Self-Organized Quantum Dots

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Self-Organized Quantum Dots by Max G. Lagally

In this, the Information Age, we hear almost daily of advances in the speed of computers, of more efficient integrated circuit chips, and of new digital marvels to improve our lives or expand the ways we spend our leisure time (1 ). During the last 40 years, computers have become more powerful as their basic element, the transistor, has become smaller and smaller. An article elsewhere in this issue (2) briefly describes how advances in the development of materials and “bottoms-up” materials-processing methods have enabled this miniaturization. The microelectronics industry has continued to respond to new technological challenges as the dimensions of integrated circuits have shrunk. The most recent “road map” for the future issued by …the road presently the National Semiconductor traveled becomes Association (3) projects advances in the technology at treacherous when least to 2012. densely packed Yet the rate of development of the microelectronics transistors can no industry, a doubling time aplonger be reduced in proximately every 18 months size and still function (expressed, in terms of the number of transistors that can properly. A new be put on a unit area of silicon, paradigm for by Moore’s law [see ref 2]) parcomputation could allels the evolution of earlier technologies (e.g., steel): after then be required. about 40 years, the rate slows. Just becoming noticeable as a deviation from Moore’s law, such a slowdown can have many causes. Ultimately, however, the road presently traveled becomes treacherous when densely packed transistors can no longer be reduced in size and still function properly. A new paradigm for computation could then be required. That paradigm is almost universally thought to be some form of “quantum computation”, although whether it will be feasible, when (if ever) it will replace computation as we know it now, and what form it will take are hotly debated issues (4). Nanoelectronic devices that may replace the transistor in future computers will perform as switches and amplifiers just as the transistor does, but will employ quantum mechanical phenomena that become significant when the size of the structure that makes up the active element of the nanoelectronic device becomes sufficiently small (5). Of the several potential candidates for quantum nanoelectronic devices, the ones that most capture the imagination are those using quantum dots (6). The term “quantum dot” has its origin in quantum well electronic devices, which by now are very common, with examples found in nearly every home in the form of the solid-state laser in CD players. Between quantum wells and quantum dots are quantum wires. The terms refer to the dimensionality of confinement of electrical charges in the structure. In a quantum well,

Figure 1. Scanning tunneling microscope image of a single QD, a Ge nanocrystal grown by depositing Ge onto a Si surface. Because Ge atoms are slightly larger than Si atoms, the strain produced by Ge trying to match the Si lattice causes a preference for the formation of such crystals, as this formation minimizes the total free energy of the combined Ge–Si film system. The nanocrystal is 3 nm high and 30 nm along the base.

charges are confined in a thin layer but are free to move in the other two dimensions. In a quantum wire, the charges are confined in two dimensions. In a quantum dot, charges are confined in all three dimensions and are spatially localized on the dot. The confinement determines the allowed energy levels of the charges (the quantum mechanical particle-in-a-box problem) and thus produces unique and spatially localized electronic and optical properties. The properties of quantum dots (QDs) can perhaps be more simply visualized by considering an analogy with the development of solids from atoms. A QD can be thought of as a large “artificial atom” (6 ). A single atom has discrete energy levels; transitions between these levels produce radiation with well-defined wavelengths. A simple model of the formation of solids from atoms, the tight-binding model, shows how bands and energy gaps eventually form from the original atomic levels as we make a large, three-dimensional solid. The properties of metals, semiconductors, and insulators are determined by the band structure of the solid and its filling with electrons. Making quantum wells, wires, and dots is effectively going backward in the process of making a large solid. By confining one dimension after another, we limit the classical degrees of freedom of the electrons and thus introduce quantum mechanical properties. In a QD, typically a nanocrystal consisting of perhaps 1,000 to 100,000 atoms (as opposed to ~1022 for a cubic centimeter of most solids), the electronic states are quantized in all three dimensions, producing discrete energy levels, just as in an atom. But, unlike atoms, which for a given element all have the same size and can be represented as spherically symmetric boxes to hold electrons, QDs of a given material (artificial atoms) can have a range of sizes and shapes (cubes, pyramids, pancakes, rods, spheres, rectangular solids). Substantial changes in fundamental electrical and optical properties will occur when the electronic energy level spacing at a given temperature exceeds the energy of an electron at that temperature. Because of the nature of their bonding, semiconductors show these quantum confinement effects at relatively large size: a dimension below several tens of nanometers will produce noticeable effects. The positions of the energy levels in the QD depend on

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Figure 2. Atomic-force microscope image of the surface of a multilayer film consisting of 20 layers of 2.5-nm-thick SiGe alloy (each producing pyramids) alternating with 20 layers of pure 10-nm-thick Si that embeds each previous pyramid layer (20 × (2.5 nm Si0.25Ge0.75/10 nm Si) on Si (001)). This process produces the uniform array of pyramids in the outer layer. The pyramids are 7.5 nm high and have 75 nm × 75 nm square bases.

Figure 3. Schematic diagram of an idealized version of the outer few layers of the multilayer film shown in Fig. 2. This “artificial crystal” of pyramidal QDs would have unique quantum mechanical properties and thus novel electronic or optoelectronic applications.

its size and shape and are thus tunable by controlling size and shape, producing unique optical and electronic properties that have attracted considerable recent interest ( 6, 7 ). The discrete energy levels, in which charges can be placed and held, make QDs potential candidates for computing applications and for optoelectronic devices such as lasers and optical switches. Nanocrystals can be fabricated by various means. For example, researchers have been able to synthesize chemically macroscopic quantities of CdSe nanocrystals and tune their size by slightly varying the synthesis conditions (8). Precipitation of semiconductor nanocrystals out of an organic liquid proceeds by injecting a set of precursors into a hot liquid. Nucleation occurs, the temperature drops, and the resulting nanocrystals become coated with a layer of organic material that keeps them from fusing. The organic coating may also provide electronic passivation. Others have used deposition from an atomic or molecular vapor onto a crystalline surface to produce QDs. Figure 1 shows an image of a QD made by atomic-vapor deposition, a Ge nanocrystal consisting of about 10,000 atoms grown by depositing Ge on a Si surface (9 ). The synthesis of such dots teaches us much about the kinetic and energetic pathways by which crystals grow in various environments (8, 10 ). Using individual dots (or in some cases a large number of uncorrelated dots), many scientists have recently begun to probe the unique properties of artificial atoms (7). Although single QDs have value, ordered arrays of QDs (artificial crystals, in analogy with artificial atoms) are much more interesting because quantum mechanical interactions between dots can make possible unique computing and optoelectronic applications. Because the QD electronic structure depends on dot size and the interactions between QDs depend on their spacing, uniformity in size and spacing (as-

suming a fixed shape) now become important considerations. It is thus not enough to make mono-size-disperse nanocrystals; they also must be organized into a regular structure. “Colloidal crystals” up to 50-µm large made from 2nm CdSe nanocrystals, with near-atomic precision in their size and spacing, have been demonstrated ( 9 ). The protecting layer that coats individual nanocrystals also acts as a precise spacer when the nanocrystals pack to form the artificial crystal. By modifying the chemistry of the spacer layer, the “lattice parameter” of the artificial crystal and hence the electronic coupling between the QDs can be varied. If the arrays are formed at a solid interface, the crystallographic axes of the QD crystals align as they assemble. Optical spectroscopy shows both effects of confinement and of dot-to-dot interactions ( 11 ). For computing applications, one would like to be able to create arrays of QDs in Si single crystals, as all of our present semiconductor technology is based on Si. Ge or GeSi alloy nanocrystals grown by vapor deposition (either by atomic-beam deposition or by chemical vapor deposition, the decomposition of larger molecules over a hot surface) offer this potential (see Fig. 1). The formation of these Ge nanocrystals is determined by the strain that results when Ge, which is slightly larger than Si, is added on top of the Si lattice. As the Ge tries to form a layer on the Si lattice with a oneto-one correspondence of the atoms, strain builds up until the Ge can no longer form a layer, but forms pyramids instead (9, 10 ). Effectively the minimization of the free energy of the combined Si/Ge system controls the formation of the pyramids. (The same effect occurs in other strained layered thin-film systems [12]). One can thus readily form an assembly of 3-nm-high nanocrystals over a complete 10-cmdiameter (or larger) Si wafer simply by allowing nature to perform the self-organization. Unfortunately, a single layer

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of such QDs is not as uniform in size and spacing as we need. A trick has been discovered, however: if the layer of QDs is embedded in Si and then Ge is grown again and this process is repeated, the system improves its self-organization (10). Figure 2 shows a QD array that results after 20 alternate layers of Si and Ge have been grown. Figure 3 is a schematic diagram of what the top few layers of this artificial crystal might look like: a regular 3-D array of uniformly sized and spaced pyramidal nanocrystals. Finally, how might one use such QDs in computing? One scenario of the ultimate scale of computing will involve use of single-electron transistors (SETs), which store a bit of information by the presence or absence of a single electron, marooned on a QD in the middle of the transistor. Single fabricated SETs have been demonstrated recently. Figure 4 shows schematically how self-organized QD arrays may play a role in this future. It shows a field-effect transistor (compare Fig. 8 in ref 2 ) with a layer of self-organized QDs, each of which can hold a charge. One can imagine scaling the whole device to a size at which only one QD resides within each transistor, giving a large array of SETs that may be able to communicate with each other quantum mechanically without the need for connecting wires. To make this vision of the ultimate technology of the Information Age a reality will require the continued efforts of chemists and materials scientists to provide the knowledge of materials and materials processing that serves as the underpinnings of the microelectronics industry. Literature Cited 1. See, for example, the article on Man of the Year (W. Isaacson, p 46) and associated reports (pp 76 and 78) in Time Magazine, Dec 29, 1997/Jan 5, 1998. 2. Campbell, D. J.; Kuech, T. F.; Lisensky, G. C.; Lorenz, J. K.; Whittingham, M. S.; Ellis, A. B. J. Chem. Educ. 1998, 75, 297– 312.

Figure 4. A potential application of QDs in transistors. The diagram shows a field effect transistor with a buried layer of QDs. The standard field effect transistor consists of a source and drain for flowing charges through a channel and a gate, which can control the flow of charges with a voltage that makes the channel effectively wider or narrower. Charging the QD layer provides an extra level of control. Reducing the size of the device until only one QD remains underneath each gate would produce a coupled array of single-electron transistors, the ultimate in storing bits of information.

3. The National Technology Roadmap for Semiconductors; Semiconductor Industry Association, 1997. Semiconductor Industry Association, San Jose, CA 95110; http://www.semichips.org/ (accessed January 1998). Copies may be obtained by contacting www. sematech.org. 4. Lloyd, S. Sci. Amer., Oct. 1995, p 140. 5. Two easy-to read summaries are Goldhaber-Gordon, D.; Montemerlo, M. S.; Love, J. C.; Opitek, G. J.; Ellenbogen, J. C. Overview of Nanoelectronic Devices. Proc. IEEE 1997, 85, 521 and Montemerlo, M. S.; Love, J. C.; Opitek, G. J.; Goldhaber-Gordon, D. J.; Ellenbogen, J. C. “Technologies and Designs for Electronic Nanocomputers.” MITRE Technical Repor t No. 96W0000044, The MITRE Corporation: McLean, VA, July 1996. For copies of these reports, downloadable slides, and extensive tutorial information, see http://www.mitre.org/research/ nanotech (accessed January 1998) or contact [email protected]. 6. Reed, M. A. Sci. Amer., Jan. 1993, p 98; Levi, B. G. Phys. Today, May 1996, p 22–24; May, M. Amer. Sci., May/June 1996, 84, 337–338; Dagani, R. C&E News, 1998, 76, 27–29. 7. McEuen, P. L. Science 1997, 278, 1729–1730, and references cited there. 8. Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993, 115, 8706. 9. Mo, Y.-W.; Savage, D. E.; Swartzentruber, B. S.; Lagally, M. G. Phys. Rev. Lett. 1990, 65, 1020. Mo, Y.-W.; Lagally, M. G. J. Cryst. Growth 1991, 111, 876. 10. For a review, see Liu, F.; Lagally, M. G. Surf. Sci. 1997, 386, 169. See also http://mrgcvd.engr.wisc.edu/lagallygroup/index.html (image archives); accessed January 1998. 11. Murray, C. B.; Kagan, C. R.; Bawendi, M.G. Science 1995, 270, 1335–1338. 12. For example, Grundmann, M. et al. Phys. Rev. Lett. 1995, 74, 4043; Phys. Rev. 1995, B52, 11969. For an animation, a QD quiz, and additional information on Group III-V QDs, see http://sol.physik.TU-Berlin.de/htm_grdm/nano/qdquiz.html; accessed January 1998.

Max Lagally is in the Department of Materials Science and Engineering, University of Wisconsin–Madison, Madison, WI 53706. [email protected].

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