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Properties of Point Defects in Semiconductors

Properties of Point Defects in Semiconductors. Dr. Blair R. Tuttle Assistant Professor of Physics Penn State University at Erie, The Behrend College. Semiconductor review and motivation Point defect calculations using ab initio DFT Applications from recent research:

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Properties of Point Defects in Semiconductors

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  1. Properties of Point Defects in Semiconductors Dr. Blair R. Tuttle Assistant Professor of Physics Penn State University at Erie, The Behrend College

  2. Semiconductor review and motivation Point defect calculations using ab initio DFT Applications from recent research: Donor and acceptor levels for atomic H in c-Si Paramagnetic defects Energies of H in Si environments Hydrogen in amorphous silicon Hydrogen at Si-SiO2 interface Outline © Blair Tuttle 2001

  3. Properties of solids Semiconductors Conductors Insulators E E E Band Gap > 2 eV Band Gap< 2 eV occupied N N N • Wires • Switches • Barriers © Blair Tuttle 2001

  4. Silicon as prototype semiconductor Tetrahedral Coordination 4 bonds per Si Diamond Structure: E-Fermi N Semiconductor: Eg = 1.1 eV : E © Blair Tuttle 2001

  5. Doping in c-Si P-type Boron acceptors N-type Phosphorous donors e - h+ -1 +1 N E E © Blair Tuttle 2001

  6. Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Gate Source Drain Lds ~ 90 nm tox ~ 2.0 nm Vsd ~ 2.0 V © Blair Tuttle 2001

  7. Compensates both p-type and n-type doping Passivates dangling bonds at surfaces and interfaces Hydrogen related charge traps in MOSFETs Participates in metastable defect formation in poly- and amorphous silicon Forms very mobile H2 molecules in bulk Si Forms large platelets used for cleaving silicon Hydrogen in Silicon Systems For more details see reference below and references therein: C. Van de Walle and B. Tuttle, “Theory of hydrogen in silicon devices” IEEE Transactions on Electron Devices, vol. 47 pg. 1779 (2000) © Blair Tuttle 2001

  8. Etot = total energy for bulk cell with Nsi silicon atoms and NH hydrogen atoms. mH , mSi = the chemical potential for hydrogen, Si The charge q and the Fermi energy (EF). Concentration of defects: H in Si © Blair Tuttle 2001

  9. Donor level is the Fermi Energy when: Calculate Eform for H at its local minima for each charge state q = +1,0,-1 Calculate valence band maximum to compare charge states Acceptor and Donor levels for atomic hydrogen in crystalline silicon © Blair Tuttle 2001

  10. Semi-empirical Tight binding (TB) Classical Potentials Ab intio Quantum Monte Carlo (QMC) Hartree-Fock methods (HF) Density Function Theory (DFT) Choose Method For more details on a state-of-the-art implimentation of DFT: Kresse and Furthmuller,”Efficient iterative schemes for ab intio total-energy calculations using a plane wave basis set” Phys. Rev. B vol. 54 pg. 11169 (1996). http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html © Blair Tuttle 2001

  11. Solve the Kohn-Sham equations: Review of DFT For more details see review articles below: W. E. Pickett, “Pseudopotential methods in condensed matter applications” Computer Physics Reports, vol. 9 pg. 115 (1989). M. C. Payne et al. “Iterative minimization techniques for ab initio total-energy calculations” Review of Modern Physics vol. 64 pg. 1045 (1992). © Blair Tuttle 2001

  12. Local density approximation (LDA) Calculates exhange-correlation energy (Eex,cor) based only on the local charge density Rigorous for slowly varying charge density General gradient approximations (GGA) Calculates Eex,cor using density and gradients Improves many shortcoming of LDA Choose {ex, cor} functional For more details see reference below: Kurth, Perdew, and Blaha “Molecular and solid-state tests of density functional approximations: LSD, GGAs, and meta-GGAs” Int. J. of Quantum Chem. Vol. 75 pg. 889 ( 1999). © Blair Tuttle 2001

  13. Bond lengths, lattice constants ~ 1 – 5 % (low) Binding and cohesive energies ~ 10 % (high) Vibrational frequencies ~ 5 – 10 % (low) Valence bands good valence band offsets for semiconductors Wavefunctions good Hyperfine parameters Results of DFT-LDA © Blair Tuttle 2001

  14. Poor when charge gradients vary significantly (better in GGA) Atomic energies too low: EH = -13.0 eV Barriers to molecular dissociation often low, Example: H + H2 = H3 Energy of Phases, Ex: Stishovite vs Quartz Semiconductor band gaps poor ~ 50 % low Shortcomings of DFT-LDA © Blair Tuttle 2001

  15. Cluster models (20 – 1000 atoms) Defect-surface interactions Passivate cluster surface with hydrogen Wavefunctions localized Periodic supercell (20 – 1000 atoms) Defect-defect interactions Wavefunctions de-localized Bands well defined Choose boundary conditions © Blair Tuttle 2001

  16. Localized pseudo-atomic orbitals Efficient but not easy to use or improve results Plane Waves Easy to use and improve results: Choose basis for wavefunctions © Blair Tuttle 2001

  17. Convergence calculation Total energy for defect at minima Relative energies for defect in various positions Accuracy vs. Computational Cost Variables to converge Basis set size Supercell size Reciprocal space integration Spin polarization (include or not) Testing Convergence © Blair Tuttle 2001

  18. Plane waves are a complete basis so crank up the G vectors until convergence is reached. Convergence: Basis size DE [eV] EPW [Ryd.] © Blair Tuttle 2001

  19. Prevent defect-defect interactions. Electronic localization of defect level as determined by k-point integration Steric relaxations: di-vancancy in silicon Coulombic interaction of charged defects Convergence: Supercell size For more details see reference below and references therein: 1. C. Van de Walle and B. Tuttle, “Theory of hydrogen in silicon devices” IEEE Transactions on Electron Devices, vol. 47 pg. 1779 (2000) 2. http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html © Blair Tuttle 2001

  20. Reciprocal space integration For each supercell size, converge the number of “special” k-points Data for 8 atom supercell: Convergence: k-point sampling © Blair Tuttle 2001

  21. Convergence data at Epw = 15 Ryd. N=64, Kpt=2x2x2 results converged to within 0.1 eV © Blair Tuttle 2001

  22. Bandstructure of 64 atom supercell Bulk c-Si Bulk c-Si + H+BC L G X L G X Bulk bands retained even with defect in calculation © Blair Tuttle 2001

  23. Results for H in c-Si EForm Eglda H+1 • H0 and H+1 at global minimum • H-1 at stationary point or saddle point • Will lower its energy by moving to Td site H0 H-1 EFermi 0.5 eV 1.0 eV For more info see: C. G. Van de Walle, “Hydrogen in crystalline semiconductors” Deep Centers I Semiconductors , Ed. by S. T. Pantelides, pg. 899 (1992). © Blair Tuttle 2001

  24. Hydrogen in Silicon Solid = LDA, Dashed =LDA + rigid scissor shift E in eV E(0,-)E(+,0) E(+,-) U-corr Exp. 0.51 0.92 0.72 -0.41 LDA 0.46 1.07 0.77 -0.61 © Blair Tuttle 2001

  25. Si 3sp3 H 1s 001 H0 defect level chemistry 110 Defect level derived from Si-Si anti-bonding states For more info see: C. G. Van de Walle, “Hydrogen in crystalline semiconductors” Deep Centers I Semiconductors , Ed. by S. T. Pantelides, pg. 899 (1992). © Blair Tuttle 2001

  26. Metal Oxide Semiconductor Field Effect Transistor (MOSFET) Gate Source Drain Lds ~ 90 nm tox ~ 2.0 nm Vsd ~ 2.0 V © Blair Tuttle 2001

  27. Si 3sp3 H 1s 001 H0 in silicon = paramagnetic defect 110 For more info see: C. G. Van de Walle and P. Blochl, “First principles calculations of hyperfine parameters” Phys. Rev. B vol. 47 pg. 4244 (1993). © Blair Tuttle 2001

  28. Atomic Ho in c-Si D center defects in a-Si Pb centers at Si-SiO2 interfaces E’ centers in SiO2 Atomic Ho in SiO2 Paramagnetic Defects © Blair Tuttle 2001

  29. Hyperfine parameters All electron wavefunctions are needed !!!! For more info see: C. G. Van de Walle and P. Blochl, “First principles calculations of hyperfine parameters” Phys. Rev. B vol. 47 pg. 4244 (1993). © Blair Tuttle 2001

  30. Hyperfine parameters for Sidb Isotropic Parameters For more details see: B. Tuttle, “Hydrogen and Pb defects at the Si(111)-SiO2 interface” Phys. Rev. B vol. 60 pg. 2631 (1999). © Blair Tuttle 2001

  31. Binding energy for hydrogen passivation Related to the desorption energy Compare to vacuum annealing experiments H passivation of defects © Blair Tuttle 2001

  32. Si 3sp3 H 1s 001 Atomic hydrogen in Silicon 110 H0 min. energy at BC site, EB ~ 0.5 --1.1 eV In disordered Si, strain lowers EB ~ 0.25 eV per 0.1 Ang H+ (BC) and H-(T): Negative U impurity Neutral hydrogen in Si is a paramagnetic defect © Blair Tuttle 2001

  33. H2 complexes in Silicon H2 min. at T site EB ~ 1.9 eV per H atom 0.6 eV less than free space H2* along <111> direction EB ~ 1.6 eV per H atom H+ (BC) + H_(T) © Blair Tuttle 2001

  34. H passivation of strained bonds Si 3sp3 2 H 1s 2 (Si-H) Hydrogen atoms remove electronic band tail states in a-Si EB ~ 2.3 eV per H atom (roughly the same as H2 in free space) Negative U complex (equilibrium state includes only 0 or 2 H) © Blair Tuttle 2001

  35. Passivation of a 5-fold Si defect Si-H Bond Frustrated Bond • 5-fold Si defects are paramagnetic: • D center in a-Si & Pb center at Si-SiO2 interface • EB ~ 2.45 eV per H for Si-H at Si-interstitials in c-Si • EB ~ 2.55 eV per H for Si-H at a 5-fold defect in a-Si © Blair Tuttle 2001

  36. H passivation of dangling bonds Si 3sp3 H 1s Si dangling bonds paramagnetic EB ~ 4.1 eV for H-SiH3 EB ~ 3.6 eV for pre-existing isolated Sidb in c-Si EB ~ 3.1 - 3.6 eV for pre-existing isolated Sidb in a-Si © Blair Tuttle 2001

  37. Hydrogen in SiO2 H0 favors open void EB ~ 0.1 eV Very little experimental info on charge states Defect is paramagnetic H2 free to rotate EB ~ 2.3 eV per H atom © Blair Tuttle 2001

  38. Binding Energy per H (eV) 0.0 1.0 2.0 3.0 4.0 H at pre-existing isolated silicon dangling bond (db) H0 (free) & SiO2 H in c-Si H at pre-existing db with Si-H in a cluster e.g. a Si vacancy H2* in c-Si H2 (free) & SiO2 H2 in c-Si H at pre-existing “frustrated” Si bond (Si-H H-Si) in a-Si © Blair Tuttle 2001

  39. Hydrogenated Amorphous Silicon Egap ~1.8 eV ln(DOS) Energy Electronic Band Tails  Strained Si-Si bonds Intrinsic paramagnetic defects: [D] ~ 1016 cm-3 5-15 % Hydrogen  [H]~ 1021 cm-3 © Blair Tuttle 2001

  40. Si-H behavior in a-Si:H • [D] concentration thermally activated with Ed ~ 0.3 eV • Hydrogen diffusion thermally activated Ea ~ 1.5 eV 1019 Spin Density [cm-3] 1018 1018 1017 Spin Density [cm-3] 1017 1019 1020 1021 H Evolved [cm-3] Hydrogen in (Si-H H-Si) clusters evolves first Dilute Si-H bonds stronger 1016 1.2 1.6 2.0 1000/T [ k-1] S. Zafar and A. Schiff, “Hydrogen and defects in amorphous silicon” Phys. Rev. Lett. Vol. 66 pg. 1493 (1991). © Blair Tuttle 2001

  41. Simulated annealing Monte Carlo: bond switching Molecular Dynamics: add defects Compare results to experiments Modelling a-Si:H V q © Blair Tuttle 2001

  42. Energy of H in a-Si EB (eV) 0.0 1.0 H Ea~1.5 eV Clustered Si-H 2.0 Ed~.3 eV H at frustrated bonds 3.0 Isolated Si-H bonds 4.0 B. Tuttle and J. B. Adams, “Ab initio study of H in amorphous silicon” Phys. Rev. B, vol. 57 pg. 12859 (1998). © Blair Tuttle 2001

  43. Si-SiO2 Interface M. Staedele, B. R. Tuttle and K. Hess, 'Tunneling through unltrathin SiO2 gate oxide from microscopic models', J. Appl.Phys. {\bf 89}, 348 (2001). © Blair Tuttle 2001

  44. Thermal vacuum annealing measurements [PB] versus time, pressure and temperature Data fit by first-order kinetics Rate limiting step: EB = 2.6 eV Si-H dissociation at Si-SiO2 interface H ER EB=2.6 eV SiO2 (Si-H) Sidb [Si-H] [ Sidb + H ] Si © Blair Tuttle 2001 K. Brower and Meyers, Appl. Phys. Lett. Vol. 57, pg. 162 (1990)..

  45. Energy of H at Si(111)-SiO2 interface EB (eV) 0.0 H in SiO2 1.0 H in Si EB~2.6 eV 2.0 3.0 Isolated Si-H bonds 4.0 © Blair Tuttle 2001

  46. Si-H Desorption Paths © Blair Tuttle 2001

  47. H2 passivation of Sidb (or Pb ) Thermal Annealing Experiments H2 H ER EB=1.6 eV SiO2 Pb (PbH) [Pb + H2 ] [ (PbH) + H ] Si Possible Reactions Theory 1. Sidb + H2(SiO2) => Si-H + H(SiO2) ER = 1.0 eV 2. Sidb + H2(SiO2) => Si-H + H(Si) ER = 0.0 eV © Blair Tuttle 2001

  48. Path for H2 dissociation and for H-D exchange Exchange of deeply trapped H and transport H is low ~ 0.2 eV © Blair Tuttle 2001 B. Tuttle and C. Van de Walle, “Exchange of deeply trapped and interstitial H in Si” Phys. Rev. B vol. 59 pg. 5493 (1999).

  49. H2 dissociation in SiO2 Thermal Annealing Experiments H H2 ER EB= 4.1 eV H SiO2 [H 2] [ H + H ] Si Reactions Theory 1. H2 (SiO2) => 2 H(SiO2) ER = 4.4 eV 2. H2 (SiO2) => 2 H(Si) ER = 2.4 eV © Blair Tuttle 2001

  50. H0 diffusion in SiO2 Energy Contours (0.1 eV) Y position (Ang.) X position (Ang.) • Experiments  Ea = 0.05 – 1.0 eV • Classical Potentials  Ea = 0.6 -- 0.9 eV • LDA & CTS Theory: • Ea = 0.2 eV • Do = 8.1x 10-4 cm2/sec © Blair Tuttle 2001 B. Tuttle, “Energetics and diffusion of hydrogen in SiO2” Phys. Rev. B vol. 61 pg. 4417 (2000).

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