GaAs Quantum Dots

SEMICONDUCTORS A N D SEMIMETALS. VOL. 60

CHAPTER 2

Molecular Beam Epitaxial Growth of Self-Assembled InAs/GaAs Quantum Dots Yoshiaki Nakata and Yoshihiro Sugiyama QUANTUM ELECTRON DEVICES LABORATllRY FUIITSULABORATORIES LTD ATSUGI.KANACAWA. JAPAN

Mitsuvu Sugawara OPTIC'AL SEMICONOUCTOR DEVICES

LABOKATORY

FUIITSULABORATORIES LID ATSUGI,KANAGAWA, JAPAN

I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . 117 THESTRANSKI-KRASTANOW GROWTH MODE. . . . . . . . . . . . . . . . 119 1. Energy- Balance Model,for Islcind Formation . . . . . . . . . . . . . . 119 2. InAs Island Growfh . . . . . . . . . . . . . . . . . . . . . . . . . 121 3. Multiple-Layer Growth anti Perpendicular Alignment of Islands . . . . . . 125 4. In-Plane Alignment of Ishncis . . . . . . . . . . . . . . . . . . . . 130 111. CLOSELY STACKED InAsJGaAs QUANTUM DOTS. . . . . . . . . . _ . _ _ 132 1. Close Stacking of InAs Islunt6 . . . . . . . . . . . . . . . . . . . . 133 2. Photoluminescence Properties . . . . . . . . . . . . . . . . . . . . 137 3. Zero-Dimensional Exciton Corlfinenwnt Evaluated by Diamagnetic Shifts. 140 I V . COLUMNAR InAsJGaAs QUANTUM DOTS. . . . . . . . . . . . . . . . . 143 v. S U M M A R Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I52 11.

1

I. Introduction The atom-like density of states in quantum dots should drastically improve the performance of optical devices, especially semiconductor lasers, and should also be instrumental in the development of novel optoelectronic and single-electron devices. Since high-performance lasers, including quantum-wire and quantum-dot in active regions, were first proposed theoretically by Arakawa and Sakaki (1982), fabricating these low-dimensional 117 Copyright 1 1999 by Academic Press All rights of reproduction in any form reserved. ISBN 0-12-752169-0 ISSN 0080-8784/99 $3000

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quantum nano-structures has been a major interest in semiconductor research. In particular, 111-V nano-structures such as GaAs/AlGaAs, InGaAs/GaAs, and InGaAs/InP are major targets in optical and electronic device applications. Numerous challenges in quantum-wire and quantum-dot fabrication have been reported during the last two decades. The most straightforward technique is to laterally pattern the quantum-well structures through a combination of high-resolution electron beam lithography and dry or wet etching (Petroff et al., 1982; Reed et al., 1986; Miyamoto et al., 1987; Gershoni et al., 1988). Other techniques exploit regrowth of epitaxial layers, such as fractional layer growth on a vicinal substrate (Petroff et al., 1984; Fukui and Saito, 1987), selective growth on a patterned substrate (Kapon et al., 1989, 1992), and cleaved-edge overgrowth (Goni et al., 1992; Pfeiffer et al., 1993; Wegscheider et al., 1995). However, artificial structures fabricated in these ways did not take full advantage of engineered energy states, and some had drawbacks. For example, lithography- and etching-based technologies caused damage to the crystals, such as impurity contamination, defect formation, and poor interface quality. Further, there were serious problems in the fabricated structures themselves, such as large size, low density, and size irregularity. Significant quantum-size effects advantageous to, say, optical devices appear when the size is less than the exciton Bohr radius. Moreover, millions of the structures should be densely packed, with size uniformity on the atomic scale, to obtain the desired optical signal. Unfortunately, no technique could succeed in achieving all of these requirements. Self-assembling, a novel way to fabricate quantum dots, is now being welcomed as the most promising approach in overcoming the various problems with previous techniques. This process exploits the three-dimensional island growth of highly lattice-mismatched semiconductors. The growth of InAs on a GaAs substrate is a typical example, where the lattice mismatch between InAs and GaAs is about 7%. Dislocation-free highdensity coherent islands of InAs are self-assembled on the GaAs substrate, accompanied by a wetting layer. Typical InAs self-assembled islands have a dome or pyramid shape with a base length of about 20 nm and a height of a few nm. Since the exciton Bohr radius is 10 to 20nm in an InAs-GaAs system, the island size is small enough to exhibit the three-dimensional quantum confinement effect. Actually, well-separated photo-emission spectra from discrete energy states have been observed (Mukai et al., 1994; Grundmann et al., 1996). Room-temperature lasing from the quantum-dot quantized levels has been achieved, and the threshold current has decreased and is now close to that of strained quantum-well lasers (see Chapter 6). Though self-assembling is a new way to form quantum dots, the growth

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process itself is not new but is simply a Stranski-Krastanow (SK) mode growth (Stranski and Krastanow, 1937). InGaAs/GaAs islands grown via the SK mode were observed and evaluated by several groups in the mid-1980s (Schaffer et al., 1983; Lewis et al., 1984; Glas et al., 1987; Houzay et al., 1987). However, the research did not attract broad interest, at least as it applied to quantum dots. That SK InAs islands on a GaAs substrate might work as quantum dots was proposed by Tabuchi et al. (1992). Since then many works have identified the islands as quantum dots with threedimensional quantum confinement, primarily on the basis of their optical emission properties (Leonard et al., 1993; Mukai et al., 1994; Marzin et al., 1994; Oshinowo et al., 1994; Moison et al., 1994). Three-dimensional island growth, now the center of interest in semiconductor material and device research, is known as self-assembled growth. In addition to the InGaAs quantum dots treated in this volume, a variety of dots of other semiconductor materials have been fabricated through self-assembling processes. These include InGaP (Carlsson et al., 1995; Reaves et al., 1995), CdSe (Arita et al., 1997), and GaN (Tanaka et al., 1996, 1997). In the near future, this new material category will improve various optical devices like semiconductor lasers in many aspects (see Chapter 7) and in wavelength regions ranging from infrared to red to blue. This chapter focuses on the molecular beam epitaxial (MBE) growth of InAs islands on a GaAs substrate. Section 11, briefly reviews the three well-known growth modes and a simple energy balance model for island formation, and then describes the growth process of InAs three-dimensional islands with various diagnostic results. Then, Section I11 introduces the perpendicular stacking of InAs islands, called closely stacked quantum dots, and Section IV introduces columnar-shaped quantum dots. Perpendicular stacking increases the island size primarily in the growth direction and enables us not only to tune the emission wavelength but to narrow the spectrum linewidth caused by the island-size fluctuations. By comparing the structural and optical properties of different types of dots, we can see the perpendicularly stacked columnar shaped quantum dots’ advantages. 11. The Stranski-Krastanow Growth Mode

1. ENERGY-BALANCE MODELFOR ISLAND FORMATION The crystal growth on a bulk substrate occurs in one of three distinct modes, schematically shown in Fig. 2.1; Frank-van der Merwe (FM), Volmer-Weber (VW), and Stranski-Krastanow (SK). While growth proceeds layer by layer in the FM mode, VW growth causes three-dimensional

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Frank-van der Merwe mode

Volmer-We&r mode Island

Epitaxial layer

FIG. 2.1. Three types of growth mode on a substrate; Frank-van der Merwe (FM); Volmer-Weber (VW); and Stranski-Krastanow (SK). In the F M mode growth proceeds layer by layer. In the VW mode growth occurs as three-dimensional islands on the substrate. The SK mode is a combination of the FM and VW modes, where the growth of a severalmonolayer-thin film, called a wetting layer. is followed by cluster nucleation, leading to island formation.

islands on the substrate, if the film has a higher surface energy than that of the substrate. SK growth is a combination of the FM and VW modes, where the growth of a several-monolayer thin film, called a wetting layer, is followed by cluster nucleation and then to island formation. Which growth mode occurs depends primarily on the difference in the surface energy between the substrate and the grown material and on the strain energy accumulated in the grown materials as a result of lattice mismatch. In the strained-layer growth of semiconductors discussed here, the SK growth mode has been found to dominate. Why islands form in the lattice-mismatched epitaxy can be understood by a simple model of energy balance (Tu et al., 1992). Let us compare the total energy between a coherently strained film on a substrate and strain-free islands made by the same number of atoms as in the film. The total energy is supposed to consist of the strain energy due to lattice mismatch and the surface energy. The strain-free islands are, for simplicity, assumed to be cubic shaped with a side length of X . Instead of releasing the strain energy, the cubic islands have greater surface energy due to the increased surface area. The island energy is lower than the film energy, then, when the island is larger than a critical value determined by the surface energy, y , and the in-plane strain, E, as

x > x,K

y/&2

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When E # 0, there is always a value of X above which the island is in the lower energy state; that is, when the side length of the islands is greater than X,, the island configuration will be favored. This indicates that, given sufficient growth temperature and time, islands are always formed in the strained layer epitaxy. In contrast, the present strained-layer epitaxial growth using metalorganic chemical vapor deposition (MOCVD) and MBE enables us to obtain coherent strained layers over 1% lattice mismatch without dislocations, which tells us that strained-layer epitaxy occurs under metastable conditions, and that surface kinetics also play an important role. Though the present energy balance model looks too simple, in Eq. (2.1) we see that the critical size is inversely proportional to the square of the strain and that we will have smaller islands as the lattice mismatch increases. In the following sections, we will see that this simple rule explains actual island growth rather well. 2. InAs ISLAND GROWTH

When InAs is supplied to a GaAs substrate, three-dimensional island growth occurs followed by the two-dimensional growth of a wetting layer. Before we move on to the islands’ perpendicular stacking, let us see in detail how the growth of individual islands proceeds. With MBE growth, the reflection high-energy electron diffraction (RHEED) pattern gives us important information on the surface state. When the layer-by-layer growth proceeds, RHEED shows streak patterns. The RHEED pattern transits to spots when three-dimensional islands start to grow. For the post-growth surface morphology evaluation technique, we use atomic force microscopy (AFM), from which we know the shape, size, density, alignment, and the distance between neighboring islands. We can get similar information from plan-view transmission electron microscopy (TEM) even when islands are covered by overgrown layers, we can also evaluate defects, such as dislocations and stacking faults. Cross-sectional TEM is quite useful for observing cross-sectional shape and height of the islands, and how the islands are stacked perpendicularly and interact with each other. We will see this in Sections I11 and IV. For the growth of InAs islands, a conventional MBE was used with metallic In, Ga, Al, and As, as source materials. The substrates were (001)-oriented GaAs. Before growth, they were thermally cleaned at about 680°C for one minute under an arsenic pressure of 1.2 x lo-’ Torr. InAs islands were grown on a GaAs (100 nm)/AlGaAs (50 nm)/GaAs (400 nm) buffer layer and covered with a GaAs (50 nm)/AlGaAs (50 nm)/GaAs (100 nm) cap layer. The substrate temperature for the growth of InAs was

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varied between 470 and 560°C, and was 650°C for the growth of the buffer layer. The substrate temperature was monitored by a pyrometer calibrated by the melting temperature of In-A1 alloys. The growth rates of InAs and GaAs were approximately 0.1 and 0.75 pm/h. In other words, it takes about 10 seconds to grow one monolayer (ML) InAs and about 1.3 seconds to grow one ML GaAs. The arsenic Torr and was 1.2 x pressure used for InAs island growth was 6 x Torr for buffer-layer growth. These values were measured by an ion gauge at the substrate position. Two arsenic cells were used, both set at 6 x lop6 Torr. The arsenic pressure was changed abruptly at the interface by switching one of these cells on and off. After 60-second annealing of the InAs islands, GaAs layers were overgrown. The variation of the RHEED pattern and the diffraction intensity are shown in Fig. 2.2. During the growth of the buffer layer, the surface was

Growth time (s)

2 0 ~ 1 div. 1

FIG.2.2. Variation of the RHEED pattern and the reflection intensity for the various stages of growth of lnAs islands. The pattern transition from streaks to spots began as the growth of lnAs reached around 1.6 monolayers at 16 seconds, indicating that two-dimensional growth transited to three-dimensional island growth. The reflection intensity reached an almost constant value at the 1.8-ML InAs supply. The pattern went back to streaky at the 6-ML GaAs growth, showing that 6-ML GaAs completely covers the InAs islands and almost flattens the surface.

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As-stabilized (2 x 4) and then transited to c(4 x 4) reconstruction while the substrate temperature dropped to 510°C. The leftmost photograph in Fig. 2.2 is the [ l l O ] azimuthal RHEED pattern obtained before InAs growth. The lp-order fractional diffractions were clearly observed. Immediately after the InAs growth started, the fractional-order reflections disappeared, and the transition from streaks to spots started as the growth of InAs reached around 1.6 M L (at 16 seconds), indicating that a two-dimensional layer growth transited to a three-dimensional island growth. When the GaAs supply started to overgrow the InAs islands as a cap layer, the spot intensity rapidly decreased. The pattern went back to streaky at the 6-ML GaAs growth, showing that the 6-ML GaAs supply fully covers the InAs islands and almost flattens the surface. The island size and density were evaluated by ex-situ AFM operated in the air. Figure 2.3 shows AFM images of the island surfaces grown with the InAs supply of 1.3, 1.6, 2.1, and 2.6 ML. These images refer to different epilayers grown under the same conditions. The scanned area is 0.5 x 0.5 pm2. The island growth started at an InAs supply of about 1.6 ML, as seen in the change of RHEED pattern. As the amount of InAs supply

(c) 2.1 ML

(d) 2.6 ML

2 0.5 x 0.5 pm FIG. 2.3. AFM images of the islanding surfaces when the InAs supply was 1.3, 1.6, 2.1, and 2.6 MLs. The islanding growth starts at the 1.6-ML supply, as seen in the change in RHEED pattern. As the supply amount increases, the dot density rapidly increases and the dots coalesce.

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increased, the island density rapidly increased, and the islands began to coalesce when the amount of InAs exceeded approximately 2.3 ML. Figure 2.4 shows the in-plane base diameter and the density of the islands as a function of the amount of InAs supply (InAs nominal thickness (ML)). As depicted in the figure, growth proceeds from the two-dimensional growth of a wetting layer to the nucleation of InAs islands at about a 1.6-ML supply, to the increase in the island density, and finally to the coalescence of neighboring islands at about a 2.3-ML supply. Figure 2.5 shows the base diameter and density of islands grown with the 2.1-ML InAs supply as a function of the growth temperature. The AFM images of islands grown at each temperature are also shown. As temperature increases from 470 to 56OoC,the island diameter increases from 15 to 45 nm and the density decreases correspondingly. This temperature dependence is due to the surface migration lengh of TnAs, which increases as the temperature increases. Figure 2.6 shows the plan view (a) and the (1 10) cross section (b) of TEM images for InAs islands grown with a 2.5-ML InAs supply. Observable were

lnAs nominal thickness (ML) FIG. 2.4. In-plane diameter and density of islands as a function of the InAs nominal thickness. The growth proceeds from the two-dimensional growth of a wetting layer, to the nucleation of InAs islands at about 1.6 ML supply. to the increase in the density, and finally, to the coalescence of neighboring islands at 2.2-2.3-ML supply.

-

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lo'*

Ts = 510°C

540°C

0 450 500 550 600 Growth temperature ( "C)

560°C 0.5 x 0.5 pm2

FIG. 2.5. Diameter and density of islands at 2.1-ML InAs supply as a function of growth temperature, and the AFM images of islands at each temperature. As the temperature increases from 470 to 560'C. the island diameter increased from 15 to 45 nm and the density decreases correspondingly.

two types of islands-small, with a diameter of 15-20 nm, and large, with about twice the diameter -which were formed probably by coalescence. While the height of most islands is 3 to 5 nm, that of the large-size islands exceeds 10nm. Contrasts due to strain were observed both in the GaAs buffer layer and in the GaAs overlayer, and they extended as the dot size increased. There are two types of defects: V-shaped dislocations and multiple stacking faults. In the upper middele part of Fig. 2.6(a), a large island accompanied by line-shaped defects on both sides could be seen. These defects are a V-shaped dislocation pair lying on two equivalent { 11l } planes. Note that both types of defect are generated from large islands and almost no defects are observed around the small islands (Ueda et al., 1998).

3. MULTIPLE-LAYER GROWTH AND PERPENDICULAR ALIGNMENT OF ISLANDS The InAs islands buried in GaAs work as quantum dots because they are smaller than the exciton wave function both in the in-plane and perpendicular directions. When we apply the TnAs island layers to the active region of

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FIG. 2.6. (a) the (001) plan-view and (b) the (110) cross-sectional TEM images of InAs islands (2.5-ML InAs coverage). Observed are small islands with a diameter of about 20nm and large islands with about twice that diameter formed by the coalescence of two islands. While the height of most islands is 3 to 5 nm, that of the large islands exceeds 10 nm. Contrasts due to strain are observed in both the GaAs buffer layer and the GaAs overlayer, and they extend as the dot size increases. There are two types of defect to be observed: V-shaped dislocations and multiple-stacking faults.

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optical devices, multiple-layer stacking of the island layer is often required to obtained enough interaction between confined electrons and the electromagnetic field. This is immediately understood if we think of multiple quantum-well lasers. Figure 2.7 shows the cross-sectional TEM images of the stacked island structures grown with the intermediate layer thickness of lOnm (a) and 20nm (b). For the multiple-layer stacking, the growth sequence shown in Fig. 2.2 is simply repeated. These intermediate-layer thicknesses are much greater than the island height of about 3-5 nm. In the 20-nm structure (b), the islands form independently of the lower-layer islands. AFM images show that the mean island size and the density are almost constant in all island layers. When the intermediate layer is reduced to 10 nm, the islands align in the perpendicular direction and the size increases as we move to the upper layers. This perpendicular alignment of islands is due to the strain fields induced by the lower layer islands. Xie (1995) provided an analytical description of correlated island formation in the growth direction under strain fields. His explanation follows: Islands on the first layer produce tensile stress in the GaAs intermediate layer above the islands. Let 1, be the effective length of the lateral strain field extent at the GaAs surface. The InAs that forms the next layer impinging inside I, around the lower island preferentially migrates from regions of higher to lower lattice mismatch and accumulates just on top of the lower islands. Thus, the InAs can achieve an energetically lower thermodynamic state due to lower lattice mismatch against the GaAs in tension. The strain fields induced by the islands provide the driving force for

(a) Intermediate layer: 10 nm

(b) Intermediate layer: 20 nm

FIG. 2.7. Cross-sectional TEM images taken when the intermediate GaAs layer thickness was (a) 10 nm and (b) 20 nrn. These intermediate layer thicknesses are greater than the height of the InAs islands, which is 3-5 nm. In the 20-nm structure, the island formation occurs independently between layers. When the intermediate layer was reduced to 10 nm, the islands aligned in the perpendicular direction and the size increased as growth moved on to the upper layers.

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perpendicularly aligned self-assembling island formation. In the region outside l,, where there is negligible stress, some of the impinging In atoms initiate formation of islands. Thus, in order to achieve effective perpendicular alignment, the island separation, I, should satisfy the condition of 21, > 1. This condition is achieved by decreasing the intermediate GaAs thickness below a critical intermediate layer thickness. The size and density of islands vary as the multiple-layer stacking proceeds, as seen in Fig. 2.8. When we grew 1.8-ML InAs islands using 10-nm thick intermediate GaAs layers, the average diameter of the 10thlayer islands was about 45 nm, 90% larger than the first-layer islands, which were 24 nm in diameter. The island density decreased from 1 x 10" cm-2 for the first-layer islands to 3 x 10'ocm-2 for the 10th-layer islands. These phenomena were also reported by Solomon et al. (1996). The increase in the island size and the decrease in the density can be understood by the above-mentioned strain field model as follows. The size distribution of self-assembled islands leads to spatial fluctuation of strain fields at the surface of GaAs. Supplied InAs for the growth of the next island layer preferentially accumulates on the sites with larger strain fields. Due to smaller lattice mismatch between InAs and the surface, the island becomes large. As a result, large islands are formed preferentially on the large-strainfield region, preventing island formation on the small-strain-field region. This explains the increase in the island size and the decrease in density in multiple-island growth with about a 10-nm intermediate layer. As seen in Fig. 2.8, as we further reduce the thickness of the intermediate layer below 10 nm, the increase in size and the decrease in density become less remarkable. For example, when we grew multiple layers with 3-nm thick intermediate layers, the average diameter of the 10th-layer islands was about 33 nm-40% larger than the 1st-layer islands, with 24-nm diameter- while the islands' density decreased from 1 x 10' cm2 for the 1st-layer islands to 8 x lOl0cm2 for the 10th-layer islands. This is because the thinner intermediate layer causes the strain field over small islands to become large enough to accumulate supplied InAs. Photoluminescence spectra from single-layer and multiple-layer samples with 20-nm intermediate layers at 77 K are shown in Fig. 2.9. The sample was excited by an Ar' ion laser at a power of 1 mW, and the luminescence was dispersed by a monochrometer and detected by a cooled Ge detector. The laser spot was about 100pm in diameter. The emission spectrum appeared at around 1.2 eV with a full width at half maximum (FWHM) of 90meV for both samples. Such large spectrum width is typically observed in self-assembled SK-mode islands so far reported. This is inhomogeneous broadening, caused by the fluctuation of the quantized energies among islands included in the measured area (lo6 to lo7 islands). By means of

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Intermediate layer thickness, L (nm)

FIG. 2.8. In-plane diameter and density normalized against the first-island-layer density as a function of the intermediate-layer thickness. When 1.8-ML InAs islands were grown using LO-nm thick intermediate GaAs layers, the average diameter of the 10th-layer islands was about 45m, 90% larger than the first-layer islands, with a 24-nm diameter. The island density decreased from 1 x 10" em-' for the first-layer islands to 3 x 10" cm-' for the 10th-layer islands. As the thickness of the intermediate layer was further reduced below 10 nm, the increase in size and the decrease in density became less remarkable.

microprobe photoluminescence to access a limited number of islands, a sharp emission spectrum with around 100peV is observed (Marzin et al., 1994; Fafard et al., 1994; Grundmann et al., 1995a; Leon et al., 1995; Hessman et al., 1996). When we apply SK-mode islands as the quantum dots to the laser active region, the large spectrum broadening lowers the optical (differential) gain and prevents us from achieving the high performance predicted in quantumdot lasers. For example, low gain leads to lasing from excited levels with a high density of states, increasing the threshold current. Low differential gain lowers the relaxation oscillation frequency and limits the modulation bandwidth. One exceptional device that prefers large broadening is multi-

YOSHIAKINAKATA AND YOSHIHIROSUGIYAMA

PL

77 K

Stacked island layers FWHM: 90 meV

0.9

1.0

1.1 1.2 Energy (eV)

1.3

1.4

FIG. 2.9. Photoluminescence spectra from single-layer and multiple-layer samples with 20-nm intermediate layers at 77 K. The emission spectrum appeared at around 1.2 eV with the full width at half maximum (FWHM) of 90meV for both samples. This inhomogeneous broadening was caused by the fluctuation of the quantized energies among islands included in the measured area (lo6 to lo’ islands).

wavelength optical memory, where the spectrum hole burning is exploited for data storage and the large spectrum broadening increases the memory size (Muto, 1995). The broadening of luminescence should be controlled by the structural fluctuations, especially by the island height, since the SK-mode islands have a height of 3-5nm, which is much smaller than the diameter of about 20nm. This is understood by a well-known concept that the quantized energy changes by a constant size fluctuation as the size of the confinement region decreases. Thus, if the height can be increased or more accurately controlled, emission spectrum broadening will be greatly reduced. Increase or control is achieved by means of close stacking of islands in the perpendicular direction, as will be seen in Sections I11 and IV. 4. IN-PLANE ALIGNMENTOF ISLANDS

The islands become technologically more interesting if we can manipulate their arrangement laterally as well as vertically to achieve three-dimensional arrays. There are several reports on lateral ordering, in-plane alignment, and

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control of islanding sites in specific regions, which we summarize in the following paragraphs. The short-range ordering of InAs SK-mode islands grown on (001) GaAs by MBE was reported by Grundmann et al. (1995b), who showed by plan-view TEM observation that InAs islands align in the quasi-periodic square lattice with an axis of (100). Shchukin et al. (1995) theoretically explained this spontaneous ordering by showing that a periodic array of strained islands arranged in a two-dimensional square lattice has a minimum total energy with main axes along the [loo] and [OlO] directions. Tersoff et al. (1996) presented a model showing that island size and spacing grow progressively more uniform as successive island layers are stacked. Nishi et al. (1997) observed spontaneous lateral alignment of InGaAs islands grown by gas-source MBE aligned in a direction inclined about 60" from the [Oll] direction on (311)B surfaces. Surface steps play an important role in determining strained-island nucleation. Leonard et al. (1994) and Ikoma and Ohkouchi (1995) showed by AFM and ultra-high-vacuum scanning tunneling microscopy (UHVSTM) that InAs islands form in alignment along the monolayer step edges on (001) GaAs. Kitmura et al. (1995) demonstrated that InGaAs islands grown by MOCVD preferentially form on the bunched steps on the misoriented (001) GaAs substrates, and that selective island formation on the bunched step is possible. Growth on prepatterned substrates has been extensively studied as a way to control directly the in-plane alignment or position of islands. Preferential island formation has been found either on top of the ridges or along the sidewalls of the mesa stripes and at the bottom of the V-grooves, trenches, holes, and pits. Mui et al. (1995) demonstrated the self-alignment of InAs islands on etched GaAs ridges running along the [ O l l ] and [OlT] directions on the (100)-oriented substrates. InAs islands were formed on the sidewalls of ridges running along the [llO] direction, while for the ridges running along the [OlT] direction, islands were formed on the (100) plane on and at the foot of the mesa stripes. Moreover, as the grating pitch was reduced to 0.28 mm, islands were located either on the sidewalls or at the bottoms, with none on the tops. Seifert et al. (1996) reported InP islands on InGaP/GaAs overgrown stripes lithographically defined by metal stripes 30" off from the [TlO] direction on the (001) GaAs substrates. They demonstrated that the islands aligned either on top of the ridges, at the sidewall near the mesa edges, or at the bottom of the trenches, depending on the geometry of the InGaP/GaAs overgrown mesa stripes. Similarly results were obtained by Jeppensen et al. (1996) in an InP islands/InGaP/(OOl) GaAs system. They found that InAs islands grown by chemical-beam epitaxy form in chains with a minimum period of 33 nm along the trenches, and that single or a

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few islands that grow in an array in electron-beam lithographic holes on a (100) GaAs surface. Tsui et al. (1997) and Konkar et al. (1998) tried to form InAs islands selectively on top of the mesa stripes fabricated on (001) GaAs substrates. They demonstrated selective positioning of InAs islands on the top mesas depending on the geometry. The selective island formation on non-(001) prepatterned substrates were studied. Saitoh et al. (1996) used lithographically fabricated (wet-etched) tetrahedral-shaped recesses and V-grooves on (11 l)B GaAs substrates. They found that InAs islands selectively form at the bottom of those recesses. One of the most important purposes of the study of in-plane alignment of islands is improved structural uniformity. However, this purpose has yet to be achieved. We must further improve size and composition uniformity of islands grown on those stepped surfaces and grown by selective area growth. 111. Closely Stacked InAslGaAs Quantum Dots

The alignment of islands in the perpendicular direction will make it possible to couple islands electrically in the vertical direction as we reduce the intermediate GaAs thickness to the extent that the electron wave functions of neighboring wells are overlapped. This is the same situation as multiple quantum-well transfer to a superlattice when the barrier layer thickness is reduced. Vertical coupling enables electron tunneling between quantum dots, which lead to such novel electronic applications as a single-electron tunneling device. When we think of optical-device application of quantum dots, the most promising and practical advantage of the stacking technique will be size control. By choosing the intermediate-layer thickness and the repetition number of island layers, we will be able to tune the island size (height) and thus the quantized energies to meet device requirements. In addition, according to the discussion in Section 11, the size increase in the perpendicular direction will lead to a narrowing of the emission spectrum which will be quite beneficial for lasers. This section describes the growth process, the crystal structures, and the optical properties of perpendicularly stacked islands when the intermediate GaAs layer is reduced to a few nanometers close to or comparable to the height of InAs islands. Even under this condition, InAs islands are repeatedly grown. Optical diagnostics show that the stacking of the InAs islands increases the effective size of quantum dots in the perpendicular direction due t o electrical coupling, resulting in the narrowing of the spectrum FWHM to 25 meV. We call the stacked structure closely stacked quantum dots (Nakata et al., 1997).

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1. CLOSESTACKING OF InAs ISLANDS

Figure 2.10 shows the growth sequence for the close stacking of InAs islands. The amount of InAs supply for island formation was fixed at about 1.8 ML, and the nominal thickness of the GaAs intermediate layers was set at 2 and 3 nm. Prior to and following InAs island growth, the sample was annealed for 2 minutes and 1 minute, respectively. The growth rates, arsenic pressure, and growth temperature were the same as in Section 11.1. Figure 2.1 1 shows the RHEED-pattern intensity transition, observed at the area indicated by an arrow in the inset patterns, during the growth of InAs islands. The RHEED shows the streak pattern for the two-dimensional growth in the early stage, and the change to the spot pattern for the three-dimensional growth at above a critical amount of InAs supply. The SK-mode islands also grow for the 3rd and 5th layer. Note that the 3rd- and 5th-layer islanding started when the growth of InAs reached about 1 MLabout 63% of the 1st-layer islanding (approximated 1.6 ML). The reason for the smaller critical amount for the islanding is thought to be that the strain induced by the lower-layer islands accumulates InAs preferentially or that segregation of InAs from lower islands. The transition of the growth mode from two- to three-dimensional and the existence of wetting layers, as will be shown in the TEM image (Fig. 2.14(a)), both indicate that SK-growth islands were formed even on such thin GaAs intermediate layers.

FIG. 2.10. Growth sequence for the close stacking of InAs islands. The amount of InAs supply for island formation was fixed at about 1.8 ML, and the nominal thickness of the GaAs intermediate layers was set at 2 and 3nm. Prior to and following InAs island growth, the sample was annealed for 2 minutes and 1 minute, respectively.

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0

10

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FIG. 2.1 1. RHEED pattern intensity transition observed at the area indicated by an arrow in the inset patterns during the growth of InAs islands. The RHEED pattern shows that the SK island growth occurred also for the 3rd and 5th layer. Note that the 3rd- and 5th-layer island started when the growth of InAs reached about IOML, which was about 63% of the 1st-layer islanding.

The island size and the density at each layer were evaluated by ex-situ AFM. Figure 2.12 shows AFM images of the islanding surfaces at the (a) lst, (b) 3rd, (c) 5th, and (d) 10th layers stacked with 3-nm thick intermediate layers. These images refer to different epilayers grown under the same conditions. The scanned area is 250 x 250 nm'. The upper layer islands expanded slightly as the number of stacked layers increased. Figure 2.13 shows the dependence of island size on the number (diameter) and density of stacked layers. The average diameter of the 10th-layer islands was about 33 nm-40% larger than the 1st-layer islands, which were about 24 nm in diameter-while the island density decreased from 1 x loi1 cm-' for the 1st-layer islands to 8 x 10'ocm-2 for the 10th-layer islands. The increase in the diameter and decrease in the density were caused by the strain field formed by the lower islands as in Section 1.3. TEM photography shows the overall structural features. Figure 2.14(a) is a (110) cross-sectional TEM image of a 5-island stacked structure grown with 2-nm thick intermediate layers. Each island layer was accompanied by

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250 x 250 nm2 FIG. 2.12. AFM images of the islanding surfaces at the (a) Ist, (b) 3rd, (c) Sth, and (d) 10th layers stacked with 3-nm thick intermediate layers. The upper-layer islands expanded slightly as the number of stacked layers increased.

40

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n U

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6 8 Layer number

4

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0 12

FIG. 2.13. The dependence of the island size (diameter) and density on the number of stacked layers. The average diameter of the 10th-layer islands was about 33 nm-40"/0 larger than the diameter of the 1st-layer islands (about 24 nm), while the island density decreased from 1 x 10" cm-' for the 1st-layer islands to 8 x IOL0cm-*for the 10th-layer islands.

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(a)

FIG.2.14. (a) ( I 10) cross-sectional TEM image of a 5-layer stacked island structure grown with 2-nm thick intermediate layers. Each island layer was accompanied by a wetting layer. The islands as a whole were about 22 nm in diameter and 13 nm in height, shown in the image as dark megaphone-like strained regions. (b) Plan view of a TEM image obtained from a 5-layer stacked island structure. Island density was 8 x 10'" cm-'. Size uniformity and lateral ordering were improved compared to a single-island layer.

a wetting layer, indicating that the upper-layer islands formed via SK growth, as did the 1st-layer islands. The upper-layer islands grew just on the lower-layer islands, aligning vertically. These islands as a whole had a structure of about 22 nm in diameter and 13 nm in height, shown in the image as dark megaphone-like strained regions. Figure 2.14(b) is a plan view of a TEM image obtained from a 5-layer stacked island structure grown with 2-nm thick intermediate layers. The density of the islands was 8 x 10'0cm-2, which agreed with the AFM results. What is surprising is that tht size uniformity and lateral ordering improved compared to the ordinary SK-mode islands (a single island layer). Although we attempted

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GaAs overgrowth

on lnAs islands

Annealing

(growth interruption)

137

2nd lnAs growth

FIG. 2.15. Growth process of stacked islands. The height of the InAs island after GaAs overgrowth decreased to the thickness of the intermediate layer. Then SK growth occurred on top of the lower island. This phenomenon enables us to precisely control the thickness of islands in the growth direction through the intermediate-layer thickness.

control only in the vertical dimension of the islands, uniform lateral dimension was also achieved in these closely stacked structures. Islands in each layer are seen to be spatially isolated in the vertical direction, with a 3- to 4-ML distance between the bottom of the upper-layer islands and the top of the lower-layer islands. The individual island was smaller in height than the intermediate GaAs layer thickness, and looked as if it were being buried in GaAs. The RHEED showed a streak pattern after overgrowth of GaAs and growth interruption, indicating that the interface between the overgrown GaAs and the upper InAs wetting layer is almost flat. A model to explain the formation process of this structure is illustrated in Fig. 2.15. First, the intermediate layers of GaAs overgrow away from the InAs islands, as confirmed by Xie et a]. (1995). During annealing (growth interruption after the GaAs overgrowth), the InAs of the upper part of the islands above the GaAs overlayers leave the islands and regrow to form parts of a wetting layer on GaAs. Then some of the InAs at the top regions in the remaining islands replaced with GaAs to reduce the total energy. This leads to a decrease in the island height. Similar features were also shown by Bimberg et al. (1996) and Ledentsov et al. (1996). This phenomenon enables us to precisely control the island height in the growth direction through the intermediate-layer thickness. The island-to-island distance of 3 to 4 M L is so thin that the electron wave functions of each island can be overlapped along the vertical direction. This suggests that the islands are electronically coupled and behave as a single quantum dot, which we will confirm by the optical diagnostics as follows.

2. PHOTOLUMINESCENCE PROPERTIES Light emission properties of these structures were evaluated using a photoluminescence technique with the same measurement conditions given

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FIG.2.16. (a) Emission spectra at 77 K of a single island layer and closely stacked 3-, 5-, and 10-layer island structures grown with 3-nm thick intermediate layers. The peak energy shifted to a lower energy as the number of stacked layers increased (about 90 meV in the 5-layer islands). At the same time, the broad emission spectrum of the single-island layer drastically narrowed at the 5-stacked layer to an FWHM of 27 meV-about one-third of that obtained for a single-layer island. (b) Interval layer thickness dependence on emission spectra with the five stacked layers. As the intermediate layer thickness decreased, the emission spectrum shifted toward lower energies and narrowed to an FWHM of 27 meV a t the 3-nm interval.

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in Section 111. Figure 2.16(a) shows the emission spectra at 77 K of a single island layer ( N = 1) and closely stacked 3-, 5-, and 10-layer island structures grown with 3-nm thick intermediate layers ( N = 3, 5, lo). The peak energy shifted to a lower energy as the number of stacked layers increased (about 90 meV in the 5-layer stacked islands). At the same time, the broad emission spectrum of the single-island layer drastically narrowed at the 5-layerstacked structure to an FWHM of 27 meV, which is about one-third of that obtained for a single-layer island. For a stack of 10 layers, the FWHM increased and integrated photoluminescence intensity decreased. This could be due to the increase in the total amount of strain around the stacked island structures, which induces dislocations and structural modulation. Figure 2.16(b) shows the dependence of the intermediate-layer thickness on emission spectra with the five stacked layers. As the intermediate layer thickness decreased, the emisson spectrum shifted toward lower energies and narrowed to an FWHM of 27 meV at the 3-nm thick intermediate layer. Figure 2.17 shows the excitation power dependence of the photoluminescence spectra for the 5-layer stacked islands with 2-nm (a) and 3-nm intermediate layers (b). As the excitation power increased, both samples exhibited peaks in the higher energy regime, which can be attributed to the higher-order quantized states. Note that energy separation between adjacent states was almost constant for both samples. The energy separation between the ground-state and the first excited-state emission was about 52 meV for the sample grown with 2-nm-thick intermediate layers and 44 meV for the sample grown with 3-nm-thick intermediate layers. The energy separation was smaller than that of the ordinary SK-mode islands (single-island layer) of about 70 meV, as seen in the electroluminescence spectrum (see Chapter 6). All the results observed above indicate that the electron wavefunctions between neighboring islands in the perpendicular direction overlap each other and that the stacked structure, as a whole, can work as a single quantum dot with a larger size. The proofs are (1) the red shift of the emission spectra with an increase in the repetition number; (2) the red shift of the emission spectra with a decrease in the intermediate-layer thickness; and (3) the decrease in the energy separation between the discrete energy states. As a result, we can control the quantum-dot size in the perpendicular direction by this close-stacking technique through the change in the stacking repetition number and in the intermediate layer thickness. The drastic improvement in spectrum broadening was just as expected. One direct reason for this success is that island size (height) is effectively increased, as seen above, decreasing the influence of dot size (height) fluctuation. Also, the island height is controlled more by the intermediatelayer thickness, as seen in Fig. 2.15. Finally, lateral dot size is more uniform, as seen in Fig. 2.14(b).

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0.9

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1.3

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(a)

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(b)

FIG.2.17. Excitation power dependence of photoluminescence spectra for the 5-layer islands with (a) 2-nm and (b) 3-nm thick intermediate layers. As the excitation power increased, both samples exhibited peaks in the higher energy regime, which can be attributed to the higher-order quantized states.

EXCITONCONFINEMENT EVALUATED BY 3. ZERO-DIMENSIONAL DIAMAGNETIC SHIFTS A question that often arises when we observe luminescence spectra from quantum-dot samples is whether the emission really originated from the dots and reflects the characteristics peculiar to their three-dimensional confinement. With closely stacked dots in particular, the identification is not so straightforward due to their structural complexity -namely, multiple stacked structure accompanied by wetting layers. The emission spectra in

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141

Section 111.2 indicated that the exciton states of the stacked dot form through the wave function overlap of each SK dot component, and that the perpendicularly stacked structure should be considered as one quantum dot. Magnetophotoluminescence, treated here, will give us not only the evidence of the three-dimensional confinement of excitons but also the exciton wave function extent in quantum dots. The principle can be summarized this way. The magnetic field confines excitons in the plane perpendicular to the field and increases their energy. We can determine the magnitude of other competing confinement potentials and thus the extent of the wave function by evaluating the number of energy shifts. The samples and the magnetic field direction are schematically shown in Fig. 2.18(a). The samples were five-layer-stacked InAs SK islands with 3-nm GaAs intermediate layers and, for comparison, an In,,,,Ga,~,,As/ GaAs quantum-well sample grown on a GaAs substrate by MOCVD. The In,,,,Ga,,,,As well-layer thickness was 8 nm and subjected to - 1.3% biaxial compressive strain. Figure 2.18(b) shows the photoluminescence spectra of the two samples with no magnetic field applied. Figure 2.18(c) shows the diamagnetic shifts for both samples under magnetic fields perpendicular and parallel to the sample plane at 4.2 K. In the quantum well, while the shift under a perpendicular field reached up to 7.3 meV at a maximum field of 11.8 T, the shift under the parallel field was much smaller (only 1.6meV at 11.8 T). The shift of the dots was almost independent of the field direction, and the maximum shift was 2.4meV in either direction. These results immediately give us the following insights into the difference in the quantum-confinement characteristics between the two samples. The asymmetrical shift in the quantum well is due to its onedirection quantum confinement. When the field is perpendicular to the plane, it works as a two-dimensional confinement potential for excitons in the well layer, causing large diamagnetic shifts. When the field is parallel to the plane, it affects only one direction in the quantum-well plane, since the other direction is already confined by strong potential barriers. The symmetrical, small diamagnetic shifts in the closely stacked dots show that excitons are three-dimensionally confined by an almost symmetrical confinement potential. The extent of the exciton wave function is estimated to be almost equal to the quantum-well thickness of 8 nm, since the shifts for the closely stacked dots and the quantum well under the parallel configuration are almost the same. Detailed quantitative analyses support this simple qualitative estimation (Sugawara et al., 1997). The extent of the wave function, approximately 8 nm, is smaller than the dot size observed by plan-view TEM (Fig. 2.14(a)) and definitely larger than the height of the single SK dot of about 3 nm. This indicates that the wave function of the ground-state exciton extends over

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Stacked islands (A = 1.088 (pm)) B B

QW

i;-

(A = 0.936 (pm))

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InGaAdGaAs QW

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FIG.2.18. (a) Samples for magneto-optical measurements. Five-layer stacked InAs SK islands with 3-nm GaAs intermediate layers and, for comparison, an In,~,,Ga,,,,As/GaAs quantum-well sample grown on a GaAs substrate by MOCVD. The In,,,,Ga,,,,As well layer was 8 nm thick and subjected to - 1.3% biaxial compressive strain. (b) Photoluminescence spectra of the two samples with no magnetic-field applied (from Sugawara et al., 1997. Copyright 1993 by The American Physical Society). (c) Diamagnetic shifts of emission spectra for both samples under magnetic fields perpendicular and parallel to the sample plane at 4.2 K (from Sugawara et al., 1997. Copyright 1993 by The American Physical Society).

2 MOLECULAR BEAMEPITAXIAL GROWTH

W

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100 120 140

Square of magnetic field ( T 2 ) FIG. 2.18. (c)

two or three SK dots out of five. Such exciton localization in the whole stacked structure can be attributed to the composition and/or size inhomogeneity of each SK dot components; that is, the potential minimum is formed by the coupling of the adjacent two or three SK dots with low band-edge energies.

IV. Columnar InAslGaAs Quantum Dots The advantages of the stacking technique for device applications can be summarized as follows. First, the spectrum width can be made much narrower than in ordinary SK dots. Second, the size (height) and the symmetry vary with the number of stacked layers, which makes it possible to artificially control the energy separation between the discrete quantum levels, the emission wavelength, the degeneracy of the quantum levels, the overlap integral of the electron-hole wave functions that determines the oscillator strength of optical transitions, and so forth. Though we succeeded in narrowing the spectrum width by close stacking of SK-mode islands and growth interruption (annealing) as explained in Section 111, we found that the emission efficiency was greatly damaged. The photoluminescence from the closely stacked islands rapidly weakened as the temperature rose and was barely observed at room temperature. Among

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various growth conditions, annealing after the growth of the GaAs intermediate layers (see the growth conditions in Fig. 2.10) was found to cause the most serious degradation. A large number of defects and/or impurities should have been introduced during annealing, working as nonradiative recombination centers. On the contrary, though the emission efficiency was fairly good even at room temperature without annealing, the spectrum width was reduced to 50-60 meV at most, presumably due to fluctuations in the island height and in the thickness of the spacer between the bottom of the upper-layer islands and the top of the lower-layer islands (Endoh et al., 1998). To overcome this problem, we stacked SK mode islands using even thinner intermediate layers -3 ML thick (less than 1 nm) -so that islands would physically contact each other in the perpendicular direction. This thickness is much less than the island height. As seen in Fig. 2.2, about 6 ML of GaAs supply was needed to fully cover the islands. The SK-mode islands could be grown even on such thin GaAs intermediate layers. Figure 2.19 shows the RHEED-pattern intensity transition during the stacked island growth (the GaAs intermediate layer on the first InAs island layers and the second InAs island layers). In this experiment, the first island layer was grown with the InAs supply of 1.8 ML. The intermediatelayer thickness was reduced to 3 ML from 10 ML, which is the same as that used in the closely stacked structures in Section 111. Immediately after the GaAs supply, the spot intensity decreased, showing that the growth surface was becoming flat by the growth of the intermediate layers. The spot intensity recovered to that of the first islands when the InAs supply started, showing that the second island layers grew. It should be noted that even on 3- and 5-ML thick intermediate layers, which were much thinner than the island height, second island layers grew as well as the first island layer. However, the critical amount of lnAs supply for the transition from two-dimensional layer growth to three-dimensional island growth decreased as the intermediate layer thickness has reduced: 0.84ML for the 10-ML intermediate layers, 0.76 ML for the 7-ML intermediate layers, 0.60 ML for the 5-ML intermediate layers, and 0.26ML for the 3-ML intermediate layers. These were much smaller than that for the first island layer, shown at the bottom of Fig. 2.19. Figure 2.20 shows the RHEED-pattern intensity transition when the InAs islands were repeatedly stacked using the 3-ML thick intermediate layers. The inset photographs are the AFM images of the topmost layer after 8 to 9 repetitions. The amount of InAs supply for the stacked-island formation was changed from about 0.5 ML to 0.8 ML. When the stacked islands were grown with an InAs supply of about 0.7ML, the RHEED intensity oscillated with the InAs island growth (RHEED intensity increased) and

2 MOLECULAR BEAMEPITAXIAL GROWTH

Growth time (s)

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20 s I 1 div.

FIG.2.19. RHEED pattern intensity transition during the stacked island growth (GaAs intermediate layer o n the first InAs islands and the second InAs island). The critical thickness for the transition from two-dimensional growth t o island growth decreases as the intermediate GaAs layer thickness reduces.

GaAs intermediate-layer growth (RHEED intensity decreased). This suggests that the islands were formed successfully. The AFM image of the topmost island layer grown with the 0.7-ML InAs supply shows that stacked islands were formed with the same size and density as in the first islands. On the other hand, when stacked with an InAs supply of about 0.5 ML and 0.8 ML, RHEED intensity oscillation stopped. When stacked with the InAs supply of about 0.5 ML, RHEED intensity damped at the third repetition, and the AFM image showed no island formation. This is possibly because the InAs supply was not enough for island formation. When stacked with an InAs supply of about 0.8 ML, RHEED intensity did not recover completely at 8 to 9 repetitions and islands like the first one were not seen in the AFM image. The supply of 0.8 ML is excessive. The optimum amount of about 0.7 ML is smaller than in the case of ordinary SK-mode islands. When stacked islands using such thin intermediate layers, the amount of InAs supply has to be reduced and optimized precisely.

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a

YI U

Growth time ( 5 )

40 8 I 1 div.

FIG.2.20. RHEED pattern intensity transition when the InAs islands were repeatedly grown with the intermediate layer of 3 ML. The inset photograph shows the AFM images of the topmost layer. The above results suggest that there is an optimum lnAs supply amount.

Figure 2.21(a) is a cross-sectional TEM image of the structure shown schematically in Fig. 2.21(b). InAs island layers formed with an InAs supply of 0.7 M L and GaAs intermediate layers of 3 M L were grown alternately (8 repetitions) on the first island layer formed with an 1.8-ML InAs supply. The stacked upper islands were grown on the lower-layer islands aligning perpendicularly on the first-layer islands. The islands on each layer were in contact with each other physically, and the stacked islands as a whole had a columnar shape with a diameter and a height of about 17 nm and 13 nm, respectively. All island layers were accompanied by wetting layers, seen as horizontal line-shaped contrasts in the TEM image, indicating that the stacked islands were formed by the SK mode. Figure 2.21(a) is a low-magnification image. The columnar-shaped islands were seen clearly in the quantum-well-like dark contrast region composed of lnAs multiple wetting layers and GaAs intermediate layers. In Chapter 3, we will introduce InGaAs/GaAs quantum dots with a light emission wavelength of 1.3 pm grown by the alternate growth of elementary In-Ga-As in MOCVD. The present structures look very similar to the ALS dots. Although the large islands were formed, the contrasts corresponding to dislocations and stacking faults, which observed at the coalesced large islands, as shown in Fig. 2.6, were barely observed, suggesting that the composition of lnAs was smaller than that in the ordinary SK islands.

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FIG.2.21. (a) Cross-sectional TEM image of columnar-shaped quantum dots. (b) Schematic structure. (c) Low magnification image.

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Figure 2.22 shows the photoluminescence spectrum of these columnarshaped quantum dots, measured at 300K. The peak wavelength of the ground level was 1.17pm, and that of the excited level was 1.10pm. An emission peak related to the multiple wetting layers was observed at 1.01 pm. An FWHM of the spectrum was about 42meV. This is much smaller than that for the ordinary SK-mode quantum dots of about 80 meV, indicating that structural uniformity was fairly improved. The photoluminescence intensity was also better than the SK-mode quantum dots and was over 1000 times stronger than in the closely stacked quantum dots described above, suggesting that the introduction of defects and impurities working as the nonradiative recombination centers was remarkably suppressed. The emission from the wetting layers red-shifted compared with the ordinary SK mode quantum dots. This is because multiple wetting layers were coupled electrically and formed a quantum level as a whole. The energy separation between the ground state and the wetting layer was 168meV, which is much smaller than 230meV of the ordinary SK-mode quantum dots. An excellent performance of columnar-shaped quantum dots is demonstrated in Chapter 6. Figure 2.23 plots the photoluminescence wavelength at room temperature and 7 7 K as a function of the stacked-layer number. As the layer number

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FIG.2.22. Photoluminescence spectrum of the columnar-shaped quantum dots shown in Fig. 2.21 measured at 300 K. The peak wavelength of the ground level was 1.17 pm and that of the excited level was 1.10 pm. An emission peak related to the multiple wetting layers was observed at 1.01 p m A full width at half maximum (FWHM) of the spectrum was about 42 meV.

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FIG.2.23. Photoluminescence wavelength at room temperature and 77 K as a function of the stacked layer number. As the layer number increases, the emission wavelength shifts to longer wavelength due to the size increase.

increased, the emission wavelength becomes longer due to the size increase. It is surprising that the longest wavelength at room temperature was 1.24 ym at the 23rd stacking- very close to the practically applicable 1.3 pm. Structural features of the stacked islands are summarized in Fig. 2.24. Stacked-island structures strongly depend on the intermediate layer thickness, t (nm). When t > 20 nm, stacked islands form without any correlation to the lower-layer islands. The mean island size and density are constant in all island layers, which is useful for increasing island density per unit volume. When t < 20 nm, stacked upper islands form in correlation to the lower-layer islands due to strain fields induced by the lower-layer islands. The upper-layer islands form in alignment with the first-layer islands in the perpendicular direction, and expand with an increase of the stacked-layer number. As the intermediate-layer thickness decreases almost to the island height, the size expansion of the stacked islands is suppressed, and almost equal size islands are stacked closely. In this case, the electron wave functions between neighboring islands in the perpendicular direction overlap each other, and the perpendicularIy stacked structure works effectively as a single large quantum dot. Drastic improvement of the spectrum linewidth is observed. When the intermediate-layer thickness further de-

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YOSHIAKI NAKATAAND YOSHIHIROSUGIYAMA

10 20 30 Intermediatelayer thickness, t (nm)

FIG. 2.24. Structural features of stacked islands. Stacked island structures strongly depend on the intermediate-layer thickness, t (nm). When f z 20nm, stacked islands were formed without any correlation to the lower-layer islands. When t < 20 nm, stacked upper islands were formed in correlation to the lower-layer islands due to strain field induced by the lower-layer islands.

creases to a few monolayers of less than 1 nm, which is much smaller than the island height, stacked islands are formed. This success is achieved by optimizing the amount of InAs supply for the stacked-island formation. If we use 3-ML-thick intermediate layers, the amount of InAs supply has to be reduced to about 0.7ML. The islands in the stacked structure are in contact with each other physically in the perpendicular direction and the stacked structure has a columnar shape as a whole. Even when we use these thin intermediate layers, all stacked islands are accompanied by wetting layers, indicating that the islands grow in the SK mode.

V. Summary The structural features and optical properties of quantum dots presented in this chapter are summarized in Fig. 2.25. Ordinary InAs SK-mode quantum dots on GaAs substrates show broad spectra with a typical FWHM of 80meV because of their large structural fluctuation. Since the shape of ordinary SK-mode quantum dots is rather flat, their spectrum broadening depends mainly on the fluctuation of the island height. The stacking techniques to grow the closely stacked and columnar-shaped dots

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MOLECULAR BEAMEPITAXIAL GROWTH SK islands

Close1 stacked isinds

Columnar-shaped islands

90 meV

25 meV

40 meV

Good

Poor

Good

Schematic structure PL FWHM

PL

efficiency In-plane coverage (Density) Wavelength

(300K)

40%

40%

> 1 x 10'1 cm-2

> 1 x 1011 cm-*

Clm

1.2 pm

40%

>1 x

loll

cm-2

> 1.2 pm

Frc. 2.25. Structural and optical properties of different types of dots

are very useful in suppressing island height fluctuation because the effective height can be controlled artificially by the number of stacked island layers. The luminescence spectrum was remarkably improved from 80 meV to 25 meV by the close stacking method. In columnar-shaped quantum dots, where both narrow spectrum width and high emission efficiency are obtained, we have successfully achieved low-threshold and highly efficient operation of quantum-dot lasers (Chapter 6). According to the simulation of quantum-dot laser performance in Chapter 1, the narrow spectrum width we have achieved is very promising for high-performance quantum-dot lasers that are superior to strained quantum-well lasers. If we aim at high-speed direct-modulation quantum-dot lasers, as predicted by Arakawa and Sakaki (1982), we need to further reduce the spectrum width to 10 meV (Chapter 1). The in-plane size fluctuation of our columnar-shaped dots was evaluated by AFM and found to give a broadening of about 20meV (Endoh et al., 1998). For that reason, we are now concentrating on improving in-plane size homogeneity.

Acknowledgments The authors would like to thank Dr. Hiroshi Ishikawa, Dr. Hajime Shoji, Dr. Kohki Mukai, Dr. Osamu Ueda, Dr. Akira Endoh, and Dr. Toshiro Futatsugi, of Fujitsu Laboratories Ltd., and Professor Shunichi Muto of

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Hokkaido University for their fruitful input and support. We also are grateful to Dr. Hajime Ishikawa and Dr. Naoki Yokoyama of Fujitsu Laboratories Ltd., for their encouragement and strong support throughout this work.

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