crystal-air surface interphase boundary grain boundary twin boundary stacking faults crystal...
TRANSCRIPT
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
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
• 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
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
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