Scaling the Nanowire

The preeminent physicist-futurist Richard Feynman famously declared in a 1959 address to the American Physical Society that “there’s plenty of room at the bottom.” He then invited them to enter the strange new world of nanoscale materials, none of which had actually been invented, except in Feynman’s fantastical imagination.

It took another generation of scientists before nanotechnology emerged, but Feynman’s assertion still rings true. There’s plenty of room at the nanoscale and scientists at Lawrence Berkeley National Laboratory (LBNL) in California are at the forefront in constructing new materials there.

Paul Alivisatos, director of LBNL’s Materials Science Division, is a world leader in nanostructures and inventor of many technologies using quantum dots — special kinds of semiconductor nanocrystals. Quantum dots, which are one ten-millionth of an inch in diameter, fluoresce brightly, are exceedingly stable and don’t interfere with biological processes because they are made of inert minerals. Alivisatos and his colleagues have constructed dozens of variations in which the fluorescent color changes with the dot’s size. Today life-science researchers use quantum dots as markers, allowing them to visualize with extreme accuracy individual genes, proteins and other small molecules inside living cells and fulfilling a prediction Feynman made in his famous lecture.

LBNL physicist Lin-Wang Wang likes to say that some day we will view the 21st Century as the “nanostructure” age, much as we associate Neolithic humans with the Stone Age and their descendents with the Bronze and Iron ages.

Despite their obvious usefulness, however, the behavior of materials built from nanometer particles is still not completely understood or fully predictable. Part of the problem is that electron wavelengths also are on the nanometer scale. Electrons’ quantum mechanical properties — the consequence of their wave-like behaviors — are changed by the sizes and geometries of the quantum dots, a subject that still generates heated discussion among physicists. These size and geometric changes allow electrons in semiconductor nanostructures to generate new energetic and optical properties.

Wang and his LBNL colleague Andrew Canning, a computational physicist who helped pioneer the application of parallel computing to material science, want to use computational methods to understand the emergent behaviors of novel materials, such as quantum dots, built from these exceedingly small blocks.

“There are a lot of challenges and there are still many mysteries to be solved,” Wang says. “For example, we still don’t quite understand the dynamics of the electron inside a quantum dot or a quantum rod. There is a lot of surface area in a quantum structure, much more than the same material in bulk. So how the surface is coupled with the interior states and how this affects the nanostructure properties is not well understood.”

The Rules are Different in Nanoscale

The research team is not starting from scratch, of course. There are established equations that predict the behavior of the electron wave function in these materials. The devil lies in the size of the problem.

“In terms of computation the nanostructure is challenging. For example, if you have a bulk material the crystal structure is a very small unit cell, just a few atoms, that repeats itself many, many times,” Wang says. “So computationally, you can treat bulk structures by calculating one unit cell — you only deal with a few atoms. With only a few atoms, you can represent the whole, much larger structure of the material. However, for a quantum dot or a quantum wire you have to treat the whole system together. These systems usually contain a few thousand to tens of thousands of atoms, and that makes the computation challenging.”

To solve a problem containing thousands of atoms requires new algorithms that handle the physics differently without compromising accuracy and parallel computing on a massive scale. That’s where Canning’s expertise came in.

“We know we need to solve the Schrödinger equation for these problems, but to do so fully is exceedingly computationally expensive,” Canning says. “What we did was make advances to approximate, solve the problem, and still get the physics right.”

Canning collaborated with Steven Louie’s group at the University of California-Berkeley, to improve the Parallel Total Energy Code (Paratec), an ab initio, quantum- mechanical, total energy program. The program runs on Franklin, the Cray XT4 at LBNL’s National Energy Research Scientific Computing Center (NERSC). The massively parallel system has 9,660 compute nodes, but is due to receive an upgrade, increasing its processing capability to a theoretical peak of about 360 teraflops.

“Paratec enables us to calculate thousand-atom nanosystems,” Canning says. “The calculation is fast and scales to the cube of the system, rather than exponentially, as a true solution of the many-body Schrödinger equation.”

Besides massive parallelization of the codes, the researchers also developed many new algorithms for nanostructure calculations. For example, Wang devised a linear scaling method, called the folded spectrum method, for use on large-scale electronic structure calculations. The conventional methods in Paratec must calculate thousands of electron wave functions, but the Escan code uses the folded spectrum method to calculate only a few states near the nanostructure energy band gap. That means the computation scales linearly to the size of the problem — a critical requirement for efficient nanoscience computation. Wang and Canning recently worked with Osni Marques at LBNL and Jack Dongarra’s group at the University of Tennessee, Knoxville, to reinvestigate and significantly improve the Escan code by adding more advanced algorithms.

Wang and his colleagues also have recently invented a linear scaling three-dimensional fragment (LS3DF) method, which can be hundreds of times faster than a conventional method in calculating the total energy of a given nanostructure. The code has run at 107 teraflops on 137,072 processors of Intrepid, Argonne National Laboratory’s IBM Blue Gene/P. The researchers have in essence designed a new algorithm to solve an existing physical problem with petascale computation. Wang says the LS3DF program is designed for materials science applications such as studying material defects, metal alloys and large organic molecules.

Within a nanostructure, the physicists are interested mainly in the location and energy level of electrons in the system because that determines the properties of a nanomaterial. For example, Wang says, electrons within a quantum rod or dot can occupy a series of quantum energy states or levels as they orbit the atomic nucleus and interact with each other. The color emitted by the material typically depends on these energy states.

Specifically, the scientists focus on two quantum energy levels: the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which the Escan code can calculate. The energy difference between these two levels determines the material’s color.

The color also changes with the quantum dot’s size, providing one way to engineer its properties. In principle, knowing the electronic properties of a given material lets the researchers predict how a new nanostructure will behave before actually spending the time and money to make it. It’s a potentially less expensive way to experiment with new nanomaterials, Wang says.

Solar Cells on the Cheap

That kind of predictive power led to a discovery that may contribute to energy independence for the United States. In collaboration with scientist Yong Zhang, a senior scientist at the National Renewable Energy Laboratory in Golden, Colorado, Wang and his colleagues predicted a new kind of solar cell that could be manufactured inexpensively and from environmentally friendly materials.

The prediction is based on a new kind of nanostructure architecture that takes advantage of the unique electronic properties of materials constructed from nanometer-sized units. In order for a material to generate electricity efficiently from sunlight it must have an electron excitation potential around 2 electron volts (eV). Silicon is one such material, and most commercial solar cells use silicon that is cut into thin sheets from bulk material. These solar cells are expensive and it takes years to recoup the cost of manufacturing and installation.

Wang and Zhang collaborated with Joshua Schrier, Denis Demchenko and Paul Alivisatos to propose using zinc oxide (the white stuff often found in sunscreens) and zinc sulfide (an abundant, easily produced mineral) in a novel solar cell. The two materials by themselves could never generate solar energy efficiently. The key is how they are combined.

The researchers designed an architecture with a zinc sulfide nanostructure core surrounded by a thin shell of zinc oxide to form a nanowire. Using a new code developed by Wang and a team of LBNL computational scientists, the researchers simulated the electronic wave properties of the proposed solar cell.

“We wanted to reduce the band gap,” Wang says. “By staggering the band energy alignment of the materials we calculated the overall band gap would be 2 eV, which produces a high efficiency limit of 23 percent.”

The researchers published their finding in the journal Nanoletters and got immediate response. The publication was one of the top 10 most-viewed Nanoletters articles in 2007. Wang says several groups worldwide now are working on building versions of the nanowire and testing their efficiency. If they function as predicted, the group will have invented a safe, abundant, stable and environmentally benign solar cell that can be built immediately using existing manufacturing methods.

Looking forward, the scientists are using these newly developed computational methods to help guide other new nanostructure materials. Even now, when the experimental group creates a new nanostructure, the properties are not always easy to predict.

“When you do the experiment, you don’t really know what result you are getting,” Wang says. “How to explain experiments is sometimes challenging. That’s the first task of simulation, to explain experimental results. Then the second task is to get some guidance for experimental design — to figure out what kind of experiment to do. That’s theory guiding the experiment.”

Both kinds of computation keep the group busy. Experimentalists at LBNL and collaborators at Washington University, NREL and worldwide are busy creating new nanomaterials: rod-shaped semiconductor nanocrystals that could be stacked to create tiny electronic devices; nanowires of various semiconductor materials; and quantum dots that can track tumors and help physicians diagnose and treat cancers more specifically.

There appear to be few limits to the number of nanostructures that can be created, proving once again that Feynman was right — there’s lots of room in the nanosphere.