Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session J6: Advanced Electronic Structure Methods for Defects in Semiconductors and Insulators |
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Sponsoring Units: DCOMP Chair: Shengbai Zhang, Rensselaer Polytechnic Institute Room: Portland Ballroom 253 |
Tuesday, March 16, 2010 11:15AM - 11:51AM |
J6.00001: Defects levels and band alignments at semiconductor-oxide interfaces through the use of hybrid functionals Invited Speaker: Alfredo Pasquarello The issue of aligning defect levels with respect to the band edges at semiconductor-oxide interfaces is addressed through the use of hybrid functionals. The fraction of exact exchange contained in these functionals is responsible for a systematic increase in the band gaps, but leaves the energy levels of atomically localized defect states largely unaffected provided they are aligned with respect to a common reference potential. Hence, the location of the defect levels can be decoupled from the band-gap renormalization problem, which transforms into the determination of band edge shifts. Furthermore, band-edge shifts as determined within a hybrid functional scheme are found to give an accurate description of band offsets for several semiconductor-oxide interfaces. The combination of these results gives a viable framework for positioning calculated defect levels within a band diagram, which is directly comparable to experiment. Our approach is illustrated through several applications. More practical issues will also be addressed, including the differences originating from the choice of hybrid functional and the treatment of the exchange singularity in plane-wave formulations. [Preview Abstract] |
Tuesday, March 16, 2010 11:51AM - 12:27PM |
J6.00002: Defect Physics without the Band-Gap Problem: Combining DFT and \textit{GW} Invited Speaker: Patrick Rinke In computational defect physics and chemistry the local-density and generalized gradient approximations (LDA/GGA) to density functional theory (DFT) are widely applied due to their computational efficiency. However, their predictive power is limited by intrinsic deficiencies like artificial self-interaction and the absence of the derivative discontinuity in the exchange-correlation potential (that give rise to the so called band-gap problem). We present a new formalism that combines DFT with many-body perturbation theory (MBPT) in the $G_0W_0$ approximation to overcome these deficiencies [1,2]. The formation energy of a defect is expressed as successive charging of a lower charge state, for which the defect level is unoccupied, permitting a decomposition into a lattice (DFT) and an electron addition part ($G_0W_0$) [2]. For the self-interstitial in silicon the approach increases the LDA formation energy of the neutral state by $\sim$1.1~eV in good agreement with diffusion Monte Carlo calculations [2,3,4]. For the anion vacancy in bulk MgO (also called F- or color center), which can probably be regarded as \emph{the} classic intrinsic point defect in compound insulators, it proves to be necessary to go one step further in the hierarchy of MBPT. After including the electron-hole and electron-phonon interaction the absorption energies of the neutral and the positively charged F-center become practically identical -- a fact that has impeded the F-center's characterization for decades -- in good agreement with optical absorption studies [5].\\[4pt] [1] Hedstr\"om {\it et al.} PRL {\bf 97}, 226401 (2006)\\[0pt] [2] Rinke {\it et al.} PRL {\bf 102}, 026402 (2009)\\[0pt] [3] Batista {\it et al.} PRB {\bf 74}, 121102(R) (2006)\\[0pt] [4] Leung {\it et al.} PRL {\bf 83}, 2351 (1999)\\[0pt] [5] Kappers {\it et al.} PRB {\bf 1}, 4151(1970) [Preview Abstract] |
Tuesday, March 16, 2010 12:27PM - 1:03PM |
J6.00003: Quantum Monte Carlo calculations for point defects in semiconductors Invited Speaker: Richard Hennig Point defects in silicon have been studied extensively for many years. Nevertheless the mechanism for self diffusion in Si is still debated. Direct experimental measurements of the selfdiffusion in silicon are complicated by the lack of suitable isotopes. Formation energies are either obtained from theory or indirectly through the analysis of dopant and metal diffusion experiments. Density functional calculations predict formation energies ranging from 3 to 5 eV depending on the approximations used for the exchange-correlation functional [1]. Analysis of dopant and metal diffusion experiments result in similar broad range of diffusion activation energies of 4.95 [2], 4.68 [3], 2.4 eV [4]. Assuming a migration energy barrier of 0.1-0.3 eV [5], the resulting experimental interstitial formation energies range from 2.1 - 4.9 eV. To answer the question of the formation energy of Si interstitials we resort to a many-body description of the wave functions using quantum Monte Carlo (QMC) techniques. Previous QMC calculations resulted in formation energies for the interstitials of around 5 eV [1,6]. We present a careful analysis of all the controlled and uncontrolled approximations that affect the defect formation energies in variational and diffusion Monte Carlo calculations. We find that more accurate trial wave functions for QMC using improved Jastrow expansions and most importantly a backflow transformation for the electron coordinates significantly improve the wave functions. Using zero-variance extrapolation, we predict interstitial formation energies in good agreement with hybrid DFT functionals [1] and recent GW calculations [7]. \\[4pt] [1] E. R. Batista, J. Heyd, R. G. Hennig, B. P. Uberuaga, R. L. Martin, G. E. Scuseria, C. J. Umrigar, and J. W. Wilkins. Phys. Rev. B 74, 121102(R) (2006).\\[0pt] [2] H. Bracht, E. E. Haller, and R. Clark-Phelps, Phys. Rev. Lett. 81, 393 (1998). \\[0pt] [3] A. Ural, P. B. Griffin, and J. D. Plummer, Phys. Rev. Lett. 83, 3454 (1999). \\[0pt] [4] R. Vaidyanathan, M. Y. L. Jung, and E. G. Seebauer, Phys. Rev. B 75, 195209 (2007). \\[0pt] [5] P. G. Coleman and C. P. Burrows, Phys. Rev. Lett. 98, 265502 (2007). \\[0pt] [6] W. K. Leung, R. J. Needs, G. Rajagopal, S. Itoh, and S. Ihara, Phys. Rev. Lett. 83, 2351 (1999). \\[0pt] [7] P. Rinke, A. Janotti, M. Scheffler, and C. G. Van de Walle, Phys. Rev. Lett. 102, 026402 (2009). [Preview Abstract] |
Tuesday, March 16, 2010 1:03PM - 1:39PM |
J6.00004: Charged defects in the supercell approach Invited Speaker: Christoph Freysoldt In electronic structure theory, point defects in crystalline materials are usually modelled in the supercell approach. While the isolated-defect limit (i.e. low concentrations) can be achieved by making the supercell large enough in principle, advanced electronic structure methods are limited to rather small system sizes (i.e. excessively high concentrations) in practice. For these small systems, however, defect-defect interactions may significantly alter the calculated properties. In order to apply any advanced method to point defects, the unavoidable artifacts must be corrected for. For charged defects, the Coulomb interaction between the defect and its periodic images as well as the unavoidable neutralizing background gives rise to a slow convergence of the defect energetics with respect to supercell size. Various correction schemes have been suggested over the years, ranging from Coulomb truncation over Makov-Payne corrections to scaling-law extrapolation. Unfortunately, the schemes often disagree and sometimes even worsen convergence with respect to supercell size. I will review these approaches in the light of an exact, yet tractable treatment of the electrostatics in a polarizable material, and present our new correction scheme derived from this analysis with well-controlled approximations [Phys. Rev. Lett. 102, 016402 (2009)]. [Preview Abstract] |
Tuesday, March 16, 2010 1:39PM - 2:15PM |
J6.00005: Applications of LSDA+U to defects in semiconductors and calculation of magnetic exchange interactions Invited Speaker: Walter Lambrecht The LSDA+U (local spin density approximation with Hubbard-U corrections) was originally introduced for systems with narrow bands and strong Coulomb interactions. However, it can also be used in a somewhat empirical manner to generate an orbital dependent shift potential to correct LDA band gap underestimates. In this talk I will discuss some aspects of LSDA+U. For example, does LSDA+U give a unique solution? How to choose U? What are the various flavors of LSDA+U? I will show that the ground state of rare-earth nitrides in LSDA+U depends on the symmetry of the starting density matrix and how this relates to Hund's rules and orbital magnetic moment. I will then show how we can use this approach to calculate exchange interactions in Gd pnictide compounds. In combination with the Liechtenstein linear response approach, we calculated exchange interactions in Mn-doped ScN and in Gd pnictides. In those examples we used not only the Uf for f electrons but also a Ud to shift the d-like conduction band up. In a similar manner, we used a Us to shift up the bottom of the s-like conduction band in ZnO and used this approach in an attempt to clear up the controversies over the oxygen vacancy level in ZnO. I will discuss the relation of this approach to other band gap correction approaches such as hybrid functionals and GW. It appears important to not only correct the minimum gap but the gap at various k-points and in fact separately the two band edges. Work along those lines is in progress. [Preview Abstract] |
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