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Yosuke Harashima , Keith Slevin Department of Physics, Osaka University, Japan

Numerical analysis for the m etal-insulator transition in doped semiconductors using density functional theory in the local density approximation. Yosuke Harashima , Keith Slevin Department of Physics, Osaka University, Japan. Metal-insulator transition in doped semiconductors.

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Yosuke Harashima , Keith Slevin Department of Physics, Osaka University, Japan

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  1. Numerical analysis for the metal-insulator transitionin doped semiconductorsusing density functional theory in the local density approximation Yosuke Harashima, Keith Slevin Department of Physics, Osaka University, Japan

  2. Metal-insulator transition in doped semiconductors • Disorder • Metal-insulator transition • Electron-electron interaction • ex. Critical exponent

  3. Impurity band for low concentration

  4. For high concentration

  5. Model • Donor impurities distributed randomly in space • Long range Coulomb interaction for electron-electron pairs

  6. Schrödinger equation for impurity band • = 0.32 • = 12.0

  7. Kohn-Sham equations • Auxiliary system:

  8. Exchange-correlation energy in an effective medium

  9. Local density approximation

  10. Calculation details • Real space finite difference approximation • In this study M=2 and h=18[Bohr] • Complete spin polarized case (for simplicity)

  11. Multi-fractal analysis for Kohn-Sham orbital • A. Rodriguez et al (2011)

  12. Asymptotic behavior • Extended states: • Localized states:

  13. Metal-Insulator Transition around nD ≈ 1.5 [10-7 Bohr-3]

  14. Density of states • Periodic system • Disordered system

  15. nD ≈ 0.6 [10-7 Bohr-3]

  16. nD ≈ 1.4 [10-7 Bohr-3]

  17. nD ≈ 1.9 [10-7 Bohr-3]

  18. Summary • The model taking into account, • Random positions of impurities. • Electron-electron interaction using DFT in LDA. • The existence of the Metal-Insulator transition around nD ≈ 1.5 [10-7 Bohr-3] is shown in this model. • We are calculating the critical exponents. • As extension, • Spin of electrons using local spin density approximation. • Compensation of impurities.

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