With the help of Lonestar, a supercomputer at the Texas Advanced Computing Center, computational physicist James Chelikowsky is advancing the scientific understanding of nanostructures, including quantum dots, which have novel properties with countless potential applications in many industries.

Scientists and engineers are convinced that the fledgling, interdisciplinary field of nanoscience, the science of very small structures -- those between 1 and 100 nanometers in diameter or length -- will drive the next generation of technological advancements. Just how small is a nanometer? One nanometer is one-billionth of a meter -- that is 1 X 10^-9 meters or 1/1,000,000,000 of a meter! For perspective, consider that the width of a human hair is approximately 80,000 nanometers, and a DNA molecule is about 2.5 nanometers wide.

By all accounts, nanoscience is one of the hottest areas in science and technology today. In fact, scientists from many fields, including physics, chemistry, biology, information technology, metrology (the science of measurement), and others, have turned to investigating the properties of nanostructures. Likewise, engineers are enthusiastic about the possible applications of nanotechnology to a wide array of industries, including energy, medicine, electronics, computing, security, and materials.

All this attention and enthusiasm stems from the discovery that the structure, and electrical and optical properties, of many materials at the nanoscale differ in very fundamental ways from the macroscopic or "bulk" material. Unique phenomena or "emergent" properties often appear in materials at the nanoscale and these properties have many potential and novel applications in the real world.

Although the applied use of nanoscience is limited, several industries are currently using nanotechnology. For example, nanoscale products are now used in magnetic recording tapes, sunscreens, automotive catalyst supports, markers for biological imaging, electroconductive coatings, optical fibers, and chemical-mechanical polishing. In addition, medical researchers are working at the nanoscale to develop new drug delivery methods, cancer-detection methods, and pharmaceuticals. Other promising nanotechnologies are being developed that can create artificial bone, antibodies, red blood cells, and nerve cells. The National Institutes of Health projects that many of these nanotechnologies, and more, will yield medical benefits in as little as 10 years.

However, before many of these real world applications can become reality, scientists like James Chelikowsky at The University of Texas at Austin must first uncover the properties that govern the behavior of these tiny structures -- which today, are still largely unknown.

Meet Dr. James Chelikowsky

James Chelikowsky is the W.A. "Tex" Moncrief Jr. Chair in Computational Materials in the Institute for Computational Engineering and Sciences at The University of Texas at Austin, and is a leading researcher in the computational physics of nanostructures.

He and his research group do not work with the actual nanostructures; instead, they use complex mathematical calculations and models to simulate the properties of real or hypothetical nanostructures, using high performance computers. Specifically, they employ advanced computational methods to understand the structural and electronic properties of materials in the nano-regime, such as atomic clusters, nanowires, and nanocrystals.

At such small scales, it is difficult and sometimes impossible to make measurements of the physical properties of materials, particularly structural properties. "Very often, the properties of nanostructures can be calculated mathematically better than they can be measured experimentally in the laboratory," Chelikowsky said. The field that encompasses the study of materials using computers is called "computational materials science." This field is relatively new, and provides insights into many physical phenomena that are too complex for analytical or experimental methods.

As a graduate student at the University of California at Berkeley in the 1970s, Chelikowsky studied under Marvin Cohen, one of the pioneers in computational materials science. "If you counted the number of people doing computational physics at the time, particularly on materials, you could count them on one hand. Now, there are computational materials scientists at almost all the major universities," commented Chelikowsky, "and many of them now work with nanostructures. However, I have also studied materials at larger size scales, such as my favorite material, silicon."

Chelikowsky came to The University of Texas at Austin from the University of Minnesota in 2005. "I really liked the interdisciplinary nature of my appointment -- but I primarily came to UT Austin for the opportunity to advance my research. I was attracted by the resources available at the university, especially the large-scale supercomputing systems, which are critical for my work. UT Austin is very high on the 'TOP500' list of the most powerful supercomputers in the world," said Chelikowsky, "and that is extremely attractive to a computational physicist."

Quantum Dots: Very Small Semiconductors

A semiconductor is a solid whose electrical conductivity is in between that of a metal and that of an insulator, and can be controlled over a wide range, either permanently or dynamically. Semiconductors will conduct an electrical current, but only if stimulated by an outside force, such as heat, light, or voltage. This property makes semiconductors "controllable" for a wide variety of applications, not the least of which is computer components. For example, cadmium always conducts electricity, whereas selenium always insulates against electrical current. However, when chemically combined as cadmium selenide (CdSe), the resulting crystal exhibits the properties of a semiconductor.

Chelikowsky has worked primarily with semiconductor nanocrystals called quantum dots. Quantum dots are composed of hundreds or thousands of atoms, and are typically between one and 10 nanometers in diameter. It would take about four million quantum dots, arranged end-to-end, to stretch across a penny! Quantum dots have unique properties that lie somewhere between that of a single molecule and the bulk material.

Their unique properties are usually due to quantum confinement -- the physical confinement of electronic interactions due to their small size. In fact, quantum dots are often thought of as "artificial atoms" because their electrons are confined to a very small space compared to electrons in the bulk material. Quantum dots are of particular interest because of this property, which gives them the potential to be custom-designed or "tuned" for a variety of applications in electronics, medicine, computer science, and potentially many others.

In collaboration with computer scientists and applied mathematicians at The University of Texas at Austin and several other universities, Chelikowsky is using high-performance algorithms to simulate and model the electronic properties of quantum dots. Their work is based on the principle that the properties of matter arise from the interactions among atoms, and that this can be understood mathematically.

By exploring the electronic structure of a material by calculating the distribution of electrons across a range of energies, they can predict how well a material conducts electricity, how it reacts to heat, how it responds to a magnetic field, and a whole host of other fundamental properties. Chelikowsky then collaborates with physical scientists to apply these algorithms to complex nanoscale systems such as quantum dots.

The Atom in the Middle: Doped Nanocrystals

Chelikowsky and his research group are working to understand one of the major hurdles that must be overcome before semiconductor nanocrystals such as quantum dots can be used in electronic and optical products. That is, how to effectively "dope" them. Doping is the process of adding an impurity, called a "dopant," to a material to modify its electrical properties. The electrons in these impurities enable the crystal's electric behavior to be controlled and fine-tuned for specific purposes.

Doping is nothing new; in fact, the introduction of impurities into bulk crystals forms the entire basis for modern electronics. For example, adding a dopant such as boron or phosphorous to silicon crystals can dramatically alter its electrical properties in specific ways. Doped silicon is one of the main components in modern transistors, personal computers, and diodes.

Likewise, doped semiconductor nanocrystals potentially provide the basis for a wide variety of nano-applications in the future, including solar cells, electroluminescent devices, as well as semiconductors. Chelikowsky and his group are exploring the behavior of several quantum dots that have potential for such applications, including several that they have made magnetic by adding impurities such as manganese.

The problem is that unlike bulk semiconductors used in electronics today, semiconductor nanocrystals tend to self-purify -- that is, eject the impurities, usually to the crystal's surface. Chelikowsky became interested in this phenomenon in a complicated quantum dot called cadmium selenide (CdSe), with manganese introduced as an impurity. In the bulk material, it is easy to introduce an impurity like manganese, but it is difficult in nanostructures of the same material. He and his research group decided to look at this problem and see if they could better understand why.

Often, the electrons associated with dopant atoms added to semiconductors are only weakly bonded to the crystalline structure. However, this is the desired effect because the dopants are the source of electrons that can conduct current, making it useful as a semiconductor. Although rare, these impurity atoms can move around, a phenomenon that occurs in both bulk and nanocrystal semiconductors.

In nanocrystals, however, such movement leads to the impurity atoms reaching the crystal's surface much more often and easier than in the bulk material, simply due to the large surface to volume ratio of these small structures. Simply put, the impurity atom has a much smaller distance to travel to reach the surface of a nanocrystal. Once the dopant reaches the surface, it often binds there, which defeats the purpose of doping it in the first place because the dopant can no longer contribute conduction electrons.

Chelikowsky and his research group have taken a slightly different route than most to try to understand self-purification. "Most researchers who have studied doped nanocrystals have examined the kinetic phenomenon -- how the atoms move around and eventually become bonded to the surface. Instead, we asked a different question -- we asked whether the dopant is energetically happy in the center of the nanostructure or would it be better off energetically if it moved to the surface or out of the crystal altogether," explained Chelikowsky. They hypothesized that doped quantum dots are intrinsically unstable and tend to self-purify because a high amount of energy (i.e., energy of formation) is required to bind the dopant to the nanocrystal.

Making the Calculations: A Big Job for a Big Computer

To test their hypothesis, Chelikowsky and his co-author, Gustavo Dalpian, calculated the energy levels and spatial distribution of electrons in CdSe nanocrystals, both with and without a single atom of manganese placed in the center of the crystal as an impurity. They tested CdSe crystals ranging in diameter from 1.4 to 2.6 nanometers, containing up to 293 cadmium and selenium atoms.

"When we set up this type of calculation, we start with the geometry of the electrons in the bulk material because we know how the atoms are arranged from past work. We take what we know about the arrangement of atoms, and then calculate what the energetic relationships would be if we reduced its size to say 1,000 atoms, the size of a quantum dot. To do this, we must solve an equation called the Kohn-Sham equation," said Chelikowsky.

The solution to the Kohn-Sham equation is a standard quantum mechanics problem, but Chelikowsky's group does not use the standard procedures. "The standard way to solve the equation is to express the wave functions associated with the electrons in the quantum dot as simple functions -- like sines and cosines," said Chelikowsky. "This works great for crystals because they are periodic. For example, if you could literally step into the crystal and take a look around, you would only need to know something about a little part of the crystal to know about the entire crystal because it is periodic -- it keeps repeating itself over and over."

However, quantum dots are not periodic, so they solve the equation in a different way. Rather than using sines and cosines, they solve it as an engineer would, using what are called finite difference techniques. According to Chelikowsky, "finite difference techniques work great for quantum dots because the only thing we need to put into the equation is the arrangement of the atoms within the quantum dot itself and we can ignore everything outside the dot. In other words, we set the probability of finding an electron outside the quantum dot to zero. This greatly simplifies the calculation. Nevertheless, the calculations still require large amounts of computing power," said Chelikowsky.

To perform these complex calculations, Chelikowsky and Dalpian used a custom computer code called PARSEC (Pseudopotential Algorithms for Real Space Energy Calculations). Chelikowsky and Yousef Saad at the University of Minnesota developed PARSEC in the early 1990's; since then, many others have made improvements to the code, including Dalpian. PARSEC is optimized for massively parallel computing environments.

For the large amount of computing power required to make these calculations, Chelikowsky's research group turned to Lonestar, a supercomputer at the Texas Advanced Computing Center at The University of Texas at Austin. Lonestar, a Dell Linux cluster, is one of the most powerful computing systems in the world, and is currently #12 on the top500 list of the world's most powerful supercomputers. In the larger calculation, four runs were made in order for the model to converge. Making these kinds of calculations takes so much computing power that Chelikowsky's research group is one of Lonestar's top users.

Chelikowsky and Dalpian's calculations revealed that the smaller the CdSe nanocrystal, the more energetically unfavorable it is to add the impurity atom. Although it may be energetically favorable to add a manganese atom in the bulk material, it gets less favorable as the size of the nanocrystal decreases. Therefore, setting aside the issue of kinetics, energetics alone explains why doped quantum dots are intrinsically unstable and tend to self-purify.

Chelikowsky thinks this discovery applies to other quantum dot systems as well. In addition, he and Dalpian proposed that growing CdSe or similar nanocrystals in an anion-rich solution would make doping them energetically more favorable. Now it is up to other researchers to explore their proposal experimentally to see if they can produce more stable nanostructures that engineers can then fine tune for various specific applications.

The Road Ahead…Will it be a Small, Small World?

Now, and very likely in the future, the computational science done by Chelikowsky and his colleagues ultimately serves as the underpinnings for almost all applications in nanotechnology. This technology would not be possible without researchers like Chelikowsky pushing forward the frontiers of nanoscience every day.

Chelikowsky believes that it is difficult to predict what the future might hold in the science of computational materials, especially as it applies to nanotechnology. He said, "Part of the problem is that when you work with computers, you get used to them working at a certain level and having certain computational capabilities. It's easy to fall into the trap of thinking that computers can be used for certain types of computations and not for others, and it's hard to break out of that mindset. Students sometimes get irritated when I pose a problem that is not possible to solve with today's computers or would take a year's worth of computer time to solve. But these types of problems, the ones that are not possible or too difficult right now, are exactly the ones we should be thinking about! Chances are that advanced computing resources will become available to solve these problems sometime in the future."

One very difficult nanoscale problem that Chelikowsky would like to tackle, but which is beyond today's computing capabilities, is how crystals grow and the mechanisms by which defects are incorporated into growing crystals. What's most difficult about tackling this problem are the small size and time scales involved. Chelikowsky believes that it will take a computer that is three or more orders of magnitude better than today's most powerful supercomputer to solve this problem. For now, he plans to keep that idea on the back burner until such a supercomputer comes along....

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Source: Texas Advanced Computing Center. For images and more information about Dr. Chelikowsky's work, go to http://www.tacc.utexas.edu/research/users/features/chel.php.