Progress in art and science of crystal growth and its impacts on modern society

Quartz crystals have a long history of being used as crystal oscillators, which give an accurate oscillation frequency that can be used for telecommunication systems. Since the invention of the transistor, crystal oscillators have been used in watches, clocks, computers, mobile phones, and so forth. Up to the end of World War II, naturally grown quartz crystals were used. However, to meet the demand for them, the hydrothermal synthesis of quartz crystals was developed for their large-scale production, and all crystals are now grown artificially.^1–4)

The method used for the hydrothermal growth of quartz is schematically illustrated in Fig. 2. Crystal growth is conducted in an aqueous solution of NaOH or Na₂CO₃ under high pressure and high temperature. In the upper zone, the temperature is kept slightly lower than that in the lower zone. The source quartz crystals are dissolved in the solution and transported to the upper zone, where growth occurs on seed crystals. By increasing the number of seed crystals, one can grow a large number of high-quality quartz crystals. An example of an as-grown quartz crystal is shown in Fig. 3.

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Ruby and sapphire, which belong to a group of corundum crystals, also have a long history of being used as jewel bearings. They are used in mechanical watches, and high-accuracy measurement instruments such as galvanometers and gyroscopes. The Verneuil process developed in 1902 has been employed to grow these crystals, and a modified process for mass production is still used at present.⁵⁾

A schematic illustration of the Verneuil technique is given in Fig. 4. The source material is Al₂O₃ powder, which is placed in the upper container. The powder is sent to the seed crystal in the growth chamber through a tube with oxygen gas. As shown in the figure, hydrogen gas is supplied through the outer tube to the growth chamber, where both gases react to give a high-temperature flame. The flame heats both the powder and the surface of the seed crystal to form a melt. By pulling down the seed crystal, continuous growth can be achieved. Corundum crystals are also grown by the Czochralski method.⁶⁾

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In human history, the greatest impact of crystal growth on industry was the invention of the point contact transistor in 1947 and the junction transistor in 1948. The action of a transistor would never have been observed without the realization of a single crystal growth of germanium with high purity. Bell Telephone Laboratories had a long history of growing single crystals of halides⁷⁾ and metals. The art and science of these growth technologies were applied to grow single crystals of germanium. After the invention of point contact and junction transistors, the systematic development of growth and purification technologies was greatly required, and the Bridgman and Czochralski techniques were applied to grow single crystals of germanium. A schematic illustration of the Czochralski method is given in Fig. 5. After melting the material, a thin seed is brought in contact with the surface of the melt, and then the crystal is pulled upward to start the growth.

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The purification of germanium was another key technology required to produce transistors. Pfann developed the zone-melting technique, which enabled the purification of crystals and also the doping of impurities to a predetermined level.^8,9) The invention of the transistor was the first epoch-making event that clearly showed how crystal growth is important for industry and society. After the success of germanium point contact and junction transistors, germanium took the position of the dominant material in solid-state electronics. However, silicon soon came to take this position. Since silicon cannot be grown by the Bridgman technique owing to its reaction with the crucible, the Czochralski technique was employed.

The first successful growth of a silicon single crystal by the Czochralski method was accomplished by Teal and Buehler in 1949 at Bell Telephone Laboratories.^10,11) At that time, the size of grown silicon crystals was 1 in. in diameter and 5 in. in length. The development of the Czochralski technique allowed the growth of dislocation-free silicon crystals with the diameter of 16 in. From such large-scale silicon wafers, silicon integrated circuits are produced and used in computers, cell phones, cars, and many other products.

The next epoch-making event in the crystal growth of semiconductors was the introduction of the use of epitaxial growth for devices. Theuerer of Bell Telephone Laboratories succeeded in growing a thin single-crystal film of silicon epitaxially on a silicon substrate,¹²⁾ while his group was trying to grow a high-resistivity film on a low-resistivity substrate for mesa transistors and other devices. Figure 6 schematically illustrates typical apparatus used for silicon vapor-phase growth. A mixture of hydrogen and SiCl₄ is sent to a silicon substrate heated by a radio-frequency (RF) electromagnetic wave. At a high temperature, SiCl₄ is reduced by hydrogen resulting in the growth of silicon atoms on the substrate. The growth temperature is between 1000 and 1300 °C. By epitaxial growth, one can reduce the collector resistivity of n–p–n planar transistors as shown in Fig. 7. The epitaxial growth of silicon has provided the freedom to design various types of silicon devices including integrated circuits.

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2.5.1. Liquid-phase epitaxy

The invention of liquid-phase epitaxy (LPE) by Nelson at RCA Laboratories led to a breakthrough in the crystal growth of compound semiconductors.¹³⁾ The principle of GaAs LPE is shown schematically in Fig. 8. LPE is conducted in a graphite boat of high purity, which is surrounded by high-purity hydrogen gas. Before the growth, the sliding part of the boat (slider) is at position (a) and GaAs is saturated with high-purity gallium metal contained in the well of the slider at an elevated temperature. After the saturation is completed, the slider is moved on the substrate to take position (b). Then, the temperature is decreased to start the growth. The temperature is continuously decreased to maintain growth at a certain rate. After the required thickness of GaAs is attained, the slider is moved back to position (a) so that the growth is terminated. For the growth of many layers with different types of conductivity and alloy compositions, a slider with many wells is used.

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In LPE, the growth is usually carried out under a condition quite close to equilibrium, which is extremely important for obtaining high-quality layers with a low concentration of point defects and a stoichiometric composition. The invention of LPE was a key factor leading to the successful fabrication of LDs and commercial optoelectronic devices such as LEDs. LDs operating at room temperature and in continuous-wave mode were made possible by this invention. Alferov succeeded in growing an LD with a GaAs–GaAlAs double heterostructure by LPE, for which he was awarded the Novel Prize in Physics in 2000.

The successful use of LPE in industry has promoted advances in the science of epitaxial growth and greater understanding of the growth mechanism of LPE. Figure 9 shows the growth spiral found on an as-grown surface of InP after LPE by atomic force microscopy (AFM).¹⁴⁾ It has been found that the interstep distance of a growth spiral is given by¹⁵⁾

$$\begin{equation} \lambda_{0}=19\gamma'\nu_{\text{s}}/m\Delta\mu, \end{equation} \tag{ 1 }$$

where γ', ν_s, m, and Δμ are the free energy of the side surface of the spiral step, the molar volume of the growing species, the number of spirals at the center, and the difference in the chemical potential between the growth atmosphere and the crystal, respectively. Δμ is given by

$$\begin{equation} \Delta\mu=RT\ln\alpha=RT\ln(\sigma+1), \end{equation} \tag{ 2 }$$

where α is the supersaturation ratio and σ is the supersaturation. Hence, once the interstep distance of the growth spiral is measured by AFM or differential interference contrast microscopy, one can obtain the value of the supersaturation in the vicinity of the growing surface. The interstep distance near the spiral center in Fig. 9 was measured to be 0.93 µm and the supersaturation was calculated to be 0.05 with a tentative value of γ' = 0.12 J/m².¹⁴⁾ The absolute value of the supersaturation is not very reliable because the value of γ' is calculated using the broken bond model and the latent heat of InP. However, the change in the supersaturation upon changing the growth parameters can be reliably predicted, and this gives important information to clarifying the growth mechanism.

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In general, it is very difficult to measure the supersaturation on a surface during growth. However, by this method, one can find the supersaturation as a function of growth temperature and other growth parameters. The successful measurement of the supersaturation on a growing surface was a major achievement that had not previously been obtained in semiconductor epitaxy, and this method has been applied to find the supersaturation in GaN epitaxy, which will be discussed later.

Another important achievement in semiconductor growth science was discovering the formation mechanism of macrosteps. It is well-known that macrosteps appear on a surface after vapor growth, melt growth, and solution growth. They are generated on the growing surface due to step bunching. In solution growth such as LPE, it was found that the bunching occurs as a result of a morphological instability.^16,17) This has been confirmed by micro-gravity experiments conducted in a space shuttle.^18–20)

It was also found that the impurity nonuniformity is induced in association with macrostep risers.²¹⁾ Figure 10 shows a surface micrograph of LPE-grown GaP (a) and a photoluminescence image of the cleaved cross section (b). One clearly sees that the dark lines are formed under macrostep risers.²⁰⁾ It was found that the dark lines appear because the nitrogen concentration is low in the region where the luminescence is weak.²²⁾ Nitrogen takes a substitutional site in GaP and acts as a luminescence center.

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Figure 11(a) shows a surface micrograph of GaP grown by LPE taken by a differential interference contrast microscope.²³⁾ In the figure, macrosteps and atomistic steps can be seen, the latter of which are generated by screw dislocations. An overall picture of the growth is given in Fig. 11(b). The macrosteps move slowly during the growth and atomistic steps run along the terraces of the macrosteps. The vertical growth is carried out by the propagation of the atomistic steps from the screw dislocations.

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2.5.2. Molecular beam epitaxy and metalorganic chemical vapor deposition

The next major breakthrough made in epitaxial technology was the birth and development of molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD). Cho (Bell Telephone Laboratories), and Manasevit and Simpson (North American Rockwell) respectively reported the growth of GaAs by MBE²⁴⁾ in 1970 and of GaAs, GaP, and their alloys by MOCVD²⁵⁾ in 1969. The MBE chamber designed by Cho in 1970 is illustrated in Fig. 12. Since the beginning of MBE, all the elements equipped in modern MBE systems, such as a liquid nitrogen shroud, a Knudsen cell, and a reflection high-energy electron diffraction (RHEED) system, were installed. The great advantage of MBE is the possibility of real-time monitoring of the growth process. Among the many in situ monitoring systems, the RHEED system is most powerful and has become an indispensable tool. In 1981, Harris et al. found that during the growth of GaAs by MBE, the intensity of the RHEED image oscillates with an oscillation period identical to the time for GaAs monolayer growth.²⁶⁾

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Figure 13 shows the RHEED intensity oscillation during the growth of GaAs by MBE observed by Neave et al.²⁷⁾ The intensity oscillation is explained as follows. After keeping a GaAs substrate at a high temperature under an arsenic flux, the surface becomes very flat and the RHEED intensity takes a maximum value. However, when the growth starts, the intensity decreases because the surface starts being covered by two-dimensional nuclei and the electrons are scattered in random directions.

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The RHEED oscillation is extremely useful. First, it is used to monitor the thickness of the growth layer. Control of the thickness with monolayer accuracy is often required in the fabrication of devices such as LDs, quantum well devices, and high-electron mobility transistors (HEMTs). Secondly, it can be used to detect the birth and spread of two-dimensional nuclei on the growing surface. By utilizing this principle, it was found that there are two modes of growth in MBE.^28,29) One is the step-flow mode, in which the growth is conducted by the advance of the step train in one direction without nucleation. The other is the two-dimensional nucleation mode, in which the growth is carried out by the steps generated by nuclei. Thus, RHEED oscillation is an indispensable tool for understanding the growth mechanism. This is another example of how the technological development of crystal growth has contributed to the advance of crystal growth science.

MOCVD is another important tool for epitaxy. In contrast to LPE and halogen vapor-phase epitaxy, in both MBE and MOCVD there is almost no chemical reaction by which the substrate is dissolved during the growth. This means that one can achieve growth with a very sharp interface. In the early development of MOCVD by Manasevit and his group, there was a purity problem with the metalorganic sources. However, the purity was improved drastically in the 1970's, enabling high-purity and high-quality films to be used for all devices. MOCVD is now the most important method in industry for growing nitride semiconductors.

Figure 14 shows a schematic diagram of MOCVD apparatus for the growth of GaAs. The metalorganic source can be triethylgallium instead of trimethylgallium. If one wishes to grow AlAs or GaAlAs, one can employ a trimethyl- or triethylaluminum source in addition. When the doping of an impurity is necessary, one adds supply lines to provide metalorganic zinc and hydrides of sulfur and selenium, for instance. By controlling the flow rate very accurately, the growth rate can be kept very low similarly to in MBE. Hence, MOCVD can be used for growing quantum well lasers, HEMTs, and other sophisticated devices.

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One of the largest contributions of MOCVD to growth science has been to establish the relationship between the growth rate and surface supersaturation. Akasaka et al. employed the selective-area epitaxy (SAE) of GaN to separate areas with a screw dislocation from those without.³⁰⁾ Then, they measured surface supersaturation from the interstep distance of spiral steps in the area with a screw dislocation using Eq. (1). The growth rate was obtained by measuring the height of the area after the growth.³¹⁾

Figure 15 shows a growth spiral observed by Akasaka et al. by AFM.³²⁾ It is seen in the figure that two spiral steps are generated at the center and hence m in Eq. (1) is 2. Figure 16 gives the growth rate as a function of supersaturation calculated by Eq. (1).³²⁾ In the figure, the curved line gives the theoretical growth rate calculated by Akasaka et al. using Burton–Cabrera–Frank (BCF) theory and closed diamonds show the experimental values. According to BCF theory, the growth rate is proportional to σ² in the low-σ region and proportional to σ in the high-σ region. The boundary between the two regions is calculated as σ₁ = 0.5 in this case.³²⁾ As seen in the figure, all experiments were conducted in the low-σ region and the growth rate follows a quadratic function of σ, in good agreement with the theory. On the other hand, the growth rate in the area with no screw dislocations is very low in this range of supersaturation and increases marginally at the highest supersaturation in the experiment.³²⁾

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BCF theory assumes that the growth is conducted by steps from screw dislocations and that the surface diffusion is a rate-limiting process. MOCVD is one of the best methods for the application of BCF theory. In the history of crystal growth theory, BCF theory has been applied to solution growth, but in solution growth it is not clear whether surface diffusion plays an important role. In this respect, the MOCVD conducted by Akasaka et al. is one of the best examples to which BCF theory can be applied.

Two-step growth consists of initial growth at a low temperature and successive growth at a higher temperature. At the low temperature, a thin buffer layer of poor crystal quality is grown on the substrate, and then the growth is carried out at the normal higher growth temperature. The idea is to confine a large number of misfit dislocations generated at the interface within the buffer layer.

Looking back at the history of two-step growth, in 1978, Ohnishi et al. reported deposition of a ZnO buffer layer of 13 nm thickness at 100–160 °C on a sapphire substrate by sputtering followed by the growth of ZnO at 900–1000 °C by CVD. They obtained a ZnO epitaxial layer of high quality.³⁷⁾ Then, in 1980, Nishino et al. used two-step growth to grow SiC on a silicon substrate.³⁸⁾ They deposited a SiC buffer layer on a silicon substrate at 800 °C by RF sputtering and grew SiC of good quality at 1360 °C by CVD.

Remarkable success was attained in growing a high quality silicon epitaxial layer on a sapphire substrate by Ishida et al. in 1981.³⁹⁾ They deposited an amorphous silicon film on a sapphire substrate by sputtering at room temperature. The thickness of the buffer layer is important in determining the quality of the successively grown layer and they reported that it should be 2–4 nm. The growth of silicon in the second step was conducted at 1000 °C. The quality of the film was excellent and the MOSFET fabricated with this film showed very good properties.⁴⁰⁾

Two-step growth was also applied to the heteroepitaxy of GaAs on silicon by Akiyama et al. in 1984.⁴¹⁾ To avoid the formation of an antiphase domain, a vicinal (001) substrate was employed. They grew GaAs of good quality by both MOCVD and MBE and reported an etch pit density on the order of 10³/cm². However, in their case, it turned out that the etch pits corresponded to bunched dislocations and the density of individual dislocations was on the order of 10⁶/cm², which is excellent even for HM².

The most successful application of two-step growth was attained in the growth of nitride semiconductors. Akasaki's group succeeded in growing high-quality GaN on sapphire using an AlN buffer layer in 1986.⁴²⁾ The grown crystal was optically flat without cracks, which had never been achieved by other methods. Figure 17 shows the effect of a low-temperature buffer layer on the crystal quality of GaN.^43,44) Figures 17(a) and 17(b) present surface micrographs of GaN grown on sapphire without a low-temperature buffer layer, taken using transmission and reflection light, respectively. Figure 17(c) gives an illustration of the cross section of GaN layer directly grown on sapphire, where pits, cracks and highly conductive regions are schematically shown. Figure 17(d) presents GaN crystal grown at a high temperature on the AlN buffer layer grown at a low temperature on a sapphire substrate. The film is transparent and shows a very sharp X-ray diffraction peak and strong photoluminescence band edge emission.

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High-quality AlGaN was also grown by this method.^45,46) Then in 1989, the same group succeeded in obtaining p-type GaN by doping Mg and activating it by electron beam irradiation, then they fabricated a p–n junction for the first time in the history of nitride semiconductors.^47,48) The success of the p–n junction made it possible to produce efficient blue to ultraviolet LEDs and LDs, and it can be said that their work gave blue light to the world. Akasaki and Amano were awarded the 2014 Nobel Prize in Physics for the invention of the p–n junction blue LED.

In 1992, Nakamura et al. found that p-type GaN could be obtained by the thermal activation of Mg-doped GaN, which was also grown with a low-temperature buffer layer.⁴⁹⁾ Thermal activation is ideally suited to the mass production of nitride devices and Nakamura was jointly awarded the 2014 Nobel Prize in Physics due to the invention for obtaining the p-type GaN by thermal activation. Blue and white LEDs are now ubiquitous in villages, towns, and cities worldwide. This is the best example of how a development in crystal growth technology, in this case the use of a low-temperature buffer layer, has changed society.

Superlattices have been employed to reduce the density of misfit dislocations generated at a heteroepitaxy interface. Superlattices are known to block the propagation of threading dislocations as shown by Matthews et al. as early as in 1976.⁵⁰⁾ In 1984, Fischer et al. employed a GaAs/GaAlAs superlattice to reduce the dislocation density in GaAs heteroepitaxially grown on a silicon substrate.⁵¹⁾

Umeno's group grew GaAs of good quality on a silicon substrate with an AlP, AlGaP, GaP/GaAs_0.5P_0.5, superlattice and a GaAs_0.5P_0.5/GaAs superlattice.⁵²⁾ In their case, the superlattice consisted of layers with different lattice constants, which induced a strain in the layers. By employing a superlattice, one can decrease the dislocation density of GaAs on a silicon substrate to the order of 10⁶/cm², but it is not possible to eliminate dislocations completely. To fabricate OEICs, the dislocation density should be nearly zero so that no dislocations remain in the active layer of the LD. However, if the dislocation density is not a major constraint for devices, such as nitride-based devices on silicon, one can use a superlattice as a buffer layer to reduce the dislocation density.

The idea of microchannel epitaxy (MCE) is shown in Fig. 18.⁵³⁾ As seen in Fig. 18(a), in ordinary epitaxy the grown layer becomes single crystalline by inheriting the lattice information of the substrate. However, if a dislocation penetrating the surface is present in the substrate, the dislocation will be inherited in the epitaxial layer.

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There are two ideas for preventing the propagation of dislocations. The first one is shown in Fig. 18(b). An amorphous film such as SiO₂ is deposited on the substrate and a narrow window called a microchannel is cut in the amorphous film. When the growth starts inside the microchannel, it then proceeds laterally over the amorphous film. Since the amorphous film is present between the substrate and the laterally grown layer, a dislocation in the substrate cannot propagate into the grown layer as shown in the figure. Hence, if no threading dislocations are present in the microchannel area, the grown layer becomes dislocation-free. The main idea is that although lattice information is inherited through the narrow microchannel to realize epitaxial growth, defect information is blocked by the amorphous film. This type of MCE has been named as horizontal MCE (HMCE).⁵³⁾

The second idea of MCE is given in Fig. 18(c). In this case, the growth is conducted in the vertical direction through the microchannel. The grown layer can be a slab or a rod. This idea of MCE has been named as vertical MCE (VMCE).⁵³⁾ Depending on the crystallographic orientation of the substrate, a dislocation often takes an off-normal orientation relative to the substrate surface. Then, the dislocation exits the epitaxial layer from the side of the layer as shown in the figure. Since HMCE is much more frequently used than VMCE, hereafter, we refer to MCE instead of HMCE for simplicity.

Figure 19 schematically illustrates the MCE of GaAs on a silicon substrate. To realize large lateral growth, LPE is employed. LPE has the advantage of growth with very low supersaturation, which enables large growth anisotropy to be realized, namely, a large ratio of the horizontal width to the vertical thickness. First, a GaAs buffer layer is grown by MBE or MOCVD on a silicon substrate, then the LPE growth of GaAs is conducted through a microchannel opened in an amorphous film, in this case, a SiO₂ film.^54–57)

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An optical micrograph of MCE GaAs grown on silicon is shown in Fig. 20. In the central region, an area of dislocations with a width of approximately 25 µm can be seen. A large number of dislocations are present in the region, which change the appearance of the surface. However, there are no dislocations outside of the channel region. In the case shown in Fig. 20, the width of the MCE layer (W) was 195 µm and the thickness (T) was 12 µm.⁵⁷⁾

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Figure 21 shows a cross sectional TEM image of as-grown MCE GaAs on silicon taken by Tamura of Joint Research Center for Atom Technology.⁵³⁾ It is clearly seen that threading dislocations are blocked by the SiO₂ film deposited on the GaAs buffer layer, which was grown on a (001) silicon substrate by MOCVD. It is also seen that the dislocations continue to the epitaxial layer through the microchannel, which is 5 µm in width. Since the dislocations propagate on the {111} plane, the dislocated area is broadened as growth proceeds, as seen in the figure. Hence, to realize a dislocation-free area as large as possible, one should grow an MCE layer that is as wide as possible while keeping the thickness as small as possible.

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An attempt to decrease the density of dislocation generated at a heteroepitaxy interface was reported by Tsauer et al. in 1982.⁵⁸⁾ They employed halogen CVD and grew GaAs from narrow windows cut in a SiO₂ film deposited on a buffer layer of Ge on a silicon substrate. They obtained a dislocation density of less than 10⁴/cm² in the laterally grown area. At that time, since a value of 10⁴/cm² was not attractive for GaAs-on-silicon technology for optical use, which requires dislocation free GaAs for the fabrication of LDs, this work did not draw much attention. However, once it was found in 1989 that a dislocation-free layer can be obtained in a laterally grown area,⁵⁴⁾ this technology started to attract strong interest.

Usui et al. used MCE to grow GaN on sapphire to decrease the dislocation density in 1997,⁵⁹⁾ and Nakamura et al. employed this technology to fabricate a nitride LD and succeeded in obtaining a lifetime of more than 10,000 h under cw operation at 20 °C in 1997.⁶⁰⁾ Since then, MCE has been widely used as a method to reduce the dislocation density.

The proposal by Arakawa and Sakaki⁶¹⁾ to use a low-dimensional structure (LDS) for a high-performance semiconductor laser stimulated the development of technology to fabricate wire and dot structures by crystal growth and also attempts to advance the growth science of LDSs. For the growth of a dot structure, a self-assembly process of InAs dots on a GaAs substrate was employed very successfully in 1985.⁶²⁾ In 1990, Sasaki's group tried to grow In_xGa_1−xAs (0 ≦ x ≦ 1) layers on InAs and InP substrates and found that the formation of dots occurred.⁶³⁾ These techniques utilize a self-stopping effect of the dot size induced by the strain between the dot and the substrate. Such self-assembled dots are already used in the production of quantum dot lasers, because the method gives high-density and high-quality dots. The production of quantum dot lasers is one of the major successes of crystal growth.

Regarding the science of crystal growth, the formation of dots or small islands after the growth of some layers on a lattice mismatched substrate has been studied for a long time. Such growth is known as the Stranski–Krastanov (SK) mode of heteroepitaxy. A great deal of work has been devoted to studying the growth of dots on various substrates. In this respect, the development of quantum dot devices has encouraged fundamental studies of SK growth.

However, the self-assembly technique cannot be used for the fabrication of wire structures and dots on arbitrary substrates. The positioning of the dots is also a difficult problem. If we can solve these problems, the range of LDS applications will be greatly expanded.

One of the methods used to solve these problems is to perform growth on non-planar substrates. Kapon et al. employed a substrate with grooves and obtained GaAs/GaAlAs wire structures on the bottoms of the grooves.^64,65) Fukui et al. used SAE and obtained a GaAs dot on the top of a GaAlAs truncated pyramid.⁶⁶⁾

In developing the technology for growth on a non-planar surface, a very basic phenomenon in growth science has been found. Isu et al.^67–71) and later Shen et al.^72–76) studied the surface diffusion between facets. The macroscopic surface diffusion between facets, which is known as intersurface diffusion, plays an important role in determining the final facet that appears in the growth of an LDS. By utilizing the intersurface diffusion one can create an LDS and can control its shape.

Figure 22 shows growth pyramids of GaAs grown by MBE on mesas produced by photolithography and chemical etching.⁷⁷⁾ The figure shows a scanning electron microscopy (SEM) image taken in real time during the growth. The growth was conducted by a micro-probe RHEED/SEM MBE system, which is schematically shown in Fig. 23. The micro-probe RHEED/SEM MBE system is very powerful for studying the growth of LDSs. This apparatus was developed by Ichikawa et al.⁷⁸⁾ and others.^{67,68,79–81)}

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It was found that in the MBE of GaAs the direction of intersurface diffusion is reversed by changing the arsenic pressure. Figure 24 schematically represents the growth rate distribution on a (001) facet adjacent to a (111) B facet when intersurface diffusion occurs. Here, gallium adatoms diffuse from the (111) B facet to the (001) facet under a flux of As₄. Gallium adatoms diffusing from (111) B facet are incorporated one by one at the steps generated by two-dimensional nuclei on the (001) facet.

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Thus, the intensity of the lateral flux of gallium decreases and the local growth rate decreases as the distance increases from the boundary between the two facets. The decay of the growth rate follows an exponential law, and from the slope in a logarithmic plot one can obtain the incorporation diffusion length λ_inc, which is of µm order. We define G as the ratio of R_CORNER to R_PLANAR, as shown in the figure, where R_CORNER and R_PLANAR are the growth rates at the boundary on the (001) facet and infinitely far from the boundary, respectively. A value of G of larger than unity means that intersurface diffusion occurs from (111) B to the (001) facet, while G of less than unity indicates that the flow occurs in the opposite direction.

Figure 25 gives the change in G as the As₄ pressure is increased.⁸²⁾ There are three arsenic pressure regions in which intersurface diffusion occurs in a certain direction. In regions 1 and 3, gallium adatoms diffuse from (111) B facet to the (001) facet, and in region 2 the direction is reversed. By making use of the inversion of the surface flow, one can control the shape of the growth pyramids, such as those shown in Fig. 22. During the growth, truncated pyramids with (111) B tops and {110} sides on a (111) B GaAs substrate are obtained, and as the growth proceeds the tops finally become sharp and true pyramids are formed. However, if the arsenic pressure is further increased, the direction of the gallium flow is changed and the tops again become flat, as shown in Fig. 26, similarly to in region 3 of Fig. 25. On the other hand, if the arsenic pressure is decreased, the flat tops again change to sharp tops as shown in Fig. 26.⁷⁷⁾ As seen in the figure, the truncated pyramids grown on a (111) B substrate show a reversible change in the top shape, and this phenomenon can be utilized to fabricate dot structures as explained by Fukui et al.⁶⁶⁾

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