New mathematical approach helps to simulate materials for solar cells and LEDs

June 22, 2012 // By Paul Buckley
A multidisciplinary team of researchers at MIT and in Spain has found a new mathematical approach to simulating the electronic behavior of noncrystalline materials.

The approach paves the way for the future development of new devices such as lower-cost solar cells, organic LED lights and printable, flexible electronic circuits.

The researchers said that the new method uses a mathematical technique that has not previously been applied in physics or chemistry. Even though the method uses approximations rather than exact solutions, the resulting predictions turn out to match the actual electronic properties of noncrystalline materials with great precision.

Jiahao Chen, a postdoc in MIT’s Department of Chemistry and lead author of the report, said that finding this novel approach to simulating the electronic properties of ‘disordered materials’ - those that lack an orderly crystal structure - involved a team of physicists, chemists, mathematicians at MIT and a computer scientist at the Universidad Autónoma de Madrid. The work was funded by a grant from the National Science Foundation aimed specifically at fostering interdisciplinary research.

The project uses a mathematical concept known as free probability applied to random matrices - previously considered an abstraction with no known real-world applications - that the team found could be used as a step toward solving difficult problems in physics and chemistry. “Random-matrix theory allows us to understand how disorder in a material affects its electrical properties,” said Chen.

Typically, figuring out the electronic properties of materials from first principles requires calculating certain properties of matrices - arrays of numbers arranged in columns and rows. The numbers in the matrix represent the energies of electrons and the interactions between electrons, which arise from the way molecules are arranged in the material.

To determine how physical changes, such as shifting temperatures or adding impurities, will affect such materials would normally require varying each number in the matrix, and then calculating how this changes the properties of the matrix. With disordered materials, where the values of the numbers in the matrix are not precisely known to begin with, this is a very difficult