Conceptual progress for explaining and predicting semiconductor properties
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Conceptual progress for explaining and predicting semiconductor properties Marvin L. Cohena) Department of Physics, University of California at Berkeley, Berkeley, California 94611; and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (Received 4 June 2011; accepted 1 September 2011)
After some background discussion, this review will focus on some recent developments in the areas of theoretical studies of semiconductor electronic structure, photovoltaics, semiconducting boron nitride nanotubes, and the search for modified semiconductors and insulators with higher superconducting transition temperatures. The background discussion covers the evolution of studies of solids, which changed dramatically after the development of quantum theory. These conceptual changes resulted in methods for calculating properties of materials and theoretical frameworks for interpreting experimental measurements. In some cases, the theoretical approaches have been successful in predicting new materials and new properties. As stated above, a few examples will be given to illustrate the development of this field. I. INTRODUCTION
The prehistory of theoretical work on condensed matter systems involves the belief that solids are made of atoms and atoms can be understood using quantum theory. The first part goes back to theorists like Einstein, Boltzmann, and Drude at the beginning of the last century, whereas the second part relies on the atomic and quantum theories of Bohr, Dirac, Schrödinger, Heisenberg, and others in the 1920s. Calculating properties of solids based on knowing about the properties of their constituent atoms started in the 1920s and 1930s with the work of Born, Sommerfeld, Bethe, and others, but the actual applications to explaining and predicting properties of solids took many years. As in the study of atoms, a critical part in developing an atomic and ultimately a quantum theory was the use of optical spectral studies. However, because solid state spectra are broad and relatively featureless compared to atomic spectra, unraveling their message was difficult. In the 1960s and 1970s, the optical properties of semiconductors originating from interband electronic transitions were essentially explained by an international experimental– theoretical collaboration.1 On the experimental side, reflectivity, modulated reflectivity, and photoemission techniques provided the theorists with reliable data to build semiempirical theories. The most popular of these was the empirical pseudopotential method (EPM),2,3 where the crystalline potential was determined by comparing the calculated optical properties with the experimental data. This approach was not just a fitting scheme. It was based on a theoretical model in a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.328 J. Mater. Res., Vol. 26, No. 22, Nov 28, 2011
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which each ion of the crystal had an appropriate potential to simulate valence el
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