Empirical relation between Pauling electronegativity and self-energy cutoffs in local-density approximation-1/2 quasi-pa
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esearch Letters
Empirical relation between Pauling electronegativity and self-energy cutoffs in local-density approximation-1/2 quasi-particle approach applied to the calculation of band gaps of binary compound semiconductors Mauro Ribeiro Jr., Office of Operational Research for Business Intelligence & Technology, Principal Office, 412N Main St., STE100, 82834 Buffalo, USA Address all correspondence to Mauro Ribeiro, Jr. at [email protected] (Received 19 February 2016; accepted 18 April 2016)
Abstract The local-density approximation (LDA)-1/2 technique has been successfully applied to surmount current limitations in density-functional theory to determine excited-states properties of solids via LDAs to the exchange-correlation functional. The main task to properly apply this technique is to choose the “cut-off” radius to truncate the long-ranged self-energy function, originated by the procedure of removing the spurious self-energy of electrons (and/or holes). The usual procedure is by choosing an extreme of the variation of the band gap as a function of this cutoff. This work examines the relationship between that cut-off parameter and the electronegativity difference between cation and anion in binary compounds calculated self-consistently with LDA-1/2.
Introduction Compound semiconductors have been at the core of modern technology regarding optics and light emitting diodes (LEDs),[1] integration with silicon and electronics,[2,3] and countless applications from telecommunications to optical fiber communications.[4] In particular, binary semiconductors represent a class of materials specially grown using modern techniques such as chemical vapor deposition (CVD),[5] and are rapidly evolving to incorporate and even substitute silicon in some microelectronic devices and transistors.[6] Density-functional theory (DFT),[7,8] together with modern exchange-correlation functionals,[9] has been a remarkable tool to predict crystal structures, lattice parameters, phase transitions, phonon dispersion curves, mode Grüneisen parameters, effective charges, dielectric constants, elastic constants, bulk and internal strain parameters, and many other ground-state properties of solids.[10,11] However, DFT, through common local-density approximation (LDA) or the generalized-gradient approximation (GGA) respectively and their many ramifications, is not able to deal with excited states[12] due to an nonanalytical behavior of the exchange-correlation energy functional, intrinsic to DFT, which emerges as a discontinuity of the functional derivative of the exchange and correlation energy when calculating the “eigenvalues” of the one-particle densityfunctional equation for the ground state.[13,14] As a result, band gaps predicted by the LDA to the exchange-correlation functional are generally underestimated by 40% on average,[13,15] as well as other electronic properties such as energy barriers in chemical reactions, dissociation energies of molecular ions, charge transfer excitation energies—not to mention the
overestimation of bindi
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