Crystal-Air surfaceInterphaseboundary

Grainboundary

Twin Boundary

Stacking Faults

Crystal BoundaryCrystal-Crystal Low

angle

Highangle

2D DEFECTS(Surface / Interface)

Anti-phase Boundary

Homophase

Low angle

High angle

Based on axis

Based on angle of rotation

Based on Lattice Models

Twist

Tilt

Mixed

Special

Random

CSL/Other

Based on Geometryof the Boundary plane

Curved

Faceted

Mixed

Picture ARM-UC Berkeley4

Curtesy S. Van Tenderloo

Interphase

Low angle

High angle

Based on axis

Based on angle of rotation

Based on Lattice Models

Twist

Tilt

Mixed

Special

Random

Epitaxial/Coherent

Based on Geometryof the Boundary plane

Curved

Faceted

Mixed

Semicoherent

Incoherent

Wulff-type constructions

Coherence at interfaces

• Coherent interface means an interface in which the atoms match up on a 1-to-1 basis (even if some elastic strain is present).

• Incoherent interface means an interface in which the atomic structure is disordered.

• Semi-coherent interface means an interface in which the atoms match up, but only on a local basis, with defects (dislocations) in between.

Coherent interfaces

• Coherent interface means an interface in which the atoms match up on a 1-to-1 basis (even if some elastic strain is present).

• Near identical lattice parameters, often thin layers of A on B

Incoherent interfaces

• Incoherent interface means an interface in which the atomic structure is disordered.

• General case, analogous to a general high-angle grain boundary (roughly)

Semi-coherent interfaces

• Semi-coherent interface means an interface in which the atoms match up, but only on a local basis, with defects (dislocations) in between.

• Comparable to a low-angle grain boundary with a dislocation array (now called misfit dislocations)

Epitaxy

Britannica Concise Encyclopedia: epitaxy

Process of growing a crystal of a particular orientation on top of another crystal. If both crystals are of the same material, the process is known as homoepitaxy; if the materials are different, it is known as heteroepitaxy. Common types of epitaxy include vapour phase, liquid phase, and solid phase, according to the source of the atoms being arranged on the substrate.

Comment 1: “growth” is not needed here…

Comment 2: often used more generally than this

Main Types of Epitaxy

• Homoepitaxy– Growth of material on the same substrate (Si on Si)

• Pseudomorphic growth– Material adopts the lattice of substrate/matrix

• Coincidence– Material has certain spacings common with

substrate/matrix– Similar to CSL

• Cube-Cube– Major orientations are parallel, e.g. [001]A//[001]

substrate

Heteroepitaxial growth modesFrank-van der

Merwe

1

2

layer-by-layer

Volmer-Weber

trade surface for interface

Stranski-Krastanov

relieve stress

Pseudomorphic Growth

Pseudomorphic Growth

• Consider a layer of “A” on “B”, of thickness t

• Take z normal to film, x in plane• Suppose that lattice of A is larger than that

of B, and would match that of B is strained by exx along x

• Strain energy scales as texx2 (I leave to you

to work this out in detail…) per unit area

Interface Energy

• If A matches the lattice of B, the “bonding” will be good

• Energy of interface per unit area is AB

• Total energy of system– E = t*exx

2 + AB

• Hetero epitaxial growth (“lattice-mismatched” growth) permits the fabrication of dissimilar materials on the same substrate

• Strain in the growing film depends on thickness and mismatch

Thin layer - the film will elastically deform to match the in-plane lattice parameter of the substrate

Thick layer - film will revert to its unstrained lattice parameter, with misfit dislocations at the interface with the substrate

AlternativeAlternative

Alternative, dislocations

• Put dislocations at the interfaces of Burgers vector b, separation L

• Assume that these remove all the strain– b/L = exx

• Energy of dislocations per unit area will scale as b2/L (better, use Read-Shockley model or similar, Frank-Van Der Merwe)– Note: no t dependence

T TTT

Energy Balance

• For “phase transition” pseudomorphic to dislocationsE = -C1*t*exx

2 + C2(b2/L)

Dislocation Standoff

T TTT

1

2

T TTT

1 > 2

T TTT

1 < 2

1 = 2

Dislocation energy scales with shear modulus

Energy Balance

• Better, consider a half dislocation loop growing in (kinetics)

• Energy of loop = RC2b2

• Strain energy relieved = C1R2/2exx2

• For transition (remove & 1/2)E = -C1R2exx

2 + RC2b2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2

Strained

Relaxed

R

Classic Nucleation Problem

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 0.5 1 1.5 2

Islands

Similar Cases

• Thin films/precipitates can have different structures– Energy for phase change < interface energy

E = C1*V + C2V2/3(A-B)

3 nm

VNVN

B1-AlNB1-AlN

4.0 4.2 4.4 4.6 4.8

0

1

2

3

4

5

aTiN

zinc-blende

B1T

ota

l e

ne

rgy p

er

un

itce

ll (

eV

)

rela

tive

to

wu

rtzite

AlN

Underlayer Lattice Constant (Å)

Epitaxial Stabilization of B1-AlN in AlN/VN Superlattices

a VN

Energy of B1-AlN and zb-AlN vs. underlayer lattice constant (not including the interfacial energy). [Madan et al.]

zb-AlN B1-AlNw-AlN

Al N

Similar Cases

• Nanoparticles can have different structures– Energy for elastic strain < surface energy

E = C1*V + (CA-CB) V2/3A

Stranski-Krastanow Growth

• Formation of 3D structures (q-dots) preceded by wetting layer

• Relieve strain energy, increase surface energy

E = C1V2/3+C2V

Comments

• Similar to CSL boundaries, one can have dislocations of the coherency between the two materials at an interface

• A step at the interface is normally a different type of dislocation – sessile (immobile)

• There is more….

Interphase

Low angle

High angle

Based on axis

Based on angle of rotation

Based on Lattice Models

Twist

Tilt

Mixed

Special

Random

Epitaxial/Coherent

Based on Geometryof the Boundary plane

Curved

Faceted

Mixed

Semicoherent

Incoherent

Wulff-type constructions

Picture ARM-UC Berkeley30

Curtesy S. Van Tenderloo