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Atomic Orbitals

Atomic Orbitals. s -orbitals. p -orbitals. d -orbitals. H B. H A. H A - H B. = H 2. Chemical Bonding. Overlap of half-filled orbitals - bond formation. Formation of Molecular Hydrogen from Atoms. Overlap of filled orbitals - no bonding. Periodic Chart. Crystal Bonding.

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Atomic Orbitals

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  1. Atomic Orbitals s-orbitals p-orbitals d-orbitals

  2. HB HA HA - HB = H2 Chemical Bonding Overlap of half-filled orbitals - bond formation Formation of Molecular Hydrogen from Atoms Overlap of filled orbitals - no bonding

  3. Periodic Chart

  4. Crystal Bonding sp3 antibonding orbitals sp3 bonding orbitals Silicon Crystal Bonding

  5. Semiconductor Band Structures Silicon Germanium Gallium Arsenide

  6. Intrinsic Semiconductor Aggregate Band Structure Fermi-Dirac Distribution

  7. n-type Semiconductor Aggregate Band Structure Donor Ionization Fermi-Dirac Distribution

  8. p-type Semiconductor Aggregate Band Structure Acceptor Ionization Fermi-Dirac Distribution

  9. Temperature Dependence Fermi level shift in extrinsic silicon Mobile electron concentration (ND= 1.15(1016) cm3)

  10. No Field Field Present Pictorial representation of carrier trajectory Carrier Mobility Carrier drift velocity vs applied field in intrinsic silicon

  11. Effect of Dopant Impurities Effect of total dopant concentration on carrier mobility Resistivity of bulk silicon as a function of net dopant concentration

  12. The Seven Crystal Systems

  13. Bravais Lattices

  14. Diamond Cubic Lattice a = lattice parameter; length of cubic unit cell edge Silicon atoms have tetrahedral coordination in a FCC (face centered cubic) Bravais lattice

  15. z z z y y y x x x Miller Indices 100 110 111

  16. Diamond Cubic Model 100 110 111

  17. Cleavage Planes Crystals naturally have cleavage planes along which they are easily broken. These correspond to crystal planes of low bond density. In the diamond cubic structure, cleavage occurs along 110 planes.

  18. [100] Orientation

  19. [110] Orientation

  20. [111] Orientation

  21. [100] Cleavage

  22. [111] Cleavage

  23. Czochralski Process

  24. Czochralski Process Equipment Image courtesy Microchemicals

  25. Czochralski Factory and Boules

  26. CZ Growth under Rapid Stirring Distribution Coefficients CZ Dopant Profiles under Conditions of Rapid Stirring

  27. Enrichment at the Melt Interface

  28. Zone Refining Si Ingot Heater Ingot slowly passes through the needle’s eye heater so that the molten zone is “swept” through the ingot from one end to the other

  29. Single Pass FZ Process

  30. Multiple Pass FZ Process Almost arbitrarily pure silicon can be obtained by multiple pass zone refining.

  31. “Dangling Bonds” Vacancy (Schottky Defect)

  32. Self-Interstital

  33. Dislocations Edge Dislocation Screw Dislocation

  34. Burgers Vector Edge Dislocation Screw Dislocation Dislocations in Silicon [100] [111]

  35. Stacking Faults Intrinsic Stacking Fault Extrinsic Stacking Fault

  36. Vacancy-Interstitial Equilibrium Formation of a Frenkel defect - vacancy-interstitial pair “Chemical” Equilibrium

  37. Thermodynamic Potentials E = Internal Energy H = Enthalpy (heat content) A = Helmholtz Free Energy G = Gibbs Free Energy For condensed phases: E and H are equivalent = internal energy (total system energy) A and G are equivalent = free energy (energy available for work) T = Absolute Temperature S = Entropy (disorder) Boltzmann’s relation

  38. Internal Gettering Gettering removes harmful impurities from the front side of the wafer rendering them electrically innocuous. High temperature anneal - denuded zone formation Low temperature anneal - nucleation Intermediate temperature anneal - precipitate growth

  39. Oxygen Solubility in Silicon

  40. Oxygen Outdiffusion

  41. Precipitate Free Energy a) - Free energy of formation of a spherical precipitate as a function of radius b) - Saturated solid solution of B (e.g., interstitial oxygen) in A (e.g., silicon crystal) c) - Nucleus formation

  42. Substrate Characterization by XRD Bragg pattern - [hk0], [h0l], or [0kl]

  43. Wafer Finishing Ingot slicing into raw wafers Schematic of chemical mechanical polishing

  44. Vapor-Liquid-Solid (VLS) Growth Si nanowires grown by VLS (at IBM)

  45. liquid A B solid Gold-Silicon Eutectic A – eutectic melt mixed with solid gold B – eutectic melt mixed with solid silicon

  46. Non-bridging oxygen SiO4 tetrahedron Silanol Silicon Dioxide Network

  47. Thermal Oxidation One dimensional model of oxide growth Deal-Grove growth kinetics

  48. Oxidation Kinetics Rate constants for wet and dry oxidation on [100] and [111] surfaces

  49. Linear Rate Constant Orientation dependence for [100] and [111] surfaces affects only the “pre-exponential” factor and not the activation energy

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