Carter spoke about their work at an international quantum theory conference in Georgia on Monday.

“People are impressed,” Carter noted. “But scientists are always questioning, ‘What are the flaws?’ ”

Carter and Huang formulated an equation that allows researchers to predict much more rapidly the characteristics of semiconducting materials before they are made. The equation calculates the kinetic energy of electrons in semiconductors from the electron density, allowing portions of these materials to be easily simulated on a computer.

These simulations provide information about real-life properties of the material.  Researchers can then apply this knowledge to design new technologies, including lighter car frames and smaller electronic devices.

“I would say that we had the first inkling about a year ago that this was going to work nicely,” Carter explained. “It took a while to prove it and to do all the tests that needed to be done to show that it was really the breakthrough we hoped it would be.”

Carter and Huang, who share authorship of the article outlining their findings, submitted the final version of their paper for publication at the end of October 2009. Physical Review B, a journal of the American Physical Society, published their work online on Jan. 26.

Before this discovery, the theory using the electron density could only accurately predict characteristics of metals. When trying to predict characteristics of non-metallic substances, however, the accuracy was poor. This left a gap in understanding the properties of non-metallic substances, which are used in many modern technologies. For years, scientists had been searching for an equation that worked for both types of materials.

“This is a pretty old question, so my target was very clear,” Huang said. “[It] was just to try to extend this method to treat semiconductors.”

In 1927, Llewellyn Hilleth Thomas and Nobel laureate Enrico Fermi proposed the original equation, which related the characteristics of atoms and molecules to electron density. They asserted that electron kinetic energy was related to electron distribution throughout a material. In 1964, Pierre Hohenberg and Nobel laureate Walter Kohn proved that the 1927 equation could be applied to real materials. But an equation that accurately related kinetic energy to density remained to be found.

In 1996, Carter started working on a solution to the problem. Huang joined the search three years ago to pursue his doctoral thesis.

“It is a tough problem,” Huang said. “I took on the project and just tried my best.”

“[Huang] was able to derive, and found in the literature, some hints of something we had left out of our previous description,” Carter said. “It’s really his beautiful work that made this happen.”

Following subsequent analyses of Huang’s findings, Carter and Huang came up with an equation that Huang described as a “compromise,” since it works for both metals and non-metals. The solution lay in addressing the difference between the response of metals and semiconductors to electrical fields.

 “We just found a missing key in the equation and then tested it,” Huang explained, noting that — for the new equation’s potential impact ­— the solution was relatively simple.

 “We didn’t expect the result to be this good,” Huang said. “We were both very surprised and very happy, because we only introduced one extra parameter. The equation didn’t change a lot from the previous one, which is very important.”

“It’s the first breakthrough in the last 10, if not 25, years,” Carter added. “[But] we know this is a very hard problem, and there’s a lot more to do.”

Correction: An earlier version of this article stated that Chen Huang GS had been working on the project for one year, when in fact he has been working on it for three years. The headline for this article has also been updated.

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