 10 nm, which were annealed at (a) 275, (b) 300 and (c)

3258C. The crystallization process can be likened to that of

the a-Si/SiO2 system as follows. Crystalline Ge islands of

about 20 nm in radius start to form at 2758C, and these

Y. Wakayama et al. / Thin Solid Films 350 (1999) 300±307306

Fig. 11. Plane-view TEM images of postannealed Ge ®lms of 10 nm initial

thickness: (a) 2758C, traces of detached islands are observed; (b) 3008C,

island-B is formed as indicated by an arrow even in this crystallization

stage when the nucleation starts near island-A; (c) 3258C, the size distribu-

tion of (c) is also shown in (d).

Fig. 10. (a) The crystallite is spherical when radius r is less than di/2. Then,

the free energy change follows Eq. (3). The crystallite can be regarded as

cylindrical if r exceeds di/2. Then, the free energy change follows Eq. (1).

(b) Change in the free energy accompanying the crystallization process.

The thicker di is, the larger rc becomes compared with those expected in

Fig. 9a.

correspond to islands-A for Si. Relatively small islands,

islands-B, were observed only among or near islands-A,

as indicated by arrows in Fig. 11b. Crystallization was

completed at 3258C, as shown in Fig. 11c. Then, the size

distribution was bimodal, as shown in Fig. 11d.

The average size of Ge islands was smaller than that of Si

islands. This may be because the change in the interfacial

energy through crystallization, that is sco 2 sao, of Ge/SiO2

is greater than that of the Si/SiO2 system. Moreover, traces

showing that the Ge islands detached form the surface were

often observed for the Ge/SiO2 system, as indicated by

arrows in Fig. 11a. Some of the c-Ge islands were consid-

ered to detach from the surface during specimen preparation

for TEM observation. We assume that this is likewise due to

the increase in the interfacial energy through crystallization.

Recently, self-assembly techniques using gas-phase

deposition methods have been regarded as promising candi-

dates for the fabrication of quantum-dots. However, ambig-

uous factors, such as the diffusion length of highly mobile

atoms supplied to the substrate or the nucleation ratio of

islands, make it dif®cult to design nanometer-scale materi-

als precisely. In particular, the broad size distribution of the

quantum-dots is a crucial problem. On the other hand, the

solid-state process mentioned here provides another

approach to achieve size uniformity of semiconductor dots

on a nanometer scale.

4. Summary

We investigated the crystal growth of amorphous thin

®lms with a clean surface on the SiO2 substrate. It was

emphasized that the thickness of the amorphous ®lms is

the dominant factor affecting the crystallization process.

The crystalline islands examined here indicated bimodal

size distribution. This is a result of two-step crystallization

process as follows. First, the agglomeration of the crystal-

lites was triggered after they reached the critical radius rc to

minimize the total energy. At this step, the islands have

basically a uniform radius. Next, crystallization was

completed by further thermal annealing, forming small

islands with a broad size distribution. The main point is

that a high size uniformity of the islands could be obtained

under moderate thermal annealing conditions by taking

advantage of the in¯uence of the Si/SiO2 interface.

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