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We propose developing techniques for engineering the band structure of semiconductors, thus, altering their optical properties so as to transform them into dramatically more efficient solar energy converters. We will engineer the band structure by optical hyperdoping via femtosecond laser irradiation that leads to higher levels of doping than are possible using other methods. To better understand and optimize the dynamics of optical hyperdoping, we will develop new mathematical tools for modeling the hyperdoping process, focusing on the quantum mechanics associated with the unusual band structure, as well as methods for understanding and controlling the non-equilibrium process itself. The multidisciplinary team of PIs will integrate expertise in mathematics and continuum modeling of optical hyperdoping (Michael Brenner), theoretical chemistry and modeling at the quantum level (Alán Aspuru-Guzik), materials science of optoelectronic materials (Eric Mazur), and chemistry of surfaces and interfaces (Cynthia Friend) to make a concerted attack on creating and understanding new materials with transformative potential and broad impact.