The Muppet’s Guide to:The Structure and Dynamics of Solids

5. Crystal Growth II and Defects

Crystal Growth

• All growth processes require conditions that promote formation of a crystal such as:

– Condensing from a supersaturated solution

– Freezing from a melt

– Evaporation

• Different methods needed for different materials

Growth from SolutionEvaporation of the solvent causes super-saturation and hence the solute comes out of solution

Growth from the melt

• Czochralski growth– Liquid encapsulated Czochralski growth

• Bridgman growth (directional freezing)– Interface shape– Thermal considerations

Czochralski growth (crystal pulling)

Czochralski growth (crystal pulling)

• A seed is lowered into the melt

• The seed is rotated and withdrawn

Czochralski growth (crystal pulling)

• A seed is lowered into the melt

• The seed is rotated and withdrawn

• A rod or boule of crystal forms

• Industry standard for Si and Ge

Pure Material

Melt + Impurities

Czochralski growth

• A seed is lowered into the melt

• The seed is rotated and withdrawn

• A rod or boule of crystal forms

• Industry standard for Si and Ge

"Smithsonian", Jan 2000, Vol 30, No. 10

Liquid encapsulated Czochralski growth

• Growth takes place in a pressure vessel

• The melt is covered in boric oxide (B2O3) which is viscous and un-reactive

• This allows an over-pressure of inert gas to be applied so as to contain the melt – important for GaAs and CdTe (volatile components)

Bridgman growth

• Boat is moved through the temperature gradient in a tube furnace

• Growth of the crystal is by directional freezing of the melt

T

x

solidliquid

Directional freezing

• Material is contained in a capsule

• A concave growth surface allows secondary nuclei to form at the walls of the tube

• A convex growth surface causes secondary nuclei to be crowded out by the main crystal in the advancing solid

Freezing direction, x

solidliquid

solidliquid

Hot Zone or Float ZoneCrucible free growth or anneal

Also used to remove impurities

Impurities

Crystal

Melt

Ck

C

Segregation coefficient:

For k<1, impurities stay in melt

Diffusion mechanism

Layer by Layer Growth

For epitaxial growth we want the layer to stick:

• Energy to remain on surface, Ea

• Energy to diffuse on surface, Ed

• Cohesive energy, Ec

• Strain Energy, (U)

Thin film Growth Modes

Growth mode depends on energies when atoms arrive at substrateImage Courtesy, Nessa Fereshteh Saniee, PhD Thesis, UoW 2014

Epitaxial growth

• Molecular beam epitaxy

Co-evaporation of the elements that make the compound at UHV

Base pressure of chamber <10-10Torr. Growth pressure <10-9Torr

Sputtering

Base pressure of system <10-7 Torr. Growth in Ar <10-3 Torr

Pulsed Laser Deposition (PLD)

Images Courtesy, Nessa Fereshteh Saniee, PhD Thesis, UoW 2014

Laser produces a plasma of material

which is then deposited on a

substrate. Good for oxides and high

melting point materials

Heterostructures

Dislocation/Disorder

Lattice Match through Rotations

Pt[100]//FeCo[110]

45° Rotation of unit cells

aPt=3.9242ÅaFe=2.8665Å

2 4.0538Fea A

4.0538 3.92423.3%

3.9242Miss match

inac.cea.fr/Images/astImg/479_1.png

Disorder in crystalline materials

• No such thing as a perfectly ordered material• Many materials are technologically of value because

they are disordered/imperfect in some way:

silicon devices – controlled levels of deliberate impurity additions (ppb) p-type : B Si B + h

n-type : P Si P + e

steels – additions of 0.1 to 1 at.% other metals to improve mechanical properties and corrosion resistance

• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects

Types of Imperfections

• Dislocations Line defects

• Grain Boundaries Area defects

Imperfections in Solids

Linear Defects (Dislocations)– Are one-dimensional defects around which atoms are

misaligned• Edge dislocation:

– extra half-plane of atoms inserted in a crystal structure– b to dislocation line

• Screw dislocation:– spiral planar ramp resulting from shear deformation– b to dislocation line

Burger’s vector, b: measure of the magnitude and direction of lattice distortion.

Dislocations – linear defectsSource:- growth- stress- temperature

Evidence:- metals more deformable than

predicted (but can be strengthened by impurities)

- spiral growths on surface of some crystals

- reactions occur at active surface sites

Types: edge, screw, intermediate

Transmission electron micrograph of Ti alloy – dark lines are dislocations(Callister: Materials Science and Engineering)

Edge dislocation

– partial plane of atoms

– lattice distorted where plane ends

Dislocations characterised by the Burgers vector, b-for metals, b points in a close-packed direction and equals the interatomic spacing

(Callister: Materials Science and Engineering)

Heterostructures

ct t┬

Buffer Layers

┬ ┬

┬

Screw dislocation• partial slip of a crystal

• on one side of dislocation line, crystal has undergone slip; on other side, crystal is normal

• continued application of shear stress causes dislocation to move through crystal

Shear stress

(Callister: Materials Science and Engineering)

Edge, Screw, and Mixed Dislocations

Edge

Screw

Mixed

(Callister: Materials Science and Engineering)

Interfacial (planar) defects

• boundaries separating regions of different crystal structure or crystallographic orientation– External surfaces (see final section of

module)– Internal boundaries

• Layer Interfaces (2D)• Region Interfaces (3D)

• Freezing - result of casting of molten material– 2 steps

• Nuclei form • Nuclei grow to form crystals• Crystals grow until they meet each other

– grain structure

Planar Defects in Solids

nuclei crystals growing grain structureliquid

(Callister: Materials Science and Engineering)

Polycrystalline Materials

Grain Boundaries• regions between crystals• transition from lattice of one

region to that of the other• slightly disordered• low density in grain

boundaries– high mobility– high diffusivity– high chemical reactivity

Adapted from Fig. 4.7, Callister 7e.

Grain boundaries

D = b/

b

Internal surfaces of a single crystal where ideal domains (mosaic) meet with some misalignment: high-angle and small(low)-angle.

NB – in polycrystalline materials, grain boundaries are more extensive and may even separate different phases

Small-angle grain boundary equivalent to linear array of edge dislocations

bonding not fully satisfied region of higher energy, more reactive, impurities present.

(Callister: Materials Science and Engineering)

Planar Defects in Solids 2

• Another case is a twin boundary (plane) – Essentially a reflection of atom positions across the twin

plane.

• Stacking faults– For FCC metals an error in ABCABC packing sequence– Ex: ABCABABC

(Callister: Materials Science and Engineering)