# Materials Science and Engineering/Derivations/Models of Micro and Nanoscale Processing/Surfaces and Interfaces
## Pseudomorphic Growth

Occurs with similar lattice constant and structure
Growth types depend on processing conditions
Lattice typically needs to be less than 0.5%
Grow diamond tin and zincblende possible because interface energy is low enough to stabilize phase
Metastable growth - thickness beyond which the phase transforms to stable phase
Interface energy effect becomes smaller

## Misfit Accomodation

Coherently strained - becomes energetically favorable to form misfits
Glide and leave a misfit dislocation
Dislocations can multiply
Nucleate a dislocation at surface
Glide and remove strain at film

### Critical Thickness

Thermodynamic quantity
Kinetics determine whether dislocations form
Depend on temperature - grow metastable film to higher thickness

### Kinetic Phenomena

Treatment of kinetics

#### Mathews

Dislocation motion
Assume Boltzman like jump
Strain energy relief rate is proportional to v
Tendency to overestimate extent to which it is possible to grow strained film

#### Dodson and Tsao

Improved understanding
Dislocation motion also dependent on stress
Revisit with atomistic models

#### Nucleation of a Dislocation Loop

Treat nucleation similar to nucleation of phase transition
Energy per unit length of dislocation and step at the surface
Closed 1D defect loop
Shear over area distance equal to the Burger's vector
Calculate the critical energy to create a stable loop
Nucleation loops very unlikely
Comparison with growth on mesas
Most patches remain dislocation free
Estimate concentration by looking at how density depends on size of patches

## Types of Defects

* Stacking faults
* Interfacial misfit dislocations
* Threading screw dislocations
* Growth spiral
* Stacking fault in film
* Stacking fault in substrate
* Hillock
* Precipitate or void

### Stacking Fault

Two-dimensional feature
Use substrates with ledges on surface
Ensure that the surface is free of patches of oxide
Propagate existing ledges - choice of stacking determined

### Modes of Heteroepitaxy

Transition depends on temperature
Rough film evolves into islands

#### Frank-Van der Merwe Growth

Pseudomorphic growth
Add Ge and achieve pseudomorphic growth

#### Volmer-Weber Growth

Island, "3D"

#### Stranski-Krastanov Growth

Starts 2D, becomes 3D

### Highly strained surface

Reduce strain by developing roughness
Hydrogen induced embrittlement
Rediscover analysis
Strain relief process results in islanding
Pertubation in strained surface
Square wave with amplitude c
Strain energy times volume per unit area
Increase surface area by creating wave
Critical stress
With a critical stress, there is a wavelength above which the pertubation is stable
Longer wavelength corresponds to smaller rate of growth
Surface energy cost too high with high k number
Instability possible through evaporation
Islanding is a method of strain relief
Kinetic mechanism is surface diffusivity
Relieve stress through islanding or misfit dislocation
Activation energy of glide : 0.1 ev
Activation energy of surface diffusion : 0.5 eV
Islanding at high temperature
SiGe greater than critical thickness
Want islanding: high temperature

### Volmer-Weber Growth

Occurs with wide range of materials
Single crystal film
Crystallographic orientation templated by substrate
Film can be single crystal and still contain many defects
Growth by any mechanism other than Frank-Van der Merwe is not epitaxy
Nucleation of islands
Island growth
Growth of GaAs on Si
Always grow with islands
Islands start pseudomorphic
Growth errors lead to dislocations
Slight island rotations
PbTe on CaF2 - Volmer-Weber Growth
Ag on NaCl - with stacking faults
Epitaxial alignment
Interface energy that is strongly dependent on orientation of substrate to island
Growth of islands with particular energies
Interface energy minimization leads to epitaxial alignment
Iron on gallium arsenide
Match every other atom
Matching forms a deep cusp
CdTe on GaAs
Many metal-metal combinations
Same relationship to FCC
Grow epitaxial films by Volmer-Weber
Avoid defects if possible
To avoid SK and VW growth:
* Work with lattice matched systems
* Live with strain
* Manage strain relief

### Pseudobinary solution

Lattice matched substrate
GaAs and GaSb form pseudobinary solution
Plot relationship by plotting lattice constant as function of mole fraction

### Strained Layer Superlattices

Grow a layer with small critical thickness
Grow another layer with low critical thickness with misfit in opposite direction
Cancel effects of distortion
Grow strained layer superlattice

### Graded Layer

Learn how to engineer dislocations
Threading dislocation
Not enough strain to produce islanding
Enough strain to cause dislocation to glide
Threading dislocation concentration low in substrate
Begin with graded layer and create GaAs layer
Compound semiconductor with direct band gap on silicon