Tufts Rpic Crystal

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Tufts Rpic Crystal

  1. 1. Crystal Growth <ul><li>1.) INTRODUCTION: </li></ul><ul><ul><li>Melt growth, solution growth and vapor growth. </li></ul></ul><ul><li>2.) Process for crystal growth from melt : </li></ul><ul><ul><li>2.1 Directional solidification/Bridgman process. </li></ul></ul><ul><ul><li>2.2 Zone melting and floating zone. </li></ul></ul><ul><ul><li>2.3 Czochralski method. </li></ul></ul><ul><ul><li>2.4 Liquid encapsulated Czochralski. </li></ul></ul><ul><li>3) Convection and segregation </li></ul>
  2. 2. 1) Introduction <ul><li>Motivation for growth of single crystals </li></ul><ul><ul><li>Research (physics/materials): </li></ul></ul><ul><ul><ul><li>Properties of solids are obscured by grain boundaries (to understand solids we must understand crystals). </li></ul></ul></ul><ul><ul><ul><ul><li>Metals </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Semiconductors </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Superconductors </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Protein crystals </li></ul></ul></ul></ul>
  3. 3. Applications <ul><ul><ul><li>Uniform properties on microscopic level </li></ul></ul></ul><ul><ul><ul><ul><li>Micro-devices: electronic, optical, and mechanical </li></ul></ul></ul></ul><ul><ul><ul><li>No creep, fatigue… </li></ul></ul></ul><ul><ul><ul><li>Beautiful objects </li></ul></ul></ul>
  4. 4. Methods for Crystal Growth <ul><li>Directional solidification from the melt ~ cm/hr </li></ul><ul><li>Solution growth (supersaturation) ~ mm/day </li></ul><ul><li>Vapor growth (sublimation-condensation) ~ µm/hr </li></ul><ul><li>Thin layers </li></ul><ul><li>Boules </li></ul>
  5. 5. a.) Growth from the melt: <ul><li>Conditions: </li></ul><ul><ul><li>Material must melt congruently (no change in composition during melting) e.g. Yttrium iron garnet (YIG) is grown from solutions because it does not melt congruently. </li></ul></ul><ul><ul><li>Material must not decompose before melting. e.g. SiC is grown from vapor phase (sublimation-condensation) because it decomposes before melting. </li></ul></ul><ul><ul><li>Material must not undergo a solid state phase transformation between melting point and room temperature. e.g. SiO 2 is grown from solution (hydrothermal growth) because of a α-β quartz transition at 583°C. </li></ul></ul>
  6. 6. Advantages of solidification: <ul><li>Fast (~ cm/hr ); growth rate depends on heat transfer (not on mass transfer). </li></ul><ul><li>Variety of techniques developed (e.g. crystal pulling and directional and zone solidification). </li></ul>
  7. 7. b.) Growth from solution: <ul><li>For materials that: </li></ul><ul><ul><li>(i) melt non congruently or </li></ul></ul><ul><ul><li>(ii) decompose before melting or </li></ul></ul><ul><ul><li>(iii) undergo a solid state phase transformation before melting or </li></ul></ul><ul><ul><li>(iv) have very high melting point. </li></ul></ul><ul><li>Classification is based on the solvent type. </li></ul><ul><li>Key requirement: High purity solvent which is insoluble in the crystal. </li></ul>
  8. 8. b.1) Molten salt (flux) growth: <ul><li>Common solvents: PbO, PbF 2 , B 2 O 3 , KF. </li></ul><ul><li>Used for oxides with very high melting points (or melt congruently, decompose or undergo a solid phase transformation). </li></ul><ul><li>e.g. Yttrium iron garnet (YIG) is grown from solutions because it does not melt congruently. </li></ul><ul><ul><li>Advantages: carried on at much lower temperatures than melt growth. </li></ul></ul><ul><ul><li>Limitations: very slow; borderline purity, platinum crucibles, stoichiometry is hard to control. </li></ul></ul>
  9. 9. b.2) Metallic solution growth: <ul><li>Liquid phase Epitaxy – for high quality epitaxial layers of III-V compounds and boules; </li></ul><ul><ul><li>GaAs from Ga solution (melt with > 50% Ga). </li></ul></ul><ul><ul><li>GaSb from Ga solution (melt with > 50% Ga). </li></ul></ul><ul><ul><li>Terary III-V compounds (solid solutions of III-V compounds): Ga 1-x ln x As, GaAs x P 1-x . </li></ul></ul><ul><ul><ul><li>Advantages: growth at lower temperatures than melt growth yields high quality. </li></ul></ul></ul><ul><ul><ul><li>Limitations: very slow = small crystals or thin layers. </li></ul></ul></ul>
  10. 10. b.3) Hydrothermal growth: <ul><li>Aqueous solution at high temperature and pressure (e.g. SiO 2 is grown by hydrothermal growth at 2000 bars and 400 °C because of α-β quartz transition at 583°C). </li></ul>
  11. 11. c.) Growth from the vapor phase: <ul><li>Boule growth: only when other methods are not useful (SiC, AlN sublimation-condensation). </li></ul><ul><li>Thin layers, i.e., vapor phase epitaxy: extensively used (chemical vapor deposition, sputtering). E.g. SiC is grown from vapor phase (sublimation-condensation) because it decomposes before melting. </li></ul>
  12. 12. 2) Processes for crystal growth from the melt : <ul><li>2.1 Directional solidification, i.e. Bridgman process </li></ul><ul><li>2.2 Czochralski Method (CZ) and LEC </li></ul><ul><li>2.3 Zone melting and floating zone (FZ) </li></ul>
  13. 14. It’s a Boy!! Born May 8, 2001 at 10:35 p.m. Weight: 14 lbs, 9 oz Length: 15 inches Crystal growth furnace for SUBSA investigation, destined for Space Station Alpha in May 2002.
  14. 15. Directional Solidification, i.e. Vertical Bridgman Growth <ul><li>Charge and the seed are placed into the crucible </li></ul><ul><li>Conservative process: no material is added or removed from either solid or liquid phase, except by crystallization (R.A. Laudise). </li></ul><ul><li>Axial temperature gradient is imposed along the crucible. </li></ul>
  15. 16. <ul><li>Growth: Interface is advanced by moving the container or the gradient (furnace/ heat source). </li></ul><ul><li>Seeding: part of the seed is molten </li></ul>
  16. 17. Advantages of the Bridgman Process: <ul><ul><li>Simple: in confined growth, the shape of the crystal is defined by the container. </li></ul></ul><ul><ul><li>Radial temperature gradients are not needed to control the crystal shape. </li></ul></ul><ul><ul><li>Low thermal stresses result in low level of stress-induced dislocations. </li></ul></ul><ul><ul><li>Crystals may be grown in sealed ampules (stoichiometry of melts with volatile constitutes is easy to control). </li></ul></ul><ul><ul><li>Relatively low level of natural convection; Melt exposed to stabilizing temperature gradients (VB only). </li></ul></ul><ul><ul><li>Process requires little attention (maintenance). </li></ul></ul>
  17. 18. <ul><li>Drawbacks </li></ul><ul><ul><li>Confined growth: container pressure on the crystal during cooling. </li></ul></ul><ul><ul><li>Hard to observe the seeding process and growing crystal. </li></ul></ul><ul><ul><li>Level of natural convection changes as the melt is depleted, forced convection is hard to impose. </li></ul></ul><ul><ul><li>Ampule and seed preparation, sealing, etc., does not lend itself to high throughput production. </li></ul></ul><ul><li>Applications: </li></ul><ul><ul><li>Melts with volatile constituents: III-V (GaAs, lnP, GaSb) and II-VI compounds (CdTe). </li></ul></ul><ul><ul><li>Ternary compounds (Ga1-lnxAs, Ga1-xlnxSb, Hg1-xCdxTe). </li></ul></ul>
  18. 19. Liquid Encapsulation Advantages: Properties of a good encapsulant - Prevents contact between the crystal and the melt - Reduced nucleation - Thermal stresses are reduced - Reduced evaporation - Melting temperature lower than the crystal - Low vapor pressure - Density lower than the density of the melt - No reaction with the melt or the crucible Best encapsulans: - B 2 O 3 - LiCl, KCl, CaCl2, NaCl Crucible Encapsulant Melt Crystal
  19. 20. Bridgman growth with the Submerged Baffle <ul><li>H ~ 1 cm </li></ul><ul><li>low dT/dr </li></ul><ul><li>no free surface </li></ul><ul><li>forced convection </li></ul><ul><li>H(t) ~10 cm </li></ul><ul><li>large dT/dr </li></ul><ul><li>free surface </li></ul>Gr  g     T  H 3  2
  20. 21. 2.2 Czochralski Method (CZ): <ul><li>Conservative process: no material is added or removed from either solid or liquid phase, except by crystallization. </li></ul><ul><li>Charge is held at temperature slightly above melting point. </li></ul><ul><li>Seed is dipped into the melt and slowly withdrawn. </li></ul><ul><li>Crystal grows as the atoms from the melt adhere themselves to the seed. </li></ul>
  21. 22. Advantages: <ul><ul><li>Growth from free surface (accommodates volume change). </li></ul></ul><ul><ul><li>Crystal can be observed. </li></ul></ul><ul><ul><li>Forced convection easy to impose. </li></ul></ul><ul><ul><li>High throughput; large crystals can be obtained. </li></ul></ul><ul><ul><li>High crystalline perfection can be achieved. </li></ul></ul><ul><ul><li>Good radial homogeneity. </li></ul></ul>
  22. 23. Drawbacks: <ul><li>Materials with high vapor pressure can not be grown. </li></ul><ul><li>Batch process; hard to adapt for continuous growth; result: axial segregation. </li></ul><ul><li>The crystal has to be rotated; rotation of the crucible is desirable. </li></ul><ul><li>Process requires continuous attention (seeding, necking) and sophisticated control. </li></ul>
  23. 24. Drawbacks (continued): <ul><li>Melt is thermally upside down. </li></ul><ul><li>Temperature gradients are high to control the crystal diameter. </li></ul><ul><li>High thermal stresses. </li></ul><ul><li>Shape and size of the crystal is hard to control if temperature gradients are low. </li></ul>
  24. 25. Liquid encapsulated Czochralski method (LEC) <ul><li>Advantages: </li></ul><ul><ul><li>Materials with high vapor pressure can be grown. </li></ul></ul><ul><ul><li>Retains most of CZ advantages: growth from a free surface, etc. </li></ul></ul><ul><ul><li>B2O3 prevents reaction between melt and crucible: prevents reaction between melt and ambient; dissloves oxides (eg. Ga2O3). </li></ul></ul>
  25. 26. Drawbacks: <ul><ul><li>Some loss of volatile constituent. </li></ul></ul><ul><ul><li>“ Contamination” by B 2 O 3 . </li></ul></ul><ul><ul><li>B 2 O 3 is too viscous below 1000 °C. </li></ul></ul><ul><ul><li>Encapsulant becomes opaque towards the end of growth. </li></ul></ul>
  26. 27. 2.3 Zone melting and floating zone: <ul><ul><li>Nonconservative process: material is added to molten region. </li></ul></ul><ul><ul><li>Only a small part of th charge is molten (except the seed). </li></ul></ul><ul><ul><li>Axial temperature gradient is imposed along the crucible </li></ul></ul><ul><ul><li>Molten zone (the interface) is advanced by moving the charge or the gradient. </li></ul></ul>
  27. 28. Advantages : <ul><ul><li>Charge is purified by repeated passage of the zone (zone refining). </li></ul></ul><ul><ul><li>Crystals may be grown in sealed ampules or without containers (floating zone). </li></ul></ul><ul><ul><li>Steady-state growth possible. </li></ul></ul><ul><ul><li>Zone leveling is possible; can lead to superior axial homogeneity. </li></ul></ul><ul><ul><li>Process requires little attention (maintenance). </li></ul></ul><ul><ul><li>Simple: no need to control the shape of the crystal. </li></ul></ul><ul><ul><li>Radial temperature gradients are high. </li></ul></ul>
  28. 29. Drawbacks : <ul><ul><li>Confined growth (except in floating zone). </li></ul></ul><ul><ul><li>Hard to observe the seeding process and the growing crystal. </li></ul></ul><ul><ul><li>Forced convection is hard to impose (except in floating zone). </li></ul></ul><ul><ul><li>In floating zone, materials with high vapor pressure can not be grown. </li></ul></ul>
  29. 30. 3) Convection and segregation
  30. 31. Enclosure Heated from Below
  31. 32. Natural buoyancy forces moving boundary less difficult predict (at S/L interface) hard to predict, model and control Magnitude: Features: V ~ w L unsteady: Gr > 5,000 turbulent: Driving mech. Forced Convection L and  T = f (time)  ° f (time) Growth process: all CZ, FZ Comparison of Natural and Forced Convection
  32. 33. c) Impose forced convection - Accelerated Crucible Rotation Technique - Coupled Vibrational Stirring - Rotating Baffle Control of Crystal Homogeneity a) Reduce natural convection: - Reduced gravity (µg) - Magnetic fields - Submerged baffle b) Enhance natural convection - centrifuges
  33. 34. No motion of phase boundary Beginning of motion Mass Transfer: Solid-Liquid Interface
  34. 35. Diffusion-controlled segregation Tiller et al.
  35. 36. Perfect Mixing Scheil (1942), Pfann(1952) ∆ f S = change in solid fraction Solidified Fraction, f S • no steady state • axial inhomogeneity (k<<1)
  36. 37. Burton, Prim and Slichter’s BPS Model • assumption: 1-D flow (?) • Stagnant solute layer, at y = 0, v=0 C L = C 0 at x =  BPS at x = 0
  37. 38. Burton, Prim and Slichter’s BPS Model, cont. Levich: Kodera (1953): measurement of D [cm2/s] Levich soulution  -Czochralski only -crucible = finite melt -natural convection, -couterrotation -turbulence
  38. 39. Solute Conservation in CV: Ostrogorsky & Müller: Integral CV approach
  39. 40. Ostrogorsky and Müller: Integral control-volume approach (cont.) <ul><li> D and V D are real physical parameter; analytical solutions exist. </li></ul><ul><li>laminar and turbulent flow </li></ul>a = 1/6 Table 1  D and V ∞ for several important melt growth techniques (CZ=Czochralski, FZ = Floating Zone, Gr = Grashof number) Driving Mechanism Growth Method  D V ∞ Crystal rotation Cz, FZ V∞  L Natural Convection Bridgman V ∞ ~Gr (  /L) Weak natural convection in microgravity Bridgman V ∞ ~Gr(  /L) 1/2
  40. 41. • Cochran's ∞ rotating disc: J.Appl.Phy. 27(1956)686 • Levich (Sparrow and Gregg) Model of Ostrogorsky and Müller and Data of Bridges k eff versus growth rate R and  for Czochralski grown crystals.
  41. 42. Microscopic Inhomogeneity (1  m to 1 mm) <ul><li>Caused by unsteady conditions: </li></ul><ul><ul><li>Unsteady (turbulent) flow, temperature, composition </li></ul></ul><ul><ul><li>Crystal rotation </li></ul></ul><ul><ul><li>Vibrations </li></ul></ul>
  42. 43. Bridgman growth with the Submerged Baffle <ul><li>H ~ 1 cm </li></ul><ul><li>low dT/dr </li></ul><ul><li>no free surface </li></ul><ul><li>forced convection </li></ul><ul><li>H(t) ~10 cm </li></ul><ul><li>large dT/dr </li></ul><ul><li>free surface </li></ul>Gr  g     T  H 3  2
  43. 44. Micro-segregation (a) Bridgman and (b) Baffle Spreading Resistance in 6 cm diameter Ga-doped Ge-2%Si alloy Measurements conducted by M. Lichtensteiger at NASA-MSFC [9]

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