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Applied Surface Science 252 (2005) 1476–1480

Formation of Ge self-assembled quantum dots

on a SixGe1�x buffer layer

Hyungjun Kim a, Chansun Shin b, Joonyeon Chang c,*

aDepartment of Electrical Engineering, University of California Los Angeles, Los Angeles, CA 90095-1595, USAbNuclear Materials Technology Development, Korea Atomic Energy Research Institute, Daejeon 305-353, Republic of Korea

cNano Device Research Center, Korea Institute of Science and Technology, P.O. Box 131, Chongryang,

Seoul 136-791, Republic of Korea

Received 10 July 2004; received in revised form 12 January 2005; accepted 22 February 2005

Available online 23 May 2005

Abstract

Ge self-assembled quantum dots (SAQDs) grown on a relaxed Si0.75Ge0.25 buffer layer were observed using an atomic force

microscopy (AFM) and a transmission electron microscopy (TEM). The effect of buried misfit dislocations on the formation and

the distribution of Ge SAQDs was extensively investigated. The Burgers vector determination of each buried dislocation using

the g�b = 0 invisibility criterion with plane-view TEM micrographs shows that Ge SAQDs grow at specific positions related to

the Burgers vectors of buried dislocations. The measurement of the lateral distance between a SAQD and the corresponding

misfit dislocation with plane-view and cross-sectional TEM images reveals that SAQDs form at the intersections of the top

surface with the slip planes of misfit dislocations. The stress field on the top surface due to misfit dislocations is computed, and it

is found that the strain energy of the misfit dislocations provides the preferential formation sites for Ge SAQDs nucleation.

# 2005 Elsevier B.V. All rights reserved.

PACS: 85.30.V; 81.15.H; 61.16.B

Keywords: Ge self-assembled quantum dots; Molecular beam epitaxy (MBE); Transmission electron microscopy (TEM)

1. Introduction

Semiconductor quantum dots (QDs) in heteroepi-

taxial systems have been attractive because of their

extensive optoelectronic applications such as lasers

and photodetectors [1,2]. Carriers in QDs are confined

* Corresponding author. Tel.: +82 2 958 6822;

fax: +82 2 958 6851.

E-mail address: presto@kist.re.kr (J. Chang).

0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved

doi:10.1016/j.apsusc.2005.02.141

three dimensionally, and thus the optoelectronic

properties of QDs are different from those of bulk

materials, quantum wells and quantum wires. The

shape and the size of QDs are important parameters in

determining their optoelectronic properties [3,4]. Size

and shape uniformity of QDs should bewell controlled

for enhanced performance of devices.

Ge self-assembled quantum dots (SAQDs) on Si

have served as a simple model system because the

system consists of two components. Buried misfit

.

H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480 1477

dislocations formed between a Si substrate and a SiGe

buffer layer have been interesting because it can be

employed as a tool to control the distribution of Ge

SAQDs. The previous work [5] shows that the

distribution of Ge SAQDs can be controlled by the

density of the buried dislocation networks.

Thework ofKimet al. [6] pointed out that there exist

three different types of effective sites for the nucleation

and growth of Ge SAQDs: (i) the intersection of two

perpendicular buried dislocations, (ii) a single disloca-

tion line and (iii) the region beyond one diffusion length

away from any dislocation. According to the work, the

density ofGe adatoms increases homogeneously on a Si

substrate at the beginning of deposition. After the initial

stage of low Ge coverage, Ge adatoms diffuse to the

effective sites due to the fact that the lattice constant of

the locally strained effective sites are close to that ofGe.

Consequently, Ge adatoms dwell longer at the effective

sites, and form Ge SAQDs [7].

In this work, we observed the regular distribution of

Ge SAQDs grown on a relaxed Si0.75Ge0.25 buffer layer

causing low density of misfit dislocations to investigate

the spatial relationship between misfit dislocations and

preferential formation sites of SAQDs. The Burgers

vector of each buried misfit dislocation is carefully

determined with plane-view TEM. The preferential

formation sites of Ge SAQDs are observed with cross-

sectional TEM micrographs. We have paid attention to

the strain energy of the buried misfit dislocation

network observed in TEM micrographs.

2. Experimental procedure

An 800 A thick Si0.75Ge0.25 layer was grown on a Si

(0 0 1) substrate at 550 8C. A Si0.75Ge0.25 layer is

under compression as grown, which makes the surface

of the layer wrinkle. A 100 A thick Si cap layer was

deposited on a Si0.75Ge0.25 layer at 600 8C subse-

quently to keep the surface of a Si0.75Ge0.25 layer flat

by equilibrating the stress state.

The buffer layer consisting of a Si0.75Ge0.25 layer

and a Si cap layer was annealed at 700 8C for 30 min

afterward. The postgrowth annealing resulted in

approximately 10% relaxation of the buffer layer.

The composition of the relaxed buffer layer was found

to generate misfit dislocations with a relatively large

separation distance.

Ge dots were nucleated on both a Si (0 0 1) substrate

and a Si (0 0 1) with the buffer layer. A 4.5 A thick Ge

layer was deposited first on Si at 280 8C so as to

minimize alloying between Si and Ge dots [8]. Ge dots

were grown subsequently at 650 8C with a constant

growth rate of 0.05 A/s. All epitaxial layers were grown

using a molecular beam epitaxy (MBE, Riber EVA32).

The size and the shape of nucleated SAQDs were

characterized using a Park Scientific atomic force

microscopy (AFM) in contact mode. TEM specimens

for (0 0 1) plane-view and h1 1 0i cross-sectional

observations were prepared by chemical thinning in a

room-temperature HF/HNO3 solution and by ion-

beam thinning using a Gatan 660 Ion-Beam thinner

with a cold stage respectively. TEMmicrographs were

taken with a Philips CM30 and a JEOL 2000FX

transmission electron microscopy. Buried misfit

dislocations and the nucleation sites of Ge SAQDs

were observed with plane-view and cross-sectional

TEM images. The Burgers vector of each dislocation

was determined by the g�b = 0 invisibility criterion.

3. Results and discussion

Fig. 1 shows AFM morphologies of Ge SAQDs

grown on two different types of substrates. In the case

of Ge SAQDs nucleated on a Si (0 0 1) substrate

(Fig. 1(a)), Ge dots are distributed randomly. Ge

SAQDs grown on the relaxed buffer layer (Fig. 1(b)),

however, are well aligned along two orthogonal lines.

The relaxed buffer layer provides preferential forma-

tion sites of Ge SAQDs. It was also observed that the

buffer layer promotes the formation of Ge SAQDs.

Aplane-viewTEM image corresponding toFig. 1(b)

is shown in Fig. 2(a). Lines representmisfit dislocations

nucleated at the interface between the relaxed buffer

layer and a Si (0 0 1) substrate, and small dots are Ge

SAQDs. The misfit dislocation lines are found to be

generated along two orthogonal lines of [1 1 0] and

½1 1 0� in order to accommodate the lattice mismatch

between the substrate and a partially relaxed

Si0.75Ge0.25 layer. The composition of the buffer layer

induces relatively large separation distance of a few

hundred nanometers between adjacent misfit disloca-

tions. The density of misfit dislocations can be easily

controlled by changing the composition x of SixGe1�x

because the lattice parameter of Ge is 4% larger than

H. Kim et al. / Applied Surface Science 252 (2005) 1476–14801478

Fig. 1. AFM images of Ge SAQDs showing different mode of

distribution depending on the presence of a buried misfit dislocation

network.

Fig. 2. (a) A (0 0 1) plane-view TEM micrograph of Ge SAQDs

grown on the relaxed Si0.75Ge0.25 buffer layer. The projection of the

Burgers vector of each misfit dislocation is marked as arrows. (b) A

schematic view of a [�1, 1, 0] misfit dislocation line and the four

possible Burgers vectors on two {1 1 1} planes.

that of Si. Ge SAQDs are found to bewell aligned to the

buried misfit dislocation lines, and it should be noted

that Ge SAQDs form at a certain distance from the

misfit dislocation lines.

The Burgers vector of each dislocation in Fig. 2(a)

was determined by the g�b = 0 invisibility criterion

with four different g vectors i.e., 1 3 1; 1 3 1; 1 1 1 and1 1 1: The Burgers vector of each dislocation line is

projected on the (0 0 1) plane and represented by

arrows in Fig. 2(a). It is assumed that all the Burgers

vectors make an acute angle with the [0 0 1] direction.

The slip system of the diamond structure such as Si

and Ge is h1 1 0i{1 1 1}, and misfit dislocations on the

interface between a Si (0 0 1) substrate and a relaxed

SiGe layer are known to be a mixed edge-screw type

with the Burgers vector oriented 608 from a

dislocation line direction [9,10] as observed in this

work. Fig. 2(b) represents a schematic diagram of a

½1 1 0� misfit dislocation line lying on a (0 0 1) plane

and the four possible Burgers vectors. The slip plane is

either (1 1 1) or ð1 1 1Þ plane, which is inclined to

(0 0 1) plane with an angle of 54.78. From the

determination of the Burgers vector, it is found that Ge

SAQDs are nucleated at one side of the buried misfit

dislocation, which is offset to the corresponding

Burgers vector direction. The position of one array of

SAQDs is marked by a dashed line in Fig. 2(a) along

the corresponding [1 1 0] dislocation line.

In order to investigate the relationship between

buried misfit dislocation network and preferential

formation sites of Ge SAQDs rigorously, h1 1 0i cross-sectional TEM micrographs are examined. Fig. 3(a)

shows such a cross-sectional micrograph viewed along

[1 1 0], in which misfit dislocations are indicated by

arrows. The average distance between a dislocation

H. Kim et al. / Applied Surface Science 252 (2005) 1476–1480 1479

Fig. 3. (a) A [1 1 0] cross-sectional TEMmicrograph. White arrows

represent buried misfit dislocations. (b) A schematic view of a Ge

SAQD and the corresponding misfit dislocation.

Fig. 4. The contour of the computed unit strain energy on the top

surface: solid lines represent underlying misfit dislocation lines and

dotted lines indicate the intersections between the slip planes of the

dislocations and the top surface. The Burgers vector of each dis-

location line is also marked (minimum,maximum and the number of

contour levels: 3 � 10�7, 4.5 � 10�6, 11).

line and a Ge SAQD in Fig. 3(a) is found to be

650 � 13 A. The distance agrees well to the lateral

distance between a misfit dislocation and the position

where the slip plane of the dislocation intersects the

top surface of the 900 A thick buffer layer as shown in

Fig. 3(b). Ge SAQDs thus grow at the specific

positions where the slip planes of buried dislocations

intersect with the top surface. This fact suggests that

the distribution of Ge SAQDs can be manipulated by

utilizing a buried misfit dislocation network.

A two-dimensional array of long straight disloca-

tions with the same configuration as shown in Fig. 2(a)

is constructed in order to compute the elastic stress field

of the array of dislocation lines. The stress field due to a

dislocation line is calculated using the Li’s formula [11]

under the assumption of isotropic linear elasticity, and

the image stress field due to the free surface is computed

using the method of Gosling andWillis [12]. The strain

energy is computed assuming Hookean elasticity.

The array of misfit dislocations and the correspond-

ing strain energy per unit volume on the top surface are

shown in Fig. 4. The unit strain energy is normalized by

mb/{4p(1 � n)} with m and n being the shear modulus

and the Poisson’s ratio of the buffer layer respectively.

The maximum value of the normalized strain energy is

4.76 � 10�6. The contour of the normalized unit strain

energy shows that the region of the maximum strain

energy is offset to the intersection line of each slip

plane, where Ge SAQDs form preferentially as

observed experimentally. Ross [13] showed that the

nucleation of Ge SAQDs occurs approximately at the

point of the maximum tensile strain (exx + eyy) due to asingle dislocation. In the case of a dislocation network

comprising several perpendicular misfit dislocations,

however, the nucleation sites of Ge SAQDs are not

always corresponding to the region of the maximum

tensile strain of the dislocation network involved. The

strain energy of buried dislocations is likely to be an

important factor for the distribution of Ge SAQDs, and

SAQDs are nucleated on the top surface by reducing the

strain energy due to buriedmisfit dislocations. Based on

the results, it is concluded that the intersection of two

perpendicular buried dislocations is energetically most

favorable site for the formation of Ge SAQDs among

three effective sites proposed in [6].

4. Summary

Systematic AFM and TEM observations were

performed to investigate the relationship between

H. Kim et al. / Applied Surface Science 252 (2005) 1476–14801480

misfit dislocations and the distribution of Ge SAQDs.

Ge SAQDs form randomly on a Si (0 0 1) substrate,

whereas they are nucleated along misfit dislocations

buried in a relaxed Si0.75Ge0.25 buffer layer. Both

plane-view and cross-sectional TEM images clearly

show that Ge SAQDs grow at specific positions where

the slip planes of misfit dislocations intersect with the

surface of the buffer layer. The computation of the

stress field of the buried misfit dislocation network

observed experimentally shows that the location of Ge

SAQDs is well aligned with the region of the

maximum strain energy due to the dislocation

network. This result implies that a uniform distribu-

tion of Ge SAQDs can be successfully achieved by

utilizing a uniform network of misfit dislocations

generated in a partially relaxed SiGe buffer layer.

Acknowledgements

This work was supported by ‘‘Korea Institute

of Science of Technology Vision 21st program

and R&D Program for NT-IT Fusion Strategy of

Advanced Technologies’’. The authors are grateful to

Dr. M. Fivel from GPM2, Institut national poly-

technique de Grenoble (France) for helpful discus-

sions on the computation of image stresses.

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