Predictive Calculations of Properties of nanostructures and bulk Materials for Applications in
Electronic, Clean Energy, and Other Industries
Diola Bagayoko, Guang-Lin Zhao
Department of Physics and High Performance Computing Laboratory
Southern University and A & M College, Baton Rouge, Louisiana 70813
From the dawn of quantum calculations to the late 1990s, ab-initio theoretical calculations have woefully under- or overestimated the band gaps of semiconductors and insulators. Density functional theory calculations have underestimated the band gaps of numerous semiconductors by 30 to 50% or more. In fact, most semiconductors were theoretically predicted to be metals (i.e., negative band gap). On the other hand, Hartree-Fock calculations have led to band gap values that are two to five times greater than the experimental ones. The above situation, in analogy to the UV catastrophe of black body radiation, is referred to as the band gap catastrophe. We present the Bagayoko, Zhao, and Williams (BZW) method that has resolved the above long-standing problem consisting of the woeful underestimation, by theory, of the measured band gaps of semiconductors, nanostructures, and of insulators. This underestimation was widely ascribed to shortfalls of density functional theory (DFT). Derivative discontinuity, self-interaction, and other features of local density approximation (LDA) and of other implementations of DFT have been cited to explain the noted underestimation. BZW described a well-defined “basis set and variational” effect that accounts for most of the underestimation and introduced an ab-initio computational method that avoids this effect [Phys. Rev. B (PRB) 60, 1563 (1999); PRB 74, 245214 (2006); and PRB 76, 037101 (2007)]. Following a detailed description of the BZW method that rests in part on the Rayleigh theorem, we review ten years of its successful application (a) to reproduce experimentally measured band gaps (GaN, C, Si, 3C-SIC, 4H-SiC, AlAs, ZnSe, w-InN, InAs, AlN, etc.) and (b) to predict unknown band gaps (c-Si3N4, c-InN, and w-InN) of semiconductors. We show the confirmation of these predictions by experiment. Further, we note that the BZW method is expected to resolve the theoretical underestimation of the energy gaps of atoms, molecules, and of nuclei (in the shell model). We conclude with suggested applications of the BZW method for predictive calculations of properties of semiconductors and of nuclei that could inform and guide the design and fabrication of semiconductor-based and other devices. The BZW method is expected to be unavoidable in theoretical studies of nanostructures for which quantum effects are ubiquitous and non-negligible. Acknowledgments: Work funded in part by the Department of the Navy, Office of Naval Research (ONR, Award No. N00014-05-1-0830), NASA (Award No. NNG 05G146G), and the National Science Foundation (NSF, Award No. HRD 0503362). Contributors to the work reported here include G. L. Zhao, T. D. Williams, Y. Luo, L. Franklin, and H. Jin.
The High Performance Computer Laboratory in Physics and the recently acquired LONI resources provide an adequate platform for the performance of our calculations and for MD and MC simulations that are done by Dr. J. D. Fan and Dr. Pui-Man Lam.
1. “Unusual Optical Properties of Aligned Carbon Nanotube Mats in Infrared Energy Region.” G. L. Zhao, D. Bagayoko, and L. Yang, J. Nanosci. Nanotechnol. 9, 1603-1606 (2009).
2. Comment on “Band gap bowing and electron localization of GaXIn1-XN” [J. Appl. Phys., vol. 100, page 093717 (2006)]. D. Bagayoko, L. Franklin, G. L. Zhao, and H. Jin, J. Appl. Phys. 103, 096101 (2008).
3. Comments on “Band structures and optical spectra of InN polymorphs: Influence of quasiparticle and excitonic effects,” D. Bagayoko, L. Franklin, H. Jin, and G. L. Zhao. Phys. Rev. 76, 037101 (2007).
4. “Calculated Optical Properties of Wurtzite InN,” H. Jin, G. L. Zhao, and D. Bagayoko. Journal of Appl. Phys. 101, 033123 (2007).
5. “Density Functional Band Gaps of AlAs.” H. Jin, G. L. Zhao, and D. Bagayoko. Phys. Rev. B73, 245214 (2006).
6. “Optical Properties of Aligned Carbon Nanotube Mats for Photonic Applications.” G. L. Zhao, D. Bagayoko and L.Yang. Journal of Appl. Phys. 99, 2006
7. “Structural, Elastic, and Electronic Properties of Carbon Nanotubes Under Uniaxial Strain,” A. Pullen, G. L. Zhao, D. Bagayoko, and L. Yang. Physical Review B 71, 205410 (2005). (Mr. Pullen is a former Timbuktu Academy Scholar currently pursuing a Ph.D. in Physics at Caltech.)
8. “Density Functional Band Gap of Wurtzite InN.” Diola Bagayoko and Lashounda Franklin,
Journal of Applied Physics, 97, 123708, 2005.
9. “Predictions of Electronic, Structural, and Elastic Properties of Cubic InN.” Diola Bagayoko,
Lashounda Franklin, and G. L. Zhao, Journal of Applied Physics 96, 4297-4301, 2004.
10. “Effective Masses of Charge Carriers in Selected Symmorphic and Nonsymmorphic Carbon
Nanotubes.” G. L. Zhao, D. Bagayoko, and L. Yang, Phys. Rev. B 69, 245416, June 2004.
11. “Electronic Structure of Short Carbon Nanobells.” G. L. Zhao, D. Bagayoko, and E. G. Wang, Modern Physics Letters B., Vol. 17, 375 (2003).
12. "Predicted Electronic Properties of Cubic Silicon Nitride (c-Si3N4), D. Bagayoko and G. L. Zhao. Physica C 364-365, Pages 261-264, 2001.
13. “Local-Density-Functional Prediction of Electronic Properties of GaN, Si, C, and RuO2” G. L. Zhao, D. Bagayoko, and T. D. Williams. Physical Review B60, 1563, 1999.
14. “Ab-Initio Calculations of the Electronic Structure and Optical Properties of Ferroelectric Tetragonal BaTiO3.” D. Bagayoko, G. L. Zhao, J. D. Fan, and J. T. Wang, Journal of Physics: Condensed Matter, Vol. 10, No. 25, 5645 (June, 1998).
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